Part 1: definitions

You can't define "mentions".

You are trying to assert a set of invariant linguistic rules. This is an impossible task.

Words are defined by their context. X is not(everything else).

I suspect you are somewhat aware of this. And yet here you are trying to browbeat into believing that your interpretation of words is the one and only true interpretation.

In case we do need to establish that you can't define anything objectively:

Me: I challenge you to define "Word".
You: Words.
Me: Define those words.
You: More Words.
Me: Define those words.
Etc.

You can choose infinite regression or circular definitions.

Part 2: Interpretations

There is no single correct interpretation.

Every single person who reads a sentence interprets it as they will.

You can't stop them interpreting it howsoever they choose.

The idea that your personal interpretation of, say, the Liar's paradox is correct and everyone else is wrong is a level of hubris even I don't aspire to.

I get that you are trying to establish a common ground for productive dialogue. But you can't do it.

The only person who interprets things identically to you - is an identical copy of you.

Each and every person has a unique response to every experience. Their response is their response. You cannot force them to respond the same way you do.

Part 3: Meaning

Meaning is relationships. Relationships change. Ergo, Meaning changes.

The meaning of words depends on context. Part of the context is the observer.

As you grow and change, your perception of meaning changes.

Mathematics chases after inherent meaning by stripping away relationships to find the essence of a thing.

Of course, in a world where meaning is contextual - the essence is the relationships.

All of which to say: meaning is in the eye of the beholder and changes as you change.

Coming on strong

It is possible you are deserving of more respect than I'm currently giving you... but for someone apparently sure of their position - you are peddling a whole lot of BS.

Your interpretation of the Liar's paradox is YOUR interpretation. RusselA's interpretation is his.

Can the paradox be interpreted in that way. Yes. Valid interpretation.

Right and wrong can get bent. Each interpretation exists.

Language is subjective.

I struggle to understand how anyone with the slightest awareness of linguistics can turn around and proclaim a given interpretation to be definitive. And yet here you are trying to tell RusserlA that his interpretation is wrong.

For shame.

Or do you genuinely believe that you can define... anything?

This is a natural process. You seem to take a pejorative view of mathematical evolution. — fishfry

There is mathematics - and there is the justification/explanation of mathematics.

Applied mathematics is concerned with whether the results are useful. I'm more than fine with this.

It is where pure mathematics tries to establish a foundation of knowledge that I am disgruntled. The effort is laudable - but mathematicians have gotten themselves stuck in a dead end and appear unwilling to extricate themselves.

Axiomatic Mathematics is the show piece of mathematics within which reside logic, formal languages and the majority of mathematical proofs.

But it doesn't work. Axiomatic Mathematics can't define axioms. As deal breakers go - this is one.

There is an argument that a flawed system is better than no system. "We know axiomatic mathematics is flawed - but it is better than nothing".

Except that axiomatic mathematics without axioms isn't merely flawed - it doesn't exist. The axiom bit is not negotiable. You can define axioms or you can't.

As it stands, axiomatic mathematics strives to find the essence of meaning by stripping away extraneous fluff like relationships.

In fact, meaning resides entirely in those relationships.

All progress in modern thought is emphatically despite axiomatic mathematics. The presumption of objective truth has been a catastrophic mistake in modern thought.

There is nothing to be lost by discarding axiomatic mathematics.

As it happens, we can describe relationships. The thing that axiomatic mathematics is trying to dispose of is exactly where knowledge, understanding, meaning and... everything is.

Mathematics' insistence that the path to truth is in defining inherent properties is holding back human progress.

To be fair - mathematics is merely making explicit general societal assumptions. By making implicit assumptions explicit, mathematics makes it much easier to understand what our assumptions are and consider them critically.

I do think that the idea of an objective universe is a dead end and mathematicians should have examined their failures more critically. And we still need the rigour and pedantry of the mathematical process.

No changing of the rules. — jgill

That is debatable.

The central problem is that the rules aren't, and cannot be, defined.

When nobody knows exactly what the rules are, it is hard to determine whether the rules are being followed consistently.

We could spend decades arguing back and forth over whether mathematicians are applying rules consistently to the staircase paradox. And we will never come to a conclusion without a definite and unambiguous statement of what the rules are.

It is impossible to have a definite and unambiguous statement of what the rules are. Definitions are relational. X is not(Everything else). Roughly: A defines B and B defines A.

Any definition of rules (or axioms or anything else) results in infinite regression or circular definitions.

This is where mathematics is stuck. In order to make clear, unambiguous mathematical statements, we first need clear, unambiguous (mathematical) statements.

There is no starting point to jump start mathematics.

..................

I didn't mean to sucker you into a debate on the foundation of mathematics...

But mathematics doesn't have a foundation (c.f. foundational crisis in mathematics).

As much as mathematicians really, really want to make categorical statements - they can't. Anymore than philosophers have managed to establish a fixed point to build philosophy on.

To be clear - I'm not a nihilist. We can and do describe the relationships things have.

It just sp happens that you can either describe X, or the relationships of X but not both.

In this universe - we can describe the relationships of X.

Yet again you respond with assertions but no justification for your position.

Why?

You aren't even trying to show me that I'm wrong.

If you want to win trolling points; reddit has upvotes and downvotes to keep score.

You have no clue what you are talking about. — Lionino

I assure you, the feeling remains mutual.

The simplest set is the empty set, which is not nothing but something that has no parts. — litewave

That seems a lot like a definition of nothing to me.

One of the sub-threads here is that all definitions are circular.

An empty set is defined by set theory. Set theory is defined by the axioms of set theory. The axioms of set theory are defined by something else which is defined by something else which is defined by something else...

This results in infinite regression or circular definitions.

As a result axiomatic mathematics cannot define the meaning of anything. Hence "The Foundational Crisis in Mathematics" among other things.

The good news is that I can't definitively prove that a mathematical point and an empty set are equivalent to "nothing".

The bad news is no-one can demonstrate they are not equivalent, either.

And this brings us to the age old questions: What can we know with certainty? What can we describe?

For example, all definitions related to Quantum Mechanics are circular (this isn't just a mathematics problem). Our perception of what fields and waves are - derives from the universe we are trying to describe.

Quantum Mechanics says that electrons look like (other) bits of universe. This bit of the universe looks similar to that bit of the universe.

It isn't wrong. But it doesn't explain anything.

The reason 's answer is so good is because we can describe the relationships (oppositeness) of things. Indeed - we can only describe relationships.



I believe the standard prize is "a sense of pride and accomplishment". I'm told it nourishes the soul.

I'll certainly consider your suggestion of a physical prize. But I have been assured that "Exposure" is superior to mere material possessions.

I am not sure where you got that from — Count Timothy von Icarus

https://youtu.be/DIL37Rkt4m0?si=8veEEon_DGHD7uNb&t=183

With specific reference to human language.

It seems to me one can dispense with theism, recognize that More is Different and that humans have more cortical neurons than any other species, and thereby have a basis for recognizing a uniqueness to humans. — wonderer1

At which point the question becomes how much difference qualifies as distinct vs mere degree of difference.

Would you prefer to believe that Random Evolution "gave" some higher animals the "mechanism" of Reasoning? — Gnomon

I think that "reasoning" is a lot less special than many humans suppose.

Perhaps more isnt so different after all. — Joshs

Yes - this is a significant part of where I'm coming from.

Emergent

Human reasoning isn't special. Recursive thought (thinking about thinking) is the same mechanism as all other thought.

So - Everything is relationships. Neural networks are physically and notionally, networks of relationships.

I'd like to compare a single relationship to a brush stroke on a paint canvass.

A single stroke of paint tends not to have much in the way of inherent meaning.

Many strokes of paint form the portrait or landscape that we find compelling/moving/boring...

The whole picture forms a shape that we find meaningful.

A single relationship is largely meaningless. Many relationships with multiple loops of connection form a compelling shape.

In a universe composed of relationships - there is little value in comparing individual relationships. Whether a relationship is the signifier or signified is irrelevant.

The Mona Lisa isn't any one brush stroke.

When we perceive the face of a smiling woman - it doesn't matter that the shape is composed of brush strokes, lit LEDs or atomic particles. What matters is that we recognise the shape.

Patterns

One of the neat features of patterns is that they are scale agnostic. Language can describe the patterns we see from sub-atomic up to the visible universe.

Similarly, patterns are material agnostic. We can see a face in the moon and animals in clouds. Okay - those specific examples aren't terribly useful... but it does mean we can look at a bunch of RGB LEDs and perceive Arnold Schwarzenegger telling the hapless victim "I'll be back!".

The downside (if you are invested in human thought being unique) is that learning mathematics and learning to walk are the same process.

We can argue that the "attempt-fail-pain-retry"/"attempt-succeed-reward-reinforce" loop of mathematics is longer (more abstract) and humans are especially good at delayed reward/failure.

's description of specialness is plausible when a small difference of degree can make the difference between success and failure at a given task.

Clearly humans are special enough to have accomplished (*gestures broadly*) all this. But when running away from the bear, you just need to be faster than your companions.

Humans probably are better at learning, retaining and applying patterns - but I see no reason to think that wolves don't have much the same appreciation of rolling hills as apokrisis describes for humans.

No definitions

The interpretant need not be an "interpreter." We could consider here how the non-living photoreceptors in a camera might fill the role of interpretant (or the distinction of virtual signs or intentions in the media). — Count Timothy von Icarus

One of the defining features of a relational universe is that perception is unique to each observer. In General Relativity, space appears time-like and time appears space-like under certain conditions.

It isn't merely that semiotics can't define the signifier - the signifier changes according to the observer. It isn't that there is a fixed thing that we just happen not to be able to define - there are no fixed things.

Truth is, literally, in the eye of the beholder.

The Mona Lisa doesn't exist. Each person viewing the Mona Lisa experiences their relationships with the Mona Lisa.

[accusative]
You know that the two people looking at the Mona Lisa are seeing different things. And then you assume that there is one single correct perception that all the others are distortions of.
[/accusative]

The Mona Lisa is your perception of it. Your experiences are real.

You, semiotics, mathematics and the majority of philosophers are trying to demote experience to a second class citizen subservient to some special reality that can't be directly observed, can't be described but gives rise to each individual's perception.

Wrap up

When you only have a hammer... H'mm wrong aphorism.

When we can only describe (networks of) relationships; describing relationships is trivial. Describing anything else is impossible.

Human thought is manipulation of relationships. We don't have anything else to manipulate.

There is a possibility that there are processes outside the ability of language to describe. In which case - tough titty. Nothing we can do about that.

We know that we can describe (but not define) relationships.

Language is an aspect of the universe. manipulating language is manipulating the universe.

To understand the nature of language is to understand the nature of the universe.

We can't define semiotics, or mathematics, or humanity.

But we can manipulate the bejeezus out of relationships.

Perception as pattern matching isn't new.

However, we can go beyond it being a nice theory. A relationship based description of cognition is the only game in town.

Argumentation from authority is a fallacy.

I get that you think you are right.

For my part, I'm pretty sure I know what I'm talking about.

You reiterating your assumptions, claiming you are right by fiat - isn't an argument.

Saying your dad can beat up my dad isn't an argument.

The very fact that you think someone else can put me in my place tells me you don't actually understand the position you are trying to defend. If you understood it - you'd be able to present the evidence to me yourself.

As it stands - you are telling me I'm wrong but providing no justification for that position.

It is almost as if you aren't trying to persuade me you are right. It looks somewhat as if you are trying to defend your own beliefs without understanding where those beliefs are coming from.

If I really wanted, I would tag Tones and he would inundate this thread with corrections on your post. — Lionino

I would be delighted to engage with someone who knows the difference between a dialogue and a sermon.

Your claim that a given sentence has a fixed (nonsensical) meaning in all possible languages across the entirety of time and space is simply absurd.

Your claim that formal languages are not axiomatic systems is straightforwardly counterfactual. ZFC set Theory is the axiomatic system for which the axiom of choice was invented. This is an easy lookup. No-one who has the slightest knowledge of axiomatic mathematics thinks otherwise. This suggests to me that you a regurgitating something you heard - not talking about things you understand.

If you can find a single instance of a non-circular definition - you can rub that in my face.

I thought your post on the metaphysics of mathematics was interesting - but when you claim that a sentence has a fixed meaning (albeit nonsensical) you demonstrate beyond reasonable doubt that you don't understand the questions you are asking.

"Context matters" is basic English comprehension.

TL;DR

I don't mind that you think I'm wrong. The feeling is mutual.

I'm bothered that you aren't trying to show me exactly how I'm wrong.

You appear to be going out of your way to avoid presenting an actual argument. On a Philosophy Forum.

It looks to me like you aren't trying to persuade me. It looks to me like you are trying to preserve your own unfounded beliefs.

Care to demonstrate that you know what you are talking about rather than merely declaring it?

And please do sick any tame lapdogs on me. (no typo - bring it).



I think General Relativity is physics done right.

The significant difference between Quantum Mechanics (QM) and General Relativity (GR) is that QM tries to describe an objective universe that can't be directly experienced, while GR describes what an individual observer sees.

In my estimation, most people struggle with GR because they are trying to interpret it from a Newtonian/Eucildean framework.

So the twin paradox is paradoxical given the assumptions of a fixed, objective universe in which The Law of Identity holds - but is just a description of what we would see in GR.

cannot imagine a framework without his implicit assumptions about the world. In his perception, a paradox is always a paradox. But the "twin paradox" is only a paradox within Newtonian/Euclidean space. In GR - the "twin paradox" isn't a paradox of any kind. It is simply what is observed.

GR is such a fundamentally different approach to knowledge that there is no path from Newtonian Mechanics (NM) to GR. GR cannot be constructed using NM. There is no iterative set of steps from one to the other.

Albert Einstein had to go back to first principles. The theories of relativity are built from the single observation that the speed-of-light-in-vacuum is constant for all observers. His theories then take this observation to its ultimate conclusion.

Trying to comprehend GR while holding onto the assumptions of "objective reality" is impossible. Each observer experiences a different reality. Changing the relationships (relative velocity) in GR changes the perception of what reality is. Talking about a singular objective reality isn't meaningful within GR. No observer is "the correct observer" and every observer perceives a different universe - similar, connected, but unique for each observer.

Relational universe

Context Matters.

Meaning is defined by context. Einstein was referring to physics - but the universe is relational in every aspect.

The world you experience is genuinely different from the world everyone else (individually) experiences.

Not chaotically different. There are many similarities - but no two people's experiences are identical.

Everyone knows that experience is subjective. But most are still trying to understand a relational universe in objective terms.

The fixed, objective knowledge that craves doesn't exist. A relational (subjective) universe cannot be understood from the perspective of an objective worldview within which objects are static (The Law of Identity).

I may be hearing Heraclitus playing the lyre here, but it seems to me that “oppositeness” is the simplest possible building block of the universe. — Thales

Yes, yes, yes, yes, yes.

So much yes.

You win all the prizes. This is the right answer.

Some more agreement

I call them relationships or connections or differences - Opposites/oppositeness is just as good a name.

A rose by any other name...

So - yes - there is some fundamental quality of oppositeness and this quality is the building block of the universe.

Way back in the OP - I stated that the minimum possible oppositeness (relationship, connection, difference) is a directed edge in a graph.

Does this make sense to you as a minimum oppositeness. How do you picture/imagine a universe made out of pure oppositeness.

To be clear: I'm impressed with your description of oppositeness and I want to listen to you develop the idea more. Stepping away from the conventional "particle" centric models seems to me to be a huge step.

I think that recognising this oppositeness nature of the universe is the lynch pin. That it is impossible to describe a particle based universe - and (relatively) trivial to describe an oppositeness universe.

You don't have to ... anything. I'm not expecting immediate agreement. I am already sincerely impressed by your insight. I would be honoured to agree, or disagree, with any further thoughts on the matter you have.

Not necessarily. The Diagonal paradox can be extended to a sequence of smooth curves that converges to a limit curve in the complex plane in which the disparity of lengths is infinite. — jgill

First: I like the example. I do enjoy coming across these sorts of things.

Second: Mathematicians have a long career of coming across inconsistencies and hurriedly changing the rules so that this particular inconsistency no longer counts.

You may remember that I don't think anything other than relationships exist. I don't think Euclidean space, points, lines or triangles exist.

{Exist = can be described}

The relationships of a triangle do exist. We can describe those relationships.

In the staircase paradox there is a presumption of a continuous manifold within which exist infinitely divisible lines of arbitrary length.

And the definitions of all those terms are circular.

As such, inconsistency in mathematics occurs when people try to describe things that are indescribable.

So long as we only ever try to describe describable things, there is never any inconsistency. But trying to do something impossible always leads to some kind of system error.

We can, then, describe the relationships of our hands. We cannot describe our hands.

We can describe how (the relationships of) our hands pick up (the relationships of) a ball.

The distinction between X and Relationships-of-X is usually irrelevant since we can only ever describe "Relationships of X".

Mathematics tries to describe X. To the extent that descriptions of X and descriptions of X's relationships share common ground this appears to work.

But:

• The Law of Identity defines X as static. X's relationships change.
• Relationships are quantised (there is a minimum measurable change).

This means that the staircase paradox cannot actually define a continuous space or a continuous line. There are no demonstrably continuous relationships for a continuous space to be similar too.

There is no definable limit for a staircase to approach.

P.S.

That isn't very clear.

Simplified:

We can only describe the relationships of X.

Number lines, continuous spaces, points and lines are defined to be static.

It is not possible to describe static (or continuous) objects using dynamic and discrete relationships.

Why can't we just choose to say the set of all sets that do not contains themselves is the highest in order and so is not included in itself? What in math or language requires that include itself in itself? — Gregory

I think Axiomatic Mathematics is wholly mistaken. At the same time, I'm trying not to mislead you about Godel's incompleteness theorems and Axiomatic Mathematics in general.

I think Intuitionism(sp?) is giving up too easily - but it is arguably at least as well founded as axiomatic mathematics (which isn't saying a lot, but...).

Godel is pulling on a piece of string and seeing where it leads: Given a set of assumptions; what conclusions can we draw.

Godel's specific arguments are about what an axiomatic system can say about itself.

As such, the self-referential nature of Godel's arguments is baked into the premise

Godel could have asked different questions - but the questions he asked were specifically and explicitly self-referential. Removing the self-referential bit doesn't leave anything behind - it is all about self-reference.

Axiomatic Mathematics is wrong but the question is right

Axiomatic Mathematics cannot definitively define axioms. Without axioms, Axiomatic mathematics is nothing.

Godel's theorems are part of axiomatic mathematics and fatally flawed even before we reach the self-referential stage.

However, the question of what we are able to say about the universe we inhabit remains a legitimate question.

For example, if we describe electrons as having wavelike properties we are describing one part of the universe in terms of other parts.

Our sense of waves and wavelike properties come from our experience of the universe. We then try to describe the universe by saying that electrons behave (somewhat) like waves.

We are describing the universe as being similar to the universe.

This isn't wrong, of course. We can compare and measure similarities and differences between parts of the universe.

But there is no explanation. We can't step outside the universe and objectively describe it independent of our experience within it.

We are here

All of our experience, understanding and knowledge derives from our existence within the universe.

When we try to describe the universe itself (physics) we find that our measuring sticks are part of the thing we are trying to measure.

We can still make measurements. The Earth's circumference is roughly 40,000km. And a metre is one ten millionth of the distance from the north pole to the equator through Paris.

{The metre is now defined as the distance travelled by the speed of light in vacuum in a particular time.}

As a species, we are getting pretty good at measuring things. But we can't explain what we are measuring.

We don't know what distance is. From small scale to large scale, we can measure distance - but we have no clue how to create it from first principles. We can describe what we observe; but not why we observe in the first place.

Not nihilism

We cannot explain the universe. All of our explanations have the universe as a given.

All we can do is describe/measure one piece of universe using other pieces of universe.

This is a limit on knowledge - if you expect omniscience. We can't explain the universe.

We can describe what the universe is, though.

We cannot say what an electron is. The intrinsic properties of an electron are permanently outside our ability to speculate upon.

We can measure electric fields (whatever they are).

This makes zero sense. — Lionino

This makes zero sense to you.

Okay. Fine.

You're not giving me anything to work with.

You provide no clue as to why you perceive my statement regarding meaninglessness to be meaningless.

You've made a statement with no associated context or argument.

Do you agree with everything else I say, but this specific statement is causing you problems?

Those "sets of axioms" are the logical language chosen. — Lionino

And that Logical language has a set of axioms that need a set of axioms that need a set of axioms.

Formal languages are, very specifically, axiomatic systems. They don't just magically exist as handy off-the-shelf starting points.

This is the fundamental problem with the axiomatic approach to knowledge: there is no fixed, known starting point. You have a choice between infinite regression of definitions or Circular definitions.

You are right, that whenever possible, mathematicians prefer a formal language over a natural language to describe new axioms. However, formal languages have axioms that need to be described (just like every other axiomatic system).

In practical terms, the first axiomatic systems were described by natural languages - So this rock solid foundation of formal languages turns out to be built on a foundation that can't be defined.

The only difference between a natural language and a formal language is the degree of obfuscation between the two.

Formal languages cannot and do not define anything with any more precision than natural language (c.f. circular definitions and infinite regression).

You've got a post on metaphysics and mathematics on the front page right now that directly refers to the foundational crisis in mathematics. This is that crisis: axioms cannot be defined.

Also makes zero sense. — Lionino

Again: why make this statement?

Meaning of words

You declare: "This makes no sense" as if a given sentence has a fixed, objective meaning independent of context.

Even axiomatic mathematics recognises that the meaning of a given sentence is relative to the axioms.

A sentence in one axiomatic system can be true while it is false in another axiomatic system.

You appear to be implying that meaning is independent of context. That a sentence always has a fixed meaning (or lack thereof).

This presumption is not unique to you. It is, however, impossible to justify.

Mathematicians have been trying to pin a single fixed meaning to a set of axioms since the first axiom. It can't be done.

Meaning always depends on context. Truth depend on context. Not sometimes. Not when we feel like it. Always.

Axiomatic mathematics wants axioms to have a fixed meaning but knows that meaning of statements within an axiomatic system depend on the axioms of the system.

Pick a lane. Are axiomatic statements context dependent or not?

You can't define statements in a formal language according to their axioms - and then turn around and claim that the statements of the formal language are fixed and independent of context when used to describe the next axiomatic system.

The confusion in your thread on Grundlagenkrise and metaphysics of mathematics is entirely down to an inconsistent approach to language in which sometimes meaning is contextual and sometimes it is inherent.

Recognising that all meaning is context dependent and being consistent with respect to this observation causes everything to neatly slip into place.

The idea that because something doesn't make sense to you - it therefore cannot make sense to anyone else is utterly unsustainable.

Many people cannot make sense of General Relativity. Are we to suppose that their perception is necessarily universal and that General Relativity is nonsense?

Is that really how you think knowledge works?

Is my perception of your statements the only possible way to interpret them?

Roundup

At some level you know that meaning is context dependent. You know that different people interpret the same words differently.

All I'm pointing out is that there are no exceptions.

Axiomatic mathematics is trying to find fixed axioms while defining axiomatic systems contextually. One or the other has some potential to succeed. Mixing the two just leads to confusion.

Principle of explosion — 180 Proof

Now you're getting it!

You are absolutely right. The Principle of Explosion is a prime demonstration of the ridiculousness of Logic.

The Principle of Explosion tells us that given an inconsistency, every conceivable statement is inconsistent.

Some people mistakenly believe that The Principle of Explosion is constrained to a single system.

However, as you so perspicaciously draw attention to; The mechanism of The Principle of Explosion is entirely unconstrained:

Given any inconsistency - we can show that any statement is simultaneously true and false.

And since The Principle of Explosion is an observation, not a deduction, there is no cop out clause.

The Principle of Explosion applies everywhere it can apply.

It is so refreshing to meet someone who can actually read what the Principle of Explosion actually says. Thank you for bringing it to our attention.

First Order Logic is a subset of Axiomatic Mathematics.

Axiomatic Mathematics is predicated upon deterministic progression from a set of axioms.

In order to specify exactly one, unique, progression from a set of axioms we need to know exactly how to interpret a given set of axioms.

As such, for any given set of axioms we need a set of axioms that uniquely defines how to interpret that set of axioms.

In order to uniquely understand axioms we need axiom^2. In order to understand axioms^2 we need axioms^3. In order to understand axioms^3 we need axioms^4. ....

This leads to infinite regression or a closed loop of circular definitions (A defines B and B defines A).

Axiomatic Mathematics has one job: define axioms. It is impossible to uniquely define a set of axioms.

Without axioms, axiomatic mathematics isn't a thing.

First order Logic, a subset of axiomatic mathematics, doesn't exist.

Technically: it is impossible to define axiomatic mathematics and first order logic. We haven't actually proved they don't exist - just that we cannot say anything meaningful about them.

For all practical purposes, we can treat them as if they don't exist. The distinction between "can't be described" and "don't exist" is moot.

Right. The so-called "Liar's paradox" seems quite silly, akin to something a third grader thought up at recess. — Leontiskos

Godel's incompleteness theorems use the same basic structure as The Liar's paradox. As such, it is worth understanding the principles of contradiction/paradox.

Part 1: There are no lies

It is impossible to definitively define what a lie is.

A lie is not the truth. The truth is not a lie.

All definitions are circular (A defines B and B defines A).

Part 2: Squiggles don't lie

Sentences do not have any inherent meaning.

All descriptions are of the form: X is not(Everything Else).

That is, The Liar's Paradox as a set of symbols with no connection to anything else has no inherent meaning.

When we read a sentence, we create meaning as part of the process of interpreting the symbols.

The perception of a lie doesn't exist in written words - it exists in your mind.

Silly

You are right that the Liar's paradox is a silly misattribution within which lies cannot be defined and meaning exists within the observer, not arbitrary symbols.

However, understanding exactly why the paradox is not very paradoxical illuminates the nature of understanding and has direct implications in our pursuit of knowledge.

"The set of all sets that do not contain themselves". Obviously this top set could not self reference. I would say the same of Godel — Gregory

"Applying the rules consistently breaks down. Therefore we do not apply the rules consistently".

If you apply the rules of naive set theory - those rules lead to a contradiction. Therefore the rules of set theory cannot possibly be correct (The Principle of Explosion).

When you have to make an exception to the rules in order for things to work - your rules don't work.

As such - I don't think your comparison to an inconsistent set theory and its ad hoc fix is very helpful.

More pertinently - Godel was specifically working within the rules of axiomatic mathematics and exploring the limits of those rules. If he had to step outside those rules then the whole point of the exercise collapses.

The whole point of Godel's incompetenesses is: Given premise; what can we say?

For the incompleteness theorems to exclude themselves would be to disregard the whole point of the exercise in the first place.

It seems to me that geometry/space is what has presente a foundation for all mathematics. — Gregory

Yes-ish.

You have to exist in order to have a concept of mathematics. The universe has to exist for you to exist for you to conceive of mathematics.

So - yes - absolutely - mathematics is founded on the existence of the universe.

The trouble is that a full understanding of mathematics requires a full understanding of the universe as a pre-requisite.

Your concept of numbers derives from your experience of the world around you.

But no-one can define the universe in a fixed, objective manner.

Axioms

Given a set of axioms we can create an axiomatic system.

But...

In order to uniquely define a set of axioms we need a set of instructions that describes how axioms should be interpreted: axioms^2

In order to accurately interpret axioms^2 we need a set of instructions the describe how axioms^2 should be interpreted: axioms^3.

...

Etc, etc and also etc.

So - yes - we do in fact take the universe as a foundation and explore that foundation. But we can't say anything definitive about that foundation. Consequently we cannot say anything definitive about anything derived from that foundation.

So - we are free to propose the existence of the real number line - but we cannot say anything meaningful about it. Any definition faces the problem of axioms - infinite regression (or a closed loop of A defines B and B defines A).

No matter how hard we try - we are only ever able to describe the relationships of X, never X itself.

As with Zeno's paradoxes where we see space dissolve into nothing (or parmendian pure being), numbers must have a basic unity that holds them from infinite divisione. If we have 1, then we have 2 halfs, which each is one, so 1 is two. This can go on forever- as with divisione of a line. Numbers are synthetic (Kant)and nah platonic (Plato). A number is not a set. 7 is not the set of 7 ones. Sets are applied by us TO numbers which WE can choose how to group — Gregory

In mathematics - a paradox (inconsistency) demonstrates a faulty set of axioms.

Zeno's paradox demonstrates that some assumption (such as the continuous nature of space) is mistaken.

I would argue that zeno's paradox is a demonstration that space is not, in fact, continuous. That space cannot be infinitely divided - just as we currently believe matter cannot be infinitely divided (c.f. electron is a fundamental particle).

I'm a neophyte to semiotics.

Initial reaction on watching the video:

• This mostly seems sensible to me.
• I'm uncomfortable with the usage of "things" and "objects"/"objective".
• This seems to wildly overcomplicate things.
• I'm deeply uncomfortable with the idea that humans are qualitatively different, not just quantitatively different. (I think this is connected with ideas around emergence).

Cognition is uniquely human

The idea that humans have a unique ability to understand signs is a direct callback to the divinity of humanity.

It implies that humans have access to a special mechanism that isn't part of the rest of creation.

To believe in this version of semiotics, I am tasked with believing that God gave humanity access to mechanisms that are not available to mere mortal animals.

Even with a more mundane "emergent behaviours" justification, this seems to me to exhibit characteristics of trying to fit the evidence to the prejudices.

Things & Objects

A thing is its relationships.

In principle there is nothing wrong with referring to "thing" when we mean "the relationships of thing". Not least because "thing" is always "the relationships of thing". "Thing" without relationships is moot, irrelevant.

At a surface level - the interlocutors are referring to networks of relationships as things and I was totally onboard...

However, there appears to be an assumption that it is possible to define the terminology. To specify what semiotics is. That the notion of signs is a fixed, static target.

I can understand the urge to define the subject. The presumption of definitions is near universal. But words are their relationships - When semiotics fails to be consistent in this regard it fails at its primary purpose.

-------------------------------------------------------------------------------------------------

State of play

(Some) people can see that descriptions are relational.

Process philosophy and semiotics are approaches to knowledge based on this observation.

Even knowing that all definitions are relational, and that relationships change; these subjects are still assuming the existence of fixed definitions.

Fixed definitions

We know that we can't define X. We can only describe the relationships of X, not X itself.

Even so, the idea of a fixed X persists. Semiotics claims to be an X - A static subject matter - a fixed point of knowledge.

The first problem of semiotics is defining what semiotics (and all related terminology) is.

In trying to define itself, semiotics contradicts its premise

Interlude

I'm not sure how hard I need to sell this. Your general/academic knowledge of philosophy is far greater than mine and you've been investigating this subject matter for some time.

You've demonstrated that you have the individual pieces.

On the other hand, I'm describing a universe where nothing can be defined and meaning/knowledge/understanding are in permanent flux.

This is territory diametrically opposed to The Law of Identity.

In a world where the meaning of a sentence changes while you are reading it; logic doesn't apply.

There is no way to start from an assumption of a static objective universe and arrive at a dynamic universe of changing relationships.

We have to go back to first principles, disposing of all the assumptions predicated on The Law of Identity. Like, for example, the idea that mathematics has some fixed, objective reality. Or that semiotics and process philosophy can be defined.

Humanity exists

No-one has ever described a single instance of a fixed, unambiguous definition independent of relationships.

Our concept of X has always been "the relationships of X".

Semiotics cannot define what semiotics is except through descriptions of relationships. As relationships change, semiotics changes.

We already operate without fixed definitions.

Denying the possibility of fixed knowledge isn't nihilistic. We never had static meaning. Its absence isn't going to cause modern society to collapse.

Mathematics never defined what axioms are, let alone a single axiom. Logic cannot specify the fixed initial state from which deductions progress. Every definition in Quantum Mechanics is circular.

And still we have society and communication.

Rebuilding from first principles

Once we stop trying to do the impossible, everything else (the possible) is trivial in comparison.

We can describe relationships (with respect to other relationships).

That is it. That is our foundation; our First principle.

Any and all effort invested into describing relationships is productive.

Effort put into defining semiotics is wasted - it is an impossible task.

The difficult task is to stop attempting the impossible. "Define your Terms!" has been a defining mantra of modern thought. Possible or not - the habit of trying to define terms runs deep, to the point that subjects specifically addressing the relational nature of meaning are still reflexively trying to define their terms.

You already know how to describe relationships. The trick is not to conflate descriptions with definitions. Descriptions are possible. Definitions (c.f. The Law of Identity) are not possible.

Wow, I did not see that coming. More than 2500 years of mathematical development flushed down the toilet in a few seconds! — alan1000

Yup. Sort of. Descartes, Gödel, Alfred North Whitehead and The Foundational Crisis In Mathematics (among many others) have covered much of this territory before. It gets ignored because it is inconvenient - but this isn't entirely new.

Evidence

Try creating a non-circular definition.

Different approaches

Gödel's incompleteness theorems talk about the limitations of a system referring to itself.

Descartes observes that nothing can be proven outside one's own existence.

Alfred North Whitehead formalised process philosophy.

The foundational Crisis in Mathematics is a number of different people pointing out that axiomatic mathematics cannot establish a firm foundation from which to proceed.

General Relativity demonstrates that the assumptions of Newtonian Mechanics do not apply to the universe.

Context matters: the meaning of a thing depends (entirely) on the context.

Subjective experience exists.

Count Timothy von Icarus provides several relevant quotes in response to NOS4A2

Precedent

This really isn't out of the blue.

Mathematicians have tried really hard to establish a set of definite, unambiguous axioms. It can't be done.

Every statement within a (closed) system is one part of the system describing other parts.

All definitions are necessarily circular.

More pertinently: every definition is by reference to other things.

Bold, Underline & Italics

We can describe the relationships of X. We cannot describe X.

There is nothing complicated here. Whatever X is - we cannot access it. We cannot experience X. We cannot describe X.

In this respect I am simply reiterating an observation that is over two millennia old.

"Relationships of numbers" is a defining property of the relational number line (the line of negative and positive integers). But you deny the existence of number lines. Can you develop this point? — alan1000

We cannot describe X. We can describe the relationships of X.

The majority of the time this distinction doesn't matter. When sitting at the dining table it would be redundantly pedantic to note that we are experiencing the dining table's relationships rather than the dining table itself.

However, in pure mathematics, philosophy and metalanguage discussions the distinction becomes crucial. Such as when we are discussing whether 0.999... = 1.

Relative vs Objective: Change vs Static

The Law of Identity states that objects (like the number line) are static, unchanging.

A defining characteristic of relationships is that they change.

As you change, grow and learn, your relationships with concepts changes. Your understanding of numbers now is significantly different than when you were first being taught to add and subtract.

Each person has (slightly) different ideas of what numbers are, and the significance of them.

There are, of course, similarities. Common experiences create similar networks of relationships. An ordered series of numbers (1<2<3<4<5<...) is a near universal experience. It is easy to confuse many apparently similar subjective experiences for objective truth.

Your understanding of the number line is dynamic. Your sense of knowledge and meaning changes.

The concept of "number line" that you posses is constantly evolving, developing, changing.

In closing

That all concepts (such as number lines) are dynamic is in direct opposition to The Law of Identity.

It is a big step to swallow in one go.

However, the individual components are simple enough observations:

• Meaning is defined by context.
• Understanding is subjective.
• The universe changes.

These aren't shocking, groundbreaking revelations.

It just so happens that a static number line with fixed (true) rules is a direct contradiction of these observations.

"Hurr durr - "absolutely no absolutes" sounds silly so you are wrong".

Language does not work according to the principles of logic.

Heck, Logic doesn't work by the principles of logic.

The Liar's paradox exists as a valid sentence. Your brain doesn't (I assume) implode just because you read: "This sentence is a lie."

Language describes networks of relationships. That is all language does.

A network of relationships isn't wrong or inconsistent. One network of relationships does not rule out any other network of relationships.

A network of relationships is just.... a network of relationships.

We can compare and contrast different networks; but one network never precludes another. Just as one painting doesn't prevent certain other painting existing; or one melody preclude the existence of other melodies; so one sentence does not preclude another.

sense

You are struggling to make sense of the idea that there are "absolutely no absolutes". This seems like a paradoxical statement to you.

However, the sentence is just squiggles on the screen. The universe isn't offended by particular squiggles. Squiggles don't break the laws of the universe and summon supernatural being. Squiggles are just squiggles.

The idea of paradox and inconsistency exists in your head - not in the written squiggles.

You interpret the squiggles. You apply meaning to the squiggles.

Paradoxes are a you problem - not a squiggle problem.

The very fact that you perceive certain squiggles to be paradoxical indicates that you have misunderstood something.

There are no inherently wrong squiggles. Your perception that some squiggles are paradoxical doesn't come from the squiggles.

Paradox

So - in light of this - can you explain why you think certain squiggles are paradoxical? Can you define 'contradiction'? Can you point to an instance of a contradiction and say how one squiggle precludes another?



Everything is made out of universe stuff.

Thoughts are made of universe stuff. We are made of universe stuff. The universe is composed of 100% Grade A universe stuff.

The only thing left to do is describe "universe stuff".

Euclidean Geometry

The problem with triangles and Euclidean Geometry is that all definitions are circular. A defines B and B defines A for all A and B. (X=not(Everything Else))

Lines, planes, angles and geometry each define all the others in a perpetual ouroboros snake of definitions.

This applies to every possible definition. We cannot define "universe stuff" in a non-circular fashion.

Trying to describe the universe in terms of Euclidean Geometry (or non-Euclidean Geometry) necessarily leaves us in a closed loop of saying the universe is like Euclidean Geometry and Euclidean Geometry is like the universe.

However

What we can do is describe relationships by relation to other relationships.

That is it

That is everything we can do. There isn't anything else.

We can contrast, compare and describe relationships with respect to other relationships.

This makes things simple.

We cannot describe triangles or spatial geometries or electrons as intrinsic entities.

When we stop trying to do impossible things - the possible things are easy.

It is possible to describe one set of relationships by relation to other sets of relationships. All the mucking around with objective definitions is a waste of effort.

We just describe the relationships we see and we have described the universe. Done and dusted.

Simplest

The simplest (smallest) relationships we describe (by relation to other relationships) are the "building blocks" of everything else.

My sincere apologies for my entirely unjustified "rant" towards you in another thread. It was immature of me.

I must admit, I was somewhat discombobulated by the extent of your (prior) understanding.

In any case, my response was irrational. I am sorry for my behaviour.

Nicholas Rescher - "Process Metaphysics: An Introduction to Process Philosophy"

W. Norris Clarke - "The One and the Many: A Contemporary Thomistic Metaphysics"

-St. Maximus - Ambiguum 7

-Charles Taylor - Hegel

Thank you for linking me up with Process Philosophy.

I had intended a more substantive post than this... But I find myself digesting your linked posts and process philosophy.

I'll be back.

The question is predicated on a faulty assumption.

Number lines do not exist (or, at least, cannot be described).

Definitions

All definitions are of the form: X is not(Everything Else)

The real numbers as intrinsic values are a phantom; an illusion.

When we describe numbers we actually describe the relationships of numbers.

'1' is understood by its relationships with '2', '3', '-4.8776', 'apples', ...

When we talk about X we are actually talking about X's relationships.

Infinitesimals

While it is worth considering what the smallest possible relationship is...

The difference between 0.999 recurring and 1 is (in part) their relationship(s) to each other.

The relationship between 0.999... and 1 defines a difference between them.

Indistinguishable

A relationship and a difference are, for all practical purposes, the same thing.

The presence of a relationship between two perceptions demonstrates a difference between those perceptions. We can distinguish between them.

0.999... is different from 1 because we perceive a difference.

The nature of difference

'Difference' is defined as not(not Difference).

0.999... is different to 1 - but we can only understand that difference by comparing it to other differences.

Sorry to be weird at you

I know this isn't the sort of answer you were looking for - but the question is only troublesome because of the mistaken belief that number lines exist.

It is flat impossible to objectively describe number lines (or anything else).

All descriptions are of relationships. We can describe the relationships of numbers. And we can describe relationships in comparison to other relationships.

This is the structure of all knowledge. This is the mechanism of understanding.

The real number line, as an objective entity has never been described; can never be described.

We can, and do, describe the relationships of numbers. This dense network of relationships is our concept of what numbers are.

I very much like and appreciate your description of the current state of knowledge.

Impossible assumption

There is an impossible assumption at the core of modern thinking.

Attempting to fit observations into this impossible shape leads to the intellectual landscape that you describe.

Identity

I would recommend looking into the origins of mathematical philosophy in Pythagoras. The Greeks had the insight that only number could be completely knowable; the expression A=A (the law of identity) offered an intrinsic certitude that things in the material/sensory world could only aspire to. — Wayfarer

The law of identity is the greatest mistaken assumption.

Part 1: Definitions

All definitions are circular. A defines B and B defines A.

Specifically: for all X: X is not (Everything else)

It doesn't matter what X is intrinsically. Each X is defined by its relationships to everything else.

The things we understand, are the relationships of X, not X itself.

The essence of integer 1 cannot be described. The relationships of '1' are our concept of oneness.

It doesn't matter if '1' obeys the Law of Identity. intrinsic '1' can vary chaotically and it wouldn't impact our concept of '1' - the relationships of '1'.

Part 1; is a standalone argument. All definitions are the relations a thing has. All descriptions are of relationships. Whatever intrinsic properties an object has are irrelevant. Our descriptions are of the relationships between objects - not the objects themselves.

Part 2: Change

Stacking static objects does not produce change.

Static x Static = Static.

No matter how many real number lines and Euclidean planes you stack together - a bunch of things that don't change is just a pile of not changing.

Describing things that don't change cannot give any insight into a universe that does change.

Static numbers by themselves tell us nothing about the world. We are interested in the way numbers change.

Oh! - but numbers don't change. We are interested in whatever it is that does change.

Part 2: This is the same argument as above expressed in different words. Things that don't change have no bearing on things that do change. Change cannot be due to things that don't change.

Metaphor

We can describe relationships. (X=not(Everything Else). The parts of science that work are describing relationships.

Things change. The Law of identity is counter-factual straight out the gate.

Of course trying to describe a changing universe using only static objects leads to some bizarre results.

It would be ludicrous enough even if we could describe intrinsically static objects. But every description is of the relationships things have. Not only is describing static objects pointless - it is impossible.

The Law of Identity is a barking mad assumption and it leads to profound confusion and overly complex descriptions.

Sure, Quantum Mechanics works - but describing static objects (fields, quarks, leptons, ...) is pure flim flam.

It is entirely irrelevant what an electron is. The only thing that can be described are an electron's relationships.

And the defining characteristic of relationships is: they change.

Deduction

I have a deck of cards containing one card - the jack of spades.

I draw one card. It is necessarily the jack of spades.

This is just induction.

I'm not seeing how deduction is different to induction.

In all cases, probabilities are based on current information applied to a given situation. Ignorance of the full context may cause any probability to be misjudged, including probabilities that are perceived to be certainties.

Induction

From over here, Induction and deduction appear to be identical (excepting that deductions are perceived to be certainties).

I have no problem with deduction being the same as induction - I'm just confused by the redundancy. I don't understand why you are describing the same thing twice and calling them different names.

Or I'm missing a critical difference...?

Fun video!

I like what you are putting down. This seems very reasonable to me.

However, I find myself unclear as to your distinction between deduction and induction.

Pattern Matching

and pure logical and verified deductive thought takes the most time out of all approaches. — Philosophim

I see pattern matching.

Where you describe sheep and goat parts, I would generalise these as shapes or patterns. We see a pattern and then later compare our memory of the pattern with new experiences to determine how we interpret the new experience. - just as you describe.

Perceiving, storing and comparing patterns is the subject of your first post.

Your second post covers inductions which I take to be a refinement of the pattern matching where you examine how well patterns match and create a hierarchy from exact matches (probable) through general similarity (possible) and vague correspondence (plausible), to stark disjunction (irrational).

This all seem eminently sensible to me.

However, you also refer to deduction and logic as preceding induction.

I think your description of induction is sufficient to cover all human knowledge exploration. And yet you appear to imply the existence of another mechanism that you haven't addressed.

Could you go into more detail regarding the mechanisms of deduction?

If you’ve seen a relationship, and in fact it is all you ever see, what does one look like? — NOS4A2

Relationships look like everything you experience.

If you only ever experience relationships - then relationships look like everything you experience.

So you are saying "I think therefore I am" is not a rigourus argument. — Gregory

I'm saying the usual interpretation (that we can only know our own existence with certainty) is limited.

It is true that we can only know our own existence with certainty.

However - our existence encompasses our entire existence. Everything you think, feel and do is part of your existence.

Using our (certain) existence as a basis, we can make statements about the nature of our existence:

• Sensory Data exists.
• For each X we perceive in Sensory Data: X is not(Everything Else).
• We do not perceive anything that is not Sensory Data.
• We cannot describe X without relation to other Sensory Data.

Thus we have a clear and certain statement regarding the limits of knowledge and description.

We can describe things in relation to other things. Our understanding of things is contained entirely within the relationships between things.

We can describe the relationships of tables and chairs. We cannot describe implicit properties, essence or identity of tables and chairs (absent relationships).

You are trying to criticise me for your interpretations.

However, you cannot prove your existence to me beyond all possible doubt ...

Firstly, "proof" only pertains to logic and mathematics, not matters of fact. — 180 Proof

This is sheerest nonsense.

I feel as though you are trying to gaslight me.

Do you really mean to say that proofs are not intended to demonstrate facts?

Were you in such a hurry to gainsay that you forgot to pay attention to what you were writing?

Can you elaborate your point, please?

Secondly, "beyond all possible doubt" is neither a necessary condition nor sufficient condition for any claim to have a(n objective) truth-value. — 180 Proof

Is this "objective truth" in the room with us now?

People have been looking for objective truths for a long time.

As it stands - all definitions are circular: for all X: X = not(Everything Else).

Our best definition of "true" is: true is not(not true).

I don't know what you think is objectively true - but if you ever manage to describe it you will have achieved something that no philosopher, mathematician or physicist has managed. I await with bated breath.

Thirdly, whether or not you/we believe "beyond all possible doubt" any X exists is neither a necessary condition nor sufficient condition that that X exists. — 180 Proof

Sort of.

You are free to speculate about the existence of things we cannot measure or describe.

However, if we cannot describe something - it is moot whether we believe that thing exists or not.... We can't even describe what it is that doesn't exist.

So, you are free to declare that things we cannot comprehend exist. You can never be proven wrong. But nor does it lead to a further line of enquiry.

Lastly, given that you/we/I lack compelling, reasonable grounds to doubt any X exists, believing that that X exists is reasonable until such grounds for doubt are evident. — 180 Proof

If you can describe it, it is possible.

If you cannot describe it, then it is of no relevance.

When you sit down at a table; you can describe the relationships of the table. You cannot describe the table sans relationships.

Solipsism isn't (just) about what we can prove - it is about what we can describe.

The reason we can't prove anything objectively is because we can't describe anything objectively.

We can, and do, describe relationships (aka Sensory Data).

Summary

You have a belief in objective truth. This belief leads you to try to interpret the world in an impossible fashion. You are trying to apply impossible standards and perceive confusion when those standards are not met.

Your belief is widespread. However, it has no basis.

Every description is a description of relationships. We can describe the relationships of X; we cannot describe X.

What of the cogito. I think therefore i am? What is this relative too? Fichte says it's related to others but the existent of a single personality seems objective to me — Gregory

Good question.

You exist.

Your existence encompasses your entire existence.

Your thoughts and your experiences are aspects of your existence.

Each part of your existence illuminates the other aspects. Your conception of consciousness is that it is not everything else.

Each of your individual conceptions is a network of relationships.

Your concept of a tree has a link to your concept of a leaf, of roots, of bark, of dogs peeing, of the one summer you climbed and scraped your shin...

A sufficiently dense web of relationships creates a compelling shape that we experience as meaning. The components of that shape are relationships.

A personality can (should) feel compelling without needing to be objective. The relationships between your experiences form something real and unique - just not something objective.

You, a thing, are describing things. You cannot describe a relationship in the absence of things. X is a thing. Everything else are things. — NOS4A2

It depends what we mean by "thing".

Various people have spent significant effort in trying to describe intrinsic properties, essence or identity in an objective, context independent way. These efforts have failed.

All definitions are circular. A describes B and B describes A.

Objective definitions don't exist.

We can, and do, describe things in relation to other things. We measure, for example, distance by taking one thing (a ruler) and comparing it to the distance we wish to measure.

Our understanding of everything is by comparison with everything else.

The relationships between things is all we ever see. We never see anything between relationships.

You experience relationships with tables and chairs. You don't experience the table and chair themselves. When you describe a table, you are describing relationships of the table.

The distinction between the table and the table's relationships is of little concern when sitting down to eat but is critical in meta-language and metaphysics discussions.

Axiomatic Mathematics

Axiomatic Mathematics specifically tries to describe tables while excluding table's relationships. This is impossible. The effort invested is wasted.

All our descriptions have always described the relationships of a thing. Your conception of a table is of a table's relationships, not the table itself.

Pardon my intrusion — 180 Proof

You are most welcome.

therefore "should be dead and buried" as well, which is self-refuting and so there's no need for — 180 Proof

You exist. This is self-evident to you.

However, you cannot prove your existence to me beyond all possible doubt (as a definite and fixed truth). The reverse also holds, of course. I am aware of my existence but cannot objectively prove my existence to you.

This is the whole Descartes thing: our senses are potentially fallible and thus nothing about the objective world can be proven.

So - "your existence is self evident" is subjectively true. Your existence is evident to you. But your existence isn't an objective truth.

This applies to every concept you can imagine. It is impossible to objectively prove anything. Your concepts and meanings are entirely subjective.

Wider issue

When faced with solipsism, people have tended to disregard it as being little better than nihilism.

It isn't obvious how human society and communication can function based solely on subjective knowledge.

However, no one has ever demonstrated objective knowledge. There isn't a single objective definition.

Your understanding is irrevocably subjective. You can't understand for someone else.

The world still works.

objective interpretation

You interpreted my declaration of the nature of the universe as an objective statement.

In a world that doesn't contain a single objective fact - how can you perceive any statement to be objective?

This isn't a rhetorical question. Why is an objective interpretation of language the default?

Truth

"The only certainty is your own existence. All else is un-provable."

A naive reading of this might be that nothing is knowable beyond the self.

For seekers of understanding this is unpalatable and appears to deny our own experience of knowledge.

There is, however, a more nuanced interpretation.

Your existence consists of everything you ever experience. Your existence encompasses everything you will ever think, dream, experience and every action you perform.

You know that Sensory Data exists because you experience it.

You know that differences exist because you experience them. There is no doubt. Differences are part of your existence, and exactly as certain as your existence (to you).

The universe is a network of relationships because that is your (subjective) experience of the universe (when you stop trying to deny that experience in favour of a fictional objective reality).

Subjective experience isn't the second class citizen of knowledge. Subjective experience is the only game in town.

TL;DR

Your perception of any statement as being an objective statement is faulty.

"Cogito Ergo Sum et al" isn't a suggestion; it is the law.

I can assert your existence because your experience demonstrates your experience to you. But your existence is not an objective fact.

Communication relies upon common subjective experiences. Experiences are always subjective. There are no objective experiences; That would be a non sequitur.

Anything with extension, that is, the sort of things that populate our universe, are infinitely divisible — NotAristotle

I think this is wrong.

Euclidean Geometry assumes/proposes infinitely divisible space - but we know it is not an accurate theory of physics.

Quantum Mechanics assumes continuous space and time - but that is an assumption going into the theory - not a demonstrated conclusion.

Fundamental particles are, currently, believed to be indivisible and I'd wager that most physicists believe that there is a bottom to physics even if we may not have reached it yet.

The idea of quantised space-time isn't strictly part of Quantum Mechanics - but the relationships between planck length, planck time and the speed-of-light-in-vacuum appears to be a significant hint towards quantisation.

So from a status quo perspective - I can see no compelling evidence to think that there are any infinitely divisible qualities to the universe. It is a possibility - but I see nothing that persuades me we should take that possibility as a given.

Change or not-change

I think that the universe must be quantised.

Mathematics has run into issues with infinitesimals within real numbers.

Along the lines of 0.999 recurring equalling 1; there is an issue deciding when a real number stops being itself and becomes the next real number.

In a continuous, infinitely divisible space; there are always infinite points between two points. Two particles travelling through such a space each traverse an infinite number of points each time period.

The trouble is, an infinite number of infinitesimal distances is... complicated...

With regard to change, the question is at what point is change measurable?

If a change is sufficiently infinitesimal, we cannot measure it. If we cannot measure a change - has a change actually occurred?

As such - the question becomes: "What is the smallest measurable change?"

Given there is a smallest measurable change - then for practical purposes, that is the quantum of change.

Mathematicians have played with this - and the answer is basically: infinitesimals don't really make sense. It is somewhat like the singularity in a black hole - all the rules break down. Mathematicians have created (several) new rulesets to apply in these circumstances but generally the idea of infinitesimals is close neighbours with dividing by zero - best avoided if possible.

Also, I am confused by some of the claims contending that everything is "part of" the universe. In a loose sense, this is true. But there is not some "thing" that is "the universe." And in that sense, the universe does not have any "parts" in the same way that a solar system does not have parts. Maybe the parts are structurally related, but there is not some existent "thing" there, it's more of a convention that helps us organize the world, thought, speech, writing. This is not true of everything. Living things, at least, are differentiate wholes. — NotAristotle

I do think there is a "thing" that is "the universe".

Holism

Holism:

Holism is the idea that systems and their properties should be analyzed as wholes, not just as collections of parts. In this view, the whole is more than the sum of its parts.

Interconnectedness:

Everything in the universe is interconnected. The nature and existence of individual entities cannot be fully understood in isolation but must be seen in relation to the larger whole.

Unity of Being:

Reality is fundamentally one unified whole. Differences and distinctions within this whole are secondary to the underlying unity. — ChatGpt

Holism isn't just an interesting approach to knowledge. It is the only possible approach.

You exist

As above, your existence is the only thing you know for certain. And everything you think, feel and do is part of that existence.

Your existence is a single, connected whole. You, I think, recognise this.

Everything you experience is an aspect of your existence.

Your experience of stars and planets and the connecting space around them are aspects of your existence.

This, right here, is the nature of the universe.

Your ability to think and experience is an aspect of the universe.

You cannot separate yourself from the universe. You cannot separate yourself from your experiences.

You can communicate because you are an aspect of a universe that facilitates communication.

The distinctions you perceive are measured in terms of your other experiences.

Show that two points are not connected

It is impossible to show that two points are not connected.

Everything you are capable of experiencing is connected to everything else. Whether conceptual or physical your ability to reference two things demonstrates their connectedness.

Every part of the universe is connected to every other part of the universe.

You cannot shave off chunks of the universe.

Each part of the universe is defined by every other part of the universe: X = not(Everything else).

All this to say: You cannot show an absolute distinction between any two things. All things are connected.

Try to memorize this number by single digits: 24777977
Now try to remember it by grouping it: 24-777-977 The second is much easier. — Philosophim

Bitesize isn't quite the same as simple - or at least, not the idea of simple I had in mind.

Talking is a complex physical, biological and mental process. To the extent that the existence of the universe is a pre-requisite for talking, it is a complex process albeit one we engage in frequently.

As such - my point on this matter was that the perception of simplicity (i.e. starting from a minimal foundation) may be misguided. Specifically, we spend the first years of our lives learning to walk and talk and building a broad foundation of awareness of the basic mechanics of the universe.

I would argue that new knowledge is absorbed and integrated more rapidly the more of that foundation the new knowledge connects to. Ideal knowledge flow would involve wide kinaesthetic activation.

Problem Spaces

*discussion, not disagreement*

The more I interact with your ideas, the more familiar and relatable they become.

Generally, people don't immediately see the value in an argument. Rather, people integrate the components of an argument over time as they interact with it.

That is, a person starts in some initial state and incrementally approaches understanding.

A child doesn't understand arithmetic on first presentation but becomes incrementally more familiar with exposure.

This applies to Artificial Intelligence training too.

I'd argue that this incremental approach to solutions is a majority of human cognition.

There is, however, a known pitfall with this mechanism: Local maxima...

Maxima



A hill climbing algorithm can get stuck at a local maxima and never find the global maxima.

This is a common problem with training AI where the best fit finds a local maxima solution but misses the global maxima. In complex problem spaces there is no clear mechanism for determining whether the current solution is a local or global maxima.

Knowledge and Induction

In light of the above, what is your understanding of the process of cognition? Are your thought processes strictly logical? strictly asymptotic (approaching a solution incrementally)? A mixture? something else?

If relevant - what would you expect two disputants with different local maxima to a given problem to do?

The thing is everything, without which there would be no relationship or any other contrived measurement. — NOS4A2

But you (and everyone else) cannot describe a thing in the absence of relationships.

for all X
{

• X=not(Everything else)

}

The intrinsic properties, essence or identity of X are irrelevant. X is not what it is - X is its relationships with everything else (what it is not).

With this in mind - I fail to see how a thing is anything, let alone everything.



There are, indeed, many, many examples of relative concepts. Relative morality is, of course, an entire thing by itself.

We define words in relation to other words. Likewise for concepts - an idea takes on significance and meaning in relation to other ideas.

Your subjective experience is, of course, relative to yourself. You assimilate new experiences in light of previous experiences. Your taste in music is subjective (relative to yourself).

However, no one has ever managed to nail down a single example of a definite, unambiguous absolute.

There are no absolute definitions. There are no absolute truths. There are absolutely no absolutes.

This is a limit on knowledge. We will never be able to described a fixed point. We can only ever compare one thing to another. Language can only describe relationships. Language cannot describe an absolute.

The idea of absolute knowledge (omniscience) or absolute truth has a venerable history and was undoubtedly a driving force behind axiomatic mathematics (the home of mathematical proofs). However, the universe doesn't work that way.

In our universe, meaning is relative. A change over there impacts the meaning over here. Any change in relationships anywhere (slightly) changes meaning everywhere. Each observer perceives their own truth. Truth is dependent on context and your lifetime of experiences is a major context for your appreciation of what is true.

Connected

The universe is a single connected entity within which differences can be discerned.

All definitions/descriptions are of the form: X is not (Everything else).

Changing X changes (Everything else). And vice versa: changing (Everything else) changes X.

There have been extensive efforts made to establish some fixed point. These efforts have not borne fruit.

Where X is defined by its relationships to (Everything else); removing those relationships to find intrinsic properties, essence and identity is counter productive.

Listening

feels that I am not properly listening to him. For my part, I am addressing the core of my disagreement with his position: any claim (direct or indirect) to objective (fixed) knowledge is counter factual.

As such - I rather think I am engaging directly with what apokrisis is saying.

Pompous ass

Yeah - I'm a smug git who thinks they knows what they are talking about.

I'm practically begging to be knocked on my ass. I mean, I've declared Formal Logic and Axiomatic Mathematics to be so wrong that they barely qualify as illusions...

Nothing new under the sun

The limitations of objective knowledge aren't a closely guarded secret.

All definitions are circular. The universe is a connected whole.

These are simple observations.

There are whole branches of philosophy dedicated to holism, and Axiomatic Mathematics really can't specify what axioms are without getting stuck in a closed loop of circular definitions.

And yet, it seems, everyone still wants to find objective (fixed) truth!?

Despite clearly(?) understanding the nature of dichotomies, Peircean Logic is still trying to approach objective truth. (picking on an illustration from this thread - the sentiment applies more widely).

So annoying

The observations of context mattering and the universe being a connected whole are just that: observations.

There is no (rational) gainsaying.

I become annoying when I insist that these observations apply. It is not possible to have or approach objective truth. Trying to apply the principles of objective truth cannot work in a holistic universe.

It is annoying because it is just a reiteration of the observations: Given the observation of a relativistic universe; the universe is relativistic.

Unless you can point to a single instance of a fixed point, independent of relationships, there is no counter-argument.

Note: Peircean Logic accepts that the limit can't be reached but proposes it can be approached. A point is fixed, or it isn't. In terms of definitions - a definition is circular - or it isn't. There is no path for a circular definition to cease being circular.

So...

I can sit here and proclaim that words do not have intrinsic meaning; There are no absolute, unambiguous definitions; Mathematical proofs don't exist; The particles and fields of Quantum Mechanics are phantasms...

And in the absence of any fixed point - all I'm doing is re-stating our observation that context matters. As such - there is no rebuttal. Words don't have intrinsic meaning, there are no non-circular definitions and mathematical proofs are sheerest fantasy.

The thing is...

The notion of objective (fixed) truth should be dead and buried millennia ago. Peircean Logic should not be trying to approach objective truth even as an unreachable limit. Quantum Mechanics shouldn't be trying to define particles when every definition is circular.

Axiomatic Mathematics should have folded the moment it failed to definitively and unambiguously specify a set of axioms. Axiomatic Mathematics had one job - specify some axioms...

At this point there is nothing rational behind the assumption of an objective (fixed) truth.

Back to roots
Simplest

We can only describe (networks of) relationships.

The simplest relationships is a directed edge.

A directed edge isn't defined in any absolute sense.

We can combine arbitrarily many directed edges into arbitrarily large and complex structures.

The universe is an iterated network of relationships.

We can't describe something that is not an iterated network of relationships.

There are no options here. No-one has ever described a single intrinsic property. The essence of an object is permanently outside our experience.

Quarks, leptons and fields are circular definitions. Our concept of a field is a direct consequence of the things we are trying to describe using fields. A describes B, B describes A.

Any feeling of comprehension regarding Quantum Mechanics is an illusion.

We can, however, describe networks of relationships. If we describe something it is (necessarily) a network of relationships.

X=not(Everything else)

This is the linchpin observation. If you can find an exception - my position collapses.

There is no one substance, like matter, but an unfathomable many substances, individuated by their location in space and time. — NOS4A2

I'm not sure I see a distinction here.

One thing with many aspects (due to relative position in space-time) seems functionally equivalent to many things whose only distinction is their relative position in space-time?

In any case, if the difference between things depends (solely) on the relationships between them (e.g. position in space-time) then there is no value in considering the things.

It seems to me that the critical component is the relationships that differentiate.

I agree that relative position (relationships) individuate. Given this, individual substances have no intrinsic properties, essence or identity. In this light the distinction between one substance and many substances is moot.

The only thing of relevance to discuss is the relationships (position) that gives rise to the distinct perceptions.

It sounds like nominalism drowns in contingecies (and infinity?) But numbers in general do this. 1 can be divided unlessly so that there is no base unit — Gregory

I'm a big fan of describing what can be observed (nominally nomanalist).

The real number line and the imaginary number plane are concepts that can't be observed. Infinitely dividing 1 isn't a practical exercise.

As noted, if we attempt to find the properties, essence and identity of the number 1 by stripping away everything else - we end up with nothing.

What we can describe are the relationships between things. The useful parts of numbers are the differences between 1, 2 and 3.

As suggests - Bertrand is still clinging to realist/universalist assumptions. He is trying to elucidate the essence of numbers where no such essence exists. The same effort invested into describing the relationships of numbers is much more productive and, I would argue, closer to the principles of nominalism.

But this makes analytics impossible, since it implies that a local material change to reality causes the meaning and hence definitions of the rest of reality to change. — sime

I think this only applies to analytics of objects.

Analysing relationships (c.f. Graph Theory) is evidently practical albeit distinct from objective analysis.

I agree with what you are saying but I think the problem is in trying to preserve objective analytics within a relational (connected) system.

That is - it is true that local changes affect meaning and definitions globally. This is an issue when you assume static meaning and definitions.

However, in a holistic system it is the relationships and how they change that are the focus. It isn't a problem that meaning changes when that is the nature of the system that we are trying to understand.

As you say - the bias towards the existence of particulars over a united whole, especially among nominalists, is passing strange. But at least some of the resistance appears to arise from attempting to apply objective (isolationist/intrinsic) assumptions to relativistic (holistic) systems.

Objective analytics don't work in a relativistic system - but that doesn't mean that a relativistic system can't be analysed - just that the mechanisms of analysis are different.

The way out of circularity is hierarchy. — apokrisis

What I am reading is: "All definitions are circular, but..." or "Knowledge is dichotomous, except..."

We have a solid observational foundation that you appear to feel the need to refute or minimise.

But even at the level of the logic, we have an upgrade available that makes much sense of what ought to be seen. — apokrisis

I hope I'm misunderstanding your intention, but "ought to be seen"!?

This reads as an outright rejection of reality in favour of mysticism. "only through special, super dooper peircean logic and a wholesale rejection of the evidence of our senses can we approach truth".

The world looks exactly like how you expect it to look – that is normal psychology. — apokrisis

The world is exactly what it looks like. Your reading comprehension is lacking if you think these two statements are equivalent.

Absolute knowledge

I think you (and Peircean Logic) are clinging to the idea of absolute, objective knowledge.

While you concede that it can't be achieved in and of itself - you still think it is something that can be approached in the limit.

This is a mistaken belief.

In an objectivist paradise where non-circular definitions exist and every point is fixed and immutable; then objective knowledge is a rational and attainable goal.

Here, in reality, things are their relationships with everything else. Meaning, knowledge and significance change every time relationships change.

Knowledge is relationships. Stripping away relationships to reach the essence of a thing is discarding the very knowledge that you are seeking.

The objectivist perception of knowledge doesn't apply in a relational universe.

Logic

Dichotomies and Logic are incompatible.

For those raised with the presumption of logic there might be some inertia in correcting this presumption.

Peircean logic recognises that logic is constrained - but persists with the fallacy of fitting the round peg into the square hole.

Knowledge (along with the rest of the universe) is fundamentally relational.

Relativistic

There is no amount of hoop jumping that can turn a relationship into a fixed point.

Subjective experience cannot be converted into objective knowledge. The context of subjective experience is the knowledge you are seeking. To strip the context is to remove the very thing you are looking for.

Solipsism told us we couldn't prove anything objectively. General Relativity told us the universe is relativistic. Context tells us the world is relativistic.

It isn't like the evidence is hidden. The subjective nature of experience is front and centre of your existence.

The ideas of absolute knowledge, absolute definitions and a fixed point are actively harmful in our pursuit of knowledge.

Relationships aren't some second order consequence of an objective universe. Relationships are the universe.

Logic doesn't work. Logic never worked. Absolute truth isn't a limit you can approach.

Your conception of knowledge, understanding and meaning is the relationships you have built internally and externally.

Summary

You appear to be claiming that it is possible to approach (but not reach) absolute objective knowledge within a system that is relational.

This seems to me to be a claim without any justification AND a flat out contradiction of the observed evidence.

Information within a relational system exists entirely within relationships (observed, c.f. Dichotomies).

In light of this, there is no way that Peirce, Frege or yourself have sorted out logic.

You/they are making claims that are flatly refuted by the evidence.

In a system where all definitions are relative to everything else, it is impossible to have definitions that are not relative to everything else.

If somebody tries to sell me a perpetual motion machine - I know it is a scam without ever seeing the machine itself.

If someone is arguing for even the tiniest scrap of objective knowledge within a relational universe, we can be certain that they are mistaken.

Peircean logic and Systems Science speak to an internalist view of nature in which "objectivity" is what a community of inquirers hopes to arrive at in the limit. — apokrisis

For all A
{
A is NOT (Everything else)
}

Example:

• Small is not Large
• Small is not Metaphysics
• Small is not a curtain rail
• etc.

This is just a re-statement dichotomies.

The following are equivalent statements:

• A is defined by its relationships to everything else.
• A is defined by its differences from everything else.
• A is the negative space of (Everything - A).

A as an object independent of relationships is an irrelevant entity. Object A has no impact on our understanding of the relationships of A.

Even if it was possible to describe object A - Our definitions are dichotomous. The relationships of A are the entirety of A. Object A is superfluous, redundant, unneeded.

Relationships (whatever they are) are all that exists.

Flip side

Every description is a description of relationships. It is impossible to describe anything else.

Objects aren't a limit to approach; they are nothing, less than an illusion. Trying to reach understanding by stripping away extraneous relationships is exactly the wrong direction. Those stripped relationships are knowledge.

Relationships are existence.

Circular definitions

Circular definitions are an artefact of trying to define Object A.

Describing the Relationships of A is an actual description. A network of relationships has a shape. We can describe that shape. Networks of relationships are possible.

Object A (without relationships) is an impossible concept. As with non-circular definitions - they simply don't exist.

Simple

We observe context, therefore context.

The world is exactly what it looks like. And it looks like relationships. It does not look like objects.

Incorrect. — apokrisis

What I read is "yes, and..."

All definitions are circular, AND your description of dichotomies.

I agree that dichotomies have been around forever. How could it be otherwise - they are the nature of the universe.

and now stand as the metaphysical foundation for our scientific descriptions of nature. — apokrisis

Yeah... I'm not sure that everyone received that memo. Specifically, Axiomatic Mathematics and Quantum Mechanics are predicated on the idea that it is possible to have non-circular definitions.

I'm delighted that there is any acknowledgement of the nature of knowledge with respect to dichotomies. I agree that it should be foundational to scientific descriptions. I'm just noting that as it stands, your assertion of standing is more aspirational than actual.

It is in this light that I question your consistency.

Empirical evidence

You are absolutely right that knowledge of the significance of context is ancient.

And yet throughout that history science has tried to deny that evidence in favour of impossible definitions and explanations.

From solipsism it is crystal clear that it is impossible to prove anything beyond personal existence; yet mathematics pretends that proofs are possible.

Understanding with respect to dichotomies is not the same as 'objective definitions'.

They are not compatible world views.

The relationship is much the same as that between Newtonian Mechanics and General Relativity. There is no iterative path from Newtonian Mechanics to General Relativity. General Relativity does not make sense given the assumptions of Newtonian Mechanics.

Incompatible World Views

You can't have logic and dichotomies at the same time.

A relational universe is incompatible with an objective universe.

It isn't possible to comprehend one in terms of the other.

Recognising the dichotomous nature of the universe is fine (its right there). Trying to bend that evidence to fit objectivist assumptions is madness.

Prejudices should yield to the evidence, not the other way around.

Logic

A specific example of why objectivist is incompatible with relativist:

One of the assumptions of logic is that the original premise is a constant.

This seems to be a reasonable constraint. Imagine how much more complicated arguments would be if the meaning of the premise changed during the course of the argument.

Except, of course, it isn't possible to specify an initial set of premises in a fixed and unambiguous fashion. Before we can wonder if the premise is static we have to deal with never knowing exactly what the premises are in the first place.

It gets worse. In a relativistic system, the act of observing is a process. Both the observed and the observer are changed during this process (The process of observation is a change of relationships). There is no omniscient observation that leaves the target unchanged.

As a kicker we can round off with General Relativity, wherein the notion of objective truth can get bent.

The alternative: If not Logic - then what?

A consistent, relativistic (context matters, dichotomous) universe doesn't contain objective contradictions. A consistent system cannot illustrate what a contradiction is.

The universe is exactly what it appears to be. You don't need a theory to describe what you see. You just look and write down your observations.

Every statement you make is a shape within the universe. You literally cannot shape the universe into an impossible shape.

Humans are lying, hypocritical, scum bags that will behave inconsistently and contradict themselves for fun. And the Liar's paradox is just a squiggle in the universe.

Your ability to look at some squiggles and perceive a paradox is a 'you' thing.

Everything that is possible within the universe (including languages) is possible. Language works with the same mechanism as the rest of the universe. Just like the universe, everything that is possible is possible.

You do, of course, make subjective evaluations of statements.

Dichotomies

I appreciate your description of dichotomies. As far as it goes, I'm in full agreement.

However, your comment regarding the foundation of science makes me think your pragmatism is superficial. That you are holding onto old assumptions despite the evidence.

Possible is easy

I might be maligning you and you are already ten steps ahead of me... but a consistently dichotomous view works really well. Describing the universe on its own terms is productive. Like "Oh my god - it is so simple!"

Existing mistaken assumptions have been blinding us to the truth: The universe is exactly what it appears to be.

The trick is to see what is there - not what we think is there.

Time

OK if the mode of time is not Presentism but Eternalism; however, we don't yet know the mode of time. If Presentism, the 'particles' roll along their fields, like a kink in a rope moves. — PoeticUniverse

You are right - whether intermittent or continuous, Time is that which we perceive as time.

My argument is that it is far more productive to describe what we see.

We do not see particles. We do not see movement through space. We do not see Hilbert spaces or integers.

We have entire industries devoted to describing our world in terms of perpetually invisible and undetectable qualities.

Such practices should be the domain of religions - not science.

Good science is empirical. Things we can see and measure.

Quantum Mechanics runs around all the houses describing particles and fields and produces nothing better than we would get through statistical analysis of our observations.

Indeed, a straightforward statistical analysis would avoid all that mucking around trying to define undefineable quantities.

God is defined as all powerful and all knowing but super, duper invisible - you can only know him through faith. "yeah, yeah - whatever you say. Sure."

Physicists do exactly the same and its "Wow - All hail the Quantum! Praise be to the waveform collapse! How sexy is that many worlds interpretation".

The universe is exactly as it appears

What you see is what you get "WYSIWYG".

The universe is what we directly experience.

Inventing new pantheons (of gods or particles) does nothing to elucidate.

Indeed, persisting in false assumptions despite the evidence clouds our vision and hampers our perception of the reality that is right there.

Trying to understand the universe in terms of invisible fields that can't be measured is the antithesis of science.

Freedom is built into the real, and the past doesn’t determine the future, it only provides constraints and affordances. — Joshs

Whether the universe is deterministic and the possibility of free will in a deterministic universe are interesting and relevant questions.

Unfortunately, your assertion doesn't appear to be falsifiable.

Reality is a moving target. Knowledge is praxis, a way of changing how we interact with our world in ways that are useful to us. The changes we make in our interactions with the world feed back into our understanding to further change our knowledge. — Joshs

This seems reasonable to me.

There is no limit to the variety of ways we can scientifically construe our world — Joshs

No.

All definitions within a system are circular.

A description consists of one piece of universe describing another piece of universe.

A --> B --> A

We can describe what we observe (with respect to everything else we observe).

Anything else is a figment of your imagination.

Thanks to the unidirectional arrow of time, the universe is continually outside itself, continually overcoming its former states. — Joshs

If you want to conceptualise each new moment as being a brand new universe that's fine.

This argument doesn't depend on a specific definition of 'inside', 'outside' or 'universe'. It depends on us being part of the process - lacking the omniscient god like view as an entity that can observe the universe without interacting with the universe.

My position is formally an internalist epistemology. I'm a Peircean pragmatist. So problem dealt with. — apokrisis

Is that 'Pragmatist' in the same way that The Democratic Republic of North Korea is Democratic?

All definitions inside a system are circular

A defines B. B defines A.

Your quantum jargon == The universe is like the universe.

In what way is observing that the universe has similarities to itself pragmatic?

I mean - you're not wrong. But neither are you advancing knowledge.

Apology

I'm sorry (rubs nipples).

I know the intent behind theories. I know I'm denigrating the scientific method. I know I'm committing heresy of the highest order.

But all definitions within a system are circular.

There has never been a single, objective, universal, unambiguous definition of anything. Ever.

For all your ability to reference distance, you cannot define distance free of circularity.

A pragmatist would deal with reality.

Post Script

I am most gratified that I am, at least, able to communicate my enthusiasm.

Piercian Pragmatism seems nice. Personally I'm a fan of describing the universe as it is.

And a really, truly do not mean to offend anyone. I simply wish to convey that:

All definitions within a system are circular.

I’m wondering how far you’re willing to push the role of context in relation to the progress of knowledge. I’d like to we you push it to the limit. — Joshs

I feel there isn't (or shouldn't be) a choice. The significance of context is readily observed and widely acknowledged. It isn't a new insight.

Any rational viewpoint has to incorporate the role of context.

A half truth is (colloquially) a lie. Half accepting the significance of context is a denial of direct experience.

So - yes - to the limit.

socorro’s g he idea that knowledge — Joshs

More context please. I'm not sure what this is referencing.

What appears consistent or inconsistent, true false , harmonious or contradictory, is not the result of a conversation between subjects and a recalcitrant, independent reality, but a reciprocation in which the subjective and the objective poles are inextricably responsive to, and mutually dependent on each other. — Joshs

I'm somewhat allergic to the mere suggestion of 'objective' as I perceive it to be commonly bound to hidden/obscured impossible assumptions. But beyond that - yes, absolutely.

(I'm expanding the point - not arguing with you)

We are that which interacts. Interaction is a two way process. The act of observation changes us - and changes that which is observed.

Possible/impossible

We can describe our experiences with respect to our other experiences. We understand joy with comparison to misery (and contentment, ennui, pride, shame,...).

It is impossible to describe anything absent our experiences.

A connected universe directly impacts what knowledge is.

The mathematical attempt to create a universal language free of individual bias is a fundamental misunderstanding of the nature of existence.

It is an impossible task.

Knowledge and understanding aren't fixed points. They are a continuous active process. Your (everyone's) engagement with the universe is a critical part of the process.

Agreement

I agree with what you are saying but I want to keep pushing these to its ultimate conclusion.

Context has significant real world implications.

When we take context seriously we see that the explanation for large parts of mathematics isn't even wrong. The idea of understanding and significance separated from an individuals interactions is meaningless.

The effort invested in seeking objective truths (independent of context) is wasted.



So much agreement - but the devil is in the details

If you doubt that there is an objective context, how is it that almost all human beings of a particular intelligence are able to learn that 1+1 = 2? — Philosophim

• 1. The choice is not between objective and chaos. The choice is between objective and relative. They are both approaches to describing a universe with (perceived) structure.
  
  General Relativity (GR) is wholly incompatible with Newtonian Mechanics (NM). Each observer in GR makes measurements that are inconsistent with other observers (according to the rules of NM). People who try to comprehend General Relativity using the assumptions of Newtonian Mechanics are in for a very bad time.
  
  This does not make General Relativity chaotic. GR describes our universe, structure and all.
  
  To the extent that you are implying that I think our experiences are chaotic with no common factors - I have failed to communicate on a monumental level. (I am challenging assumptions that are generally taken as a given. Without the context of agreed assumptions it can be difficult to interpret language).
  
  
• 2. 1+1=2 is true within Euclidean Geometry. We know for a fact that our universe is non-Euclidean. (c.f. General Relativity). A flat plane is a passable approximation for common human experience on the surface of the Earth.
  
  Most people are raised in an environment where 1+1=2 is good enough but an astrophysicist is going to ask you the context before they agree.
  
  Non-Euclidean spaces are all the possible spaces that aren't Euclidean (flat). There are infinitely many such spaces and they include curved, bent, and discontinuous systems.
  
  As such, for all x there exists a non-Euclidean space such that 1+1=x.
  
  Which is to say, there are infinitely many more systems in which 1+1 != 2 than in which 1+1=2.

Definitions

Likely its in our definition differences. — Philosophim

A statement is a piece of universe describing another piece of universe.

In a closed system (like the universe) all definitions are circular. That is A --> B --> A.

Which is to say that according to the common conception of 'definition' there are no definitions.

We can describe A in terms of B. We can describe B in terms of A. That's it. That is the complete list of things we can do with language.

Everything else is an aspect of this mechanism of language.

Language works. We describe A in terms of B and B in terms of A and we've built society.

In the entire history of mankind there has never been a non-circular definition.

Or, more constructively, meaning is dependent on context.

What I am doing is trying to break down complex concepts into more simple and easier to comprehend ideas. People think better when you can get down to fine grained foundations, and build on top of them. — Philosophim

Do they? You have evidence of this?

Context is critical because both we and our world are in continual motion. We have a system of constructs that are organized hierarchically into subordinate and superordinate aspects such that most new events are easily subsumed by our system without causing any crisis of inconsistency. When we embrace new events by effectively anticipating them, our system doesn’t remain unchanged but is subtly changed as a whole by the novel aspects of what it encounters. — Joshs

Joshs describes how experiences (such as new ideas) are more easily digested when they largely align with our expectations for those experiences.

In this conception (which I agree with), the ease of assimilation is how closely new ideas fit within our existing framework.

Here the measure of complexity of a new idea is determined by our existing framework. A simple idea is one that can be easily incorporated into existing conceptions with minimal effort.

Contrariwise, An idea that subverts existing expectations is generally difficult to digest even when the foundation is as simple as "context matters" or "all definitions in a closed system are circular".

I wasn't familiar with Saussurean linguistics. Thank you for the references - much appreciated.

Precedence

I think a great deal of what I'm talking about has already been widely talked about inside and outside of philosophy.

What exercises me is that the entire philosophical community stops short of following through.

Solipsism is usually dismissed as being little better than nihilism - but nobody has (successfully) crafted an argument against it. It turns out that taking solipsism seriously and following it to its ultimate conclusion is productive.

"Context Matters" is a simple observation that everyone is capable of making - yet throughout philosophy and mathematics we find argument after argument bending over backwards to ignore this simple observation.

Godel's incompleteness theorems go to some trouble to explicate the nature of being inside a closed system - yet no-one appears to make the connection with our own existence within a closed universe.

General Relativity is a direct repudiation of Newtonian Mechanics and the objectivist point of view. Yet objectivist assumptions remain the de facto foundation of mathematics and (Quantum Mechanics) physics.

It is not that we lack evidence, nor awareness of the evidence.

As such, I'm not trying to demonstrate anything wholly novel. Rather I am attempting to communicate that solipsism, context and the universe being a singular indivisible whole are foundational truths.

We cannot hope to understand the universe if we continue to ignore and deny the fundamental nature of the universe.

Not Theory

Philosophy has fallen into such a state of disrepair that every person has their own opinion and every opinion is worthless.

Where is metaphysics when the choice between Kant and Hume is just that: a choice? Metaphysics struggles to make definitive statements to the point that many assume this is the natural state of philosophy.

The universe isn't a pick your own adventure. You existence isn't a structureless void where each choice is equivalent to every other.

The universe is a specific thing. "Context Matters" is an observation of the universe. This isn't just another nice idea that you can choose to believe because the weather is nice.

Context mattering has consequences. All by itself, this one observation defines the nature of knowledge.

My contention is that we already have the evidence. What we need to do is take that evidence seriously.

I think you are each asserting that it is possible to do something that is impossible.

I'm not saying you, specifically, are making a mistake. I'm saying that (almost) everyone is incorporating a mistaken assumption into their sense of what knowledge is.

Possible/impossible

You can do possible things. You cannot do impossible things.

You cannot point to something that is outside the universe.

You are part of the universe. Your thoughts are part of the universe. Language is part of the universe.

You cannot reference not-universe in any way. It is flat out, unequivocally, impossible.

"Outside the universe"

The concept of "outside the universe" is null. It doesn't mean anything.

Your concept of "outside the universe" is part of the universe. It is inside the universe.

Your concept of "outside" has been formed from experiences that are wholly contained within the universe.

There is a baked in component of "outside" that can be almost universally omitted:

"Outside of x (inside the Universe)"

"outside the universe" should be read as "outside the universe (inside the universe)".

Post illustration

I would bet dollars to donuts that even now you feel that you are conceptualising something in response to the phrase "outside the universe".

Before the universe

What came before the universe? Philosophers have already explored the fact that our sense of time is a product of the universe we inhabit. "Before Time" is a non-sequitur.

Feel

Take note of how compelling the notion of "outside the universe" feels. You know what 'outside' means. You know (roughly) what 'universe' means. Of course you understand what "outside the universe" signifies...

Physics doesn't explain squat

We can compare the differences and similarities between one piece of universe and another piece of universe.

That is what is possible. This is what knowledge is. This is everything.

Explanations in physics are equivalent to "before time", "outside space"; they contain no information.

Why is this bit of universe similar to that bit of space? Because it is.

The universe is the way it is because we observe it to be that way.

We can measure the similarities and differences. We can make note of common patterns. Any attempt to justify stuff always boils down to "because".

Comparing the universe to itself

The only thing we have available is the universe. Our thoughts and actions are intrinsic parts of the universe. The universe is our starting point - our given.

Every statement fundamentally assumes the existence of the universe.

Anything and everything we say about the universe is the universe referencing itself.

This isn't a problem or a limitation. This is simply what is.

We can, in fact, describe what is. We can observe the universe and describe what we see. This is possible.

Doing possible things is easy.

We cannot explain the universe independently of the universe. Doing so would be impossible.

Doing impossible things is futile. A waste of time and effort.

Other end of the scale



I've read a few of your recent posts. You are clearly understanding concepts with the depth and clarity that I initially perceived.

I have deep respect for the arguments you have made and the insight that they represent.

The following smack down is only possible because you are most of the way there already.



As with the Count above, My deepest respects. Think of the following as an argument made with vigour. I am arguing against a position.

Smack Down

My personal worldview is ultimately Holistic and Monistic. — Gnomon

Well Whoop dee doo! Look at Mr. Holistic. He thinks the universe is a thing.

Of course it is a whole f&^%*$g thing. It isn't an option. It's the law.

Of course you can't step outside your existence. Of course you can't step outside the universe.

What is even the alternative? That bits of the universe are disconnected but connected at the same time?

But

But when we begin to "describe" the world, in language or math, it is necessary to make "distinctions". — Gnomon

No. Stop it. No Buts.

You have the truth right there in your hands and you are turning away from it.

The universe exists and everything (EVERYTHING) is part of that existence.

Everything you think, feel, imagine, do and communicate is indivisibly an aspect of the single whole.

"Ah, but - what if it wasn't?" It is. You and every mathematician, philosopher and physicist who ever lived cannot describe anything that is not inextricably a facet of the universe.

Your words are part of the universe. Your thoughts are part of the universe. Your existence is part of the universe.

Everything that we are capable of understanding, is expressed with reference to the universe.

Context

You know that context matters. Your personal, direct experience shows you that context matters. Of all the certain truths in the universe, you can see context mattering.

And then you turn around and suggest that if we remove enough context from essential mathematical concepts we'll arrive at truth!?

In a universe where the only comparison we have for one piece of universe is another piece of universe you want to remove our only reference point in the hopes of understanding concepts in isolation!?

Connected

The universe is a connected whole. This is the foundation of knowledge/understanding/meaning/significance/...

In order to understand the universe, a good place to start is with the universe. The pieces of the universe are not disconnected (distinct).

Trying to understand the universe by assuming not-universe is silly.

99.9%

In a certain sense, I think the "entire context" matters for fully defining constituent "parts" role in any universe, and this might preclude things' being "building blocks" at all in the normal sense. — Count Timothy von Icarus

Here Count Icarus looks the universe square in the face and then just stops.

Solispism, Godel's incompleteness theorems, General Relativity, every philosophical and mathematical argument that has tried to find an essence independent of bias...

We've already considered this from every angle and we are still banging our heads against the wall.

"Context matters" is right there. It isn't hidden. There's no secret.

The only possible mechanism of knowledge is with respect to the universe.

It boggles my mind how a person can be looking right at the evidence in front of their nose and then turn around and say "But when we begin to "describe" the world, in language or math, it is necessary to make "distinctions"" as if somehow, magically, the rules don't apply to language or mathematics.

We don't have the universe plus a backup universe.

Language and mathematics don't have a secret backdoor access to an objective viewpoint independent of the universe.

Possible/impossible

This is not a debate between competing theories.

It is impossible to reference something outside the universe.

An argument that references "outside the universe" isn't even wrong. The idea of an objective viewpoint free from observer bias is meaningless.

We can compare, contrast and interact with different aspects of the universe. And that is it. That is everything we can do.

There isn't anything else we can examine. There isn't anything else we can interact with.

All your thoughts, ideas, actions, experiences and dreams are aspects of a singular universe within which you exist.

Not Nihilism

Knowledge independent of your subjective experience has always been a null concept.

Objective truth has always been meaningless.

It is possible to describe one aspect of your experiences with respect to other aspects of your experience.

Possible is so, so much easier than impossible.

Everything humans have achieved is what is possible. Aligning our expectations with reality will be orders of magnitude more productive than the alternative.

Regarding a simple universe: a single particular. Depending on one's preferred ontology, could be:
- a property (existing independently)
- an object with zero properties
- an object with exactly one property (if particulars necessarily have at least one property). — Relativist

If I were writing a computer program to create my universe; each property would be assigned to an independent variable.

This suggests to me that a particle with multiple properties is not indivisibly simple.

As to individual properties - I think we can create a further hierarchy of simplicity among properties corresponding to information content.

A property that can only have two states seems simpler to me than one which has an infinite number of continuous states (binary is simpler than the set of real numbers).

As to your table of possibilities you are implying that a property is distinguishable from an object.

I'm inclined to re-write your table as:

- a property (existing independently)
- a property with zero properties
- a property with exactly one property (if particulars necessarily have at least one property).

which in turn seems to simplify to:

- a property (existing independently)

Which then just leaves the question of whether a property, by itself, is sufficient to construct complexity.

My solution to this is an edge within a directed graph.

In every instance I could think of, relationships are not physical things, but as-if mental images, where the invisible bonds are imagined, not seen. Causal Energy/Force is invisible & intangible, so only its after-effects are detectable by human senses. — Gnomon

This is interesting. In contrast, I think the only things we ever experience are relationships (or possibly interactions which are the same thing with a different label).

From a physics perspective, the only things we ever measure are interactions. We don't see particles moving through space. We don't see particles at all.

An electron is a hypothetical particle intended to explain the specific sequence of interactions that we observe. No-one has ever seen an electron. No-one has ever seen a particle move.

What we measure are sequences of individual interactions.

Mass, momentum, charge, spin, colour are all hypothetical constructs used to describe the sequences of interactions we observe.

The idea that particles travel through space is just an idea.

A theory that had no space-time, no particles; but explained the sequence of interactions as well as Quantum Mechanics does would be exactly as real as QM.

From a mathematics perspective, there are infinitely many formulations that are equivalent to Quantum Mechanics.

A physics theory needs to explain our observations. We don't observe anything between interactions.



I'd like to get into what we can and can't describe. In the meantime I'm hoping the above diatribe gives you some insight into why I don't immediately accept your distinction between ideal, real, structure and substance.

The ‘why’ is bound up with the qualitative structure of the theory which explains and organizes the observation. As one theoretical explanation is overthrown for another, the ‘why’ changes along with it. — Joshs

Except that can't be correct.

"Because I said so." "Because God decreed it." "Because it does."

Physics runs into the same infinite recursion as asking what caused the universe. At each stage there is still the question "what caused that cause?".

If we propose that God caused the universe, we haven't moved the territory. What caused God/universe? Is God/universe eternal?

"The Higgs boson does it." What causes the Higgs boson to do it? "The quantum Field." What causes the Quantum Field?

Physics (and any other discipline) is incapable of addressing the fundamental why. Any suggestion to the contrary is smoke and mirrors.

Your perception that a physics theory addresses the why is a mistake. A very common, widely believed mistake, but a mistake nevertheless.

Quantum Mechanics (QM) works because it works. There is no reason behind QM. Given enough observations you will arrive at a statistically accurate summation of those observations.

The entire field of Quantum Mechanics is nothing more than a Large Language Model fed with a data set of observations.

Don't get me (entirely) wrong. It has taken heroic efforts to make better and better observations. We have some phenomenally precise and accurate statements of observation (albeit massively overcomplicated by needless assumptions).

I think that, properly understood, information theoretic understandings of physics and metaphysics are anti-reductive, since context defines what a thing is, rather than vice versa. — Count Timothy von Icarus

Music to my ears.

We seem to be on the same page here.

In a certain sense, I think the "entire context" matters for fully defining constituent "parts" role in any universe, and this might preclude things' being "building blocks" at all in the normal sense. — Count Timothy von Icarus

I could kiss you on the lips (or some other hyperbolic expression of affection for your ideas).

Your comment indicates to me that you have a significant understanding of what it means for the universe to be a single, connected (indivisible) entity with each part being an aspect of the whole.

I find myself mildly discombobulated. Like the dog who caught the car - I'm not sure what to do with such significant agreement. (not entirely true - but I do want to put some thought into it and I'd like to get this post out).

I'll be back.

I can see your argument - but it doesn't land because I think you are pre-supposing a distinction between hallucination and reality that I don't think is a given.

You assume that hallucinations and reality are distinct. Using this assumption of distinction you then demonstrate a distinction.

You and Searle are pre-supposing that reality is provably not an hallucination and then reaching conclusions based on that unjustified assumption.

So, Searle's argument depends upon a fallacy in which the conclusion is implicit in his assumptions. He isn't demonstrating anything. He is simply making statements about what his prejudices are.

You might agree with his prejudices - but there is no argument. There is no persuasion.

This kind of fallacy is hard (possibly impossible) to avoid (given this structure of argument). Any conclusion you draw from a set of premises must have been implicit in the premises to begin with - otherwise it wouldn't be a conclusion from those premises.

Which brings us back to the initial proposition: whatever is happening when we discuss/argue it has nothing to do with the explicitly stated mechanisms of Logic - they simply don't form a coherent whole.

A therefore B

If B is is already baked into the assumption A then we haven't demonstrated anything. At best we have made an implicit assumption explicit.

This, of course, applies to all logical statements. Logical deduction can only reveal what already existed within the premises. It cannot create something out of nothing.

Revealing hidden assumptions can be useful in its own right - but Searle is trying to present a bias free argument. This is an impossible task.



That is fine. No problem.

It would be a waste of time to learn First Order Logic and Axiomatic Mathematics just so you could understand an argument that disproves them.

My fight with you regarding logic has been entirely based around demolition of a specific mechanism that you don't even subscribe to.

Your empirical (observation) based sense of logic is far more rational than formal logic. It correlates well with the principles of science (excluding mathematics).

Reductive vs expansive knowledge

My principle aim is to spotlight the inconsistency of reductive knowledge in the face of context dependent meaning.

Axiomatic Mathematics was only ever useful as an example of the failures of reductive knowledge and I feel it was a mistake to introduce that proxy war in the first place.

In light of that...

A statement of context with respect to knowledge

If I understand what you're saying, I agree. I once sat down and asked myself, "If this is correct, what would knowing the truth be?" I realized the only way to know truth, which is what is real, would be to have observed and experienced something from all possible perspectives and viewpoints, and an understanding of all conclusions which did not contradict themselves (as well possibly the ones that do!). — Philosophim

Reductive approach to knowledge

In light of the above, it should be clear that reducing or removing context is a movement away from knowledge.

Which is to say, the reductive approach to knowledge is counter productive.

Context matters

The context of a statement matters when interpreting the meaning.

This is an observation.

A statement with no context has no inherent meaning.

The better the context is defined, the better the meaning is defined.

The better any given context is defined, the better every other context is defined.

Virtuous Circle

The better we understand a given concept, the better we understand every other concept.

If I understand what you're saying, I agree. I once sat down and asked myself, "If this is correct, what would knowing the truth be?" I realized the only way to know truth, which is what is real, would be to have observed and experienced something from all possible perspectives and viewpoints, and an understanding of all conclusions which did not contradict themselves (as well possibly the ones that do!).

It is an absolutely impossible endeavor. — Philosophim

Impossible to reach omniscience - yes. But partial understanding is better than no understanding.

We are agreeing with each other so hard here it makes me wonder how we can possibly diverge elsewhere.

Yes - truth/knowledge is the full understanding of all possible contexts. We can endeavour to approach this limit knowing we will never reach it but can come arbitrarily close.

For example, the emotion of 'dread'. While we might be able to objectively ascertain that people experiencing dread have some common physical tells, that doesn't mean it describes the individual feeling the person is experiencing. While an individual can know if they're experiencing dread by the emotions they are currently having, being able to know if another person is experiencing that same emotion, despite physical tells, is only available to that specific person. We cannot experience what another experiences. — Philosophim

Again - so much yes.

Except I would cast the net much wider. Do other people experience the colour 'red' in the way that you do? This is standard philosophical fare.

I want to take it further. Apply this to everything. Your perception of the world is rooted in your experience of the world.

I think your description of 'Dread' applies to every concept that we can feel, experience or think.

Rain is a common experience and by sharing our experiences we come to regard the experience of rain as being objective - something that everyone experiences in the same way. However your description of 'dread' applies to my experience of 'rain'.

You've talked about taking shortcuts where we don't want to build everything from first principles just to say hello to the neighbour...

Shortcuts are fine, even necessary, but they are a convenient approximation.

When doing a deep dive into philosophical knowledge we are liable to find ourselves led astray if we rely on the shortcuts as being fundamental in, and of, themselves.

It depends on your definition of 'describe'. If I describe a lemon as a yellowish sour fruit, its a description is it not?" When we say that things are impossible, we have to be very specific as you also realize that language and meaning can be very indefinite unless we make it so. — Philosophim

Yeppity yep.

That is one way to describe it, but I can describe a scenario that counters that. The integer "1" is really a representation of our ability to discretely experience. "One field of grass. One blade of grass. One piece of grass." We can discretely experience anything. Not just parts but everything. The discrete experience of "Existence". A sensation in which there is nothing else but the experience itself. No breakdowns, no parts, no relation. It is within this that relation forms when we create parts. But the experience of the whole, of being itself, is one without relation. — Philosophim

Here we part ways.

You purport to demonstrate that we consider '1' discretely.

I'm looking at your description and seeing you describe '1' using a bunch of explicit and implicit relationships.

"A blade of grass" is very different to "A field of grass".

Scenario

You sit down to read a book. The first page contains the word 'one':

"one"

And that is it. That is the entire book.

You understand 'one'. The word has some meaning for you. But simple stating the word 'one' doesn't expand your knowledge. No new information has been conveyed.

To convey information you must put that 'one' into some context - some set of relationships with other words.

Moreover

Compare your argument here with the first paragraph of your post.

As I read these two sections I see a disconnect. You are contradicting yourself. You are arguing two distinct contradictory positions. In the first paragraph you argue for the importance of context, in the latter paragraph you are arguing that we can consider things without context.

Society's mistake

I strongly suspect that this inconsistency is systemic.

Everyone knows that context is important to understanding a given sentence. At the same time, everyone knows that there is a fixed definition of the words they are using and "you are using the wrong definition".

The idea of meaning being dependent on context isn't new or surprising in any way.

And then we have everyone from philosophy through mathematics to physics arguing that there are inherent truths independent of context.

Agreement

Your first paragraph is a beautiful statement of understanding.

You obviously understand that full knowledge (truth) requires all the contexts.

This is my proposal. This is where I think we can make progress as philosophers and as humans. This is where the pursuit of knowledge lies. This is the path to all possible understanding. True, we can't reach the limit - but we can approach that limit.

The flip side

Despite this clear understanding, Everybody and their dog suddenly starts insisting that knowledge, truth, meaning, ... are inherent properties independent of context.

This isn't a rational position. It is a direct contradiction of our direct experience of the importance of context.

Even after making the clearest statement of meaning/truth/significance I have ever seen; you flip around to arguing for inherent meaning just a few paragraphs later.

It is a potentially fascinating study to see why the myth of a reductive approach to knowledge persists despite the direct evidence of the importance of context. However, my immediate goal is to make this inconsistency explicit.

Reductive vs Expansive

I'm picking on your inconsistency; but that inconsistency is representative of the entirety of modern thought. The reductive approach to knowledge is exactly the wrong direction.

Read your first paragraph and bask in its glory. Greater knowledge, understanding, truth, ... comes through greater inclusion.

Each piece of context you remove takes you further away from knowledge. Every extra piece of context takes you closer to knowledge.

You have defined what knowledge is. Commit to that definition. Be consistent in your use of that definition.

The set of finite-length strings over an at most countably infinite alphabet is countable. There are countably many strings of length 1, countably many of length 2, dot dot dot, therefore countably many finite strings. — fishfry

But a sentence is not the same as a string.

The interpretation of a sentence depends on the context/axioms. The same string in two axiomatic systems is two distinct sentences.

In regard to the paper you referenced in the OP this can probably be fixed up to reference only the possible statements in a single axiomatic system. However, the assertion that natural languages are countably infinite no longer holds given there are an uncountable infinite number of contexts for any given sentence.

Way out there take

I would go significantly further.

The interpretation of statements within an axiomatic system are determined by the context/axioms.

In order to consistently and correctly interpret a given statement within an axiomatic system it is necessary to have an accurate and complete statement of context.

That is, the axioms for an axiomatic system must, themselves, have a complete statement of context (axioms must have axioms to determine how those axioms should be interpreted).

This results in infinite regression.

Axiomatic Mathematics/mathematicians do try to mitigate this problem by using previous axiomatic systems to specify axioms for subsequent axiomatic systems; but this only obfuscates the problem, it doesn't resolve the fundamentally unresolveable issue:

Without a full and complete initial specification of context, it is impossible to derive a full and complete specification of context.

Okay. Are all ideas equally simple? Is the idea of an elephant the same as the idea of a line from the perspective of complexity?

The graph presented in the OP consists of nodes and edges. These are mathematical ideas. Do you agree that a network of nodes and edges is a simple idea?

Guess #3: "The Big Bang" (i.e. planck-radius universe). — 180 Proof

Your are proposing a self propagating construction in the Big Bang? Some process that caused reality to come into existence from a formless void?

I had in mind something like an existing pile of bricks that is constructed into a shape. You appear to be taking one step further back and proposing the construction of the bricks themselves from nothingness.

That is, I have taken the universe as a given and considered the simplest possible mechanism for the continuation of an already existing system.

You have prompted me to reconsider whether the question of genesis is amenable to some equivalent approach.

Infinite regression

A naive approach to first cause leads to infinite regression with each cause needing some prior cause.

Taking the universe as a given sidesteps the problem of genesis but doesn't really solve it. An eternal (has always existed, will always exist) universe has its own conceptual problems, not least of which is the emergence of entropy.

Anthropic Principles

I am tempted by the Strong Anthropic Principle in which the universe exists in order for us to observe it.

What is the point of a universe that isn't aware of its own existence?

However, I can't immediately see a way to make a testable hypothesis out of this.

Testable

With Simplest possible universes I can build teeny tiny complex systems (universes) and compare their characteristics with our observed universe.

The proposition that our universe can be described by iteration of a direct graph is testable.

The limitation is that I have to exist in order to make those teeny tiny universes and compare them to our observed universe.

I have to take my existence (and the existence of the universe) as a given.

I'm pretty sure this is a hard limitation. But your comments have prompted me to have another consider - and there is a little tickle in my mind that is suggesting such consideration is worth some effort.

The idea of connections making up everything (like some sort of code that determines what particles are where) is attractive to me because every particle with mass must be made up of others unless mass is a trait like location and could be coded for by these connections. — Igitur

I'm glad I could tickle your brain bone a little. I'm not disagreeing with you - more refining a point I think is relevant:

As noted in the OP, I think that this is the mechanism of our observed universe.

Relevance

We have a direct graph with nodes and edges and Change A.

The closest thing to a dimension in this directed graph is an edge.

Space, time, mass, charge and consciousness are all emergent features of changing nodes and edges (according to me).

Edge as the fundamental unit of the universe

Instead of particles being the fundamental unit, we have the space between as the fundamental unit.

If an interaction is "one rearrangement of edges between nodes" we suddenly find that we don't have to think about what happens between interactions.

There is no space in which particles move. Like frames of a film, a series of interactions can give the impression of continuous movement in space.

Note: In real, genuine, actual physics we observe interactions. We never observe anything between interactions. The notion of particles travelling through space between interactions is entirely theoretical.

Our conception of space is based on trying to understand the sequence of interactions that we observe.

There are explanations of sequences of interactions that exhibit complex behaviour without the need for dimensions, mass, charge, spin or momentum as a priori assumptions.

We don't need to assume space time in order to observe the sequence of interactions that we see.

Having no parts is not 'Nothing'. The Fundamental can't have parts because those parts world be more fundamental; thus, the fundamental consists of only itself; — PoeticUniverse

It looks like we are in agreement here. Yes - a distinctive property of the very simplest thing is that it is indivisible. If it were divisible into component parts it would clearly not be 'simplest'.

I'm a little nervous about conflating 'fundamental' with 'simplest' insofar as an electron is described as a fundamental particle in Quantum Mechanics but is not simplest in regards to being composed of multiple, distinct properties.

It looks like your point regarding the persistence of fields vs electrons is making the same point?

Further discussion of simplest/fundamental

An ocean wave is emergent behaviour of large numbers of 'particles'.

If we cut a human up into smaller and smaller pieces looking for the fundamental unit of humanness we find ourselves with a mess of giblets and rather less essential humanity. Likewise for the fundamental waveness of a wave.

As such I can sort of, vaguely, see an argument that a wave is indivisible.

But, as a matter of practicality, we can divide a wave into component parts. A wave is divisible and hence not fundamental/simplest.

A mathematical point is, I would argue, indivisible. It is not composed of subunits. However, I think that a mathematical point is a complicated way of saying 'nothing'. Having a pile of mathematical points is functionally equivalent to having a pile of nothing.

A set is a container. The only inherent property of a set is that it contains. In principle, a set is independent of physics and not subject to reduction to physical fundamentals. A set is a candidate for simplest/indivisible.

An edge within a directed graph is a link. As with sets, the edges within a graph are supposed to be independent of specific physics.

Agree/Disagree

Having no parts is not 'Nothing'. The Fundamental can't have parts because those parts world be more fundamental; thus, the fundamental consists of only itself; it does not get made and it cannot break, so there is no sub-dividing it. For example, a wave would be continuous and have no parts. Waves are also ubiquitous in physical nature. The Fundamental has to be the simplest, by the necessity shown above. We can also see this trend as we look more and more 'downward' — PoeticUniverse

I agree wholeheartedly.

An electron is temporary, as is all else but the permanent quantum fields. An electron can be annihilated by a positron, but electrons can persist awhile in the right emvironment. — PoeticUniverse

The Real Number line is a typical representation of the mathematical concept of field. This field can be divided into the individual real numbers. This does not seem to fit our definition of simplest.

Just for funsies. Are you thinking of a human building a physical universe from raw materials, or a god creating a dynamic world from scratch? — Gnomon

As noted earlier, somewhere, I find myself constrained such that I require my own existence as a pre-requisite for... pretty much everything. At the moment I have no conception of how I would create myself and a universe out of sheer void. I have to take the existence of a universe as a given and work from there.

But concrete is loose sand bound together by a mineral matrix, the binder. — Gnomon

Well... funnily enough. Given the binder, it is sufficient by itself.

The little revolution I'm trying to foster is regarding the necessity of the bits between structure.

A network of relationships doesn't require us to define what the relationships are binding. The structure of the relationships is enough by itself.

Pursuit of knowledge: scenario 1

We wish to understand, say, consciousness. We want to drill down to the very core of what consciousness is to arrive at the heart of the conception.

As with when I was chopping up people earlier in this thread, we find that chopping up concepts into their component pieces tends to leave us with a messy pile and no sign of the original concept.

The definition of madness is doing the same thing over and over again and expecting different results.

Going all Sweeney Todd on concepts to find their essence is just murder. Philosophy finds itself chasing its own tail because a reductive approach to knowledge just lead to corpses.

Scenario 2

Concepts are defined by what they are not.

The significance of the Integer 1 is its distinction from the Integer 2 (and 3, 4, apple, infinity,...)

To fully understand consciousness, we need to fully understand everything that is not consciousness.

Everything is a single connected whole and each piece is an aspect of the whole.

Yes - hippy dippy "everything is one" except seriously.

Your experiences are part of your existence. If you try to consider your existence in isolation from your experiences you are liable to find you don't exist anymore.

In order to argue, you first need to exist. Every argument you engage in requires your existence. If you try to divorce the process of argument from your existence your argument ceases to exist.

That is circular

"If each idea is defined by every other idea, then reasoning is circular; there is no starting point."

Yes.

We are living inside a closed system. When you point to something it is one piece of universe pointing at another piece of universe.

When you describe something you are using one piece of universe to relay information about another piece of universe. Your concepts of the universe all derive from the universe.

Physics is literally describing the behaviour of the universe in terms of the behaviour of the universe.

Not Nihilism

Understanding the relationships between things is knowledge.

The relationship between the integers 1 and 2 is our understanding of those integers.

Context matters

Everyone knows that context matters.

Dial that up to 11 and keep going.

Context is everything. Without context there is nothing.

This isn't new territory.

Probably the bit (or qbit), right? 1 or 0, nothing more complex. Presumably, you can say everything about any of the other candidates (except perhaps ideas) with bits. — Count Timothy von Icarus

Reasonable answer - but I'm going to disagree.

In order to build a computer, the bits have to have specific relationships. There has to be structure between individual bits.

So while bits are notionally simple, by the time you can build anything with them you have stealth included some assumed structure. The bits+structure is less than trivial (simplest).

There is still the potential for a very simple system - but without an explicit statement of the structure, I'm inclined to think you are hiding more complexity than you realise within your implicit assumptions.



If I may impart my own spin to your thoughts...

I think your scepticism is/was well placed.

Physics faces the same problem as philosophers:

What caused the first cause.

Physics as a statement of observations is fine: "If we do x we observe y".

Physics as an explanation is less founded than Lord of The Rings by J.R.R. Tolkien. At least Tolkien understood what an allegory was.

Saying the Higgs boson did it isn't an explanation when you don't understand why the Higgs boson does it. As explanations go it is no different to saying God did it. It doesn't explain. It is a null statement.

It isn't clear to me that individual physicists understand that physics cannot explain observation - only describe it. I fear the myth of physics as explanation is near universal.

"This is what we observe" is in no way equivalent to "this is why we observe...."

Copied and edited from another thread

These can be boiled down to stillness and motion. The stillness of objects is sustained against the motion of relationships. Motion is as ubiquitous as the stillness it moves against and neither objects nor stillness nor relationships nor motion is first, or last, or the essence, or the true being. Because they are all at once in the paradox, which is the being, the substance, the related ones. — Fire Ologist

Beautiful. I would be interested in an expansion of your concept of 'paradox'. Context makes it appear relevant and I can see several ways in which our understanding of our own existence and communication could evoke chicken and egg notions of precedence.

Otherwise, you point is well made and taken.

Course correction

• My argument between objects and relations is mis-focused. You are right that it doesn't matter whether a given perception is illusion.
• I'm actually arguing against impossible assumptions. My perception is that there is one large multifaceted assumption that is impossible.
• Description has a mechanism. Some things can be described. Some things cannot be described.

Mistaken assumption

It is widely assumed that it is possible to describe an object.

This is wrong. It is a futile effort.

The Integer 1

The integer 1 has a set of relationships with the integer 2. Likewise for 3, 4, one million, -69, an apple,...

All these relationships form a pattern. This pattern is our conception of what the integer 1 is.

With many interconnected relationships we have a compelling sense of what something is.

If we were to remove each relationship to get to the essence of 1... we would eventually find we are left with nothing.

The integer 1 is the set of relationships it has with everything else. The integer 1 outside our universe with no relationships to anything is indistinguishable from nothingness.

Descriptions

A description is a network of relationships.

The mechanism of language is to build a network of relationships.

Essence

The typical process for finding the essence of meaning, significance, etc; is to strip away all the miscellaneous chaff until we are left with the essential core of the thing we are examining.

This is why this mistaken assumption is so devastating to the pursuit of knowledge.

Every philosophical, mathematical and physical discussion that tries to get to the core of a matter by stripping away all the extraneous concepts, assumptions and frippery is dooming itself to futility.

This is my argument

The assumption that meaning, significance or what have you, is an essential quality of a thing is the single greatest mistake of modern thought.

The significance of a thing is the sum total of its relationships with everything else. Remove the relationships and you have nothing.

This illusion is only here in distinction from some other that (which other can be an illusion as well, or anything, as in comparison to “this” particular illusion, the other need only be a “that”.) — Fire Ologist

I would hate to put words in your mouth - but your post screams to me that you already see this. You already know that every "this" needs all those "thats" in order to have significance.

Is it true?

Is language the process of creating relationships? Yes.

Read a dictionary. Examine those definitions. A simple empirical verification.

For a really fun time, consider the equations of Quantum Mechanics. An equation is a network of relationships.

Every mathematical equation is a little (or large) network of relationships.

It doesn't matter what the essence of the integer 1 is. It was never relevant. What we manipulate and use is the network of relationships.