logic. — Philosophim

You keep using that word. I do not think it means what you think it means.

First Order Logic is not the same thing as you are talking about.

It is clear you have some sense of what Logic implies to you - but you aren't communicating that understanding.

One of the features of informal languages is that they do not have strict definitions. Informal Logic is pretty much whatever you want it to be.

In contrast, First Order Logic and Axiomatic Mathematics are strictly falsifiable. I don't pick on Axiomatic Mathematics just because I like bullying mathematicians. Axiomatic Mathematics provides a (relatively) known, fixed target.

I've presented arguments relating specifically to the mathematical specification of Logic. Your counter has been to make statements regarding something that has nothing to do with First Order Logic.

It isn't that what you are saying is necessarily wrong. It is that it doesn't apply to the specific mathematical artefact that is Formal Logic.

Edit: From what I can see, your idea of Logic is Empirical. Observation is the determinant of truth. This is a reasonable foundation. However, First Order Logic has nothing to do with empirical observations. It is specifically designed to be independent of any particular universe.

You can, however, analyse the conditions under which they occur, which are different. Hence their possible distinguishability by analysis. — jkop

The premise doesn't appear demonstrated to me.

You assert that there exists some difference between hallucination and reality that can be analysed to show the difference between the two.

I don't see why this difference must exist. I can see that it might exist. But as an a priori for a philosophical position I am deeply sceptical.

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.

So it doesn’t matter whether we’re talking about seeing object and their relations or just relations of relations, the epistemic meaning of the sense data we perceive is dependent on the nature of our conceptual schemes. Do you agree with this? — Joshs

I haven't previously come across Wilfred Sellars. I've has a quick dash through some summaries and added him to my reading list.

I strongly agree that perception and thought are intimately connected.

For the rest, I'm concerned you are asking me if I'm still beating my wife. In reading the question I have the feeling I'm being asked to agree to a conceptual framework.

Specifically, I think that everything is an aspect of a singular whole. I can perceive differences between senses, thought and language, and in a casual conversation I'd readily accept the distinctions. But in the midst of constructing philosophical foundations I'm much more reluctant to make an implicit agreement that epistemic knowledge is not just an aspect of conceptual schemas.

Further, I think language is primarily proscribed by the nature of the universe. While there are cultural influences, the core mechanism of language is not culturally dependent. In practise, almost nobody uses formal logic in everyday conversation.

As such, I question the premise that particular conceptions of how language function have a significant impact compared with the actual mechanisms of language.

My point is that we can invent an infinite number of distinctive ways of viewing and analyzing the world. The proof comes in its application. I hope this lengthy reply answered your questions and added a little more clarity to my points. Let me know what you think! — Philosophim

I'm liking your approach the more I play/argue with it. My specific argument regarding objects/relationships is misguided. More details below but as a gist - I still feel there are hidden assumptions in your statements that run the risk of invalidating parts.

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.

Ideas. — RogueAI

It is possible to consider the entire history of philosophy as an examination of ideas.

I struggle to imagine any scenario in which that history can be boiled down to "the simplest conceivable building block".

I can see ideas being a building block - just not a simplest building block.

Furthermore, there appears to be a wide variety of different ideas. Are you stating all ideas are trivial? or do you have a specific idea in mind as being a foundational starting point?

What do you think makes ideas simple? The lack of a physical component?

An electron is directly a quantum of the quantum electron field, which field appears to be fundamental. — PoeticUniverse

There is some ambiguity in your statement. Are you saying an electron is fundamental, or the quantum electron field?

In either case... Okay. And?

I don't know how to engage with your comment. I don't know if you are just expanding on the idea of fundamental properties in Quantum Mechanics or you are correcting a misapprehension you think I have.

Perhaps you are just adding your own snippet to the conversation.

My expectation from philosophy forums is a discussion of ideas. A dialogue.

Your expectation doesn't have to match mine. It just means I'm likely to bug you to expand on your point until I can see something I can engage with.

The simplest fundamental would have no parts, which is fine, for elementary 'particles' would be rather stable arrangements of it, such as in QFT (Quantum Field Theory). — PoeticUniverse

'Nothing' is certainly simple... but it isn't really a building block.

A field is hardly simple. You have an n-dimensional continuous field which can be infinitely sub-divided.

It took Russell hundreds of pages of dense mathematics just to get to 1+1=2. I'd have to look to see if there is any construction for real numbers.

It is true that Euclidean Geometry (and many non-Euclidean counterparts) take a field of some kind as a given.

In this sense, fields are certainly foundational/fundamental to large parts of mathematics and physics.

However, it isn't clear to me that Fundamental == Simple.

I'm not saying you are wrong - I'm saying you will have to do much more than mentioning the idea of fields to persuade me that fields constitute simple, let alone simplest.

Guess #1: A vacuum fluctuation.

What is the simplest possible component of change we could apply to that building block?

Guess #2: To make measurements with – interacting via – (massless) quanta. — 180 Proof

This is a good answer. I see where you are coming from. A vacuum fluctuation is among the smallest discrete measurements we can make in physics.

Furthermore, going to direct observations in physics potentially bypasses hidden assumptions in the way we think about things that may lead us to regarding complex concepts as simple.

On the downside, it isn't clear how to use a single interaction as a building block.

To get as far as a single observable interaction, Quantum Mechanics tells us we need a space/field within which that interaction can occur and the interacting components need a mechanism of interaction.

I'm not disagreeing with you. I'm wide open to the idea that an interaction is, itself, a fundamental building block. And that an interaction is potentially very simple.

Under what circumstances could an interaction (Quantum Fluctuation) be simple and constructible?

The second sentence is granted, but the first sentence is not immediately intelligible. Suggest review Robinson's "h" and reconsider. — alan1000

Sorry, sticking "Robinson's "h"" into google isn't showing results I immediately recognise as relevant.

Can you give more context or a direct link, please?

You cannot say, "This and that are connected" without both "this" and "that". — Philosophim

I see your arguments and they seem well formed given your assumptions. We have enough commonality that we are clearly drawing from similar enough experiences to communicate.

I can see how it would be annoying if you felt I was derailing your thread with my pet theory. Tell me to bugger off if you feel like it.

However, I'm not just nitpicking in order to find a hook. I have some sense of what you are trying to do in presenting a framework of thought and communication. I think others have made similar efforts before and met with lacklustre success because you are (mistakenly) assuming a fundamentally objective universe.

As such, I suggest steering the discussion towards the question of whether it is, in principle, possible for two Cooperative participants to arrive at a definite solution.

Onwards

My disagreement is with your fundamental perception of discreteness.

In the above quote you state that "this" and "that" are requirements for a connection to exist.

I disagree. I think that "this" and "that" are illusions created by the connection.

It is the relationships between 'Left' and 'Right' that define each of them. Similarly with 'Hot' and 'Cold', 'Tall' and 'Short', ....

Distance, time and velocity are meaningless terms without their relationships to each other. We measure time via periodic movement in space.

These examples won't convince you. I'm not trying to convince you (yet).

What I'm interested in is whether you can imagine a relationship centred reality as distinct from your current perception of an object centred reality?

Can you imagine the possibility of some other universe existing with only relationships? Are objects a requirement for a universe to exist?

For my part, I can see your assumption of the primacy of objects over relationships. I'm not in doubt about what it is you believe. I disagree with it.

What type of argument would you present given that we disagree over the indirect part of perception?

We both agree that we directly experience Sensory Data. You perceive that Sensory Data as having been caused by objects (hence you have indirect perception of objects). I perceive Sensory Data and more Sensory Data.

What reason can you give me to believe your indirect perception of objects is an accurate representation of reality?

Its only proven as long as "There are some lemons that are not yellow" is not introduced. — Philosophim

What do you mean "introduced"?

Are you saying there is a second round of axiomatic systems where we introduce more axioms?

The very strong impression I get is that you have an intuition about what is true and you are trying to fit that intuition into systems without understanding the intuition yourself let alone communicating it to others.

I can't see the argument you are making. What I see is:

"Yes, Yes, but when we introduce stuff then something."

Since I've seen you understand and use effective arguments, this non-statement tells me that your prejudices have come up against a set of facts that don't fit. In a panic, you are re-iterating your prejudices rather than forming an argument which would require examining those prejudices against the new evidence; a process that you can already see will be deeply uncomfortable for your prejudices.

I'm not accusing you of anything nefarious. This is a natural (and usually unconscious) mechanism.

As a rule, people will try every possible alternative before examining and changing their prejudices. If there is a chance that shouting loudly "OVER THERE!" will work then you (or your subconscious) will give it the good old college try before taking the risk of learning and developing.

Learning is painful enough without some dick saying "Look! Over here! This person is learning!"

I could, of course, be reading too much into a post that forgot to bring the argument.

Segue...

Learning and argument in the absence of Logic

Since Axiomatic Mathematics has been hoisted by its own petard in the form of The Principle of Explosion; and informal logic bears only a passing resemblance to the now defunct formal logic; how can we best understand the processes of learning and argument?

A story of survival

The trick to surviving is being good at survival.

The newly born mammal that instinctively seeks its mother's milk has a better chance of passing on its genes than one that doesn't.

The foal that can stand and run within hours of birth has a greater chance of evading predators than one that takes months to stand up.

Having a genetic instinct can be a great aid to survival, but developing such an instinct takes many, many generations.

Mimicry

The parents of a baby have survived long enough to have a baby. If the baby mimics the behaviour of the parents it is taking on behaviours which have already been shown to be successful.

When you started to learn your native language you started by mimicking the sounds and shapes.

As the process continues the depth increases. Each mimicked behaviour is associated with events. We only do the "poo poo" mimic when we have a particular feeling.

When you first started learning to multiply and divide you didn't have an innate understanding of the Set Theoretic derivation of natural numbers. You just followed a particular pattern of behaviours that everyone agreed was the right pattern in that circumstance.

Calculus is just a matter of learning and following a particular set of steps in a particular set of situations.

Consequences of Mimicry, learning

Learning through mimicry is fast. One of the great strengths of humans is their ability to absorb a large number of different behaviours in a short time and, as a rule, present those behaviours at the right time.

It isn't practical for everyone to analyse each new piece of information, weigh all the competing theories and come to an objective conclusion based on the evidence. If you had to build everything from first principles working from Plato through to Russell before you could accept what the math teacher is telling you we'd still be flinging excreta at each other.

Just learn the behaviour, learn the rules for when to apply it. Done. Maybe later we'll refine the behaviour and the rules but all you have to do in this moment is memorise and apply.

A downside of mimicry is that conformity is king. Accurate and appropriate application of mimicked behaviours is (or was) a matter of life or death. The wrong ritual meant the hunt failed, or the crops failed, or the bed was within reach of the bear.

Complex Mimicry

A set of behaviours and the rules about when to apply them can be arbitrarily complex. Circumstances can overlap such that multiple behaviours are applicable with sophisticated rules about which take precedence or how to combine behaviours.

Nor is mimicry static. We refine and improve based on our experiences.

Knowledge

This story about mimicry has one particular feature I'd like to underline: Logic isn't necessary.

The initial justification for mimicked behaviours was that the person being copied had lived long enough for you to come along and copy them.

Survival of the fittest applied to behaviours. (quick shoutout to Richard Dawkins' 'Memes').

A cat learns what behaviours result in food, or scritches, or being left the hell alone.

Animals are able to learn and adapt to situations without the use of formal logic.

Humans can, arguably, learn more behaviours with a greater depth of complexity for when and where to apply them but that is a difference of degree, not of kind.

The tale of the Pacific Cargo Cults

Some Pacific Islanders would make hats and gesticulate at the sky in the hope of bounty from the heavens.

During World War II, American supply bases were setup on remote Pacific islands. Planes would be guided in using radio headsets and semaphore. The planes often carried food and other luxuries.

When the American's departed the islanders tried to call down fresh bounty by mimicking the ground crew. They didn't know that essential parts of the ritual included very specific hats and membership of the United States of America Armed Forces.

Phones

The majority of people happily use a mobile phone to call up that funny video without knowing how one works.

Physicists can plug values into formulas, perform the appropriate rituals and extract useful results. But any physicist who claims to fully understand General Relativity or Quantum Mechanics is stretching the truth.

If you've ever met an accountant, or worse, an economist you will know that they confidently perform the prescribed tasks with little comprehension of the tools and processes.

Recent research has found that Depression is not due to serotonin or dopamine deficiencies. No one knows why anti-depressants work.

The whole history of medicine is rituals that at least a few people survived so they kept doing them to the next victim.

The mechanism of Axiomatic Mathematics is a ritual: Follow these deterministic steps. (Did you know, computer programs are axiomatic systems. They start with an initial condition and then iterate those conditions using a set of rules. (This isn't me being quirky about where I apply definitions - Computational axiomatic mathematics is an entire thing)).

Thoughts

My thoughts consist of networks of relationships. These networks have shapes

I compare shapes in my mind. Some shapes mesh together well. These seem true, valid, justified to me.

Some shapes are discordant. Their existence distorts and corrupts other shapes until it is barely possible to recognise what those shapes signify. These indicate a faulty relationship. One or more of my internal relationships is incorrect.

Fixing the networks when a fault has been identified can be laborious. It largely comes down to a matter of trial and error of changing relationships until they once more form a harmonious result.

Discordant

An axiomatic system is in error if it produces contradictions. Networks of relationships are in error if they are discordant.

I think these two descriptions share a common observation.

We have a case of "I know it when I see it" that is really hard to pin down without running into trouble. In the case of axiomatic mathematics, as soon as you define what a contradiction is, you have proven everything to be inconsistent.

Now, imagine a network of relationships. Imagine every possible network of relationships. Can you see them?

Notice how one network does not preclude another?

In principle, you can have every possible network of relationships in your mind at the same time (I'm sure you have a large mind).

Networks of relationships do not contradict each other simply through the nature of their shape.

If we find some concepts to be discordant with each other it is not due simply to their physical form.

We could beat around the bushes, but the significant determinant is you.

Without you

Without you there is no meaning, no significance, no discord.

A tiger crouching in the bushes is just a shape in the universe; no more, or less, significant than any other shape... until you give that shape significance. You walking past that bush gives the shape significance. You determine how you respond to the networks of relationships that you perceive around you (and within you).

If you abstract away your existence there is nothing left.

You need to exist to perceive. You need to exist to think. You need to exist to argue.

Your existence is the foundation of your perceptual universe.

Trying to make statements as if you don't exist is futile. If you don't exist you can't make statements. If you don't exist you can't decide what is meaningful.

Summary

Everything is relationships.

Among these relationships is the relationship between your existence and everything you do and experience.

If you try to sever this relationship, you cease to exist.

While optimally, we should use distinctive contexts that lead to clear deductive beliefs, — Philosophim

Could you define 'distinct' for me, please?

Everything I see is connected. Connection seems to me to be one of the fundamental properties of the universe.

This means that everything is an aspect of a single connected whole.

Your use of 'distinct' gives me the impression that you think we can chop off bits of the universe and consider them in isolation.

The idea of 'hard distinction' makes no sense to me. The things we experience are part of the universe. Saying they are not connected appears counter-factual to me.

I do, of course, agree that there are observable differences. Indeed, 'difference' is another fundamental property of the universe.

Given these two fundamental properties, they must both be aspects of the same thing.

So, I see difference and connection as intimately connected concepts that cannot be separated. Each one is part of and requires the other.

Beyond this, I think that every concept we hold is defined by its connection to all the other concepts. The connections a concept has IS the concept.

Remove those connections to other concepts and you are left with nothing.

As it stands, your references to distinctions run counter to my direct experience. Or I don't understand your concept of distinction.

I think you have a severe misunderstanding. — Philosophim

Right back at ya, big fellow (in a friendly, affectionate and non-gender assumptive manner).

Common terms

Formal and informal:

Logic existed before mathematics formalised it.

Natural languages (such as English) evolve over time. There are no explicit rules about what can and can't be done with natural languages. There are conventions, but even these evolve with the language and are more what you'd call 'guidelines' than actual rules.

Informal logic is an aspect of natural languages and has no strict rules.

Axiomatic Mathematics is an attempt to improve on natural languages by providing strict rules that are applied consistently. Mathematics refers to these strict systems as formal systems (as opposed to natural languages being informal systems).

Formal Logic isn't the same as informal Logic.

It is like films that are "inspired by..." If you look closely you can see hints of the original story - but by and large they went in their own direction.

The mechanism of Axiomatic Mathematics (including formal Logic)

Part 1

An axiomatic system has a set of axioms (assumptions).

These axioms can be anything. Absolutely anything. There is no constraint on what axioms you choose.

"Unicorns exist" is a valid axiom. "All lemons are yellow" is a valid axiom. "BlubBlubBlub" is a valid axiom.

The axioms determine what the next valid statements in the Axiomatic System will be. In the case of "BlubBlubBlub" it would be convenient to have another axiom in the set which tells us what rules apply to "BlubBlubBlub" to construct the next statement.

Part 2

The rules that are explicitly or implicitly part of the axioms are applied to the initial set of axioms to get subsequent statements that are part of the axiomatic system.

This is repeated with subsequent stages include any new statements that have been generated.

The process ends when no new statements can be generated or when two statements contradict each other.

Some Axiomatic Systems do not terminate.

E.g.
Valid, non terminating axiomatic system:
{
"A"
"Append "A""
}

This system contains "A", "AA", "AAA", "AAAA", "AAAAA", ...

The statements do not appear to contradict other statements therefore this is a valid axiomatic system and each statement within the system is proven.

Proof

A proof only exists within a specific axiomatic system.

If you change the initial axioms you have changed the axiomatic system - it is now a different, distinct, axiomatic system. A statement is defined by its context. The same words can appear in two different axiomatic systems and be proven in one system and inconsistent in another system.

Proof = "consistent within an axiomatic system"

Your belief in the reality or otherwise of a given axiom is irrelevant. If "All lemons are yellow" is a statement within a consistent axiomatic system then "All lemons are yellow" is proven (within that axiomatic system).

Loose ends

Axiomatic Mathematics works on the basis of anything not disproven is proven.

An axiomatic system is inconsistent if it contains a contradiction. It is almost always impossible to show that an axiomatic system is consistent.

One of the problems is that axiomatic systems actually include all statements that are valid according to the rules of the axioms. Some of these statements cannot be found by iterating on existing statements.

Most significant axiomatic proofs rely on axiomatic systems that cannot be proven to be consistent. They are believed to be consistent. Mathematicians have tried hard to find contradictions within these systems. The longer a system goes without a contradiction being demonstrated, the more confidence that system is given as a consistent system

Important features to note

There are no subjective judgements on what is real.

The determination of proof is entirely based on consistent or not consistent.

There are no arguments over whether the axioms are justified, real, true, meaningful, significant or anything else.

If a set of axioms leads to a consistent system; those axioms are proven.

As much as I clown on Axiomatic Mathematics; mathematicians went to serious efforts to build a system free of bias.

Your personal opinion on what is true is irrelevant. What can you show?

It is a huge credit to mathematicians that they tried incredibly hard to make their assumptions explicit and their arguments falsifiable.

You pointing at a blue lemon does not disprove "all lemons are yellow" as far as Axiomatic Mathematics is concerned.

The Blue Lemon

What is blue? Define blue. Is blue the same category as yellow? can a lemon be both blue and yellow?

Is what you are pointing at a lemon? Is a real lemon equivalent to a conceptual lemon? Are lemons a figment of your imagination?

Are all lemons identical? How different can one lemon be from another lemon and still be a lemon?

Do I exist? What is the meaning of existence? And etc, etc and and etc.

Mathematicians sought a solution that doesn't involve all the mucking around in philosophy forums.

"Given a set of statements and associated rules; do we arrive at a contradiction? yes or no?"

Formal (mathematical) logic is not the same thing as informal (English) arguments.

Evidence based belief sounds weak to me...like its reasonable behavior of a sheep or a follower. I don't question faith unless I have to... — Kizzy

Your posts read like stream of thought. In your second post, particularly, you seem to be riffing on the ideas of existence, hallucination and nihilism.

The primary relationship between your written ideas appears to be temporal.

I think knowledge/understanding is directly correlated with the network of relationships we have between ideas. Any given idea primarily exists as its relationship to all the other ideas. The shape of those relationships is where we perceive meaning and significance.

By presenting your ideas as a single, chronological list of thoughts you strip away much of the rich interplay of concepts.

I suspect that given a long enough list of thoughts it would be possible to statistically analyse the frequency and position of ideas to get a sense of your internal structure of relationships.

As such, I recognise what you are saying as genuine reflections of what you think and believe.

However, I'm not going to do statistical analyses on your stream of consciousness. Partly because no-one has time to do that but mainly because the process of creating structure on the page out of structure in the mind is an essential component of dialogue.

The effort to represent our internal shapes in an external format is part of learning and growing.

Even if no-one reads what we write, we learn from the process of structuring our writing. By examining and considering our thoughts as we express them we can change our ideas even before we engage with other people.

Stream of consciousness can be a useful insight into our own thoughts but as a form of communication with other people it lacks an essential element of self-reflection.

Next

The Principle of Explosion is why inconsistency is a problem. — Treatid


Sure, but you never pointed out the inconsistency that destroys Axiomatic math. — Philosophim

As a demonstration of the principle, consider two contradictory statements—"All lemons are yellow" and "Not all lemons are yellow"—and suppose that both are true. If that is the case, anything can be proven, e.g., the assertion that "unicorns exist", by using the following argument:

1. We know that "Not all lemons are yellow", as it has been assumed to be true.
2. We know that "All lemons are yellow", as it has been assumed to be true.
3. Therefore, the two-part statement "All lemons are yellow or unicorns exist" must also be true, since the first part of the statement ("All lemons are yellow") has already been assumed, and the use of "or" means that if even one part of the statement is true, the statement as a whole must be true as well.
4. However, since we also know that "Not all lemons are yellow" (as this has been assumed), the first part is false, and hence the second part must be true to ensure the two-part statement to be true, i.e., unicorns exist (this inference is known as the Disjunctive syllogism).
5. The procedure may be repeated to prove that unicorns do not exist (hence proving an additional contradiction where unicorns do and do not exist), as well as any other well-formed formula. Thus, there is an explosion of true statements. — Wikipedia

Here we have the contradicting statements "All lemons are yellow" and "Not all lemons are yellow" proving that "unicorns exist".

Exactly the same process can be used to prove "unicorns don't exist".

We have a free proof machine. Plug in any sentence and we can prove that sentence is true.

If everything is provable, including the direct contradiction of everything; then proof is meaningless.

The trouble is that everything is provable. It is right there. We can plug in any sentence whatsoever and prove that sentence to be true.

The Principle of Explosion works for any sentence. Not "any sentence in a given system", not "the particular sentence I happen to feed into it".

The Principle of Explosion applies to every single sentence in every single language real and imagined.

You ask me to point to the specific inconsistency that destroys Axiomatic Mathematics...

You test my ability to take all posts in good faith.

The Principle of Explosions works with any contradiction. The contradiction doesn't have to be part of a particular Axiomatic System.

You can see how it works. Any contradiction anywhere, just once, means that every sentence and its contradiction are proven to be true,

Are you suggesting that the contradiction built into this example doesn't apply because it is made up?

Given that the made up contradiction clearly and obviously applies to The Principle of Explosion because we can see it being applied right here in this example, I'm genuinely confused as to what you are expecting.

Threshold

The threshold here is: "is it possible to state a contradiction".

An entirely consistent system doesn't contain the concept of contradiction. It is (in principle) impossible for a consistent system to describe a contradiction.

If it is possible to describe a contradiction it is already far, far too late.

The only way to have a consistent system according to The Principle of Explosion is if there are no contradictions anywhere, ever.

Just the possibility of one single contradiction anywhere in all of time and space doesn't just kill Axiomatic Mathematics, it removes it from existence.

As soon as The Principle of Explosion was stated it was Game over man, game Over!

I've read through the thread. There are some darned good points being made.

My interpretation of your paper is that you have outlined the mechanism for categorisation, applied that categorisation to modes of perception, and organised that categorisation into a hierarchy.

As far as the process is concerned, it seems very reasonable to me. I can see and understand the reasoning behind each step.

Categorisation is a powerful tool. But...

Difference does not imply (hard) distinction.

There are infinite (unlimited) possible categorisations

When spring cleaning and deciding what to throw out you could categorise by one of:

1. Least used in the last year.
2. Least sentimental value.
3. Least functional.
4. ...

You can combine these categories to create a hierarchy. There are infinite (unlimited) hierarchies.

You have chosen a set of categories and placed them in a hierarchy that produces the result you want.

Any conclusions you draw are observations about the categories and hierarchies you have chosen; not conclusions about the individual members.

You may feel that the prejudices that guided you in choosing your categories are justified. Your intuition may be right.

As it stands, all you are saying is "Given my prejudices: my prejudices".

Your prejudices could well be accurate. They are formed as a consequence of your experiences; it isn't like they are completely without foundation.

The trouble is that you are assuming your prejudices and then trying to communicate.

For example, it is obvious to you that there are distinctions. This existence of distinctions doesn't need to be justified or proven: they are right there! Just look! How are we looking at the same world and not instantly agreeing on this!? If I could just force people to understand these words in the way that I understand them...

Edge Cases

Every possible category has edge cases.

When you built your categories you had in mind clear examples that illustrated the nature of the category. A clear vision of an objective, unambiguous scale of thought and perception that everyone could readily see and agree on; that would lead to a renaissance of rational discourse inside a rational framework. (or something like that).

In practice it seems that everyone is going to extremes to define every word in the most perverse manner possible and then using those perverse interpretations to twist your straightforward statements into a knot of incomprehensibility. Suddenly everything is an exception or an edge case and you have to take a step back to even remember what your point was in the first place.

If only someone would invent a rigorous formal language that always held a fixed interpretation for every viewer.

Early Set Theory ran into trouble because some pedantic bastard found an edge case that destroyed the theory. The fix involves everyone agreeing not to do the thing, because if you do the thing everything breaks. So don't do the thing. (Russell's Paradox).

The point being that you are not the first.

The definition of madness is doing the same thing over and over again and expecting different results

The first (implicit) lesson from philosophy is: If you think you have resolved the problems of communication; you've made a mistake.

Communication itself works (more or less). But when you try to nail it down it squirts out from underneath the nail and leaves a nasty odour behind.

99.9% of theoretical mathematics is an effort to nail down unambiguous meaning. And that effort has been wasted.

Based on your guide to rationality, is it better to ignore the last two millennia of attempts to codify a universal language that is understood equally by all; or should we question why it seems so hard?

The Delusion of a Shared Universe (Why is it so hard?)

The concept of an objective universe is that there is a single, definite, objective universe that is the same for everyone. Given this assumption it seems rational to assume that descriptions of that universe should be the same for everyone.

This is wrong.

On a trivial level, two people regarding the Mona Lisa in the Louvre Museum see different things. One is standing a little to the left of the other and is a little shorter. One has only just arrived from a dazzling bright summer day and their eyesight is still adjusting to the relative dimness indoors. Each has a (slightly) different perception to the other.

In general relativity, two observers in different inertial frames disagree on whether two events are simultaneous or not. They each have accurate measuring equipment and accurately observe the same pair of events. One observes that the events happened simultaneously. The other observes that there was a measurable period of time between the two events.

In Newtonian Mechanics, all observers would observe two simultaneous events as being simultaneous.

In Relativity, two distinct observers will make distinct measurements. A Relativistic universe is fundamentally not an objective universe.

The rich man's perception of poverty bear's little resemblance to the poor man's. Someone who has lived in an abusive environment all their life has no knowledge of any other way to live.

A long, cold drink after being stuck in traffic for four hours with no air conditioning, in the middle of a Florida summer, and you've been contemplating whether it is worth drinking your own pee or if the windscreen washer fluid reservoir is drinkable... is a viscerally different experience to your normal morning cup of generic beverage.

Enough Similarity to be misleading

After a little back and forth we can all agree that 'up' is the direction away from the centre of mass of the Earth.

This could give the impression that 'up' is an objective concept. An idea that is accessible by everyone but ultimately independent of any single person. In actuality, each person has a set of experiences that they associate with the word 'up'. Each and every time a person reads the word 'up' they interpret it based on the sum total of their experiences.

As a rough approximation, it sometimes works to assume that the meaning of words exists outside of people. Common events create an aggregate average experience that might appear universal.

The rarer an event or the more closely examined an event; the less the average experience has any relevance.

First steps

Do you recognise the pattern where you have what seems like a solid, clear idea in your head but the harder you try to set that idea down in unambiguous terms that everyone should understand... the more it slips through your fingers?

I think this pattern is the major motivation behind Axiomatic Mathematics.

I think this pattern is reflected in many (possibly most) philosophical arguments.

A good first step might be to stop repeating the same thing over and over again because all those previous times they just weren't trying hard enough... and realise this is information about the nature of the universe.

Facetious

Of course people have felt that communication is flawed and thought about the problem.

If all that was needed was a slight tweaking of existing concepts the problem would have been solved long ago.

Going all the way back to first principles is daunting. Especially when it isn't clear what those first principles would even be.

On the other hand, I can see that you you put a lot of work into communicating your ideas and... it shouldn't be this hard.

Fortunately I'm available to tell you that it is so hard because you are trying to describe a relativistic universe in objective terms. This is impossible.

Describing a relativistic universe in relativistic (subjective) terms is trivial in comparison.

Is your purpose in this thread simply to critique the assumed pre-eminent role of math and logic in the ascertaining of truth ( in which case you have a lot of company, not only in philosophy but in the social sciences)? Or is your aim also to critique what you understand to be the cutting edge of ideas in philosophy and the sciences ( in which case you run the risk of reinventing the wheel)? — Joshs

Part 1

Bear with me - this may not seem like I'm answering your question but I have a plan.

The universe is exactly what we perceive. Alternatively, existence is what we experience.

There are a bunch of (or one large) mistaken assumptions that are blocking our collective ability to see clearly.

For example, it is impossible to describe non-Sensory-Data.

All the time and effort expended on trying to do impossible things is wasted. Worse, our expectations for what the answers should look like are impossible. So, even when a correct answer is staring us in the face we reject it because it doesn't conform to our (impossible) prejudices.

On the flip side, our direct experience is informed by being part of a functioning universe.

We already know that our personal experience is subjective. The idea of subjectivity isn't new or surprising.

Trying to understand the nature of subjectivity from an objective viewpoint is futile.

The only way to accurately describe the universe is from a subjective perspective. Trying to force subjective experience into an objective framework just causes confusion.

You keep on referring to me my, I. Would you be amenable to getting rid of these terms and instead just describing a constantly changing center of activity that we mistakenly refer to as a ‘self’? — Joshs

There is one existence and everything is an aspect of that existence.

This isn't some New-Age metaphor about how we should all live in harmony.

Every part of the universe is connected. There is no clear delineation where one part ends and another part begins.

Again, this isn't an original idea. The difference is that we aren't just tossing off a neat idea and moving on. The connectedness of the universe is an essential, fundamental trait. The fundamental (smallest) component of the universe must include the concept of connectedness. Connectedness has to be baked into the very fabric of the universe, it isn't an emergent behaviour that can arise from not-connected things.

A practical upshot of this is that our understanding of any single concept is determined by the sum total of all our other concepts.

For All A and All B
{
A is the difference between A and B.
B is the difference between B and A.
}

Note that things that are connected must also be different. Connections don't just connect, they also differentiate.

Following from this we get a sense of what 'self' is that isn't that far from your intuition, I think.

Agreement

I'm fairly confident that your subjective experience of 'self' is very similar to my experience of 'self'.

If we were to discuss matters of existence and identity in purely subjective terms we could rapidly reach consensus and seek out new avenues of exploration.

The trouble is that there is an expectation that valid conclusions must take the shape of 'objective statements' in a 'logical structure'. Subjective experience cannot be described in an objective framework.

It is an impossible requirement.

Language is, of course, already subjective.

This leads to situations where people successfully discuss ideas (using languages that are already subjective) and then get stuck when trying to express those ideas in an objective/logical framework. They can feel that they are communicating and then get frustrated when they can't fit the round peg of subjective experiences into the square hole of objective definitions.

I was only introducing a commonly accepted definition of solipsism, which isn’t unclear at all, and wondering if it corresponds to your use of the word. And if it doesn’t, how does your use differ? — Joshs

That is a fine definition of solipsism.

Bear in mind that I've stated that the self encompasses your entire experience.

This is, among other things, a question of knowledge. What do we know? What can we know?

Solipsism represents the line in the sand. You can know yourself and the direct experiences that are part of yourself. You cannot know anything else.

Attempting to know 'anything else' is a waste of time.

So, what about the existence of other people?

You have experiences that you associate with the concept of other people. Those experiences exist. There is no question about the existence of those experiences.

The non-sequitur arises when you question whether those people exist beyond your perception of them.

The closest I think I can parse this is: "Do the people that I experience exist outside the universe?"

You don't have to prove that people exist outside of your experience. That is irrelevant. All the things that you cannot and do not experience have exactly zero impact on you.

Note: I know you weren't arguing for or against solipsism. I am taking every opportunity to underline the point that subjective experiences are real. Subjective experiences are the bedrock of your existence. non-subjective-experiences are irrelevant. You will never experience objective experiences.

Trying to fit your subjective knowledge into an objective framework is a waste of effort and time.

Is your purpose in this thread simply to critique the assumed pre-eminent role of math and logic in the ascertaining of truth ( in which case you have a lot of company, not only in philosophy but in the social sciences)? Or is your aim also to critique what you understand to be the cutting edge of ideas in philosophy and the sciences ( in which case you run the risk of reinventing the wheel)? — Joshs

Part 2

More ambitious.

The critique is somewhat incidental albeit a necessary step.

We have two world-views that are fundamentally incompatible with each other. There is no incremental (step-wise) path from one world-view to the other.

Given objectivism it is impossible to fully grasp relativism (and vice versa).

We've seen this before between Newtonian Mechanics and General Relativity. General Relativity is not an evolution of Newtonian Mechanics. They are incompatible systems.

General Relativity is built up from first principles using only the observation that "the speed of light in vacuum is the same for all observers".

By far the largest obstacle to understanding General Relativity is trying to interpret it from the perspective of (objective) Newtonian Mechanics.

We are continuing the work of General Relativity except that our single observation is solipsism.

As such, I have two purposes:

1. Use the principles of solipsism to illustrate a relativistic system of thought.
2. Undo the mistaken assumptions of objectivism which obscure the relativistic nature of the universe.

Of these two tasks, the second is the most difficult by orders of magnitude.

The universe is relativistic. Describing the universe (including things like existence, meaning and thought) in relativistic terms is trivial. For comparison, describing the universe in objective terms is impossible.

Describing a relativistic system in relativistic terms is a joy. Everything fits together and just works.

But if you are still holding onto objective assumptions nothing makes any sense. Proof is an artifact of objective assumptions. It isn't meaningful in a relativistic system.

In a relativistic system, what you observe is the relativistic system. Your existence isn't proven by a chain of logical statements. Your existence is your observation of your existence (or more simply - you are).

Next

Axiomatic mathematics must have distinctions between systems in order to exist. But the boundaries can't be seen. There is nothing to measure. They are the poster child of belief without evidence. — Treatid


I don't understand what you're stating here. Could you give an example? — Philosophim

The Principle of Explosion

The Principle of Explosion is why inconsistency is a problem.

Note: Here's a link to Wikipedia's description of the Principle of Explosion: https://en.wikipedia.org/wiki/Principle_of_explosion

It is in plain English and doesn't require a mathematics background to understand. Anyone on these forums is likely to find it quite straightforward.

Note 2: An inconsistency occurs when two statements contradict each other or a single statement contradicts itself (c.f. Liar's Paradox).

The Principle of Explosion shows how a single contradiction in a system means that we can contradict every possible statement in that system.

In Axiomatic Mathematics, statements within a consistent system are proven. Statements in an inconsistent system are garbage.

For Axiomatic Mathematics to work there needs to be statements that are not inconsistent.

The Principle of Explosion says it applies to any system that contains an inconsistency but does not otherwise explicitly define what a system is or what the scope of a system is.

However, we can examine the mechanism of explosion.

The Wikipedia example is written in English and uses contradiction phrased using English sentences.

Can we apply the Principle of Explosion to other English sentences? Clearly we can.

Can we apply it to all other English sentences? Yes.

Can we apply it to German sentences? Well... yes...

The explosion relies on the initial contradiction. The subsequent statements don't even have to be in a specific language or even meaningful.

The mechanism of The Principle of Explosion means that given a single inconsistency, every single statement that could possibly be made can be shown to be inconsistent.

Somebody forgot to include a stop function.

Check for yourself

The Principle of Explosion says that given a single contradiction every possible statement in every possible language is inconsistent.

And you can see the process for yourself. Axiomatic Mathematics has gone bye bye and you don't need a mathematics degree to understand why.

This... is significant. Axiomatic Mathematics is a Grand Illusion that never existed.

Don't take my word for it. Examine The Principle of Explosion for yourself. Determine for yourself that the allusion to 'system' is a red herring. The Principle of Explosion necessarily applies to every conceivable statement.

Try re-writing The Principle of Explosion so it can be constrained. See if you can save Axiomatic Mathematics.

Hint: This isn't due to a typo or some quirk of an informal language. This is the result of mathematicians being so desperate to preserve Axiomatic Mathematics that they very carefully did not fully examine one of the principles they relied upon.

Extraordinary Claims require extraordinary evidence

I have made an extraordinary claim: "Axiomatic Mathematics doesn't exist".

I have provided evidence: The Principle of Explosion isn't constrained.

You don't need to take anyone else's word on this. This is within your ability to determine for yourself.

I will tell you that I'm not misrepresenting anything but you really don't need to trust me. Just read The Principle of Explosion and understand how it works.

My argument centers on the Idealist conception of self expressed in the definition. — Joshs

I... agree with what you are saying.

I'm confused as to why you think this is an argument against solipsism or its' underlying observations.

You point out that the definition of 'I' or 'self' is unclear. I agree with this.

I think you are then making an (unstated) assumption that if we cannot define the strict meaning of words then arguments involving those words are meaningless and we shall all just give up.

Why can't we strictly define words?

Imagine a closed system that you are part of. You are not outside the system looking in. You are inside the system. You are part of the closed system.

You wish to talk about this system you inhabit.

Anything you say is within the system. If you point at something, it is inside the system.

If you try to describe the system as a whole, your description is inside the thing it is trying to describe.

You would be using the universe to describe the universe.

It is like trying to describe a sheep using only references to that sheep: "A sheep's head looks like... the sheep's head." "The Sheep's wool is soft like the sheep's wool and covers the body in the way that the sheep's wool covers its' body."

You can get more creative: "The sheep's head is smaller than its body." "The tail is at the opposite end to the head."

This is, of course, where we are. We are inside the universe.

We can take one piece of the universe (a one metre ruler) and compare it to the circumference of the Earth through the poles. We can say this circumference is a little over 40,000km.

This works.

What is distance? What creates distance? Given nothing (a formless void) how would you create distance? How did distance come into being?

An electron

An electron has properties we describe as wavelike. What is a wave? A wave is something we observe elsewhere in the universe.

An electron has properties that are like other parts of the universe.

Okay. One piece of universe has similarities to other pieces of the universe.

This isn't nothing. We can enumerate those similarities and differences. We can measure and compare similarities.

However, sooner or later we need to admit that we have described a property of electrons using the result of those electrons. An ocean wave is composed of (among other things) electrons. We then describe properties of the electron using that macroscopic idea of waves.

We are describing electrons using electrons.

Definitions

The above is true of all definitions. We can compare (measure) different distances. But if we try to define what distance is we end up saying that distance is like this other thing that we can't define.

Assumption: definitions work by comparing and contrasting

It is extremely obvious to me that all descriptions describe one thing in relation to other things. "A zebra is like a horse with stripes."

If this doesn't seem obvious to you I would love to get some insight into how you think information is conveyed.

Next

There are no (logical or mathematical) proofs. — Treatid


Can you prove this? — Philosophim

A: "There are no proofs."

B: "You must prove to me that there are no proofs for me to accept your statement."

Proof is the de facto standard of modern scientific argument. It is the accepted mechanism of ensuring that an argument is rigorous and actually justifies the claims made.

Pushing for that rigour is justified.

Cutting yourself off from any mechanism that would question 'proof' and 'logic' is anti-rational.

You have defined a position that is unassailable. "If there are no proofs then it is impossible to prove there are no proofs. Therefore, obviously, the proposition that there are no proofs is wrong Q.E.D."

A proof of the non-existence of proofs

A contradiction in Logic disproves the axioms.

Logic (and Axiomatic Mathematics) start with a set of premises (axioms) which define an initial condition and a set of rules for reaching new statements within that system. If a statement within the system is both true and false at the same time, then there is some fault with the initial axioms. The Premise is mistaken.

The universe is a system. If a contradiction were to appear inside the universe then, logically, the universe must disappear in a puff of logic.

According to Axiomatic Mathematics, there are many inconsistent systems. These systems exist within the universe. Why hasn't the universe poofed out of existence.

Axiomatic Mathematics part 2: Separation

Axiomatic Mathematics (and formal logic) are instantly dead if a single contradiction invalidates the entire system.

So each Axiomatic System must be independent of every other Axiomatic System. An individual system may be invalidated but this has no impact on all the other independent systems.

This works great.

It is a Lie

The separation between Axiomatic (or Logical) systems doesn't exist.

There is no measurable quality that demonstrates the distinction between two systems.

A mathematician has to tell you that two sets of statements are distinct. There is nothing you can see, feel, touch or hear that will tell where to draw the boundary between axiomatic systems.

Axiomatic mathematics must have distinctions between systems in order to exist. But the boundaries can't be seen. There is nothing to measure. They are the poster child of belief without evidence.

If everything is connected then Logic, Axiomatic Mathematics and the whole universe are inconsistent. By the rules of Axiomatic Mathematics inconsistent systems have no information content.

Axiomatic Mathematics needs a distinction between systems to exist.

Good luck trying to demonstrate one of these distinctions.

Where we are going we don't need proof

Logic is a theory of arguments. It (tries to) describe how a form of communication works.

Before communication we have experience.

Descartes didn't argue your self awareness into existence.

Before you can argue about what it means to exist, what 'self' is or all the rest of it; you first need to exist (whatever that means).

As far as certainty goes - your existence is the pièce de résistance. There is nothing better. It is all downhill from here.

Caveat

Your existence encompasses the whole of your existence. All your experiences are part and parcel of your existence. You are as certain of your direct experiences as you are of anything else.

Logic never persuaded you that you feel pain and pleasure. You feel pain and pleasure because... you do.

We can (indeed, must) use our personal experiences as the solid foundation upon which to build... everything.

Solipsism says we cannot know anything with certainty except the self.

This isn't wrong - but the self includes everything you ever experience. When you stub your toe on a table; that experience is certain. Definite.

If we only talk about your experiences; we are limited to everything you can possibly experience.

You have only ever been able to talk about your experiences.

"The only certainty is your own existence." isn't a statement of limitation. Your existence is EVERYTHING of significance.

P.S. The universe is consistent

You can't cause bits of the universe to evaporate by making the wrong symbols.

There are no statements that have to be wrapped in a little knot of pearl in order to prevent the death of the universe.

A physical sentence isn't wrong. It isn't right either. These words don't have any meaning. They are just shapes in the universe.

When you read these words you decide on their meaning and their significance.

If you decide that a sentence is wrong - fine. It is still just a bit of universe shaped in a particular way.

The universe doesn't think the liar's paradox is a paradox. It is just squiggles on (virtual) paper.

Not all the squiggles on paper make sense to the people reading them. This isn't a squiggle problem. This is a people problem.

You, personally, decide how you will respond to what you read.

You have never been persuaded by Logical Argument. You have found squiggles that made sense according to your personal experience.

That is the final arbiter of your understanding. Your experience determines what you find plausible and implausible.

Right and wrong (truth and false) are entirely subjective opinions determined by each individual.

The symbols on the page are just symbols on the page. A symbol isn't true or inconsistent.

Your interpretation of a symbol is not the symbol.

P.P.S.

Once we get past the idea that symbols have any kind of inherent meaning; we can start to consider how similarities of experience between people enables the use of those 'meaningless' symbols to communicate meaning to other people.

Which is to say - of course language works. Of course we are able to communicate.

That doesn't mean the mechanism bears any similarity to the fairy tale we, as a society, have been telling ourselves for far too long.

Kind of like this from physicist Karen Barad? — Joshs

It certainly seems like it at first glance. I will look into her in more detail.

Thank you very much for this reference.

I appreciate it, but we're on the philosophy boards. — Philosophim

I'm about to come in hot. I can do this because you are making clear statements of position that I can engage with.

Thank you for that.

We can claim things are possible or impossible, but its all about proving it. — Philosophim

No. It isn't.

Remember solipsism?

It is impossible to prove anything beyond all doubt (except, perhaps, your own existence is self-evident to you).

To the best of my knowledge there is no accepted counter argument.

I'm sure many people think solipsism is silly, bordering on nihilism. That doesn't mean the underlying observations are wrong.

There are no (logical or mathematical) proofs.

One may not like this observation. This observation doesn't care.

It is the nature of the universe that you cannot have definite proofs (as defined by formal logic and axiomatic mathematics).

If you genuinely want to understand the nature of the universe then, sooner or later, you are going to have to come to grip with the fact that this is the nature of the universe.

Rant

I want to rant longer and harder because this is such an important point.

I suspect that solipsism is a deliberately obtuse interpretation of the observations in order to make it appear less relevant. But it isn't wrong.

Solispsism destroys Axiomatic Mathematics. Even in the absence of an alternative, solipsism is a clear statement that we must go back to the drawing board.

It isn't even subtle.

The mental gymnastics required to adhere to Axiomatic Mathematics in the face of (the observations leading to) solipsism is truly world leading. And this is from (rational) mathmaticians.

This (Proofs/Axiomatic Mathematics) goes beyond "Absolute belief without proof". It is "asbolute belief despite overwhelming evidence to the contrary).

Belief in the existence of proofs is religious in nature.

I've no doubt there was a time when it seemed to be a rational approach to knowledge. Then Descartes happened.

{Actually, the principles of solipsism were recorded over two thousand years ago. Descartes was more of a brush up than a genesis of the ideas. We've had two millenia to get our house in order. It is, perhaps, time we started facing upo to the truth no matter how uncomfortable that may be.

(It really isn't that uncomfortable. Once you stop trying to do impossible things and go with the flow (possible things); it is astonishing how quickly all the pieces fit together).}

In conclusion

Do you have a specific reason why we should disregard solipsism and the observations that lead to it?

Actually, whereas Descartes may have proven “thinking” exists, his leap to proving his own existence is less certain. He argued: — Thales

I don't think 'proof' is relevent here. Or at least not as the result of a chain of Logical Deduction.

Your existence is evident to you. Not as a matter of argument but as a matter of experience.

If we get into the weeds - we don't know what 'thinking', 'existing', 'experience' or 'self' mean in a definite manner.

Descartes' statement is more along the lines of: "There is definitely something/I have a sense of self".

The 'Ergo' (therefore) part of Descartes' statement seems to me to be a mistake. He doesn't exist because he thinks. His thoughts are an aspect of his existence.

This may feel a little nihilistic if we interpret this as "we know something but we can't define what that something is".

I think people expect to be able to define things in definitive terms and give up when it turns out that isn't possible.

My argument is that this is a piece of knowledge that we can work with. It isn't possible to define anything in absolute terms. What systems can function in the absence of concrete definitions? It is evident we inhabit a system that works without having absolute, fixed definitions.

There's a good summary in the following post if that helps.
https://thephilosophyforum.com/discussion/14044/knowledge-and-induction-within-your-self-context/p1 — Philosophim

People are good at Categorising things. It is a powerful tool and has almost certainly been instrumental in our success as a species.

I like the style/rigour of what you are doing. But I think what you are trying to do is impossible.

No matter where you start - it is impossible to create definite, unambiguous definitions.

Yes, it would make communication clearer and faster if we had rigorous definitions that everyone understood and agreed with. That isn't reality. People have been trying to create a solid, unimpeachable foundation to build on since forever. They haven't succeeded because it is an impossible task.

For example, I think you cannot justify the distinction you make between thought and experience.

Thought and experience are aspects of a single whole. You can't have thought without experience and vice versa.

Wordlviews

1. There are objects with properties that give rise to relationships between objects.

2. There are relationships.

Both these worldviews agree on the existence of relationships. Adherents of the first worldview attempt to explain observed relationships through the properties of objects.

The second worldview describes the nature of relationships by describing relationships.

Relationships are a fundamentally distinct concept from objects.

An object is a static singleton. An object has properties. These properties are also static. These static properties give rise to dynamic relationships... somehow?

A relationship, in contrast, changes. A relationship connects. A relationship presents difference.

It is not possible to build a relationship using only objects.

Fundamental Unit

The fundamental unit of the universe is a relationship.

The universe is a network of relationships that changes.

Why? Because we can see that is what it is.

The universe changes, so it must be composed of stuff that can change. The universe is connected so it must be composed of things that connect. The universe is diverse so it must be composed of differences.

Objects do not have these properties. The universe is not composed of objects.

We label the things Relationships.

Language

Language builds networks of relationships.

Why? Because language is part of the universe. The basic ingredients of the universe are the basic ingredients of everything in the universe.

It is these networks of relationships that convey meaning.

Individual words are placeholders for other networks of relationships. We can connect existing networks of relationships together to build new networks.

Any given statement is a network of relationships.

A network of relationships, by itself, is just a shape. Words on the page are just shapes. Shapes don't intend anything.

When you read you incorporate the shape of the language into your own shape (you, also, are a network of relationships). The way you incorporate new shapes into yourself depends on your existing state and the way it interacts with the new shape.

Corollory

Static objects cannot describe a dynamic universe.

At the same time, Relationships cannot describe static objects.

Descriptions work by describing unknown objects using altered descriptions of known objects.

A unicorn is a horse with a horn. You know what a horse is, you know what a horn is. By combing the two we convey what a unicorn would look like.

If you were to experience something without any precedent you wouldn't be able to convey your experience.

"It was like nothing you have ever seen before."

Challenge Time

If you can describe a static object you will have shown that I'm wrong and that I don't know what I'm talking about.

The two main arguments I'm going to fall back on will be:

A. You haven't actually described anything. "Objects are not relationships" is not a description of an Object.

B. What you have actually described is relationships. My default position is that if you manage to describe something it must have actually been a (set of) relationsips in the first place.

This is, of course, a blatant attempt to get you to engage with the ideas of what language is capable of and what it isn't capable of.

Can you describe something that has no similarities to any of your previous experiences?

@Kizzy,

I've watched the video. I was tickled by the portmanteau of 'experience' and 'internal' to give 'insperience'.

It isn't clear to me what problem you are seeing and what solution you are presenting. As such, I'm going to do some creative interpretation of what I think your point is while using the opportunity to expand on my own views.

You seem to be covering similiar ground to the article by Searle that jkop linked earlier in the thread.

I will assert that there is a common dogma in modern thinking that assumes the existence of a definite reality that exists separately from our subjective perception of it.

You express this idea as a distinction between the emotional experience of real nature versus a different pseudo experience when seeing a movie or screen. Searle presents hallucinations as his version of psedo reality.

You both believe/assume an objective reality that is distinct from our subjective experience of that reality and this informs your interpretations.

While the belief in an objective reality distinct from our subjective perceptions is widespread - it is a belief without evidence.

Integers

Integers are whole numbers: 1, 2, 4, -6,...

Except those examples aren't integers. '1' is a reference to an integer. A label for the concept of an integer. Integers themselves do not have physical form.

Note: this isn't new. c.f. Platonic Ideals.

So, Integers cannot be sensed as physical objects but they are still real. Aren't they?

Integers are as real as God. "There is no way to measure them but they determine how things work."

I am not saying anything about God. I am saying that the arguments used regarding the presence of God apply directly to Integers.

Belief in Integers is equivalent to belief in God. You can believe in them if you wish but they are defined to be free from evidence.

Note: Absolute faith without proof is a relativiely modern interpretation of Christian belief. It isn't, as I understand it, a requirement for belief. I am only interested in the related arguments for the existence of an invisible, undetecable, unmeasurable entity and applying those arguments to Integers.

Definition of an Integer

Definitions are hard. Mathematicians have invested a huge effort into defining basic concepts and the end result is that even their very best definitions contain a disturbing amount of handwaving

Fortunately we don't have to get to complex.

The Laws of Thought are: The Law of Identity, The Law of the Excluded Middle and The Law of non-Contradiction.

These are the explicit axioms (assumptions) of Axiomatic Mathematics which is the branch of mathematics that contains all the Proofs (including Formal Logic).

The integer '1' obeys the first Law of Thought (Identity). 1 is always itself. It doesn't change. 1=1.

All well and fine.

Now... do something constructive with that integer.

You could.... change it into... itself.

And that is it. That is everything you can do with the integer by itself. You can imagine it sitting there doing nothing.

The problem with static, unchanging objects is that they are static. They don't do anything.

Change

Previously we considered that your existence is self-evident; and includes your entire existence.

An aspect of your existence is your awareness of the existence of change. Whatever the exact nature of change, you are as certain of its existence as you are your own existence.

Mathematics is the discipline of describing a changing universe based on the assumption that things don't change.

Note: This applies to Axiomatic Mathematics which is not all mathematics.

An electron

Electrons are just like Integers.

No-one has ever seen an electron. It is impossible to measure the properties of an electron.

Again, this is not a new revelation. Electrons are a hypothetical particle invented to explain the observations we make. This is what a theory is.

Except that electrons don't change. The same axioms for Axiomatic Mathematics are part of the mathematics of Quantum Mechanics (The Standard Model of Physics).

Note: Quantum Mechanics is an incredibly successful theory that predicts observations to incredible levels of accuracy and precision. However, there is no way to start with the assumption of Identity (non-changing) and arrive at a changing universe.

This is a straightforward contradiction which, in mathematics, is devestating for the theory.

Quantum Mechanics does work - but it cannot possibly work according the the stated mechanisms.

Sensory Data

Sensory Data (whatever it actually is) changes.

Sensory Data isn't a window into the Real Objective Universe. Sensory Data is that universe.

Our experiences aren't a translation of an objective universe into subjective experience. Our experiences are the universe. Not in a solipsistic "we make the universe sense".

In a - What We Experience Is What Is There (WWEIWIT) way.

We don't need to infer reality from our Sensory Experience. Our Sensory Experience is our direct experience of reality.

Objects in Mathematics are defined as unchanging.

Sensory Data changes.

You know this. You can see this.

This isn't complicated. Do you experience change?

If yes: you do not live in an objective universe.

The idea of a fixed, objective universe is attractive. It makes arguments easier when the target isn't moving around all over the place. But it isn't true. It is obviously not true.

You can try describing unchanging objects until you are blue in the face - but it will get you precisely nowhere in understanding a changing universe.

Thank you for the feedback.

@jkop, Thank you for the link to Searle. An intertesting read. While I agree with his qualms regarding perception I don't think his argument rises to the status of 'refutation'. It is a rebuttal but it isn't sufficiently definitive to be considered the undisputed status quo. And, as it happens, I think he is mistaken.

{Searle presents the concept of perceiving a tree and hallucinating a tree. He argues that these two perceptions must be distinct - one 'sees' a tree the other 'not-sees' a tree. According to Searle, these two perceptions are distinct whereas previous philosophers conflated them into a single definition of 'see'.

He admits that the perception for both real tree and hallucinatory tree are identical but then distinguishes between them. He declares one an hallucination and the other real without any basis upon which to make that distinction. He just 'magically' knows that one is a real perception and the other isn't.

It is like arguing that two empty sets are distinct.

{All empty sets in mathematics are indistinguishable. As such, by convention, there is just one empty set.}

Searle is arguing that two indistinguishable perceptions are distinct becuase... he says so?}

Clarification

I think that objects do not exist.

I think that Sensory Data does exist.

I think that Objects and Sensory Data are distinct i.e. Object != Sensory Data.

These statements can be taken as a statement of axioms or as a definition of terms. (More on definitions in just a moment).

Solipsism is an interpretation based on observation and assumption.

The observation (that we only experience Sensory Data) is not, itself, solipsism.

Certainty

"Cogito Ergo Sum" - René Descartes ("I think, therefore I am").

This statement signifies that the only thing we can know with certainty is our own existence. The existence of everything else cannot be proven beyond all doubt.

Solipsism takes this to an extreme and proposes that everything else is a figment of the imagination (or some equivalent).

Existence

You know that you exist. What does it mean to exist? What is the definition of existence? Why do you exist?

If we haven't fully defined existence how can we be sure that we do, actually, exist?

All standard philosophical fare that has been discussed on these forums with each person coming to their own conclusions that may or may not overlap significantly with anyone else's.

At this point we can throw our hands up in disgust, declare ourselves nihilists, and give up on everything...

Or we can work with what we have.

What we have

You exist.

Your existence encompasses your entire existence. Everything you think, dream, feel and otherwise experience is part of your existence.

Sensory Data exists.

We haven't defined what Sensory Data is in any definitive sense. We experience something that we label Sensory Data. Just like we experience existence and label it Existence.

We haven't shown that Sensory Data isn't just another name for Existence.

This is what we have

There are no exceptions. There are no loopholes. This is the nature of existence.

LOOK! There! Did you see it?

This is the nature of existence. We have a property of existence. We label parts of our existence without knowing for certain that these parts are distinct from the other components of our existence.

If you were hoping for absolute, definitive, definitions then you are disapponted. But knowing what isn't is a piece of knowledge we can work with.

Tie back

Philosophers, mathematicans and physicists have been looking for definitive, absolute truths to build upon. Objective truths. An Objective Universe.

Our (your) direct experience tells us that this isn't possible.

When you tell me that I can't definitevely define Sensory Data you are right. I can't.

This applies to every word and concept you can imagine.

Look at the responses in this thread and see how much people are depending on particular definitions that they can't quite state in a definitive fashion... or simply saying such definitions are not possible.

This is something you are already familiar with as philosophers. You already know that objective definitions are a hard problem.

Don't fight this result. Lean into it. Accept it. Then work forward from there.

Once you accept that there can be no definitive, objective, definitions philosophy (and mathematics and physics) become orders of magnitudes easier.

"Once you stop trying to do the impossible, everything else (the possible) is trivial in comparison" - Misquoting Arthur Conan Doyle through Sherlock Holmes.

Conclusion

I have some sense of how this might come across but this is, at heart, a very simple argument:

No-one has ever figured out how to definitevely define existence (or anything else). This is positive information about the nature of the universe we inhabit.

Accept this insight. Work with it rather than against it.

{granted - it may not immediately be clear how to use this information.

It isn't as difficult as it might seem at first. We already don't have any definitive, absolute, definitions. Everything we have achieved thus far has been done in the absence of any single global definition.}