I’m not trying to make a point indirectly with rhetorical questions. The questions are sincere, and I want
you to answer sincerely.

At this time, I’m not trying to contest your assertions. You see I’m in error re: map/terrain.

Maybe you can pick one question — the one whose answer you deem most helpful — and answer it.

You indicate numbers are immaterial.

What are numbers abstracted from? Is an abstraction a derivative of its antecedent? Does a number have any type of connection to matter? Can a number have an application to matter and yet have no connection to matter? Can abstract numbers measure material things without establishing any type of connection to the material thing measured?

When we use numbers, do we make some type of contact_connection with the numbers? Is there a sense of “use” that involves no type of contact _connection?

Does a map have some type of relationship _connection with/to terrain?

Map in the sense of formalism is distinct from map in the sense of a graphic showing a Cartesian coordinate grid of intersecting streets?

I have revised my understanding of a formalism. If I can use the form of an equation as a formalism, then I can say $a+b=c$ is an example of a formalism.

What is its relationship to the concrete numbers that plug into its variables?

There is a difference in degree between refer to and specify.

Refer to can connect one thing to another generally.

Specify connects one thing to another with a concrete exactness (precision).

A formalism can refer generally to its powerset. $a+b=c$ in reference to only itself is useless. We only know how to use an equation when we know its powerset, which tells us the range of specific (precise) numbers (referred to generally by the formalism of the abstract equation) that can plug into the abstract form of the equation.

An abstract equation might be a set; it might be the set of all possible numbers that can plug into it meaningfully.

Formalisms measure regularities of nature. — ucarr

No they don't. As I wrote: formalisms ARE USED to measure or describe the regularities of nature (e.g. arithmetic IS USED to count apples in a barrel). — 180 Proof

If formalisms refer generally to their powerset of possible concrete numbers that can plug into the abstract form of the formalism, then they do measure the regularities of nature, which is to say they are generally and existentially involved in concrete measurements of regularities of nature because they constrain the range of concrete numbers that can do the measuring.

Abstractionism does not break the chain of causality connecting, existentially, formalisms to regularities of nature.

Formalisms (axiomatic or otherwise) are abstract and therefore do not refer beyond themselves to concrete matters of fact (e.g. entropy), rather they are used as syntax for methods of precisely measuring / describing the regularities of nature. — 180 Proof

Formalisms measure regularities of nature. — ucarr

This is how I read your statement.

No they don't. As I wrote: formalisms ARE USED to measure or describe the regularities of nature (e.g. arithmetic IS USED to count apples in a barrel). — 180 Proof

This is your argument supporting your claim I mis-read your claim.

You seem to be implying that guidelines for best arrangement of signs (syntax) for the sake of effective communication are exclusively generalizations.

You propound your implied characterization by pointing out how your statement presents the critical verb "measurement" in the passive voice, whereas my statement presents it in the active voice. This emphasis on the passive voice is your effort at distancing formalisms from regularities of nature_matters of concrete fact.

Obviously, by definition of formalism, there is a chain-link of narration linking the meaning of formalisms (axiomatic or otherwise) with how they're applied directly by their agents to things in nature. The degree of elaboration of the components of the narration (and the narrative "distance" accreted) never breaks the chain-link of narration connecting the formalisms to their objects.

sine qua non | ˌsinā ˌkwä ˈnōn, ˌsinē ˌkwä ˈnän |
noun
an essential condition; a thing that is absolutely necessary: grammar and usage are the sine qua non of language teaching and learning.
ORIGIN
Latin, literally ‘(cause) without which not’.
The Apple Dictionary

In my understanding, axiomatic system = sine qua non. If something is essential to a following thing that is the consequence of the first thing, then the first thing refers beyond itself specifically to the following thing.

There appears to be an idea floating through the zeitgeist of the scientific age that generalizations, i.e., abstractions, run parallel to the concrete and specific creations of nature. In my understanding, a generalization is a thinking process that utilizes cognitive compression of multiple applications of the generalization. This cognitive process produces the axiomatic system.

Although the cognitively compressed idea, while occupying its compressed state as an abstraction, seems not to be directly tied to any one of the many objects of its meaning, this in fact is a falsehood.

Claiming formalisms do not refer beyond themselves parallels claiming the distinction between a verb in the active voice and a verb in the passive voice has no connection to the grammar specifying a distinction between the two voices.

Formalisms measure regularities of nature. — ucarr

No they don't. As I wrote: formalisms ARE USED to measure or describe the regularities of nature (e.g. arithmetic IS USED to count apples in a barrel). — 180 Proof

.

Your above quote makes it clear beyond doubt you're using the distinction of the passive voice of the verb from the active voice of the verb to defend your denial of the following:

Formalisms measure regularities of nature. You say (above) regularities of nature are concrete matters of fact. Since formalisms measure regularities of nature, and regularities of nature are concrete matters of fact, formalisms measure concrete matters of fact. — ucarr

So, our debate over formalisms referring to things beyond themselves comes into focus here as a specific argument point you make in which you do the very thing you deny the possibility of doing: basing your defensive argument upon a grammatical formalism: English verbs have both an active and a passive voice, such that, per your argument, the grammatical formalism about the voice distinction, when it refers to that distinction in application, defends against :

Since formalisms measure regularities of nature, and regularities of nature are concrete matters of fact, formalisms measure concrete matters of fact. — ucarr

The premise behind your defensive argument is the following: formalisms (English verbs have both passive and active voice) do refer to concrete matters of fact, with the purported supporting fact in this instance being: "Because I wrote my claim with the verb in the passive voice, my claim 'formalisms do not refer beyond themselves to concrete matters' stands."

As you assume (in contradiction to what you say), formalisms do refer to things beyond themselves. So, by your own assumption (and debate maneuver), your claim to the contrary is false.

Facts describe real things. As you describe formalisms:

...they are used as syntax for methods of precisely measuring / describing the regularities of nature. — 180 Proof

The regularities of nature are concrete matters of fact — 180 Proof

Formalisms measure regularities of nature. You say (above) regularities of nature are concrete matters of fact. Since formalisms measure regularities of nature, and regularities of nature are concrete matters of fact, formalisms measure concrete matters of fact.

Thus,

Formalisms (axiomatic or otherwise) are abstract and therefore do not refer beyond themselves to concrete matters of fact (e.g. entropy)... — 180 Proof

falsely denies that formalisms refer beyond themselves to concrete matters of fact (e.g. entropy).

...you also say formalisms do = regularities of nature — ucarr

False. Stop shadowboxing with your strawmen, you're further confusing yourself. — 180 Proof

Here's your own language:

Formalisms (axiomatic or otherwise) are... used as syntax for methods of precisely measuring / describing the regularities of nature. — 180 Proof

Formalisms (axiomatic or otherwise) are abstract and therefore do not refer beyond themselves to concrete matters of fact (e.g. entropy)... — 180 Proof

rather they are used as syntax for methods of precisely measuring / describing the regularities of nature. — 180 Proof

Why are these two statements not a contradiction? — ucarr

Map-making does not "contradict" using a map for navigating terrain.. — 180 Proof

Premise - Formalism = (a technical term for) narrative

Question - When you write a map, do you simultaneously read it? If so, then reading and writing are merged as an identity. Also, they are symmetrical, which is to say, if writing and reading are merged, then reading and writing are merged (when you read something, it doesn't enter your understanding directly; you read what's written, and then your comprehension of what you've read writes what is written onto the plane of your memory).

Symmetry cannot be contradictory, but if the distinction between writing a map and reading a map is erased by symmetry, then there is contradiction, thus pointing up the illogic of your two sentences taken together.

Why are "regularities of nature" not concrete matters of fact? — ucarr

The regularities of nature are concrete matters of fact from which physical laws are generalized (i.e. abstracted) physical. I haven't claimed or implied otherwise — 180 Proof

Above you say formalisms $≠$ concrete matters of fact; above you also say formalisms $=$ regularities of nature. Next you say matters of fact and regularities of nature $=$ each other. How is it your statements about formalism are not contradictory?

Formalisms (axiomatic or otherwise) are abstract and therefore do not refer beyond themselves to concrete matters of fact...rather they are used as syntax for methods of precisely measuring / describing the regularities of nature. — 180 Proof

Why is it the case that formalisms, when they measure_describe the regularities of nature, do not refer beyond themselves to concrete matters of fact_the regularities of nature?

How are "matters of fact" concrete but not empirical? — ucarr

Where are you getting this? This question has nothing to do with what I've argued. — 180 Proof

empirical | imˈpirək(ə)l |
adjective
based on, concerned with, or verifiable by observation or experience rather than theory or pure logic: they provided considerable empirical evidence to support their argument.
The Apple Dictionary

The empirical includes matters of fact verifiable by observation. Since logic doesn't do any observing, instead it being done by humans not theorizing abstractly but observing real things, logic, through humans, connects with the world of empirical experience, and thus my question is pertinent to your statement.

If self-descriptions ("formalisms...do not refer beyond themselves") have nothing to do with the world (nature), instead being interested only in themselves only self-referential, how are they meaningful and useful? — ucarr

Are the disciplines of epistemology and ontology merely products of human translations? — ucarr

Idk what you mean by "translations" — 180 Proof

...that physical laws are computable does not entail that the physical universe is a computer. — 180 Proof

By your own words, we see that scientific measurement (at least sometimes) is a translation from the empirical to the cognitive.

Uncertainty is a precision problem.

More precision means more information.

According to Chaitin's incompleteness, sufficiently higher precision will indeed at some point exceed the amount of information that the system can decompress.

According to the literature on the subject, both incompleteness and imprecision ("uncertainty") can be explained by the principle of lossy compression that results in a particular maximum amount of information that could ever be decompressed out of the system. — Tarskian

Does a lossy axiomatic system also necessarily omit consequential facts because of measurement limitations described by Heisenberg Uncertainty? — ucarr

Yes. Technically, the resulting imprecision is the due to the fundamental properties of wave functions.

However, the paper mentioned , Calude & Stay, 2004, "From Heisenberg to Gödel via Chaitin.", connects uncertainty to Chaitin's incompleteness:

In fact, the formal uncertainty principle applies to all systems governed by the wave equation, not just quantum waves. This fact supports the conjecture that uncertainty implies algorithmic randomness not only in mathematics, but also in physics.

They conclude that it is not possible to decompress more precise information out of an axiomatic system than the maximum precision imposed by the fundamental properties of wave functions. — Tarskian

precision | prēˈsiZH(ə)n |
noun
technical refinement in a measurement, calculation, or specification, especially as represented by the number of digits given: a precision of six decimal figures
The Apple Dictionary

When we look at the triad of entropy_uncertainty_incompleteness through the lens of imprecision, which is about exactness, we see that the informational dimension of nature is not fully containable within human observation, whether of the scientific type, or of the humanities type.

Does this tell us something about the incompleteness of nature, or does it tell us something about the incompleteness of human cognition?

Given the limits of measurement and decompression, does 180 Proof have a cogent point?

...that physical laws are computable does not entail that the physical universe is a computer. — 180 Proof

180 Proof

Does this argument cast doubt on whether we can know reality beyond its human translation?

Are the disciplines of epistemology and ontology merely products of human translations?

Is Platonic Realism correct: humans dwell within a (cognitive) dark cave, sealed off from direct and complete experience of reality? Plato, however, thought he saw a way out of shadowy perception by means of reasoning beyond appearances.

Can we hope to eventually reason beyond the current state-of-the-art observations limited by imprecision of measurement and incompleteness of decompression? Or is it the case the limited measurements of the wave function and the limited decompression of axiomatic systems reflect existential limitations embedded in nature?

Now perhaps we come to a crux of the faceoff between the sciences and the humanities. If the observer is always entangled with the observed, does that mean the two great modalities of discovery: the what and the what it’s like of the what are linked by the biconditional operator?

The biconditional linking sciences and humanities writ large is the biconditional linking nature and sentience.

Option 1 – If humans can see nature beyond measurement and decompression limitations, then sentience is inevitable because its seeds are embedded existentially.
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Option 2 – If sentience and nature are creatively and strategically incomplete, without biconditional linkage, then existential limitations of knowing and being are always in effect. There’s a gap separating the two, however, the knowing of being, and the being of knowing of being, make a close approach to each other. This close approach, always incomplete, keeps the game of sentience going creatively because the two infinities, although incommensurable, are entangled in an evolving, inexhaustible complexity.

Formalisms (axiomatic or otherwise) are abstract and therefore do not refer beyond themselves to concrete matters of fact (e.g. entropy)... — 180 Proof

...rather they are...measuring / describing the regularities of nature. — 180 Proof

Why are these two statements not a contradiction?

Why are "regularities of nature" not concrete matters of fact?

How are "matters of fact" concrete but not empirical?

If self-descriptions ("formalisms...do not refer beyond themselves") have nothing to do with the world (nature), instead being interested only in themselves, how are they meaningful and useful?

Does a lossy axiomatic system also necessarily omit consequential facts because of measurement limitations described by Heisenberg Uncertainty? — ucarr

Yes. Technically, the resulting imprecision is the due to the fundamental properties of wave functions. — Tarskian

Do you have any interest in the Beckenstein bound, from the Holographic Principle (Gerard t'Hooft)? It describes a limit to the amount of information that can be stored within an area of spacetime at the Planck scale. Among other things, this limit establishes the physical nature of information. There's an algorithm for measuring the Beckenstein bound: it's a fraction of the area of the event horizon of a black hole.

:up:

... for any system that does work, as it goes forward in the systematic process of doing work, the work builds up complexity of detail. This building up of complexity can be observed in two modes: phenomenal (entropy) and epistemic (logic). — ucarr

...logic is not "doing work" — 180 Proof

What is symbolic logic without the reader? It's marks on paper. No work. Really, it's non-existent without the writer. Logic that has meaning and works always assumes the interaction between a human and the marks on the paper: Aristotle's intelligent agent meets intelligibility. Work.

This leads to the conclusion that axiomatic systems are a form of compression of complexity and that the increase of complexity is an irreversible process.

More nonsense. Formalisms (axiomatic or otherwise) are abstract and therefore do not refer beyond themselves to concrete matters of fact (e.g. entropy), rather they are used as syntax for methods of precisely measuring / describing the regularities of nature. — 180 Proof

"Formalisms that do not refer beyond themselves to concrete matters of fact (e.g. entropy)..." no work.

However, as above: Formalisms that have meaning and work always assume the interaction between a human and the marks on the paper: Aristotle's intelligent agent meets intelligibility. Work.

Formalisms are not abstract because, in their description of nature, they express the state of being (in this case: thinking) of human individuals who are, indeed, a part of nature, and therefore, human expression is nature expressing herself. There is no discrete bifurcation separating "abstract" human thought from nature.

"... rather they are used as syntax for methods of precisely measuring / describing the regularities of nature."

Why bother with measurement and description if there's no existential connection between abstract thought and nature? If formalisms are hermetically sealed off from nature, then, willy-nilly you can assign whatever meaning you like to whatever marks on paper you make, for all the value that has.

Both life and science are interesting. This because, within the realm of human thinking -- just another natural thing -- it's possible to be either right or wrong. Right and wrong draw their force and value from the interweave of nature as thinking and nature as object of thinking, i.e., nature looking at herself.

The test of syntax comes down to: can you speak the words trippingly from the tongue? The test of science comes down to: can you observe the predictions in nature? These tests bespeak the interweave between natural thinking and nature thinking about herself.

We will show that algorithmic randomness is equivalent to a “formal uncertainty principle” which implies Chaitin’s information-theoretic incompleteness. We also show that the derived uncertainty relation, for many computers, is physical. In fact, the formal uncertainty principle applies to all systems governed by the wave equation, not just quantum waves. This fact supports the conjecture that uncertainty implies algorithmic randomness not only in mathematics, but also in physics. — Tarskian quoting Calude and Stay

Calude & Stay, 2004, "From Heisenberg to Gödel via Chaitin."

The above quoted theories are interesting because they could either be right or wrong. There's something at stake. That wouldn't be the cause if human thinking weren't existentially connected to the natural world surrounding it.

Was this correct:

I am starting to believe that what you are really getting at behind the curtains here is that science and art share common features. — I like sushi

Followed by the possibility of uniting/transcending the differences held by many? — I like sushi

I simple yes/no or suffice. If it is a bit more than this then a sketchy - yet straight forward - outline would be all I need. — I like sushi

We don't live within a universe; instead, we live within a vital approach to a universe strategically forestalled by entropy_uncertainty_incompleteness. Science and Humanities are the two great modes of experiencing the uncontainable vitality. — ucarr

This is how I talk about science and humanities in broad generality. The link below will take you to the post for additional context.

ucarr post

That they overlap in ways complex and nuanced I acknowledge. Their common ground has not been my focus in this conversation. What I haven't seen (I'm not implying such literature doesn't exist) is a general description of how they differ. Through both lenses: similarity and difference, the view of the comparison is complex and nuanced.

I feel a measure of satisfaction with my "What" Vs "How" binary. Again, this binary entails a complex and nuanced interweave of both "What" and "How." A loose translation into English might be: What is meets What it's like to experience what is.

This language points toward The Hard Problem. Looking objectively at subjectivity is hard to do. Is consciousness purely subjective? "Not exactly," says science when it attempts to detach the observer from the observed. QM tells us there is no purity of observational detachment.

QM entanglement tells us something about consciousness: it interweaves the objective and subjective. Does this dovetail with the holism you see?

In each problem, ultimate pattern arises from the particular information preserved in the face of the combined fluctuations in aggregates that decay all non-preserved aspects of pattern toward maximum entropy or maximum randomness — Tarskian

Axiomatic theories do something similar. — Tarskian

The few rules in the axiomatic theory will not succeed in decompressing themselves back into the full reality. What facts from the full reality that they fail to incorporate does not say particularly much about these facts (deemed "chance", "random", ...). They rather say something about the compression technique being used, which is the principle that chooses what facts will be deemed predictable and what facts will be deemed mere "chance". — Tarskian

As I understand it, an axiomatic system is a compressor. The algorithm that generates the axiomatic system has a focal point that excludes info inconsequential to the outcome the axiomatic system tries to predict.

Does a lossy axiomatic system also necessarily omit consequential facts because of measurement limitations described by Heisenberg Uncertainty?

It is simply not possible to decompress and reconstruct the totality of all the information about reality out of an axiomatic system that describes it (if this axiomatic system is capable of arithmetic). — Tarskian

But then again, it also does not mean that the information forgotten in the compression is "accidental" or "random". — Tarskian

Randomness is not a necessary requirement for unpredictability. Incompleteness alone is already sufficient. A completely deterministic system can still be mostly unpredictable. — Tarskian

From your sequence of quotes here, I understand that, just as you say "Incompleteness alone is already sufficient." [to cause unpredictability].

Can we generalize to the following claim: our material creation, as we currently understand it, supports: the determinism of axiomatic systems, the incompleteness of irreversible complexity and the uncertainty of evolving dynamical systems, and, moreover, this triad of attributes is fundamental, not conditional?

You have not given me any reason to read someone else's thoughts on the matter. Make your philosoophical case, ucarr, and I will respond. — 180 Proof

...is there a logically sound argument claiming there is a causal relationship between entropy and incompleteness? — ucarr

No. — 180 Proof

The issue I want you to focus upon is this: for any system that does work, as it goes forward in the systematic process of doing work, the work builds up complexity of detail. This building up of complexity can be observed in two modes: phenomenal (entropy) and epistemic (logic).

Gödel and Chaitin have shown in the epistemic mode that the full scope of the evolving complexity can not be formally tied to the ground from which it emerges. This leads to the conclusion that axiomatic systems are a form of compression of complexity and that the increase of complexity is an irreversible process.

If the forward direction of a phenomenon incorporates information that cannot be decompressed from its theory, then it will also be impossible to decompress the information needed to reverse it, rendering the phenomenon irreversible. — Tarskian

Here's a critical question: Is it true that the extrapolation from an axiomatic system to complexity irreversible to the axiomatic system cannot be certified, and thus axiomatic systems are both incomplete and uncertain?

If you think the answer to this question is "no," can you succinctly demonstrate your refutation?

If you're refusing to read Tarskian's posts linking to:

"Entropy, heat, and Gödel incompleteness", 2014, by Karl-Georg Schlesinger, — Tarskian

it's not obvious to me why you see no reason to refute Schlesinger. The title of his paper makes it clear he's worked on the question of a causal link connecting entropy and Gödel incompleteness, the very focus of my question to you.

...is there a logically sound argument claiming there is a causal relationship between entropy and incompleteness? — ucarr

No. — 180 Proof

...succinctly express your disagreement with something I have written that you wish for me to further elaborate on... — 180 Proof

How does this differ from what I've asked of you?

Regarding what exactly? — 180 Proof

Please use the links below to Tarskian's posts. After re-reading the posts, refute the citations referenced by Tarskian by: providing known facts pertinent; corroborating evidence supporting known facts pertinent; logical analysis; valid conclusions drawn from your logical analysis.

Tarskian_Schlesinger 1

Tarskian_Schlesinger 2

If a thing is not computable, thus causing attempted measurements to terminate in undecidability, is it sound reasoning to characterize this undecidability as uncertainty — ucarr

For me uncertainty refers to a situation where you don't have all the information.. — ssu

This situation - soft uncertainty - doesn't preclude uncertainty from also being applied to:

You can have all the information, yet there's no way out of this. — ssu

which is hard uncertainty.

There is a lot of text which you won't ever write, but anything you write will automatically be something you do write (and hence not in the category of all the texts you will never write). So is this a limitation on what you can write? Of course not. — ssu

I attempt to refute your above denial (underlined) with:

Is this a logical statement: ¬x ≠ x? If so, then why is it not a logically preemptive limitation on what I can write? — ucarr

Let me attempt to clarity: I'm attempting say I can't enact the negation of what I'm doing. $\rightarrow$ Anything I write will not be something I do not write.

The implicit but really strong assumption in Schlesinger's paper is that there exists exactly one lossy compression algorithm, i.e. axiom system A, for the information contained in the physical universe.

Schlesinger actually admits this problem:

https://arxiv.org/pdf/1404.7433

So, we would need a slightly stronger form of Gödel incompleteness which would make the dynamics non-predictable for any choice of axiom system A. — Tarskian

I'm glad to see I've joined some estimable thinkers who have preceded me. My gratitude to Tarskian for the citations.

According to Schlesinger, a physical phenomenon becomes irreversible and entropy will grow, if reversing the phenomenon would require using more information than allowed by Godel's incompleteness. — Tarskian

If all these alternative compression algorithms always lead to the same output in terms of predicting entropy, then for all practical purposes, they are one and the same, aren't they? — Tarskian

:up:

Are you proceeding from the premise causal relationships are not fundamental in nature? — ucarr

Nope. — 180 Proof

...is there a logically sound argument claiming there is a causal relationship between entropy and incompleteness? — ucarr

No. — 180 Proof

Please supply: known facts pertinent; corroborating evidence supporting known facts pertinent; logical analysis; valid conclusions drawn from your logical analysis.

I am starting to believe that what you are really getting at behind the curtains here is that science and art share common features. — I like sushi

..the beating heart of physics is entropy — I like sushi

This is important generally, and here more specifically. If what you say immediately above is true, then the 2$^{nd}$ law of thermo-dynamics, if, as I herein theorize, is directly and deeply tied to the always incomplete systematic utilization of heat energy for work, then there seems to me to be good reason to think incompleteness -- not the existential measurement uncertainty of the Fourier transforms applied to elementary particles, but instead the garden variety of incompleteness: not all of the potential has been utilized -- exhibits a pattern in possession of an underlying logic. If we can learn to read that underlying logic, I conjecture it will tell us a foundational story about the passage of time and events into the future.

Science: The What - the 2$^{nd}$ law of thermo-dynamics; Humanities: The How - clinical depression of the human psyche resembles the conjectured heat death of a material system wherein all is at a lifeless equilibrium, the cosmic tendency of matter energy systems. In human terms of the "how is it experienced": the no-affect grayscale of a flatlined inner emotional life.

Entropy_uncertainty_incompleteness keep our material environment alive. Life will not be understood in the terms of wholeness, completion and closure. Since vitality tends towards these things, it's natural to seek after them. I don't think we'll find them, and that's a good thing because life, the supremely good thing, depends on us not finding them.

We don't live within a universe; instead, we live within a vital approach to a universe strategically forestalled by entropy_uncertainty_incompleteness. Science and Humanities are the two great modes of experiencing the uncontainable vitality.

J could easily respond by restricting his sphere of discourse to the logical frame and asking something like, "But do they add anything as far as the logic is concerned?" But this raises the fraught question of where the logical ends and the metalogical begins, or else where the metalogical ends and the ontological begins, in any given system. — Leontiskos

Yeah. Theoreticians are still scratching their heads over the question of an inflection point linking metalogical with ontological.

Are you proceeding from the premise causal relationships are not fundamental in nature? — ucarr

Nope. — 180 Proof

So if, for example, the 2$^{nd}$ law of thermo-dynamics establishes that systematic utilization of heat is always incomplete, and that this unconstrained thermal energy always travels to a cooler state toward equilibrium in randomization, is there a logically sound argument claiming there is a causal relationship between entropy and incompleteness?

I can say “It is true that there are a hundred thalers on the table” but this adds nothing to the proposition ‛There are a hundred thalers on the table’. — J

Basically, yes. — Leontiskos

I can say “A hundred thalers exist” but this adds nothing to the concept ‛a hundred thalers’; — J

This is a bit different, as the latter possesses a conceptual existence which the former surpasses by asserting a super-conceptual existence, at least according to common language. As far as I can see things can only be true or false in one way, whereas things can exist in multiple ways. The domain of the former is propositions whereas the domain of the latter is ontological realities, and ontological realities are more variegated and complicated. — Leontiskos

Maybe QM can tell us something pertinent herein: When that tree falls in the forest without a witness, does it make a sound? No. It makes a potential sound, and in so doing, it takes its place among all of sound in its potentiality.

“Truth is not a predication.” That is, neither existence nor truth add anything, conceptually, to what they appear to be predicating ‛existence’ and ‛truth’ of. — J

I suppose Frege was the first to have pointed out the “emptiness” of the “It is true that . . .” prefix, but did he also make the parallel with “Existence is not a predicate”? — J

Aristotle's claim in the Metaphysics that to speak truth is to say of what is that it is or of what is not that it is not is very close to the truth predication question. — Leontiskos

Truth/existence predication adds something conceptually entangled: the existential_cognitive entanglement of superposition resolved, or, to put it another way: decidedness.

In quantum mechanics, Schrödinger's cat is a thought experiment concerning quantum superposition. In the thought experiment, a hypothetical cat may be considered simultaneously both alive and dead, while it is unobserved in a closed box, as a result of its fate being linked to a random subatomic event that may or may not occur. This experiment viewed this way is described as a paradox. This thought experiment was devised by physicist Erwin Schrödinger in 1935[1] in a discussion with Albert Einstein[2] to illustrate what Schrödinger saw as the problems of the Copenhagen interpretation of quantum mechanics.

In Schrödinger's original formulation, a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal radiation monitor (e.g. a Geiger counter) detects radioactivity (i.e. a single atom decaying), the flask is shattered, releasing the poison, which kills the cat. The Copenhagen interpretation implies that, after a while, the cat is simultaneously alive and dead. Yet, when one looks in the box, one sees the cat either alive or dead, not both alive and dead. This poses the question of when exactly quantum superposition ends and reality resolves into one possibility or the other.

Schrödinger's Cat

A thing is potential and undecided until it is witnessed by a sentient. Therefore, when a sentient says: It is true of what is that it is or, it is existential of what exists that it exists, s/he adds the decidedness of witnessing the superposition of the cognitively decided thing.

The undecidability results simply show that not all is computable (or in the case of Gödel's theorems, provable), even if there is a correct model for the true mathematical object (namely itself). — ssu

If a thing is not computable, thus causing attempted measurements to terminate in undecidability, is it sound reasoning to characterize this undecidability as uncertainty (about a conjectured definitive measurement)?

There is a lot of text which you won't ever write, but anything you write will automatically be something you do write (and hence not in the category of all the texts you will never write). So is this a limitation on what you can write? Of course not. You can still write anything you want. It's a bit similar with the undecidability results. — ssu

Is this a logical statement: $\neg x$ ≠ $x$? If so, then why is it not a logically preemptive limitation on what I can write?

This is not an example of a "fundamental relationship of uncertainty, incompleteness & entropy". Not even close. — 180 Proof

Are you proceeding from the premise causal relationships are not fundamental in nature?

The $2^{nd}$ law of thermo-dynamics tells us that no isolated system can convert all of its internal energy into work. Why is this statement - among its other related implications - not an implication systematic utilization of available energy is always incomplete?

If it is one of its implications, how is it the case the 2nd law of thermo-dynamics is essential to nature, but one of its implications isn’t?

"Uncertainty" is epistemic, "incompleteness" is mathematical and "entropy" is physical. I don't think they are related at a deeper – "foundational" – level unless Max Tegmark's MUH is the case. :chin: — 180 Proof

Consider a chain of causation: a) live music is performed in a radio station studio for a live broadcast; b) the live music in the studio as rendered to radio listeners is incomplete because of noise in the transmission; c) the listeners - because of the noisy transmission - are uncertain whether three successive brass instrument solos are a flugelhorn, a trumpet and a cornet, successively, or some other configuration according to the possibilities.

Even though the parallel breaks down at b) incompleteness because, in the example, it's due to the entropy of electromagnetic transduction (albeit mathematically describable), nonetheless the physics of entropy causes the incompleteness and, in turn, the incompleteness causes the uncertainty.

Our triad, in spite of variations, remains intact.

No need for proof in physical reality to perceive its facts. — Tarskian

Why is the Copernicus_Galileo debate with the Catholic Church (re: the earth orbiting the sun) not a counter-narrative to this claim?

Is there any literature that examines questions about the relationship between Heisenberg Uncertainty and Gödel Incompleteness?

The Fourier transforms won't allow us to accurately measure both position and momentum of an elementary particle; it's one measurement at a time being accurate, with the other measurement being far less accurate. — Tarskian

Is this an example of uncertainty rooted within incompleteness?

Unlike in physical reality, in arithmetical reality we typically know that a theorem is true because we can prove it... That is why arithmetical reality appears so orderly to us, while in reality, it is highly chaotic, just like physical reality. We just cannot see the chaos. — Tarskian

Here's the really big question: Is there a foundational relationship between uncertainty, incompleteness and entropy?

Consider: The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient). Another statement is: "Not all heat can be converted into work in a cyclic process."[1][2][3]

So, heat (unfocused energy) without constraints, always spontaneously flows out of an energetic system, such that necessarily only a fraction of the contained energy of a thermo-dynamical system can be converted (brought into focus) into work.

The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. It predicts whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics and provides necessary criteria for spontaneous processes. For example, the first law allows the process of a cup falling off a table and breaking on the floor, as well as allowing the reverse process of the cup fragments coming back together and 'jumping' back onto the table, while the second law allows the former and denies the latter.

So, the entropy of a thermo-dynamic system is uni-directional; it always increases; it never decreases.

The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always tend toward a state of thermodynamic equilibrium where the entropy is highest at the given internal energy.[4] An increase in the combined entropy of system and surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time.[5][6]

2nd Law of Thermodynamics

That uncertainty might be rooted in incompleteness suggests a relationship between the two phenomena.

Now we want to see if we can connect uni-directional entropy as the arrow of time to this duad in order to make a very meaningful triad: uncertainty_incompleteness_arrow of time.

Does our triad tell us that entropy insures the material existence is always moving forward into a future that is never a simple cyclic repetition of past phenomena, such as an oscillation of the universe between big bang and big crunch?

Does our triad likewise tell us that our movement towards the future is more than a statistically probable permutation of conserved laws?

Does the discovery of QM tell us that our future is truly unknown and unknowable, albeit partially predictable?

Is entropy the engine driving uncertainty_incompleteness_arrow of time?

Is entropy the mortal enemy of the T.O.E.?

"Always Look On The Bright Side Of Life"

Links to renderings:

Mozart Group

Eric Idle

North Korean Version

Art Garfunkel

Life of Brian

"Be fair" is an expression I use - perhaps it is not as widely used as I thought - to signal that there is a brighter side to what seems so depressing. It's not an accusation or criticism. — Ludwig V

It's all cleared up. I like Art Garfunkel's rendering of "Always Look On The Bright Side of Life (Monty Python)." Have you heard it?

QM tells us the observer perturbs what s/he observes. — ucarr

Isn't that old news in a new bottle? — Ludwig V

the new bottle perturbs the old news into something interesting: — ucarr

I'm suggesting that it has been over-hyped and is rather less interesting than one would have thought, given all the fuss. — Ludwig V

There's always the hope of being understood. — ucarr

Here I'm proceeding from the notion of QM entanglement connecting observer with observed. Effect: nothing is truly unseen. In the grapevine mesh of existing things, for each thing, there's always one observer who sees that thing as it is in truth. Is this not a charming article of faith warding off depression?

Be fair. Sometimes we are understood, and sometimes we manage to sort out misunderstandings. — Ludwig V

I need your help in understanding how I'm being unfair.

How do you characterize ontically and empirically the physicist and its experimental_inferential connection to planck-scale phenomena? — ucarr

My layman's best guess: only the interaction of the measuring-apparatus and "planck-scale phenomena" is manifestly ontic – quanta (e.g. photons) "perturbing" quanta – and the physicist's readings of her measurements (thereby making inferences) are empirical. — 180 Proof

Sounds right to me too. So we have a translation from ontic to empirical. Must we always suppose there's something lost in the translation?

QM tells us the observer perturbs what s/he observes. — ucarr

Isn't that old news in a new bottle. — Ludwig V

I like to think that when I zoom out to include my premise from another one of my conversations: strategic incompleteness, the new bottle perturbs the old news into something interesting: the semi- universe, by design - I'm not making a supernatural claim here but, instead, a thermo-dynamical claim - won't let us arrive at closure for either the "what" or the "how."

Oftentimes we don't know (or appreciate) it, but we're fortunate not to arrive at a final closure for things. As a matter of fact, our happiness depends upon the continual forestalling of final closure.

Well, as I've been saying, no one reads a given text exactly as another reads it. This because each individual perturbs what s/he observes individually. — ucarr

You are looking at only one side of the coin. We learn to read from each other (and we learn the language that we read and communicate in) and we learn all the skills of knowledge. Sharing and correcting — Ludwig V

Yes, our experience is rooted within interrelationships. There seems not to be any existing thing utterly isolated and alone. There's always the hope of being understood.

I suppose it means that in a given time period for a foundational theory, no one can discover a form more basic. — ucarr

So "simple" means "more basic"? — Ludwig V

"Basic" as the criterion for "simple" expresses an ideal of efficiency and clarity and certainty.

...since classical-scale systems (e.g. brains-sensoriums) cannot directly interact with planck-scale systems. — 180 Proof

How do you characterize ontically and empirically the physicist and its experimental_inferential connection to planck-scale phenomena?

Yes, as e.g. Spinoza points out, human knowledge of unbounded (infinite) reality is necessarily perspectival and therefore bounded (finite). Basic epistemic mereology (re: maps < terrain), no? — 180 Proof

Yes. :up:

I think your "strategic incompleteness" overstates the case and incoherently conflates teleology with formalism with empiricism. — 180 Proof

Okay. Your helpful analysis empowers me to see that: teleology | formalism | empiricism are a triad of modes of cognition incorrectly (logically) articulated in my premise in its present state. Also, the scope of the territory claimed by my premise is too large_inclusive.

Okay. Proceeding from the observer as an always local person, if we bind the thinking of an always local person to that always local person, then it too, is always local, and the abstraction of abstract thinking starts dissolving. — ucarr

I don't know what you mean by "bind". If a local person indulges in abstract thinking, and shares that thinking with other local and non-local thinkers, how does the abstraction of abstract thinking dissolve? — Ludwig V

QM tells us the observer perturbs what s/he observes. So, the cognition of a sentient keeps everything local to itself in the act of observing. Thus, seemingly far-ranging observations via mental gymnastics, what we call "knowing by reasoning alone," are mostly forestalled in their abstraction from the local_empirical to the cognitive_general.

So science, no less than politics, is local. By extension from this, then, my experience of relativistic effects cannot be identical to yours as each perturbs by observation in its own way. For this reason, we imbibe artistic works in search of a particularly unique voice, although it's understood each voice is singular.

I didn't understand a lot of the intervening ideas. — Ludwig V

All of my ideas are simple, even if oftentimes communicated opaquely. This is a signal shortcoming of the high-speed, low-resolution feedback looping native to the intuitive learning_reasoning process that drives the content of my writing here (and elsewhere).

I have a lot of difficulty with the idea of something true but unprovable. How could we know that such things exist, and if we do, how do know what they are? But this is a bit more specific and so it helps. I still haven't seen an example of such a truth and would love to do so. — Ludwig V

It might help to look at some examples of a false premise leading to a true conclusion. @Tarskian can probably help you with this. (With such examples, you have a true conclusion not proven by the false premise that leads to it.)

There may not be any elegant simplicity axiomatic to everything. — ucarr

But isn't that just a methodological principle that applies when there are competing theories in play? — Ludwig V

If the competing theories are incommensurable, each with strengths and weaknesses, standard practice entails looking for the elegant simplicity.

By the way, what is the criterion for simplicity? — Ludwig V

I suppose it means that in a given time period for a foundational theory, no one can discover a form more basic.

However, it occurred to me that, as a definition, "Statements about statements" captures far too much... — Ludwig V

Berkeley's Dialogues for example can be read as a philosophical text, but also as a historical or religious text. The difference is not in the text, but in the approach to the text. — Ludwig V

Here you give us a good example of statements about statements. In other words, through what lens of interpretation do you approach a given text? Well, as I've been saying, no one reads a given text exactly as another reads it. This because each individual perturbs what s/he observes individually. Thus, we have evidence cognition spins out narratives of narratives. Now we see that when we insert cognition into the "what," it becomes the "how."

True physics would be the set of all facts in the physical universe, i .e. physical reality.

Any proposed set of physical axioms does not need to be a lossless compression of physical reality either.

The compression is actually allowed to lose a lot -- or even most -- of the information contained in physical reality.

The compression merely needs to be sound. — Tarskian

If the compression deems a fact to be true, then it must indeed be verifiably true in the uncompressed reality. — Tarskian

Since "deem" is a synonym for "judge," we see that compression herein is a process of translation. Humans frequently talk about something being lost in translation.

The foundational crisis in mathematics does indeed have a distinct metaphysical sonority to it. It describes issues in arithmetic reality but it may actually also apply to physical reality, if both realities happen to be structurally sufficiently similar. — Tarskian

Representation, though essential to cognition, imposes limitations. I think Gödel, Chaitin and Zisselman are examining these limitations logically. The translation from an axiomatic system to its power set necessarily entails loss, so there is no perfect alignment all the way to identity linking a term with its translation.

If these logical limitations translate to physics, then perhaps we're looking at thermo-dynamical systems that upwardly evolve to morpho-dynamics and, from there, to teleo-dynamics with translation losses occurring throughout the process.

Now we come to the need to look at the issue of the resolution of a rendering from one form to its correspondent via translation. I'm guessing that as the level of resolution rises, it approaches intersection with an infinite value, and thus there is no axiomatic system that completely represents reality.

Now we have a concept of reality as an infinite value. This leads me to see that knowing reality is always necessarily incomplete. This reasoning is my argument for seeing how the scope of incompleteness encompasses logic, math, science, philosophy and empirical cognition. The arts, in a symmetrical configuration, are limited by the items of the previous list.

We have examination of the "what," limited by the lossy representationality of cognition on the one side; on the other side we have empirical examination of "what it's like" to be a self-conscious sentient, the "how" (they are experienced) of the predications of the other side, limited by the lossy existentiality_noumenonality of being on the other side.

Wittegenstein has already confronted much of this. However, because reverential silence in the face of the creation is no fun for philosophy, here we are, confronting it again with our own words.

And now, talking out of the other side of my mouth, let me make the following speculation: if the gap between knowing and being is strategic, then we might rejoice at the unsolvable mystery of the future.

There's always another narrative awaiting expression and, it's not a case of endless cycling through repeating patterns across a fixed totality, better known as that charming misconception: universe.

No. Instead, because of strategic incompletion, a thermo-dynamic wisdom, future is empowered to be distinct in its uniqueness, existing beyond mere permutation of the fixed axioms and conserved laws of a unified system. There is distinct locality. There is no unity.

The observer cannot be abstracted from the experiment. — ucarr

Yes. But the observer, in my book, is not an abstraction - a point of view. (At most, a point of view is a location for a possible observer.) An observer is a person. — Ludwig V

Okay. Proceeding from the observer as an always local person, if we bind the thinking of an always local person to that always local person, then it too, is always local, and the abstraction of abstract thinking starts dissolving.

If there's no omnipresent, eternal, neutral spacetime within which dynamical material things and material systems animate themselves, then we have a wide-ranging field of local events attached to the evolving relationships linking animate things.

There is no vastness of creation because material relationships pose resistance to generalization.

The simple binary of concrete/abstract hasn’t dissolved away to nothing, but it has become faint.

What would be the criterion of success? THAT would be the definition. — Ludwig V

Might it be an ability to see how cognitive objects such as language, and cognition itself, per Gödel, will generate valid statements unprovable within the boundaries of supposedly axiomatic systems?

There may not be any elegant simplicity axiomatic to everything.

I have many problems with this - and with self-reference. Not the least of which is that I'm inclined to think that if a language cannot talk about itself, then there is something it cannot talk about, so it is incomplete. Nor is there anything wrong with self-reference. Some specific uses of it are problematic, but since I'm not committed to avoiding all logically problematic uses of language by ruling them out of court in advance, I'm not much bothered by them. — Ludwig V

This calls attention to something essential in human nature: acts of communication work with logic in application. You can't communicate if you're not being logical in a public sense, which is to say logical in a way that the common people can understand.

Every academic discipline has to keep checking (and updating) its logic as it goes forward, making additions to its database. At the end of the nineteenth century, science_physics underwent a revolution with the transition from Newton to Einstein_QM. Deep ramifications about how to view the material reality are still being distilled.

Revolutionary turns in the picture of reality are best times for philosophy and philosophers.

I don't think they give rise to any major problems of philosophy. — Ludwig V

If self-reference(s) is the antecedent to "they," then I might start thinking of you as being a radical QM materialist, as I am. For what I've seen so far (not exhaustive), scientists and logicians still maintain a white knuckle grip on the Principle of Non-Contradiction. Here at TPF, many debaters think they've scored a slam dunk whenever they discover a contradiction from the opposition.

Logicians and mathematicians have adopted the project of constructing a language with a grammar that rules such statements out. That's their choice. But it seems clear that a language that include those possibilities is perfectly workable. — Ludwig V

More evidence of your radical inclination.

Yes, Tarskian's claim is particularly interesting in terms of its generality:

A statement is philosophical, if it is a statement about another statement. For example:

It is irrelevant that it is raining today. — Tarskian

It dovetails with Gödel and, with a marvelous concision, translates his premise into verbal language. Now it's easy to see that all axiomatic systems, first order, generate statements not strictly proven within the scope of the axiomatic system from which they arise. This is a powerful generalization of the premise of incompletion, both axiomatic and existential.

When we apply essential incompletion to philosophy itself, so that now we're evaluating philosophy's evaluation of something else, we find ourselves at the second higher-order: evaluation of evaluation of a proposition.

What we're seeing now is the process of how ground rules keep giving rise to more ground rules. Ha, ha, ha! We must now laugh at ourselves in our quest to compile everything into one system elegant in its simplicity.

Another nemesis of the would-be wise, standing alongside of contradiction, is the infinite series.

I'm afraid I'm completely stuck in my opinion that the example is not a philosophical statement, unless you mean that it being used as a philosophical example makes it a philosophical statement. Which I think would be unduly stretching the scope of philosophy. — Ludwig V

You can apply critical thinking to any predication. In some instances that might render you as a pedant, but you can do it.

I am wondering, however, whether self-reference may not be part of the distinction between science and the humanities. — Ludwig V

Indeed, it is. It's the heart of the difference. It's the heart of the challenge to the Newtonian physicist to change the vision to QM. The observer cannot be abstracted from the experiment. From this we understand there is no abstraction. Instead, there are relationships. Loop quantum gravity tells us there are atoms of discontinuous space. Seemingly continuous space is an effect of the limits of human eyes.

Now we see that incompletion generalized dovetails with the fall of abstraction, landing us in a world that demands a future created from... what?

...can there be science of science. I doubt if it could follow some version of scientific method, including the experimental method, so would such a discipline be scientific? — Ludwig V

Philosophers, as we've been seeing in my post, are cognitive grammarians. Thinking about thinking amounts to examination of the ground rules for any predication.

Ground rules are the foundation supporting methodology. Therefore, any discipline that generates methodology also generates ground rules. In this way, philosophy is more inclusive than science. The methodology for the scientific method might not be scientific, but it is philosophical.

History, literature, and some approaches to language are about actual human beings, not abstract concepts — Ludwig V

Is philosophy included here? Depends on what you mean by philosophy. Much philosophy presupposes an abstract observer, but Wittgenstein, of course, challenged that. — Ludwig V

This question directs some light onto what makes Tarskian's definition of philosophy interesting:

A statement about a fact is not philosophical. For example:

It is raining today.

A statement is philosophical, if it is a statement about another statement. For example:

It is irrelevant that it is raining today.

This explains in simple words what the true meaning is of Godel's incompleteness theorem.

A theory is incomplete if it can express statements about its own statements. In other words, a theory is incomplete if it is capable of philosophy.

Self-referential statements are just a special case of the general case, which is the philosophical statement. If a statement can talk about other statements, then it can also talk about itself. — Tarskian

Tarskian helps illuminate some possible essentials of consciousness via his application of Gödel to his definition of philosophy. We're looking at a spectrum of incompleteness: a) axiomatic: Russell, Gödel; b) existential: Bohr, Schrödinger, Heisenberg; c) cognitive: Tarskian.

If philosophy is an essential part of human nature, then human nature joins the list of incompleteness detailed above.