"utility, beauty, and sustainability", I would say are not components of the building, but aspects (properties) of the whole. So I agree with your sentiment, but am inclined to think that "causal relations" - which implies that they are distinct parts (components) of the whole - is not quite the right way to articulate the point. — Ludwig V
I agree with what you say. Indeed, it seems obvious. At present "emergent properties" seems to be pretty much a label for the undefined. I think the most useful approach is not to affix a label and try to answer the question "what is an emergent property", but to consider and understand cases and then work out how they are related. Then we'll know whether to pin one label on all the cases or maybe different labels for different, but similar cases. So your comments on reinforced concrete slabs seem entirely appropriate. The label doesn't help and can get in the wayI think the utility, beauty, and sustainability of a building are Emergent Properties, and the parts, features, and configurations from which they emerge are not so distinct. They can depend on each other, or emerge from one and the same part. — jkop
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. I don't think they give rise to any major problems of philosophy. 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.This question directs some light onto what makes Tarskian's definition of philosophy interesting: — ucarr
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.A statement is philosophical, if it is a statement about another statement. For example: It is irrelevant that it is raining today. — Tarskian
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
I don't think they give rise to any major problems of philosophy. — Ludwig V
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
A statement is philosophical, if it is a statement about another statement. For example:
It is irrelevant that it is raining today. — Tarskian
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
I am wondering, however, whether self-reference may not be part of the distinction between science and the humanities. — Ludwig V
...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
At present "emergent properties" seems to be pretty much a label for the undefined. — Ludwig V
The Principle exists, but only rarely applies. You have to define your language very carefully to produce one. A fundamental rule of language appears to be to design itself to avoid the possibility f being faced by one, allowing third possibilities and shades of grey. A binary choice is almost always artificial.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. — ucarr
I didn't appreciate that. I got too annoyed at the revelation that he didn't want a definition. He wanted an algorithm that would enable an AI to distinguish philosophical texts from the rest. What would be the criterion of success? THAT would be the definition.It dovetails with Gödel and, with a marvelous concision, translates his premise into verbal language. — ucarr
I hoped you would say that. So science, in the end, is grounded in human beings. Worse than that, not in a scientific, but history and philosophy. Oh dear!The methodology for the scientific method might not be scientific, but it is philosophical. — 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.The observer cannot be abstracted from the experiment. — ucarr
I'm sure you could. Thank you for letting me off the detail. I agree that the "emergent" physical property of the gate "emerges" from the design. But the design emerges from the designer. Physics cannot even recognize a design, much less apply its laws to it.I, in principle, could explain in an enormous amount of detail, why these specific components, interconnected with each other in this specific way, results in the emergent property of the design. — wonderer1
Yes. I like the idea that it is about particular cases, rather than some very general abstraction. Generality is there the hand-waving comes in.So it seems reasonable to me, to see understanding of emergence as something particular experts have, — wonderer1
So it seems reasonable to me, to see understanding of emergence as something particular experts have,
— @wonderer1
Yes. I like the idea that it is about particular cases, rather than some very general abstraction. Generality is there the hand-waving comes in. — Ludwig V
one can have a rather good understanding of how tornadoes work while being entirely ignorant of particle physics. The point generalizes to more complex and longer-lived entities, including plants and animals, economies and ecologies, and myriad other individuals and systems studied in the special sciences: such entities appear to depend in various important respects on their components, while nonetheless belonging to distinctive taxonomies and exhibiting autonomous properties and behaviors...
...
The general notion of emergence is meant to conjoin these twin characteristics of dependence and autonomy. It mediates between extreme forms of dualism, which reject the micro-dependence of some entities, and reductionism, which rejects macro-autonomy — SEP
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
What would be the criterion of success? THAT would be the definition. — Ludwig V
There may not be any elegant simplicity axiomatic to everything. — ucarr
The compression is actually allowed to lose a lot -- or even most -- of the information contained in physical reality. — Tarskian
Not if you want to reconstruct reality rather than a pale comparison. — AmadeusD
https://en.wikipedia.org/wiki/Kolmogorov_complexity#Chaitin's_incompleteness_theorem
There exists a constant L (which only depends on S and on the choice of description language) such that there does not exist a string s for which the statement
K(s) ≥ L (as formalized in S)
can be proven within S.
https://en.wikipedia.org/wiki/Kolmogorov_complexity#Compression
It is straightforward to compute upper bounds for K(s) – simply compress the string s with some method, implement the corresponding decompressor in the chosen language, concatenate the decompressor to the compressed string, and measure the length of the resulting string – concretely, the size of a self-extracting archive in the given language.
it sounds like you're apply concepts in data processing to "reality" which seems... off, to say the least. Is there a basis for it? — AmadeusD
http://www.sci.brooklyn.cuny.edu/~noson/True%20but%20Unprovable.pdf
Gregory Chaitin described an innovative way of finding true but unprovable statements. He started by examining the complexity of the axioms of a logical system. He showed that there are certain statements that are much more complex than the axioms of the system. Such statements are true but cannot be proven by the axioms of the logical system. The following motto is sometimes used to explain this:
“A fifty-pound logical system cannot prove a seventy-five-pound theorem.”
In particular, basic arithmetic is a logical system that has a level of complexity and so there are certain types of statements that are true but too complex to be proven using basic arithmetic. The main point for our story is that within basic arithmetic we can always find more complicated statements of a certain type. Hence, there are infinitely many true but unprovable statements.
https://arxiv.org/pdf/2302.08619
A proof of Gödel’s incompleteness theorems
using Chaitin’s incompleteness theorem
Abstract
Gödel’s first and second incompleteness theorems are corner stones of modern mathematics. In this article we present a new proof of these theorems for ZFC and theories containing ZFC, using Chaitin’s incompleteness theorem and a very basic numbers extension.
As opposed to the usual proofs, these proofs don’t use any fixed point theorem and rely solely on sets structure. Unlike in the original proof, the statements which can be shown to be unprovable by our technique exceed by far one specific statement constructed from the axiom set.
Our goal is to draw attention to the technique of number extensions, which we believe can be used to prove more theorems regrading the provability and unprovability of different assertions regarding natural numbers.
I'm always interested in metaphysical speculation of that kind. — AmadeusD
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?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 didn't understand a lot of the intervening ideas. But this inclines me to retort that perhaps it needs to become faint. Binary oppositions are almost always less clear and definitie than some people would like to think.The simple binary of concrete/abstract hasn’t dissolved away to nothing, but it has become faint. — ucarr
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.Might it be an ability to see how cognitive objects such as language, and cognition itself, per Gödel, will generate valid statements unprovable with the boundaries of supposedly axiomatic systems? — ucarr
Perhaps there isn't. But isn't that just a methodological principle that applies when there are competing theories in play? In any case, it only requires us to choose the simplest of available theories, so it would be hard to refute. By the way, what is the criterion for simplicity? Kolgorov complexity?There may not be any elegant simplicity axiomatic to everything. — ucarr
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
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
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
I didn't understand a lot of the intervening ideas. — Ludwig V
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
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
By the way, what is the criterion for simplicity? — Ludwig V
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
If by "observer" you mean measurement and by "observes" you mean measures, then I think you're correct here about QM. Afaik, "sentience" itself cannot "perturb" quanta since classical-scale systems (e.g. brains-sensoriums) cannot directly interact with planck-scale systems. That way leads to the dark side (imo, p0m0 / Berkeleyan nonsense :sparkle:).QM tells us the observer perturbs what s/he observes. — ucarr
Isn't that old news in a new bottle? Only physicists needed QM to tell them about the specificity of observation and its distortion in the process of communication.QM tells us the observer perturbs what s/he observes. — 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 correctingWell, 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
So "simple" means "more basic"?I suppose it means that in a given time period for a foundational theory, no one can discover a form more basic. — ucarr
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
I think your "strategic incompleteness" overstates the case and incoherently conflates teleology with formalism with empiricism. — 180 Proof
I don't understand why you include components when I thought you were saying (correctly) that utility, beauty and sustainability are the result of other components, but not one of them. I think this may be a category issue.In this sense, they are both emergent properties and components of the architecture. — jkop
"Every effect has a cause" may be true, in a way. But it does not follow that every effect must have a cause which is a specific component of the building. The cause of utility might be an effect of the totality of the building as built, rather than as a collection of components.The special sciences won't answer how they causally emerge, nor how a balanced or distributed composition satisfies the success of a building. Yet every effect has a cause, and for millennia we have known that buildings should be practical, beautiful, and sustainable. — jkop
QM tells us the observer perturbs what s/he observes. — ucarr
Isn't that old news in a new bottle. — Ludwig V
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
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
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....since classical-scale systems (e.g. brains-sensoriums) cannot directly interact with planck-scale systems (re: decoherence).
— 180 Proof
How do you characterize ontically and empirically the physicist and its experimental_inferential connection to planck-scale phenomena? — ucarr
utility, beauty and sustainability are the result of other components, but not one of them. — Ludwig V
I'm suggesting that it has been over-hyped and is rather less interesting than one would have thought, given all the fuss.the new bottle perturbs the old news into something interesting: — ucarr
Be fair. Sometimes we are understood, and sometimes we manage to sort out misunderstandings.There's always the hope of being understood. — ucarr
Well, those are all good things."Basic" as the criterion for "simple" expresses an ideal of efficiency and clarity and certainty. — ucarr
Perhaps my problem is a verbal one. "Components" suggests that they are parts of the building in the sense that the roof and the windows are parts of the building. But they aren't. I would much prefer "aspects" of the building, or of the architecture, whichever you prefer.True, but I'm not saying they're components of themselves. They're components of the architecture. — jkop
Yes, you could have parts of the building that meet those critieria. But the basic point, I think, is that they are holistic. If we say that the frontage of the building is beautiful, that's a description of the whole frontage not of any part or segment of it. If we say that the building is very practical, we mean that the building as a whole is practical.Their own components result in practical, beautiful, and sustainable parts of a building, but the building won't be successful as a building by merely having such parts.
These, in turn, must be composed (e.g. balanced or distributed) in ways that make the building successful as a building. — jkop
"Every effect has a cause" may be true, in a way. But it does not follow that every effect must have a cause which is a specific component of the building. The cause of utility might be an effect of the totality of the building as built, rather than as a collection of components. — Ludwig V
Short version - holistic aspects of the building. — Ludwig V
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
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
Be fair. Sometimes we are understood, and sometimes we manage to sort out misunderstandings. — Ludwig V
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
This is not contorted. It's perfectly straightforward. Self-reference. I've long held the heretical view that the "witness" is not decidable. Is there any reason to suppose it must be? Of course, you could assign a third truth value to undecidable sentences, but I suppose that would be cheating."This is not provable."
Assuming that this sentence is decidable, it is true or false.
If it is true, then it is (true and unprovable).
If it is false, then it is (false and provable).
Hence, the sentence is (true and unprovable) or (false and provable). Therefore, it is a legitimate existence witness for his theorem. — Tarskian
Yes. I thought that something along these lines would probably work. However, you seem to be assuming that if a theorem can be expressed, it must be true. In which case, if that assumption is correct, it is provable. Or is that idea just an assumption or an axiom or something?A better example, Goodstein's theorem, was later discovered for which the theorem itself can be expressed in Peano arithmetic but the proof cannot, making it (true and unprovable) in that context. — Tarskian
Yes. That's what puzzled me.Godelian sentences are fiendishly difficult to detect in arithmetical reality because in that context we systematically use soundness to discover truth: the sentence at hand is true because it is provable. Arithmetical vision requires calculation. It is virtually impossible to detect an arithmetical fact without calculation. — Tarskian
But not knowing why my observation is true is not the same as its being unprovable. Surely that will only work if what I observe is incapable of being proved, as opposed to my not knowing how to prove it. If I knew that it was unprovable, I think I would either not believe my eyes or at least suspend judgement.On the other hand, if we had a copy of the theory of the physical universe, observing physical Godelian facts would be trivially easy.
Unlike in arithmetical reality, in physical reality we do not need to know why exactly a physical fact occurs in order to be able to observe it. — Tarskian
Well, maybe. I think most people believe that my brain does the calculations. I can see where the ball is going to land and catch it, without consciously doing any calculations or being aware of any calculation going on in my head. It's a tricky philosophical issue.Our eyes do not have to calculate a fact in order to see it. Our eyes just see it. We are perfectly able to see things with our eyes that we do not understand or cannot possibly predict (up to a point, of course). — Tarskian
I'm sorry I don't understand that. Do you mean that my eyes may follow heuristic principles, rather than calculations? Quite likely. But then my seeing would be an educated guess, which could be proved right (or wrong) after the event.(By the way, this is a simplification because our eyes may also use "calculations" in order to "see".) — Tarskian
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