Conifold

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Conifold

Dec 20, 2024 13:13

See Gopman's thesis Emergence of Platonism in modern physics.

Conifold

Dec 20, 2024 13:13

Penrose is explicitly a Platonist with a big "P", see Geometry Matters:"To me, the world of perfect forms is primary (as was Plato’s own belief) — its existence being almost a logical necessity — and both the other two worlds are its shadows"; "I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato’s world of mathematical concepts"; etc. So are enthusiasts of the "theory of everything", like Greene and Tegmark, albeit less mystically.

Discussion on question by Miss Unders…

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Conifold

Dec 20, 2024 13:12

"The beginning" may not be there so your italics do not entail your all caps. The contrapositive is still a conditional, if there was a beginning then nothing was there. And circular arguments with random premises do not need to be refuted, their premises can just be dismissed.

Discussion on question by TheMatrix E…

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Conifold

Dec 19, 2024 11:50

Hawking proposed at one point that information is lost in black holes and it is still considered a mainstream theory, it is also lost in quantum collapse if it is 'real'. So "information is never lost" is hardly "main and all-overriding law of physics". It simply reflects reversibility of dynamics and may well be revised. Even if not, the second law of thermodynamics provides irreversibility for all practical purposes. Physicists are probably more committed to conservation of energy, but even that was revised in some early quantum theories. "Main and all-overriding laws" are open to revision.

Discussion on question by Syed: Is as…

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Conifold

Dec 14, 2024 10:58

Is there the only valid way to define a true Scotsman? All true Scotsmen agree that there is, it is just that each has their own complete with arguments in its favor.

Discussion on question by Syed: How d…

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Conifold

Dec 12, 2024 09:03

Can we know that we saw red yesterday, and it was the same red that we see today. After all, we cannot actually time travel and verify it. And as we trust our memory, faulty though it is, we'll just have to trust our imagination to let ourselves know how we would hypothetically behave, as we do in any planning. And yes, we may guess wrong, as with everything else, and/or our bet may change when it comes to making it. Italicizing and adding "actually" do not do the work you expect of them.

Discussion on question by Syed: Is th…

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Conifold

Dec 11, 2024 19:28

If only we could give stuff greater power by thinking this or that. But alas, us thinking this or that does not make it so or explain anything. Unless, of course, you have in mind the power of positive thinking, but that is something psychologists would know more about.

Discussion on question by Mikhail Kat…

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Conifold

Dec 10, 2024 06:48

Judging by the thread you linked, Artemov's mathematical arguments are not novel, and his informal philosophical interpretation of them as "proof of consistency" mathematicians find unconvincing. How exactly does this refute Giaquinto's "barren" and "untenable"? Proving or refuting rhetorical epithets is generally a dubious exercise, of course, but here they are just less polite versions of "not novel" and "unconvincing".

Discussion on question by user80226: …

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Conifold

Dec 7, 2024 15:18

If a process is fundamentally deterministic how can it produce determined outcomes? What "keeps track" of the deterministic law and "ensures" that outcomes align with it? What could possibly prevent a fundamentally deterministic process from stopping to follow the law at some point? If the answer to this is that we specified it as "fundamentally deterministic" after all, then you have your answer as well, just replace "deterministic" with "distributed so and so". Unless, of course, you have it in mind that randomness can only be an appearance produced by some deterministic 'mechanism'.

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Conifold

Nov 28, 2024 17:48

The reasoning here is not philosophical, it is physical and bad one at that. Radiant energy is neither kinetic nor potential, mass energy is neither as well. Kinetic/potential energy split is confined to classical mechanics, kinetic energy is not even Lorentz invariant. Quantum particle collisions are not elastic, "elastic" does not even make sense for them. Dragonflies, like all living beings, store energy they get from food and use it, among other things, to move their appendages, like rotating blades. For correct energy analysis of dragonfly's descent, ask on Physics SE.

Discussion on question by Annika: Is …

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Conifold

Nov 25, 2024 00:10

Even our best physical theories already defy your 'intuitions'. But both physics and metaphysics are surmises of our experience, so any substantive claims about them are a posteriori and cannot be "theorems". Ironically, large swaths of contemporary metaphysics do, in fact, purport to base themselves on 'intuitions' (modal metaphysics, for example), even as they arrive at 'unintuitive' conclusions. So perhaps one can surmise further that our 'intuitions' are generally incoherent and that is why any systematic account has to give up some.

Discussion on question by user80226: …

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Conifold

Nov 14, 2024 17:30

Is the experience of getting high on cocaine evidence of the opposite? Neither love nor high can be reduced "solely" to chemicals, neurons and electric impulses are surely involved as well. But "X cannot be reduced to" is not an argument, and "if it is all physical why isn't it behaving in the most primitive way imaginable" is a very poor argument. Physical systems can behave in very sophisticated ways, as our computers demonstrate. It is like asking why planets are not moving in just circles or ellipses if they are all physical.

Discussion between Bumble and Syed

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Conifold

Nov 14, 2024 11:59

So when we process large quantities of independent evidence it is the evidence of what kind of events, in general terms? What should hold about those events themselves (when they do not fall into repeating series), in addition to us following Bayesian norms, to make the probabilities correspondent? Not sure if this is clear enough, but do you know of works in this spirit?

Conifold

Nov 14, 2024 11:59

Such results would have to make reasonable assumptions not just about the process of assessing evidence and calculating probabilities, but also about the underlying events they attach to, as in iid limit theorems. Some formalized versions of the 'uniformity of nature', as it where, together with analysis of how 'uniform' elementary events combine into non-repeatable compounds to which Bayesian probabilities attach.

Conifold

Nov 14, 2024 11:59

But there should be results beyond such situations that illuminate in what way probabilities are still correspondent. That reduce probabilities to something (in principle) measurable in this world. Because statistical ensembles of virtual or Lewis's worlds are as detached from our use of statistics as platonic realm is from our use of mathematics.

Conifold

Nov 14, 2024 11:59

So the nature of their correspondence is non-trivial. There is a similar issue with corresponding counterfactuals and other modal claims. Unfortunately, traditional 'interpretations' of probability gloss over this by restricting to simple situations with series of trials, where the correspondence is transparent via limit theorems.

Conifold

Nov 14, 2024 11:58

Or, when they predict probabilities, those can be converted into frequencies and again measured one way or the other. So it is easy to formulate in what sense they correspond. Many Bayesian probabilities are peculiar in the sense that there is no obvious way to make such conversions, and we cannot travel to parallel worlds to see how things unfold there and tally the outcomes.

Conifold

Nov 14, 2024 11:58

@Bumble Could you give me references on convergence results? I have little doubt that Bayesianism is useful in practice and it is so because it is essentially correct, my interest is in the nature of this correctness. Most theories, deterministic or stochastic, in experimental or observational fields, predict quantities either directly measurable or computable from those, temperatures, population sizes, prices, etc.

Conifold

Nov 11, 2024 09:57

Are there known conditions on non-'repeatable' events under which one can prove that their probabilities dictated by Bayesian norms on priors and updating connect to something objective about them (not frequencies, obviously, since those do not make sense)? And, as a consequence, prove that if we consistently bet on Bayesian probabilities then we are better off in the long run, as in iid series?

Conifold

Nov 11, 2024 09:57

@Bumble What bothers me in Bayesianism is the wrong (normative) modality. For a series of iid events the law of large numbers tells us that their probabilities align with frequencies, and those we can observe.

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Conifold

Nov 9, 2024 16:34

It will take a very long time, and definitely beyond any of our lifetimes. If one’s life goal is to understand these ultimate questions then they are well advised to revise it in view of existing realities. No human longevity will be long enough, wealth and power notwithstanding, and it is much more fulfilling to contribute, however little, to developing appropriate tools and conceptions than to "wait" for humanity to do it for them. It may also well be that the "answers", as something ready for consumption, simply do not exist, and it is only the pursuit that is ultimately the answer.

Discussion on question by user80226: …

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Conifold

Nov 8, 2024 10:04

"Aliens of the gaps" objection does not work in this context. Suspending judgment on alien design does not preclude testing its consequences. And it makes a lot of predictions: that there is energy harnessing mechanism somewhere, that there are traces of the builders on planets within, that we can figure out assembly process eventually, that other spheres might be encountered, etc. The first reaction should be to study the sphere and its surroundings and test those predictions instead of concluding how "strong" an evidence the sphere is by itself. Assessing evidence is done after a study.

Discussion on question by Mikhail Kat…

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Conifold

Nov 1, 2024 20:22

@mudskipper It is reprinted in his book Truth and Other Enigmas, p.192. You can get it on Scribd on a free trial. It is also in GoogleBooks, but which pages it would show is random.

Conifold

Nov 1, 2024 20:22

@mudskipper Dummett agrees that this (MathOverflow discussed) issue is non-trivial, as one can see by reading the full paragraph that is cut off in the OP. What he says is trivial only concerns rephrasing ∀ in words.

Conifold

Nov 1, 2024 20:22

How does "something allied" convert into "the same"? And why should Dummett care about object/meta languages when his concern is that "distinction cannot be explained at all" even conceptually, regardless of formal means used? He is not talking about transition "from A(0), A(1), A(2),... to ∀x A(x)" but about transition from "all of the statements A(0), A(1), A(2),... are true to ∀x A(x)", which is, indeed, a trivial rephrasing. That there is a "gap" between "each is true" and "all are true" is written shortly after the quote. You seem to pay insufficient attention to his text.

Discussion on question by user80226: …

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Conifold

Oct 26, 2024 17:56

You should take your reflections to their logical conclusion. Religions are not scientific theories, so scientific standards are not appropriate, but they are not theories either, so why should "settling theoretical disagreements" be appropriate at all? They are ways of life that encompass traditions, culture, values, morality, etc., knowledge claims are subservient to that. It makes sense to settle disagreements within a shared way of life, as in science or politics, not across them. There is no "settling" when elements that make it meaningful are not shared. There is, at best, co-existence.

Discussion on question by Thomas Alex…

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Conifold

Oct 24, 2024 09:27

@causative Every well-formed sentence of Peano arithmetic is either true or false in the standard (or any other) model. The term is usually not applied to models because they are "complete" by definition. The truth values in them do not have to be decidable by any method available to us, now or ever.

Conifold

Oct 24, 2024 09:27

The material world is not a theory of itself, so it is not an example of "complete physics" in the relevant sense. The standard model of arithmetic is also already "complete", problem is it is not recursively representable. What you are looking for and mathematics as practiced serve different purposes. Theories and models have limitations because their purpose imposes them, removing them defeats the purpose.

Conifold

Oct 24, 2024 09:27

Words and symbols are just means of representing. What difference does it make, in principle, whether it is words, symbols, diagrams, manipulatives or some other representations? The "failures" of Gödel's incompleteness are inherent in any finite representation, not words, it is a feature, not a bug. But advanced mathematics puts very high demands on precision and compression of content, so "object manipulation as a metaphor" and other "heartful manners" are non-starters for pragmatic reasons. There is a reason mathematics evolved away from that into abstraction and symbolism.

Discussion on question by user80226: …

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Conifold

Oct 17, 2024 16:39

I think it is is still too long for many users to read through, but judging by your summary these arguments are informal and there need not be any fallacies in them to reject their conclusions. "Best" explanation is in the eye of the beholder and depends on which mechanisms one knows to exist. Beauty, efficiency and fitness of living beings were once used to infer that they had to be designed to fit their environments. And then came the evolution theory. Later still we saw fruit flies evolve their DNA in labs without any design. The old explanation ceased to be the "best".

Conifold

Oct 17, 2024 16:39

The post is too big. Remove the quotes and summarize what the arguments are briefly, people can click on the links if they need more context.

Discussion on question by Amelia Sala…

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Conifold

Oct 12, 2024 17:00

One does not need reasons to have a "thirst" for something valuable in itself. They just have it, or not. And if not then reasons will not help either, drives and emotions are not rationally controlled. Reasons only matter when what is pursued is not valuable in itself but only derivatively, to get something else. Knowledge is not of this sort, so its pursuit now is "meaningful" regardless of what happens later.

Discussion on question by shindemo: W…

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Conifold

Oct 9, 2024 04:40

That people need not be behind verbal play, or even combining concepts, was already behind the medieval 'thinking machine' of Ramon Llull and was picked up by Leibniz. LLM 'hallucinations' have a mechanism different from human hallucinations and illusions, so the name is misleading. For cogent answers, you'll have to be more specific as to what "actually mean" is getting at.

Discussion on question by user107952:…

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Conifold

Oct 6, 2024 18:13

@causative That is not very persuasive to many. They will say that Euclidean geometry is different in kind, grounded in objective reality, while Sherlock Holmes, Call of Duty, poker or chess are human inventions. What was conceived, by whom and when is moot to the ontological status, but salient to birth dates of abstract artifacts (only). We should not argue, both positions are self-consistent, represented in the literature and this will not be resolved on SE.

Conifold

Oct 6, 2024 18:13

@causative Why? We distinguish artificial and natural physical objects, one can do the same with abstract ones. Natural vs artificial kinds are a standard example. The distinction may or may not be useful or justified (by whatever criteria), but it is not inconsistent, nor is it inconsistent to hold that natural objects exist eternally while artificial ones come to exist. For example, Thomasson, Sainsbury, etc., hold that fictional characters are such abstract artifacts, and chess might as well be.

Discussion on question by user80226: …

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Conifold

Sep 30, 2024 11:05

Since the laws of physics are mathematical does it mean that physics ultimately reduces to mathematics? Tegmark thinks so. Since the only physical events we can know of are those we can perceive, directly or indirectly, does it mean that physics ultimately reduces to perceptions? Berkeley thought so. This little game can be played every which way.

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Conifold

Sep 25, 2024 09:35

@JimmyJames Your point is strange, why would people care to debate whether to call something "subset of physics" or not? The standard meaning of reducibility that this question asks about has little to do with that and is not vacuous. It is whether higher order laws (chemical, biological, etc.) simply repackage fundamental laws or "emerge" over and above them. Do some chemical laws manifest only at the macroscopic level with nothing in fundamental physics giving rise to them or are they its consequences. That is what both physicalists and their opponents care about, not verbal choices.

Conifold

Sep 25, 2024 09:35

@JimmyJames Reduction is not about using quantum physics to do chemistry in practice, but it takes more than trivialities about subsets of physical reality. The laws governing those subsets should reduce, whether it is practical to track that or not. That chemicals are made of physical parts does not imply that laws governing physical parts induce chemical laws (in full), that is not trivial at all. Known 'derivations' of chemical laws from quantum physics import some macroscopic considerations by hand rather than derive them from microphysical ones, and hence are circular as reductions.

Conifold

Sep 25, 2024 09:35

The talk of reduction has origins in philosophy of 20th century, Carnap and Neurath in the 1930s and especially Nagel's model of 1949, see SEP. References by scientists are second hand. It should also be said that the current mainstream is that chemistry has not been reduced to physics, although that was what earlier analytic philosophers believed, and full reducibility is implausible for structural reasons, see Chemical Reduction.

Discussion on question by TheMatrix E…

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Conifold

Sep 16, 2024 08:39

Why would political splits, even or otherwise, be proxies for good vs evil? There is a rather obvious political explanation akin to Smith's "invisible hand" or Le Chatelier's principle: if the equilibrium is disturbed the system adjusts by counteracting the disturbance. Political coalitions compete under majority rule, if one makes electoral gains the other tweaks its positions to even the numbers. In the long run, a 50/50 split is the expected outcome. Modern polling and media speed up adjustments and get us to the equilibrium faster. This is directly observable in election cycles.

Discussion on question by mudskipper:…

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Conifold

Sep 13, 2024 09:43

@SystemTheory Remove the distinctions, what then? That has been tried too, got very popular, Hegel, Schelling, etc. One can string words into sentences, but that does not replace an intellectual breakthrough. Cognitive science and neuroscience do not advance by mottos and wishful thinking.

Discussion on question by Meanach: Ch…

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Conifold

Sep 7, 2024 08:15

You can put the full quote into the post, there is no word limit there. And there is a big difference between saying X on one's own behalf and saying that X "has been said" by unnamed others. It is also clear in context that he is suggesting not improving on democracy by another form of government, but improving how democracy is implemented to match its aspirations as the preferred form of government.

Conifold

Sep 7, 2024 08:15

First, Churchill did not say this. What he said was (emphasis mine) "No one pretends that democracy is perfect or all-wise. Indeed, it has been said that democracy is the worst form of Government except all those other forms that have been tried from time to time." He said how to improve it right after:"but there is the broad feeling in our country that the people should rule, and that public opinion expressed by all constitutional means, should shape, guide, and control the actions of Ministers who are their servants and not their masters." Real life versions fall short of that ideal.

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Conifold

Sep 6, 2024 15:38

@MauroALLEGRANZA Intuitionistic and other non-truth-functional logics have a notion of tautology in terms of semantic models (Kripke's, Heyting algebras, etc.), see e.g. Wasilewska. Due to completeness theorems, they coincide with theorems of a suitable propositional calculus. And if one wishes to distinguish tautologies from validities, either in modal or predicate logics, they need to formally separate the propositional fragment of such logics from the rest to make sense of it.

Conifold

Sep 6, 2024 15:38

@DavidGudeman In formal propositional systems, it makes no difference what a connective represents, it is just a connective. Similarly, ◊, □ do not have to represent possibility and necessity for the logic to be modal.

Conifold

Sep 6, 2024 15:38

It is a non-classical propositional logic. To be a modal logic in the formal sense, it has to have modal operators in its syntax, not just derivative symbols reducible to connectives.

Conifold

Sep 6, 2024 15:38

The distinction applies to modal logics, i.e. systems that explicitly separate propositional logic and modal operators. In them, (propositional) tautologies are those universally valid independently of the truth conditions for modal operators. If a logic "couches modal language in purely propositional language" then it is not modal logic in the technical sense and there is no such distinction, blurred or otherwise. Validity = propositional tautology. That one informally interprets connectives of such logics in some modal sense is moot.

Discussion on question by Igor F.: Wh…

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Conifold

Sep 6, 2024 15:37

There is algebra of logic that uses more conventional algebraic notation, see Boolean algebra, for example. But the primary purpose of logic is to relate claims, not to solve equations or derive identities. There is no analog to it in algebra and forcing algebraic notation only makes the enterprise clumsy and encourages wrong associations. Natural deduction systems were specifically introduced to replace earlier Hilbert systems because the latter were too "algebraic" for logic's purposes.

Discussion on question by Zhang Hong:…

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Conifold

Sep 6, 2024 15:32

No. Wittgenstein originally thought, mistakenly, that Gödel’s proof needs the natural language interpretation of his sentence as "I am unprovable" to show that it is true but unprovable (in part, due to Gödel’s own informal remark). This mistake is reflected in the "notorious paragraph" from RFM, but Wittgenstein corrected it later while maintaining his criticism of the theorem's philosophical interpretations. History and the debate over the "notorious paragraph" are detailed in Matthíasson, Interpretations of Wittgenstein's Remarks on Gödel.

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Conifold

Sep 4, 2024 19:56

No. "Many scientists have noted that the innate/acquired distinction is ultimately a false dichotomy. All traits are influenced in their development by both environmental and genetic factors... It is a mistake to classify traits as emanating either from the germ line or the environment" SEP, Distinction Between Innate and Acquired Characteristics.