Mathematics has a massive foundational crisis with insurmountable issues. — Tarskian

So you shit on both sides of this divide? What intellectually does meet with your full approval?

So you shit on both sides of this divide? What intellectually does meet with your full approval? — apokrisis

First of all, I am fascinated by disaster tourism. I would like to take a tour of Chernobyl reactor number four.

https://en.m.wikipedia.org/wiki/Chernobyl_Nuclear_Power_Plant_sarcophagus

The Chernobyl Nuclear Power Plant sarcophagus or Shelter Structure (Ukrainian: Об'єкт "Укриття") is a massive steel and concrete structure covering the nuclear reactor number 4 building of the Chernobyl Nuclear Power Plant. The sarcophagus resides inside the New Safe Confinement structure.

My hobby would be to compare it to the open-air molten cores of the six Fukushima reactors and try to find similarities.

Secondly, I don't trust a tool until I understand its limitations. That is why you have to crash test it thoroughly.

That is why I find the foundational crisis in mathematics an exhilarating subject. I try to devour all the literature. Show me something else that goes wrong! Is it that bad?

"Mathematics proper" is fiendishly boring in comparison.

Thirdly, most programmers hate bugs. I love them. They always called me for those, because I was apparently the only one who liked working on them. There is nothing more fun than a complete mess.

Last but not least, the foundational crisis in mathematics says a lot about the universe itself, which is itself obviously also a complete mess. The metaphysical implications of the crisis are utmost fascinating.

I don't like beautiful theories. They are boring. I don't trust smooth talkers. If it is too good to be true, then it undoubtedly is.

OK.

It's not an issue with mathematics as it may seem. It's an issue with the very notion of possibility theory in systems, such as physics which quite possibly determines states in nature.

Cheers

People have used this sort of idea to create computational and communications based theories of causation, which are pretty neat. Past states of a system end up entailing future states (or a range of them). This seems right in line with the idea of cosmic Logos in some respects. It's also a version of causation that seems to deal with some of Hume's "challenges." — Count Timothy von Icarus

I think your right about this. You seem updated with the right semantic model in mind.

I am fascinated by disaster tourism....There is nothing more fun than a complete mess — Tarskian

That explains a lot ;-)

Mathematics has a massive foundational crisis with insurmountable issues. — Tarskian

That is why I find the foundational crisis in mathematics an exhilarating subject — Tarskian

Well, it's good someone is interested. :roll:

I'd like to point out counterfactuals but don't have enough information to conjecture about it.

Thoughts?

So, physicists want a "grand unified" pattern instead. Physicists seem to view this effort as essential. — Tarskian

My point was simply that I think 'Physics' as a discipline has still a 'raison d'etre' if 'a theory of everything' is impossible to achieve. I myself worked briefly in condensed matter physics, a branch of physics that is quite independent to the search of a 'theory of everything'. To some physicists might be essential, maybe even famous ones, but this does not mean that physics becomes vain if a 'theory of everything' is impossible. There still much to be discovered about physical phenomena that can be 'modeled' with current theories.

Do you mean how does causality as imagined by physics relate to causality as imagined by logic? Do they share the same root or are they antithetic? — apokrisis

I am once again focusing on this as the thesis of this thread. If one were to know the antithetic nature of what apokrisis said then it might be deduced on such gestaltism to see the bounds and limits of physics and logical determinism.

Then once again, what could a "cause" be in logic?

If physics is to be descriptive of logic, then, a "cause" would be defined by how the system of laws governing physics works, and from there to deduce what logic would be required to explain those laws in terms of decidability in logical space.

Hmm. "physics describes logic" is ill-formed. Nothing good will come of it.

My point was simply that I think 'Physics' as a discipline has still a 'raison d'etre' if 'a theory of everything' is impossible to achieve. I myself worked briefly in condensed matter physics, a branch of physics that is quite independent to the search of a 'theory of everything'. To some physicists might be essential, maybe even famous ones, but this does not mean that physics becomes vain if a 'theory of everything' is impossible. There still much to be discovered about physical phenomena that can be 'modeled' with current theories. — boundless

Indeed, physics has its merits. I don't think anybody denies that. I was just pointing out what some of its problems are, and how these problems relate to mathematical logic.

Then what is a model to you? Wittgenstein called it a picture of reality, no?

Indeed, physics has its merits. I don't think anybody denies that. I was just pointing out what some of its problems are, and how these problems relate to mathematical logic. — Tarskian

Ok, I see. Thanks for the clarification.

You can't have a physics that "describes" logic, because you can't have a physics unless you first have a logic in which to set it out.

All you might achieve is a preferred logic for doing physics.

You can't have a physics that "describes" logic, because you can't have a physics unless you first have a logic in which to set it out. — Banno

Is this chicken or egg? Physics came first in a non-anthropological manner. QED?

Is this chicken or egg? Physics came first in a non-anthropological manner. QED? — Shawn

You can study/employ/use logic without physics. But the viceversa is not true. You can't do physics without logic. That's why I said that logic is transcendental with respect to physics: it is a necessary precondition for physics. And same, I think, is true for science in general.

[...] logic is transcendental with respect to physics: it is a necessary precondition for physics. — boundless

What makes you believe that is true?

I cannot conceive doing physics without employing logic. Not even experimental physics: after all, experimental protocols seem to be based in a procedure that follows logical laws.

On the other hand, I can study/do/discuss logic without any reference to physics. Same goes for mathematics, actually.

Yes, well may I ask whether there are things that cannot be modeled in a computer?

I'm also trying to understand your argument about logic being transcendental. Do you mean to say logic is foundational to every state of change within a system, as logic seems necessary to produce change or "cause and effect" between objects that may have a relation as defined by physical laws through logic or the transcendental logic you mention.

Yes, well may I ask whether there are things that cannot be modeled in a computer? — Shawn

Well, I don't know. I think that, say, some discoveries in physics could not be made by a computer (say e.g. Newton's discovery of gravitation)
But I am not sure why you think that it would show that if that is the case then physics would have a precedence over logic. After all, computer operations too follow logical principles.

I'm also trying to understand your argument about logic being transcendental. Do you mean to say logic is foundational to every state of change within a system, as logic seems necessary to produce change or "cause and effect" between objects that may have a relation as defined by physical laws through logic or the transcendental logic you mention. — Shawn

By saying 'x is transcendental for y' I mean that 'x' is a necessary prerequiste for 'y'. It's roughly like saying that a 'functioning visual system' (x) is 'transcendental' to 'seeing colors' ( y).

Anyway, what I meant is that logic is employed in any activity in physics, both theoretical and experimental.
Using your example, any causal explanation of physical phenomena must be formulated in a way that employs logical principles (this seems true even if Hume was actually right in his skepticism about causation. Causal explanation relie on logic, even those that are not valid).

But I am not sure why you think that it would show that if that is the case then physics would have a precedence over logic. After all, computer operations too follow logical principles. — boundless

Sure, I would like to highlight your uncertainty as stemming from not knowing how logical space can exist. Is it true in how I'm framing the ambiguity?

Additionally, as @apokrisis main question, is there anything standing in the way of a direct relationship between logic and physics? I'm only saying this as it might seem interesting given logical positivists believed in a correspondence theory of language and truth through logic...

Sure, I would like to highlight your uncertainty as stemming from not knowing how logical space can exist. Is it true in how I'm framing the ambiguity? — Shawn

No, as I said I don't understand why it is relevant to the debate about physics and logic, i.e. I see the two issues as separate, but I might be wrong.

there anything standing in the way of a direct relationship between logic and physics? — Shawn

IMO, all explanations relie on logical principles. But even, say, the basic concept of 'prediction' is based on logical reasoning:

"If [some kind of theoretical statements are valid] then [ I should observe such and such in a lab]"

So, I cannot see how physics can be considered as foundational to logic (or math) when the former cannot exist, in my opinion, without the latter. Note that even if all our physical theories, explanations etc were wrong their structure has logic as a prerequisite. Explanations and predictions are based on logic.

Also, logical argumentation cannot be based on physical phenomena and their regularities. Why? Because, there is no guarantee that physical phenomena and their regularities are not contingent and if they were contingent, then logical argumentation would not be compelling.

Unless one shows that regularities in phenomena are not contingent physics cannot be foundational for logic and mathematics IMO.

Unless one shows that regularities in phenomena are not contingent physics cannot be foundational for logic and mathematics IMO. — boundless

Logic doesn't have that kind of dimensionality, but physics does. Are there any further conclusions based on this that can be said?

I am sorry but I really don't understand what are you getting at.

To me logic is a discipline that aims at understanding the criteria according to which an explanation, argumentation, theory etc is coherent.
Physical theories, conjectures, protocols, predictions, explanations etc should be coherent.
Even, say, a false explanation must be coherent in order to be considered 'false'. In fact, in order to be a true 'explanation' must be coherent.
And I believe that the criteria according to which an explanation is deemed 'coherent' cannot be based on something that is or might be contingent.

To another poster you said earlier:

If physics is to be descriptive of logic, then, a "cause" would be defined by how the system of laws governing physics works, and from there to deduce what logic would be required to explain those laws in terms of decidability in logical space. — Shawn

This might be a starting point, I think, on which we can work.

IMO, the problem I see here is that when you try to describe the laws you might infer from your observations, you already use logic and mathematics (to make them coherent and give quantitative predictions). So, I guess I can say that in order to 'ground' logic in physics, you are already assuming that logic is fundamental.

What do you think about this last paragraph? Do you think I am wrong in detecting a circuarity here? If so, why?

And I believe that the criteria according to which an explanation is deemed 'coherent' cannot be based on something that is or might be contingent. — boundless

I don't think we can have the cake and eat it too here. The way things seem is that the very notion of possibility within a system of physical laws gives rise to a logic that is modal. Modality might be a better term than contingent...

IMO, the problem I see here is that when you try to describe the laws you might infer from your observations, you already use logic and mathematics (to make them coherent and give quantitative predictions). So, I guess I can say that in order to 'ground' logic in physics, you are already assuming that logic is fundamental.

What do you think about this last paragraph? Do you think I am wrong in detecting a circuarity here? If so, why? — boundless

It would be interesting to approach your question from the perspective of a counterfactual. What would a physics look like that could not be apprehended by any form of inferential or abductive reasoning? I don't think such questions are coherent, and there seems to be plenty of evidence attesting that everything in physics can be modeled. If it is indeed true that human logic can apprehend physics in a model or what have you (I think the right term, nowadays, is a "simulation"), then the circularity dissipates.

The only question that seemingly would remain as I see it, is whether logic is this medium by which physics and even mathematics subsists on...

By the way, I might add, I believe modal logic is capable of a ad hoc proof of the necessity of formally consistent and hypothetically complete formal systems in logic if physics describes logic. Even at a deeper level, truth itself, seemingly subsists on such an assumption.

Additionally, as apokrisis main question, is there anything standing in the way of a direct relationship between logic and physics? — Shawn

Another line to take on the question is to note how both logical entailment and physical causality share a presumption about global closure. A grounding as in conservation laws or Noether symmetry.

Just one is closed for energy, the other truth.