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?

Is it perhaps like the difference (and connection) between the truths of algebra and geometry? We inquire after entailment as a formal relation. And there is the physical view that is essentially geometric – as spacetime rather matters – or the algebraic view where even geometry can apparently be reduced beyond spacetime ... but then that little tussle re-emerges again when we move up the next level of abstraction, as in topological order?

So when it comes to this tricky relation between physics and logic, I am arguing that a model of causality is the ultimate target. And in reducing reality to causality, one could go "too far" in the reductionism. Spacetime and its material content as a geometry of relations become too much to sacrifice in the attempt to continue on towards the atomistic abstractions of Boolean logic.

Mechanics can only be taken so far before it becomes an unphysical nonsense?

Maybe logic describes physics in some ways, but I don't know if physics "describes" logic. Probably only as an application/example of it?

I don't know but can physics be undertaken without the logical axioms - identity, non-contradiction and excluded middle?

Logic is just how to talk with some sort of consistency.

I don't know but can physics be undertaken without the logical axioms — Tom Storm

Well, without some presumption of coherence, at least. If the aim of physics is to produce a coherent account of how physical things are, then it presupposes coherence, and hence logic.

If physics could describe logic, then could an alternate universe with different physics describe a different logical order? It would seem that logic would be the same, no matter what kinds of physics are in play.

If the aim of physics is to produce a coherent account of how physical things are, then it presupposes coherence, and hence logic. — Banno

:up: Sounds appropriate.

That's a pretty broad question. There is a fairly popular related view in physics today called "pancomputationalism." Per this view, the universe might be profitably seen as a "quantum computer that computes itself" (as a cellular automata lattice).

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."

However, it's worthwhile to recall that when steam engines were the new hot technology physicists also wanted to think of the universe as "one giant engine/machine." Now, this conception actually did tell us a lot, but it wasn't perfect. The same is probably true here. For one, if the universe is a "computer" in this way it cannot have true continua, and yet empirical evidence is inconclusive on the question of if the universe is ultimately discrete/finitist. If it wasn't discrete, it might still be "computation-like," but it wouldn't be computation because it would involve infinite decimal values.


The ability of ZX Calculus to construct QM is interesting here but I haven't really looked into it.

in your opinion do you think physics describes logic? — Shawn

No.

And we may want to work towards OPs that are more than a single sentence long.

Logic is just how to talk with some sort of consistency. — Banno

And thus with some sort of differentiation.

So that is indeed the kind of holism that both physics and logic represent. The dialectic of global integration and local differentiation. The universals and their particulars. The laws and their initial conditions. :up:

I suppose that, per most forms of physicalism, physics does have to describe human logic in a certain sense. Can it do it? That's an interesting question.

Logic is just how to talk with some sort of consistency. — Banno

Or is it how to draw new conclusions from what is currently known?

Deductive logic does not produce anything not in the assumptions.

Inductive, abductive, and dialectic "logics" are quite different, and quite contentious.

Inductive, abductive, and dialectic "logics" are quite different, and quite contentious. — Banno

Yep. So not at all a dogmatic slumber then. :up:

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

Yes, you nailed it. I think this is the fundamental thesis upon which this thread is about.

I don't really have much to say myself at the moment. Just one question, regarding which, where do you think mathematics stands in relation to what you said?

Deductive logic does not produce anything not in the assumptions. — Banno

Except that without such logic one will not be able to draw inferences, and this will limit their knowledge. The question of how the conclusion relates to the premises is age-old, but the fact remains that one person can draw valid inferences and another cannot, even when they have access to the same set of evidence. The difference between the two is that one possesses the art of logic and the other does not. To understand why logic was invented in the first place is to understand this.

Today logic has been reduced by some to pure formalisms, divorced from the art of reasoning well, but historically speaking this is a very recent phenomenon.

...It is also worth noting that the study of the logic of logic is still logic. Godel's proofs provide us with conclusions and theorems that we were previously ignorant of. We can say that his theorems were already present before he proved them, but they simply would not have been known without Godel's proficiency in logic. It would be odd to claim that there is no significant difference between an entailment that is known and an entailment that is unknown.

If you look at model theory, you can see on the one side a collection of rules, i.e. the axioms of a theory, and on the other side, a possibly even chaotic collection of facts (or "truths"), i.e. a model.

On the one hand, a model interprets the theory if none of its facts, no matter how chaotic, violates the theory's rules. On the other hand, a theory has a particular model if every statement provable from that theory is true in that model. Not all facts need to be provable from the theory.

Logic operates on the side of the theory. Physics operates on the side of the model.

Physics is a collection of facts in which science has observed stubborn patterns. These physical patterns are often confused for a theory, but they are not.

Physics as a model, i.e. a collection of facts, may very well interpret an otherwise unknown theory, i.e. some collection of rules (and not just stubborn patterns).

If this unknown theory of physics can be expressed in the language of first-order logic, then that would be the link between physics and logic.

We suspect that this link between physics and logic must somehow exists.

However, without actually formulating a legitimate theory for physics, we can never be sure.

I don't really have much to say myself at the moment. Just one question, regarding which, where do you think mathematics stands in relation to what you said? — Shawn

Well I sort of said that geometry/topology is where they look to come the closest. Hence why Peirce’s existential graphs and Spencer-Brown’s laws of form are so appealing to some of us. Much less so category theory even it it does actively strive to lay claim to physics.

And there is the physical view that is essentially geometric – as spacetime rather matters – or the algebraic view where even geometry can apparently be reduced beyond spacetime ... but then that little tussle re-emerges again when we move up the next level of abstraction, as in topological order? — apokrisis

Classically after studying the Trivium (of grammar, logic, and rhetoric), one would study the Quadrivium:

The quadrivium was the upper division of medieval educational provision in the liberal arts, which comprised arithmetic (number in the abstract), geometry (number in space), music (number in time), and astronomy (number in space and time). — Quadrivium | Wikipedia

Astronomy, the study of number in space and time, is more or less what we now think of as physics.

"causality as imagined by logic"?

What could that possibly be?

one would study the Quadrivium: — Leontiskos

So that suggests it all comes back to "number", even for what where then the liberal arts (a way to squeeze things past the eagle eye of the Church?).

Then grammar, logic and rhetoric concern themselves with the syntax of number rather than the semantics.

So numbers carry sense both as general variables and as particular facts. Or better yet, measurements.

I would agree with all this. The point of an education is to lift us above the socio-cultural constraints of an oral world order – socially constructed in words – to a technocratic or rational world order. And that is socially constructed in numbers as signs that connect semantics and syntax into some pragmatic business of utterances and locutions.

So that would make the maths more clearly the handmaiden to the physics? Physics employs numbers in both the syntactic and semantic sense – as the scientific generality of a variable, as the particularity of a measurement.

That could be too harsh if it is recognised that logic is larger than just propositional calculus. Logic as a triadic system of inference becomes the common root of thought under Peirce. It injects the same pragmatism into the practice of philosophy too.

As in....

Many 19th-century logicians (for example, John S. Mill, George Boole, John Venn and William Stanley Jevons) took the range of logic to include deductive as well as inductive logic.

As appears from the classification, the remarkable novelty of Peirce’s logical critics is that it embraces three essentially distinct though not entirely unrelated types of inferences: deduction, induction, and abduction.

Initially, Peirce had conceived deductive logic as the logic of mathematics, and inductive and abductive logic as the logic of science. Later in his life, however, he saw these as three different stages of inquiry rather than different kinds of inference employed in different areas of scientific inquiry.

https://iep.utm.edu/peir-log/

[D]o you think physics describes logic? — Shawn

No. Physics (provisionally) explains 'the regularities of nature' and logic (exactly) describes 'the entailments of regularities as such'. The latter is, imo so to speak, the syntax of the former (i.e. physics discursively presupposes logic). Why? Perhaps because ... nature, which includes – constitutes – h. sapiens' intelligence, is a dynamic process evolving within (thermal?) constraints from initial conditions – ur-regularities.

:up:

The point of an education is to lift us above the socio-cultural constraints of an oral world order – socially constructed in words – to a technocratic or rational world order. — apokrisis

An academic education rather teaches the fine points of sophistry, suitable for bamboozling the masses.

Since employers like CNN and Harvard can only employ that many mouthpieces, a training in sophistry increasingly leads to unemployment. Even the Chinese Communist Party says that it is fully staffed now, leaving every year millions of new graduates without a suitable job.

So that suggests it all comes back to "number" — apokrisis

For the Quadrivium, but not for the Trivium. The Trivium pertains to communication, generally speaking.

I would agree with all this. The point of an education is to lift us above the socio-cultural constraints of an oral world order – socially constructed in words – to a technocratic or rational world order. And that is socially constructed in numbers as signs that connect semantics and syntax into some pragmatic business of utterances and locutions. — apokrisis

Yes, but one must begin with communication in the Trivium: Grammar (understanding language), Logic (the ability to analyze thought, and to progress in thinking), and Rhetoric (the ability to use grammar and logic in the service of persuasion). One must understand "social constructions" before moving beyond them.

So that would make the maths more clearly the handmaiden to the physics? — apokrisis

That seems like a good way of putting it.

An academic education rather teaches the fine points of sophistry, suitable for bamboozling the masses. — Tarskian

That is only half the deal though. These days you must have also fudged some data. :razz:

The Trivium pertains to communication, generally speaking. — Leontiskos

But that is the syntax, or the rules of argument construction and transmission. The geometry of relations to complement the algebra of the relatables.

I don't really know. I'm just as confused as you are.

Hegel may have made some sense with dialectical materialism as you alluded to.

But that is the syntax, or the rules of argument construction and transmission. The geometry of relations to complement the algebra of the relatables. — apokrisis

It is that, but I think the philologists would object if we were to reduce language to a social construction, or if we were to reduce it to the matter for argument or science. Language is all these things, but it is other things, too.

As appears from the classification, the remarkable novelty of Peirce’s logical critics is that it embraces three essentially distinct though not entirely unrelated types of inferences: deduction, induction, and abduction.

This is interesting. So too for Aristotle and many Aristotelians, the division between deductive and inductive logic is not so clear-cut.

I don't really know. I'm just as confused as you are.

Hegel may have made some sense with dialectical materialism as you alluded to. — Shawn

Ooh, burn! :fire:

Ooh, burn! :fire: — apokrisis

I hope not literally. :fear:

The complexity of the world is actually quite scary.

I think the philologists would object if we were to reduce language to a social construction, — Leontiskos

But I am doing the opposite. Social construction is what language allowed. (The paleoanthropology of language evolution is one of my special areas.)

So too for Aristotle and many Aristotelians, the division between deductive and inductive logic is not so clear-cut. — Leontiskos

Two sides of the same coin. Deduce the particulars. Induce the generalities.