[omon]

Wholly irrelevant, the paper is specifically concerned with recovering a dialectic between W. O. Quine and M. Dummett. Even if the question was the more general, "Is Logic Metaphysics?", knowledge of formal logics isn't even of concern. It's trivial that we can construct a plethora of axioms with their own definitions, the problem remains: to even adhere to those definitions one is exercising another intuitive logic—even in the case of computation which is an engineered construction to proxy this very intuition, otherwise we would have never been concerned with the linear properties necessary for computation to begin with.

[TheOtherHobbes]

"Intuitive" being another word for "subjective."

The experience of truth and logical consistency is entirely subjective. We can build networks of concepts that trigger the experience in ourselves and in others, but that doesn't make them objectively true - it makes them subjectively persistent and shared.

We acquired a cat recently, and it's interesting that her experience of basic spatial relationships is very different to ours.

She doesn't have the same experience of physics that we do. She sometimes gets confused by inside vs outside, and her experience of moving objects seems to be different to ours. She also gives the impression of experiencing hands and feet as disconnected objects, and not part of a gestalt "human".

We have no guarantees that from an alien point of view, our own experience of physics and of relationships doesn't have equivalent limitations. If the limitations exist, we're not aware of them. But to the extent that our cat's view of the world is probably recognisable by other cats, she's not aware of her limitations either.

It's more of a stretch, but not impossible, that our experience of logical abstraction and consistency may also have limitations. There may be non-human viewpoints where the basic subjective qualia of truth and consistency are more coherent, reliable, and inclusive than our own.

None of this can be proved, but it seems optimistic to me to believe that our version of logic is as good as logic can possibly be.

[omon]

Yet we're able to discuss topics with each other, this is the basis of Poincare's Inter-subjective reality. There must be some commonalities of experience which allows us to map our whole experiences between each other. We are definitively limited to our experience, it is impossible to discuss or probe anything outside of it when the entire world and its phenomena is only dictated through experience to us.

Experience is a language which makes meaning from the not-experience.

As Bohr put it, "We're all suspended in language."

[danharaj]

What I'm saying is that linear logic is exactly a technical exploration directly pertinent to the questions Quine and Dummett considered. And who cares if the paper is specifically about Quine and Dummett? What's the point of resuscitating such a dialogue without informing it of modern developments? To do so seems like frolicking in the graveyard. But much like philosophy of mathematics (with some exceptions like [0]), philosophy of logic to me at least seems like it prefers dusty bones to fresh developments (if 40 years is fresh...). At the very least, modern logic and its myriad connections to other fields could shed light on whether it's even worth bothering to adjudicate the interplay of Quine and Dummet's metaphysical arguments. They might be completely irrelevant at this point in our understanding except as historical footnotes.

Linear logic is in many ways a logic of logic. Both classical and intuitionistic logic can be decomposed into finer components in linear logic, which distills logical ideas into purer components of philosophical interest, like the exponentials. The links between linear logic and processes like computation makes it a much more interesting starting point for a discussion of metaphysics and logic: Its technical results tell us that not every bespoke Broccoli logic makes sense, that one can directly study the conditions of possibility of logic. It even has connections to fundamental physics [1].

> It's trivial that we can construct a plethora of axioms with their own definitions, the problem remains: to even adhere to those definitions one is exercising another intuitive logic—even in the case of computation which is an engineered construction to proxy this very intuition, otherwise we would have never been concerned with the linear properties necessary for computation to begin with.

How are we to investigate this intuitive logic without probing the technical structure of logic and finding out what is really its essence? It's not, emphatically not trivial that one can cook up a bunch of axioms. Logic doesn't come from axioms, I think we agree about that, they are just an exigent way to surface it. There are most definitely inappropriate formulations of logic. For example, S4 is an OK modal logic of necessity and possibility but S5 is hardly a logic at all because it doesn't have cut elimination, the technical correlate of deduction.

I think this attitude just serves to marginalize philosophy of logic. Technique and philosophy must be in dialogue or both will be marginalized.

[0] https://www.urbanomic.com/book/synthetic-philosophy-of-conte...

[1] https://arxiv.org/abs/0903.0340

[omon]

The author cares about that, it's his abstract. In the same way a scientist would care about the precision and conclusions of results obtained from an older study--you are forced to use the original researchers had. Of course you can verify it with new tools, but what's the point if the research is systemically flawed to begin with?

The childhood quote hammered into our ears continues to ring true: "If I have seen further it is by standing on the shoulders of Giants."- Newton

I agree that newer technical formal languages describing our own methods of sound predicate are useful, but that's excessive and even pretentious in this case. Would you use quantum computation to verify the result of addition on a classical computer? It adds nothing, especially when it is quantum computation that is being construed to emulate classical computation!

>How are we to investigate this intuitive logic without probing the technical structure of logic and finding out what is really its essence?

Its essence cannot be discovered, there are "exigent way[s] to surface it", but like experience, it's atomic. In the end the models will just become more comprehensive in terms of formalizing experience. Yet the experience of logic is the essence; how are you able to describe what makes up experience in terms of experience? If this is the purpose of these "tools" (it's not) then they ought not to be limited by objects of human experience, as the noumenon (the negation of experience) is not even guaranteed to be symbolic to objects of perception—by definition they are not.

I would be flummoxed to find fundamental physics constructed, described, and extended from axioms through logic had no connection with logic.

Philosophy of logic continues to discuss other logics, it is only that this particular article that it's of no concern to.