Maybe no "metaphysical" notion is needed and we just speak in terms of "plausibility" and "usefulness" but these seem to easily become even murkier notions. The two most common versions of pluralism (Beall and Restall and Shapiro) cited have very different notions of which logics should "count" for instance. — Count Timothy von Icarus
And so it is up to monists to show what it is that all logical systems have in common. I don't see that it can be done. — Banno
a stipulated logical monist of a certain sort, that there is only one entailment relation which all of these logics ape. — fdrake
No True Scotsman doesn't admit of an easy formalisation in terms of predicate logic — fdrake
I imagine monists are generally going to just deny this, because monism is about logical consequence relative to some non-arbitrary context — Count Timothy von Icarus
I'd also want to liken the relationship of formalisms to their intended objects, or intended conceptual content — fdrake
My intuition is also that there are other principles that set up relations between the practice of mathematics and logic and how stuff (including mathematics) works, which is where the metaphysics and epistemology comes in. But I would be very suspicious if someone started from a basis of metaphysics in order to inform the conceptual content of their formalisms, and then started deciding which logics are good or bad on that basis. That seems like losing your keys in a dark street and only looking for them under street lamps. — fdrake
My intuition is that the rules which bind coming up with mathematical formalisms are the same as those which govern writing fiction. They're in general loose, murky, descriptive, but you can tell a good description from a bad one.
If I understand correctly, you're using "deflationary" to mean restricting the interpretations of a theory to all and only the ones which are syntactically appropriate and clearly within the logic's intended subject matter. Like propositional logic and non-self referential statements. Effectively removing everything that could be seen as contentious from the "ground" of those systems. Which would then ensure the match of their conceptual content with whatever objects they seek to model, (seemingly/allegedly) regardless of the principles used to form them. Which 'deflates' truth into unanalysable, but jury rigged, coincidence.
The paper gives lots of strategies for coming up with schematic counter examples to many, many things. You can come up with scenarios where even elementary things like "A & B... lets you derive A" don't hold. So much would need to be jettisoned, thus, if The Logic Of All and Only Common Principles was taken exactly at its word, in the sense of intersecting the theorems proved by different logics.
And that's kind of a knock down argument, when you consider X is true in system Y extensionally at any rate (which is AFAIK the standard thing to do)
made me laugh out loud.folks like Banno and probably G. Russell are eternally stuck in a single paradigm, interpreting the other paradigm in their own terms. — Leontiskos
People create knowledge. I'm not following what his claims are here. Is he suggesting that we remember logic from our previous lives?My definition of logic via the Meno is something like, "That which creates discursive knowledge" — Leontiskos
If I know that Monism is true, I know that any evidence against Monism is evidence against something that is true; I know that such evidence is misleading. But I should disregard evidence that I know is misleading. So, once I know that Monism is true, I am in a position to disregard any future evidence that seems to tell against Monism.
If I know that Euclidean space is true, I know that any evidence against Euclidean space is evidence against something that is true; I know that such evidence is misleading. But I should disregard evidence that I know is misleading. So, once I know that Euclidean space is true, I am in a position to disregard any future evidence that seems to tell against Euclidean space.
If I know that LNC is true, I know that any evidence against LNC is evidence against something that is true; I know that such evidence is misleading. But I should disregard evidence that I know is misleading. So, once I know that LNC is true, I am in a position to disregard any future evidence that seems to tell against LNC .
Yep.But I would be very suspicious if someone started from a basis of metaphysics in order to inform the conceptual content of their formalisms, and then started deciding which logics are good or bad on that basis. That seems like losing your keys in a dark street and only looking for them under street lamps. — fdrake
For instance, G&P frame the position they want to argue against as: "we define logical pluralism more precisely as the claim that at least two logics provide extensionally different but equally acceptable accounts of consequence between meaningful statements." — Count Timothy von Icarus
My definition of logic via the Meno is something like, "That which creates discursive knowledge"
— Leontiskos
People create knowledge. I'm not following what his claims are here. Is he suggesting that we remember logic from our previous lives? — Banno
And how will you enquire, Socrates, into that which you do not know? What will you put forth as the subject of enquiry? And if you find what you want, how will you ever know that this is the thing which you did not know? (Plato, Meno, 80d1-4)
I have to say, I love the cheekiness of the cover. — Count Timothy von Icarus
I have to say, I love the cheekiness of the cover. — Count Timothy von Icarus
Like probably everyone on TPF, I have read about paraconsistent logic as I read about animals in a far off land, but I have never worked with it or made use of it. — Leontiskos
Are you asking me whether I think that accepting both paraconsistent and explosive logic results in the robust kind of logical pluralism? My guess is that I would answer 'no.' Paraconsistency does not entail Dialetheism. And paraconsistent logic is often used informally in everyday life (if that counts). — Leontiskos
I also haven't seen anyone in this thread who favors logical pluralism embrace Dialetheism - other than yourself, of course. They seem to be mostly Augustinians, "Lord, give me logical pluralism, but not yet!"
I also have ulterior reasons for taking dialetheism seriously, namely Marx and Hegel. Marx's notion of contradiction I have a good feel for (but because it's more extensional it's easier to untangle Marx's notion of contradiction from the logical one by dividing wholes into parts that differ), but Hegel's continues to mystify me.
Hegel's contradiction is pretty far from most paraconsistent logics, given the unity and "development" of opposites. — Count Timothy von Icarus
If you're interested though, formalization attempts have run through category theory and Lawvere is the big name here.
https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://philarchive.org/archive/CORMAA-3v1&ved=2ahUKEwjrxdPIz6CJAxURlIkEHUmyEkcQFnoECCEQAQ&usg=AOvVaw3XxnDtBEih45jE5c2zfW2d
Nlab has some stuff on this too.
I have read many commentaries on the Logic at the point. Houlgate and Wallace are my favorites (Wallace isn't quite a commentary, but he does focus on the Logic), but Taylor was useful too. Despite this and now years of effort, I find the essence chapter largely impenetrable lol. — Count Timothy von Icarus
What if in place of Kant’s Transcendental categories we substituted normative social practices? Doesn’t that stay true to Kant’s insight concerning the inseparable role of subjectivity in the construction of meaning while avoiding a solipsistic idealism? Don’t we need to think in terms of normative social practices in order to make sense of science? — Joshs
That’s what pragmatist-hermeneutical and poststructural models of practice are for. For Hegel and Marx the dialectic totalizes historical becoming. In these latter models cultural becoming is contextually situated and non-totalizable. — Joshs
It is normativity all the way down.
But I am not sure it is a useful standard in this context since it seems to allow for refuting the dominant position(s) in terms in which its advocates wouldn't recognize it. — Count Timothy von Icarus
This is what Sider refers to as a "hostile translation" on page 14. It is interpreting or translating someone's utterance in a way that they themselves reject. — Leontiskos
It is interpreting or translating someone's utterance in a way that they themselves reject. — Leontiskos
"That which creates discursive knowledge" (or perhaps just knowledge) — Leontiskos
Is there better and worse metaphysical fan fiction? That's the nub. — Leontiskos
I'd thought of Meno's "paradox" as a precursor to bits of Wittgenstein- that there are ways of understanding (knowing) that are not the result of ratiocination. These include such things as "seeing as" instead of "seeing that", "knowing how..." instead of "knowing that..." and my favourite, PI §201, that there must be a way of understanding a rule that is shown in implementing it rather than in stating it. — Banno
So the sense of "complete generality" also allows Russell to consider variations over interpretations and the relationship of interpretations with syntactical elements of languages - it's thus a highly metalinguistic notion. Which is not surprising, as the Logic Of All And Only Universal Principles would need to have its laws apply in complete generality, and thus talk about every other logical apparatus in existence. — fdrake
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