Come on. When it has a use.In virtue of what is a logic "applicable"? — Count Timothy von Icarus
why don't you explain to me why you think pluralism and nihilism are even different positions? — Count Timothy von Icarus
So we are back to puzzling over whether there are principles that hold in complete generality.If the question is "have people created systems with different logical consequence relationships?" the answer is obviously yes. — Count Timothy von Icarus
Come on. When it has a use.
Because what it means to be "truth-preserving" and thus a "correct logic" will depend on what is being preserved. — Count Timothy von Icarus
Perhaps. Although a logician's presenting a logic would be their making use of it.Do some logics lack "a use?" — Count Timothy von Icarus
In all logical systems, presumably. But I would be happy to consider any other options you might offer.What does it mean to hold in generality? — Count Timothy von Icarus
Appeal to popularity? So you are seeing the traction in the arguments here.why would monism remain the dominant position? — Count Timothy von Icarus
Appeal to popularity? So you are seeing the traction in the arguments here
Well, I've been trying to work out what you are claiming, on the presumption that you are advocating monism.Which is why I ask, what exactly do you think the monist is claiming? — Count Timothy von Icarus
This isn't an answer to the question though. What do you think is being meant by "correct logic" in these articles? — Count Timothy von Icarus
Well, even "necessary" has differing interpretations depending on which logical system one chooses - S1 through S5 for a start. And we have logical systems that are incomplete. I'm not sure what to say. — Banno
But presumably correct logic for a monist would be only those logic s that make use of the general laws of logic, whatever they might be.
If there are general laws...If correct logics are just those logics that utilize the general laws then monism is true by definition. — Count Timothy von Icarus
How so?Your understanding of each of the positions seems to make them trivial rather than controversial. — Count Timothy von Icarus
Your understanding of each of the positions seems to make them trivial rather than controversial. — Count Timothy von Icarus
There are two questions with this pluralism/monism debate: What the heck is the thesis supposed to be, and Who has the burden of proof in addressing it? The answers seem to be, respectively, "Who knows?" and "The other guy!" :lol: — Leontiskos
There are two questions with this pluralism/monism debate: What the heck is the thesis supposed to be, and Who has the burden of proof in addressing it? The answers seem to be, respectively, "Who knows?" and "The other guy!" :lol: — Leontiskos
I think it's ok for people to add on whatever significance they like to the word truth in truth-preserving. In the same way, if you lean toward ontological realism or anti-realism, you can add that onto whatever shenanigans you're doing. It doesn't change the shenanigans either way.
So you call a logic "correct" when I might call it "applicable". And Paraconsistent logic is for you "correct" when used for processing images and signals, while Lambda Calculus is "correct" when used for cryptography or AI....which is why their position is generally something like G&P's, which is that correct logics are those which capture the logical consequence relationship at work in natural language and scientific discourse, — Count Timothy von Icarus
What one? Set it out.A monist will claim there is only one logical consequence relationship — Count Timothy von Icarus
Right, so what's with complete generality? Why not say all logics. — Cheshire
So you can come up with a logic where modus ponens holds, and come up with a logic where modus ponens does not hold. Which would mean that if you wanted to find The Logic Of All and Only Common Principles (tm), you'd need to jettison modus ponens. Since it is not a common principle, since two logics disagree on whether it is a theorem. — fdrake
The cases approach allows us to say more about what logical nihilism amounts to: it is the view that for any set of premises Γ and conclusion φ whatsoever, there is a case in which every member of Γ is true, but φ is not. — Russell
Henceforth I’ll assume the interpretations approach to logical consequence, on
which logical nihilism is the view that for every principle of the form Γ |= φ there is an interpretation of the non-logical expressions in Γ and φ such that every member of Γ comes out true but φ does not. Such an interpretation would be a counterexample to the principle. If it turns out that there are no such counterexamples, and that on every interpretation of those non-logical expressions on which each member of Γ is true, φ is also true, then the principle will be a logical law, and nihilism will be false.
On the interpretations view Γ|=φ is true iff whatever (syntactically appropriate) interpretation is given to the non-logical expressions in Γ and φ, if every member of Γ is true, then so is φ. For example, if our argument is P a, a = b P b, then the interpretations approach says that the argument is valid iff there is no interpretation of P, a and b (assuming we are treating = as logical) such that P a and a = b are true, but P b is not. Models are understood as offering us different interpretations of the non-logical expressions, and hence if we find a model in which P a and a = b is true but P b is not, the principle is not true. On the interpretations conception then, logical nihilism is the view that for every argument, Γ φ, there are interpretations of the non-logical expressions in Γ and φ which would make every member of Γ true, but φ not true
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