Jul 4, 2019 06:54 PM
https://onlinelibrary.wiley.com/doi/full...phis.12127
INTRO: Logical monists and pluralists disagree about how many correct logics there are; the monists say there is just one, the pluralists that there are more. Could it turn out that both are wrong, and that there is no logic at all? Such a view might with justice be called logical nihilism and here I'll assume a particular gloss on what that means: nihilism is the view that there are no laws of logic, so that all candidates—e.g. the law of excluded middle, modus ponens, disjunctive syllogism et. al.—fail.
Nihilism might sound absurd, but the view has come up in recent discussions of logical pluralism. Some pluralists have claimed that different logics are correct for different kinds of case, e.g. classical logic for consistent cases and paraconsistent logics for dialethic ones. Monists have responded by appealing to a principle of generality for logic: a law of logic must hold for absolutely all cases, so that it is only those principles that feature in all of the pluralist's systems that count as genuine laws of logic. The pluralist replies that the monist's insistence on generality collapses monism into nihilism, because, they maintain, every logical law fails in some cases.
From this interchange we can extract a sketch of an argument:
To be a law of logic, a principle must hold in complete generality.
No principles hold in complete generality.
There are no laws of logic.
Pluralists do not intend this as an argument for logical nihilism, of course. They think that nihilism is absurd, and since many who work on non‐classical logics find the second premise plausible, they intend the argument above as a reductio on the first premise: the monist's assumption that logic must be completely general. Still, that premise has both intuitive appeal and support from historical writers on logic, and—as I will explain in the first section of this paper—nihilism is not, in the end, absurd. These two things—the plausibility of premise 1 and the non‐absurdity of the conclusion—turn this sketch of a reductio on premise 1 into a sketch of a direct argument for nihilism.
In the first part of this paper I clarify what logical nihilism amounts to. In the second, I look at the above argument for logical nihilism in more detail. Then in the third and final section, I suggest a sensible response, inspired by Lakatos' influential Proofs and Refutations. I argue that the method of lemma incorporation outlined in that book can be applied—with beneficial results—in logic, and in particular, that it is appropriate in response to the nihilist. (MORE)
INTRO: Logical monists and pluralists disagree about how many correct logics there are; the monists say there is just one, the pluralists that there are more. Could it turn out that both are wrong, and that there is no logic at all? Such a view might with justice be called logical nihilism and here I'll assume a particular gloss on what that means: nihilism is the view that there are no laws of logic, so that all candidates—e.g. the law of excluded middle, modus ponens, disjunctive syllogism et. al.—fail.
Nihilism might sound absurd, but the view has come up in recent discussions of logical pluralism. Some pluralists have claimed that different logics are correct for different kinds of case, e.g. classical logic for consistent cases and paraconsistent logics for dialethic ones. Monists have responded by appealing to a principle of generality for logic: a law of logic must hold for absolutely all cases, so that it is only those principles that feature in all of the pluralist's systems that count as genuine laws of logic. The pluralist replies that the monist's insistence on generality collapses monism into nihilism, because, they maintain, every logical law fails in some cases.
From this interchange we can extract a sketch of an argument:
To be a law of logic, a principle must hold in complete generality.
No principles hold in complete generality.
There are no laws of logic.
Pluralists do not intend this as an argument for logical nihilism, of course. They think that nihilism is absurd, and since many who work on non‐classical logics find the second premise plausible, they intend the argument above as a reductio on the first premise: the monist's assumption that logic must be completely general. Still, that premise has both intuitive appeal and support from historical writers on logic, and—as I will explain in the first section of this paper—nihilism is not, in the end, absurd. These two things—the plausibility of premise 1 and the non‐absurdity of the conclusion—turn this sketch of a reductio on premise 1 into a sketch of a direct argument for nihilism.
In the first part of this paper I clarify what logical nihilism amounts to. In the second, I look at the above argument for logical nihilism in more detail. Then in the third and final section, I suggest a sensible response, inspired by Lakatos' influential Proofs and Refutations. I argue that the method of lemma incorporation outlined in that book can be applied—with beneficial results—in logic, and in particular, that it is appropriate in response to the nihilist. (MORE)