LOGICAL NIHILISM: COULD THERE BE NO LOGIC?*

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. 1(Cotnoir, forthcoming) distinguishes two kinds of logical nihilism, the first of which is the view that natural languages have no correct logic, and the second of which is that the consequence relation is empty. The view I have in mind here is the second. 2Monism has been the default view for many centuries, but it has recently been explicitly defended by Priest (2006). Pluralists include Carnap (1937), Varzi (2002), Beall and Restall (2006), Russell (2008) and Field (2009). There is not much recent mainstream literature on this kind of logical nihilism. Cotnoir (forthcoming) discusses a related view by the same name. Two close relatives of my version of nihilism are defended by Mortensen (1989), one based on the idea that nothing is necessary, the other on the idea that nothing is true in all mathematical models. Mortensen, on my reading, is a nihilist about logical truth, though I am unsure whether he would want to generalise this to logical consequence. Nihilism is also discussed in terms of models in Estrada-González (2015). 3Beall and Restall (2006); Priest (2006); Bueno and Shalkowski (2009); Russell (2013); Cotnoir (forthcoming) 4For example “The obvious reply to this argument is that it is only truth-preservation over all situations that is, strictly speaking, validity. One of the points about deductive logic is that it will work come what may: we do not have to worry about anything except the premises.” (Priest, 2006:202) 5“...we see no place to stop the process of generalisation and broadening of accounts of