Abstract
AbstractIn this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic.
Highlights
In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible
Under the supposition that the actual logical laws are obstinate, we will be able to infer from the logical possibility of some proposition, p, from the point of view of the actual world, to the logical possibility of p at all the worlds that do not contain a violation of the actual laws of logic
We have argued that we need to make a distinction between two kinds of logical impossibility: one tied to logical difference and another tied to logical violation
Summary
If Classical Logic were the correct logic, it would be impossible to validly infer every proposition from a contradiction. If LP (Logic of Paradox) were the correct logic, it would be impossible to validly infer every proposition from a contradiction These conditionals are examples of what we call countermetalogicals.. E is false since Trivial Logic validates all inferences and F is true since Nihilist Logic invalidates all inferences.. E is false since Trivial Logic validates all inferences and F is true since Nihilist Logic invalidates all inferences.4 Countermetalogicals of this kind are commonplace in the contemporary study of logic, though they are not known by that name. When we judge that D is true, for instance, we judge that under the supposition that Intuisionist Logic is correct, validly inferring p from ¬¬ p is logically impossible.. We will show that our account of logical possibility/impossibility does help us understand countermetalogicals and logical disputes and has important implications for the relationship between logical possibility and other kinds of possibility such as metaphysical possibility, and for claims about the necessity or contingency of the laws of logic
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