In recent years, philosophers have debated the question of logical pluralism: the view that there is more than one correct logic (see my interview with Greg Restall on this very issue). The idea, roughly, is that which putative logical laws hold depends on what sorts of “cases” we take logic to be about; different kinds of cases yield different (but equally legitimate) logics. A common logical monist objection is to say that a form of argument is only a logical law if it applies in all cases. If this is true, it raises the question: what argument forms do hold in all cases? At this point in the debate, a third position becomes viable, defined by the answer: none.
Gillian Russell, a philosopher of language and logic, argues both that applying in all cases is necessary for qualifying as a logical law; and that no argument form applies in all cases. As such, she believes there are no logical laws. Much of our discussion surrounds her claim that no argument form applies to all cases. Is this really true even of the law of non-contradiction, the “law” that says that ‘A and not-A’ can never be true? Of conjunction elimination (‘A and B’ entails ‘A’)? Of identity (‘A’ entails ‘A’)? Russell runs through purported counterexamples to these laws; what’s more, she illustrates a method for conjuring counterexamples to any proposed “law”.
Consider the sentence C: “If this sentence is true, then David Ripley is a purple giraffe”. Suppose the sentence is true. Then the antecedent of the sentence (“this sentence is true”) is true. According to the inference rule modus ponens, if an if-then sentence (such as C) is true and its antecedent is true, then its consequent (“David Ripley is a purple giraffe”) must be true. It follows that if C is true, then David Ripley is a purple giraffe. But this conclusion is C: in other words, by simply supposing how things might turn out if C were true, we have proved that C, in fact, is true. So C is true, and since C’s antecedent is the claim that C is true, its antecedent is true as well. Now we can use modus ponens again to show that C’s consequent must be true. In other words, David Ripley really is a purple giraffe. QED.
This argument is Curry’s paradox. Obviously, the choice of “David Ripley is a purple giraffe” is arbitrary; a sentence of the form of “If this sentence is true, then X” can be used to prove any claim X. Now, in actual fact, David Ripley is not a purple giraffe, but a philosopher of language and logic. According to Ripley, solutions to paradoxes like Curry’s (as well as the Liar and the Sorites) fall into two broad categories: those that solve the paradoxes by messing with the meanings of important concepts (such as the meaning of “if-then”, truth, “not”, etc.) and those that solve them by changing the structural rules of inference by appeal to substructural logics.…
I have a (true) thought that Sherlock Holmes lives on Baker Street. But what is this thought about? Is it about Sherlock Holmes? If so, is it about something that doesn’t exist? Can we really have thoughts about non-existent objects? What makes those thoughts true or false, if there is no object for the thought’s content to correspond to?
Philosopher Michael Hicks distinguishes fiction-directed thought from world-directed thought. A fiction-directed thought is knowingly about fiction; it is a kind of pretense. It is crucial that thoughts about fictional entities be fiction-directed. If if I think my “thought” about Sherlock Holmes is about a real person – in other words, if it is world-directed – then I don’t have a thought at all, because the ostensive object of my thought does not exist. According to Hicks, world-directed thought is “environment dependent”. It takes the intentional state and the object of the intentional state to make a thought. If the latter is missing, then there is no thought. Thoughts about fictional entities, as well as about hallucinations and other non-existent objects, must be fiction-directed in order to qualify as thoughts. Put another way, thought about fiction only successfully happens when we play a game of pretense set up by the author.
Be sure to listen to part 1 of this interview first.