PHIL12A Section answers, 14 February 2011 - Philosophy

language and the way the world is, it is not possible to sort out the contributions of language and world sentenceby sentence.Consider a sentence such as: ‘A square has four equal sides.’ This, you might venture, is not true of TahrirSquare. How can I convince you that I did not mean to include Tahrir Square amongst the things I referred to assquares? Only by saying that what I meant by ‘square’ was ‘’shape with four equal sides’. And that would bebegging the question.There is another problem with logical necessity, separate from the Quine’s doubts that we can get clear on whatit is for a sentence to be true in virtue of its meaning. For one might forego such sentences as logically necessary,and point simply to those sentences that are true in virtue of their logical structure. We know that a ∨ ¬a istautological, and thus the clearest case of a logical necessity. But we can doubt that every sentence that followsthis schema is logically necessary. ‘John has a beard or John does not have a beard’ follows the schema, buthow could we deny that there are interesting intermediate cases in which John neither has a proper beard norlacks one entirely?Or consider the schema ¬(a ∧ ¬a) - again, as clear cut a case of a logical necessity as one could possibly find.But ‘it is not the case that the particle is spin up and the particle is spin down’ is an instantiation of the schema,and quantum physics seems to tell us that such sentences are often false.There are deep problems here about what counts as a possibility, and about what counts as a possible circumstance.Formal languages, such as First Order Logic, help us make these ideas more precise, but they do notnecessarily solve the problems for natural language.7