UC Davis Modal Logic Problems Discussion In this problem we’re going to look at the paradoxes of the strict conditional. The paradoxes of the strict condit

UC Davis Modal Logic Problems Discussion In this problem we’re going to look at the paradoxes of the strict conditional. The paradoxes of the strict conditional concern how the strict conditional interacts with necessity. When we’re using ◻ ( A → B ) to represent “If A then B” we usually have in mind a reading of ◻ Awhere it means that “A is metaphysically necessary”, where a statement is metaphysically necessary if it’s true no matter what. Some classic examples of classes of sentences which philosophers have thought are necessary truths are analytic truths (‘Frozen water is ice’), mathematical truths (‘Two plus two is four’), and truths about natural kind terms (‘Gold has atomic number 79’).

Consider the following paradox of the strict conditional:

◻ ¬ A ⊨ ◻ ( A → B ).

This is valid in S5, but has many English instances which sound invalid. I want you to give an example instance of this argument form which illustrates the claim that this argument is invalid for our intuitive account of the conditional. To do this I want you to do the following:

Task: Give a sentences of English A and B where:

1. “It is necessarily not the case that A” is true.
2. “Necessarily, if A then B” is false.

In each case spending a sentence or two explaining your answer.