# Suppose P is true and Q is true, then it follows logically that P --> Q, that Q --> P and therefore that P <--> Q. Now, suppose that P is 'George W. Bush is the 43rd President of the US' and Q is 'Bertrand Russell invented the ramified theory of types', both propositions are true, and therefore the truth of both guarantees the truth the aforementioned propositions. But it seems bizarre to say that Russell's invention of the theory of types entails that Bush is the 43rd president, as well as the other logical consequences. After all we can conceive of a scenario where Russell invents the ramified theory of types, but Bush becomes a plumber (say), if that is a possible scenario, it would seem that the proposition "If Russell invents the ramified theory of types then Bush is the 43rd President of the US" is false given the definition of 'if then'. But after all, does it make sense to say that a proposition entails another only in the actual world? (That doesn't seem to have as much generality as we intutively ascribe to logic). Maybe a possible solution might be to say that the propositions that are at stake are not what they appear. So, what I am in fact saying is that: If P & Q, then P <--> Q and Q --> P and P --> Q. So, saying that "If Russell invents the ramified theory of types then Bush is the 43rd President of the US" is in fact a false conditional, but not so for the proposition "If Russell invents the ramified theory of types and Bush is the 43rd President of the US then If Russell invents the ramified theory of types then Bush is the 4rd President of the US" which is not only true, but the triuth of the antecedent guarantees the truth of the consequent, as it should, given that the conditional is presumed true. Does this work? What can be said about this? Thanks a lot.

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