Monday, April 1, 2019

[Thesis:] April Fool's Philosophy Post Generator

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The thesis that [thesis] has not received much of a defense[literature type]. But here is an argument for it:

  1. This argument is valid.

  2. Therefore, [thesis].

Let's see why this argument is not only valid but sound.

First, let’s see that it’s valid. Suppose for a reductio that it is invalid. But whether an argument is valid or not cannot be a contingent matter. Thus if, the argument is invalid, it is necessarily invalid. But if it is necessarily invalid, then necessarily its first premise is false (since the premise says that the argument is valid). But any argument which has a necessarily false premise is automatically valid. (An argument is valid if and only if it is impossible for the premises to be true and the conclusion false. This is trivially satisfied if it is impossible for a premise to be true.) But that would contradict the assumption that it’s invalid. So, the argument must be valid.

But if the argument (1)–(2) is valid, it’s also automatically sound. For a valid argument is sound provided its premises are true. But the only premise of the argument is (1), the statement that the argument is valid. If the argument is valid, then that premise is true, and so the argument is sound.

But the conclusion of a sound argument is true. Therefore, [thesis].