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It has been said that if there is human freedom, then we are responsible for our actions. By this, it seems natural to suppose that "given that there is no human freedom (let's just suppose for the sake of argument) then it would follow that we are not responsible for our actions." But this seems an instance of what is called the "fallacy of denying the antecedent". Is this really an instance of the fallacy or is it an exemption to the case because personally I don't see any error in the form of the argument.

Translating the argument into symbolic terms quite literally, we get this: 'If F, then R. Not F. Therefore, not R.' That form of argument does indeed commit the fallacy of denying the antecedent: the premises don't logically imply the conclusion; the truth of the premises doesn't logically ensure the truth of the conclusion. The first premise says that F is sufficient for R; it doesn't say that F is necessary for R. In that case, R can obtain even if F fails to obtain. My hunch is that you're interpreting 'If F, then R' as 'R if and only if F': you're interpreting the conditional as a biconditional , i.e., as the claim that F is both necessary and sufficient for R. 'R if and only if F' and 'Not F' together imply 'Not R'. Your interpretation is understandable, because conversationally we often do intend to assert a biconditional when we use conditional language. A parent's 'If you clean your room, you can watch TV' usually means 'You can watch TV if and only if you clean your room...

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