Author: Indigo Curnick
Date: 2025-03-22
These are the solutions to the exercises given in this article, but make sure you try them all yourself first!
Yes. If only one of two people can win, and one can't even make it, then there's only one possible winner
No. There's no reason to believe that John will win the fishing contest again just because he won it before.
Yes. This is a very classic argument form, which can be summarised as
- P1: All \(A\) are \(B\)
- P2: \(C\) is an \(A\)
- C: \(C\) is a \(B\)
Yes. Another classic argument form, which can be summarised as
- P1: All \(A\) are \(B\)
- P2: No \(C\) are \(B\)
- C: No \(A\) is a \(C\)
Yes. This is a very important classic argument form called a modus ponens
- P1: If \(P\) then \(Q\)
- P2: \(P\)
- C: Therefore, \(Q\)
No, this is a logical fallacy which looks very similar to modus ponens but is actually invalid, called affirming the consequent. Premises 1 does not say the only way for the ground to be wet is if it is raining. Someone could have used a hose or a pip could have burst.
The formal form of affirming the consequent is
- P1: If \(P\), then \(Q\)
- P2: \(Q\)
- C: Therefore, \(P\)
If you ever see an argument of this form, it is invalid!
Yes. This is a classical argument form called modus tollens which can be summarised as
- P1: If \(P\), then \(Q\)
- P2: Not \(Q\)
- C: Therefore, not \(P\)
No, this is another logical fallacy similar to the modus tollens called denying the antecedent. Just as in 6) the premise does not say the only way for the ground to be wet is rain.
The formal form of denying the antecedent is
- P1: If \(P\), then \(Q\)
- P2: Not \(P\)
- C: Therefore, not \(Q\)