‘All right Poirot, I admit it’ the reverend snarled, ‘how did you know?’
‘Well monsieur, if you had killed the duchess, then she would be dead oui? And, she is dead, no?’
The reverend’s mouth fell open.
‘Come on father’ chuckled Commissioner Japp, “Too late to take that confession back.”
A reverend, with a green background. I wonder if he did it in the dining room with the candlestick.
Affirming the consequent is a logical fallacy: Basically if you know that if P then Q, and you know that Q you aren’t entitled to deduce that P. We actually employ this fallacy a lot more than we might think. Suppose you want to find out if someone snuck out of their house last night, you might reason that if they snuck out then there would be footprints outside their window; you go look outside their window and lo and behold you find some footprints. You therefore conclude that they did indeed sneak out.
Whilst this looks right, it isn’t actually deductively valid: the conditional ‘if they snuck out then there would be footprints outside of their window’ and the affirmation of the consequent (the ‘then’ bit) doesn’t necessitate the truth of the antecedent (the ‘if’ bit). After all, someone else could have been walking past their window late at night to make the footprints.
Of course, we might be making some kind of inductive inference: we know that ‘if P then Q’, Q is true and other causes of Q are unlikely and so conclude: (probably) P but we still don’t know P is true for sure.
Ok, enough critical thinking ranting. I’ve always thought the people on Poirot are very quick to admit their crimes. Basically all he does is tell them what he thinks and they confess straight away. Why not just deny it, his evidence is usually pretty weak (see Mitchell and Webb on Poirot http://www.youtube.com/watch?v=i9iQ1yU5Ops). Right that’s all for today. Pip pip!