One of the inference methods involves a chain of reasoning which goes like this:
If my calculations are correct, then my bank charges me a mystery fee on top of all the other disclosed fees and charges. If my suspicions are correct, then I bankroll the bank manager's lunches. Either the bank doesn't charge me a mystery fee or the bank manager buys his own lunches. Therefore, either my calculations are incorrect or my suspicions are unfounded.
If my calculations are correct, then my bank charges me a mystery fee on top of all the other disclosed fees and charges. If my suspicions are correct, then I bankroll the bank manager's lunches. Either the bank doesn't charge me a mystery fee or the bank manager buys his own lunches. Therefore, either my calculations are incorrect or my suspicions are unfounded.
I think I like the name of this type of reasoning more than I like the reasoning itself, as it does not present itself readily to the mind when we speak. But it does what it says on the tin: it knocks down the assumptions we have set off with.
The mechanism is quite simple: the disjunctive second premise denies the consequents of the two conditionals. In doing so we are simply using the Modus Tollens argument form twice, the result being that the final conclusion denies the antecedents. The negated antecedents are a disjunction.
We can do without the destructive dilemma in our deduction proofs – it is a derivation of other inference methods: Modus Tollens, Modus Pollens, simplification of conjunctive expressions, and addition by means of disjunction. It is therefore redundant. In fact, the destructive dilemma is like the constructive dilemma in reverse, where we postulate two conditional sentences and a disjunction of their antecedents in order to obtain disjunction of their consequents.
I find the application of the destructive dilemma in teaching counterfactual conditionals to those students who profess to have heard it all before and need to be teased or else put in their place. The first premise, the one containing two conditionals, sketches out a more or less hypothetical situation:
If you hadn’t failed Latin at school, you would be a judge now; and if you had spelt your name correctly on the exam, you wouldn’t be a miner now.
Set the second promise like this:
I am guessing that either you are not a judge or you are a miner.
Set the question like this: what can you infer from this set of sentences? Answer:
Either you had failed Latin at school or you had misspelt your name on the exam paper.
The mechanism is quite simple: the disjunctive second premise denies the consequents of the two conditionals. In doing so we are simply using the Modus Tollens argument form twice, the result being that the final conclusion denies the antecedents. The negated antecedents are a disjunction.
We can do without the destructive dilemma in our deduction proofs – it is a derivation of other inference methods: Modus Tollens, Modus Pollens, simplification of conjunctive expressions, and addition by means of disjunction. It is therefore redundant. In fact, the destructive dilemma is like the constructive dilemma in reverse, where we postulate two conditional sentences and a disjunction of their antecedents in order to obtain disjunction of their consequents.
I find the application of the destructive dilemma in teaching counterfactual conditionals to those students who profess to have heard it all before and need to be teased or else put in their place. The first premise, the one containing two conditionals, sketches out a more or less hypothetical situation:
If you hadn’t failed Latin at school, you would be a judge now; and if you had spelt your name correctly on the exam, you wouldn’t be a miner now.
Set the second promise like this:
I am guessing that either you are not a judge or you are a miner.
Set the question like this: what can you infer from this set of sentences? Answer:
Either you had failed Latin at school or you had misspelt your name on the exam paper.
"I could have been a Judge, but I never had the Latin for the judging. All in all I'd rather have been a judge than a miner. Being a miner, as soon as you are too old and tired and sick and stupid to do the job properly, you have to go. The very opposite applies to judges." - Peter Cook as E. L. Wisty
ReplyDelete