Week 3

This week we learned about conjunction, disjunction, negation, and implication.

I found vacuous truth to be the most interesting concept of this week. At first it seemed somewhat odd to conclude that if the antecedent of a statement was false, the statement would always be true. An example of such vacuous truth could be the following: If all mice are the size of an elephant, then every person on Earth is bankrupt. To a person untrained in the laws and conventions of logic, a statement such as this would seem preposterous. How can you conclude that mice being the size of elephants implies that everyone is bankrupt when it is clearly not the case that everyone is bankrupt or that all mice are the size of elephants, and that a scenario such as that would most likely never be true? It is easy to get caught up in the absurdity of the consequent/antecedent and to simply dismiss the statement as a whole based on their improbability.

The easiest way to resolve this confusion is as follows: consider implication statements to be contracts. Whenever the antecedent is true (or occurs), and only in that case, should we expect for the consequent to occur. In our case, only if all mice were the size of elephants, and everyone turned out not to be bankrupt, then and only then could we argue that the contract has been breached, and that the statement as a whole is false. Any other combination of truths of the consequent and antecedent do not need to be considered, as we've established the only possible way for the contract to be breached. By compliment, every other scenario yields a true statement.

Ultimately I think that the evaluation of an implication being true when the antecedent is false is simply a logical convention that was adopted in order for the evaluation of larger, more complex logical statements (which contain implications) to produce more intuitive and meaningful truth results.