Originally posted by AcolyteThose pesky conditionals....
True or false:
1. If a is a real number such that a^2 = 2 and a^3 = 5, then a = 2.
2. If Hitler had been assassinated in 1932, the Moon would never have existed.
3. If Hitler was assassinated in 1932, then the Moon has never existed.
All of those sentences are true, but trivially so. Whenever the antecedent of a conditional is false, the conditional itself is true. Whenever the consequent of a conditional is true, the conditional is itself true. The only way a conditional of that sort comes out false is if the antecedent is true and the conditional is false. Goes to show that using first-order logic to formalize natural languages may have some counter-intuitive consequences.
Originally posted by AcolyteI'm comfused😕, what do you mean by #2 and #3?
True or false:
1. If a is a real number such that a^2 = 2 and a^3 = 5, then a = 2.
2. If Hitler had been assassinated in 1932, the Moon would never have existed.
3. If Hitler was assassinated in 1932, then the Moon has never existed.
Originally posted by bbarrOops, I should have said "one for the non-philosphers" 😉. The convention you explain is the one used in mathematics, but I was curious as to whether this was agreed upon by philosophers as well. Interestingly, we do use such constructions in evveryday conversation, but only as exclamations, eg "If those shoes are worth £100, then I'm the Queen of Sheba!" Perhaps the convention isn't as counter-intuitive as it might seem.
Those pesky conditionals....
All of those sentences are true, but trivially so. Whenever the antecedent of a conditional is false, the conditional itself is true. Whenever the consequent of a conditional is true, the conditional is itself true. The only way a conditional of that sort comes out false is if the antecedent is true and the conditional is fal ...[text shortened]... g first-order logic to formalize natural languages may have some counter-intuitive consequences.
On a similar note, my father, who has a contract to teach people to use a sophisicated search engine, informs me that many people find the formal definition(s) of 'AND' or 'OR' confusing. (That's an inclusive or 😛)
Originally posted by AcolyteHitler was not assassinated in 1932
True or false:
1. If a is a real number such that a^2 = 2 and a^3 = 5, then a = 2.
2. If Hitler had been assassinated in 1932, the Moon would never have existed.
3. If Hitler was assassinated in 1932, then the Moon has never existed.