I am confused about how a conditional statement is necessarily true, and not false or unknown, when the antecedent and consequent are both false. According to the truth table, the sentence "If Bill Clinton is Cambodian, then George Bush is Angolan" is true. How can such an absurd sentence be true? It seems initially like the sentence could just as easily, or more easily, be false or unknown.

I am learning about the principle of noncontradiction ~(p^~p). I can see that this would work if we assume that 'p' can only be true or false. Why should I make this assumption. I can see a lot instances where we need more than 2 truth values (how people feel about the temperature of a room, for instance could have an infinite number of responses, and all would be true because the proposition is based on subjective experiences). What is this type of logic called? If this is a possible logic then can't someone argue that everything is this way?

I know affirming the consequent is a fallacy, so that any argument with that pattern is invalid. But what what about analytically true premises, or causal premises? Are these not really instances of the fallacy? They seem to take its form, but they don't seem wrong. For example: 1. If John is a bachelor, he is an unmarried man. 2. John’s an unmarried man. 3. Therefore he’s a bachelor. How can 1 and 2 be true, and 3 be false? Yet it looks like affirming the consequent. 1. X is needed to cause Y. 2. We’ve got Y. 3. Therefore there must have been X. Again, it seems like the truth of 1 and 2 guarantee the truth of 3. What am I missing?

How, if at all, is the following paradox resolved? You hand someone a card. On one side is printed "The statement on the other side of this card is true." On the other side is printed, "The statement on the other side of this card is false." Thanks for consideration!

Here's a quote from Hume: "Nothing, that is distinctly conceivable, implies a contradiction." My question is this: what is the difference between something that is logically a contradiction and something that happens to not be instantiated? For example, ghosts do not exist. Could you explain how the concept of a ghost is not a contradiction? Thanks ^^

Is it true that anything can be concluded from a contradiction? Can you explain? It's seems like its a tautology if taken figuratively because we can indeed conclude anything if we suspend the rules of reasoning, but there is nothing especially interesting in that fact in my humble opinion.

If the sentence "q because p" is true, must the sentence "If p then q" also be true? For example, "the streets are wet because it is raining," and the sentence "if it is raining, then the streets are wet." Are there any counter-examples where "q because p" could be true while "If p then q" could be false?

If the sentence "If p then q" is true, must the sentence "q because p" also be true? For example, "if it is raining, then the streets are wet" and the sentence "The streets are wet because it is raining." Are there any counter-examples where "If p then q" could be true while "q because p" could be false?

Is there a term for the logical fallacy that other people have it worse, so you should be happy? Example: I fall down a staircase, breaking my leg. The next day I go into work, and someone (inevitably) says "Phfeh! That's not bad! Let me tell you about the time *I* fell down the stairs!" I suppose this also covers the 'third world problems' saying. "You didn't get your last paycheck? Phfeh! First world problems. In Isreal they are shooting at each other!"

Can a valid syllogism be fallacious? For example God can speak Mandarin. Charity is God. ∴ Charity can speak Mandarin. David can speak Tagalog. David's bones are David. ∴ David's bones can speak Tagalog. I'm pretty sure these are valid but unsound syllogisms, and I think they both commit the fallacy of division, but if the premises were true, would the conclusion also be true? I thought of an analogous syllogism that's sound, and I just can't figure this puzzler out. Basalt is rock. Rock is natural. ∴ Basalt is natural.