I have trouble understanding what people mean when they use a phrase with the word exception. To me it sounds like a contradiction. So my question has two parts: A) Is using the term exception ever legitimate? B) Does the term "except" usually contradict the general rule that comes before it? For example, All ice cream should be taxed, except vanilla. This seems that the quantifier "all" is false if a member is excluded. For example, All students passed the final exam except Roy. Seems to me this means only Roy failed the final exam and the quantifier "all" makes the sentence false. Please help me make sense of the term exception. Thanks for your help.

Ok, I'm going to go at Godel backwards. I'm going to start from the fact that the universe exists (whatever others may think to the contrary). I'm assuming that the universe is ruled by law. It also seems to me that the universe can't contain any self-contradictions, or it wouldn't exist in the first place. So, its laws are consistent. For a similar reason, they must be complete; if some key part was missing, the universe wouldn't exist. This line of reasoning seems to lead me to: the laws of the universe are both consistent and complete. I know that Godel was talking about formal systems, but it just seems to me that the laws of the universe are *the* formal system. So, there is at least one example of a formal system that is both consistent and complete, whether or not we can articulate it. Or have I completely missed Godel's idea here? Thanks, JT

My teacher claims that he is utterly emotionless; according to him, he isn’t clouded by emotions of any form, and has no emotional desire. He argues that any emotions he appears to possess are simply superficial occurrences, with the purpose of manipulating others. He argues that he is utterly objective and consequently, completely exclusive from any form of bias. My question is that surely somebody who objectively chooses to use logic over any form of emotional guidance and has “no emotional desire whatsoever”, is therefore exhibiting a desire in itself? Surely, if one assumes logic as their only form of reasoning, the logic must be based upon basic desires and principles, therefore denoting an emotional presence? I would be grateful if somebody could enlighten me!

How do you show some conclusion of an argument cannot be derived in a complete system? Does one have to make the truth table to show that it is not valid and therefore, by definition it should be impossible for that conclusion to be derived?

What is the relationship between mathematics and logic?

I have recently stumbled upon a short book written by the Catholic theologian named Peter Kreeft. He deductively argued for Jesus’ divinity through an approach he summarized as “Aut deus aut homo malus.” (Either God or a Bad Man.) Basically, his argument works only on the assumption made by most historians. Jesus was a teacher, he claimed divinity, and was executed. So, assuming this is true he says Jesus must’ve been one of three things. One possibility is that he was a liar. He said he was divine even though he knew it was not true. Another possibility is that he was insane. He believed he was divine even though he wasn’t. The final possibility is that he was telling the truth and he was correct. He was divine. He goes through and points out that Jesus shows no symptoms of insanity. He had no motive for lying. In fact, he was executed because of his claims. That gives him a motive to deny his divinity, which he apparently was given a chance to do by according to the Jewish and Roman sources on the...

I'm a first year student of philosophy at UCLA, and I am interested primarily in philosophy of religion. I've just taken an introductory logic course which covered symbolization, sentential logic, and quantification. There are numerous other logic courses offered through the department, including metalogic, modal logic, etc, and I was wondering if AskPhilosophers could recommend a logic course to take? More specifically, I want to take a logic course that is related or will aid me in my studies in philosophy of religion. Maybe modal logic, since it deals with necessity and possibility? Thanks.

Is a "slippery slope" argument the same as a reductio ad absurdum?

Is it possible to prove that something cannot be derived (considering only well-formed-formulas) in a natural derivation system? I mean a premise P cannot yield the conclusion Q since there isn't any logical rule that justifies the inference but how can someone prove this?

Hello, I am asking this question after reading Richard Heck's answer to the question: 'Can God make a rock both big and small?'. It's more a terminological, really: What is the name of the philosophical approach that asserts logic is a universal law that cannot be broken (not even by God)? Thanks, Amit.