One of Nietzsche's most cited statements is, to paraphrase, "That which doesn't kill me, makes me stronger". Seems to me that, despite common acceptance, this is flat out inaccurate. As one example, many people survive traumatic events and are hardly stronger, instead living sometimes nearly incapacitated lives with Post-Traumatic stress disorder. Or, those with diseases such as AIDS, diabetes, or any number of diseases that can be treated. Do Nietzschian philosophers still accept this quote? Is there some other interpretation of his statement that makes it useful?

I have been studying axiomatic set theory as a foundation of mathematics and am stuck on the definition of a relation as a subset of a Cartesian product. I have two problems. The first is that a large number of relations seem to be presupposed prior to this definition: the truth-functional relations of logic, for example, or the relations of set-membership and subset. Doesn't this make the definition circular? Second, in specifying which subset of the Cartesian product is intended, a polyadic predicate is usually invoked; but isn't a polyadic predicate a relation, thus giving a second circularity? Furthermore, these are vicious circles, not harmless ones.

Hello philosophers. I was just wondering about Gödel's Incompleteness Theorem. What exactly is it and does it limit what we are capable of knowing? I have no training in mathematics or formal logic so if you could reply in lay terms, I would appreciate that. Thanks, Tim.

Is this bad logic? As all religions claim they are right and all others wrong, then only one can be right (though they can all be wrong). And is Pascal's Wager now statistically a complete waste of time with so many religions to choose from? And why should the comparative age of a religion serve to lend it credence and respectability?

I've heard that 2 to the power of 2, to the power of 2, etc... 6 times is a number so huge that we could never figure it out. Would that qualify as being infinite? And how would we be able to intelligibly come to that conclusion, or is it a "rough estimate" that we could never figure it out? Thank you for your time. ~Kris S.

In response to question 26 [http://www.amherst.edu/askphilosophers/question/26], should it not be possible for an omnipotent being to create the possibility for a contradictory object to exist?

A question about logic. When symbolizing and making inferences in natural languages that contain such terms as "it is necessary that", "A ought to do X", "A knows X", and "it is always the case that", there are extensions of classical logic, respectively, modal, deontic, epistemic, and tense logic that attempt to deal with such natural language analogues. My question is: What about propositions that contain a mixture of all the above terms? For example, there are sentences in natural language of the form “It is necessary that John ought to always know that 2+2=4." Is there a logic that can effectively handle (i.e. symbolize and correctly infer) such propositions? If so, is this logic both sound and complete? If there is no such logic, what is a logician to do with such propositions? My intuition is that things get tricky when you mix these operators together and/or the classical quantifiers. Thanks kindly for your reply, A Concerned Thinker

Is the physical world proportional? What I mean is: is it possible, for instance, that we find a solar system exactly like ours except for the fact that every object (planets, stones, animals, trees, etc.) is one thousand times longer or less long? What if only twice longer? And what about a different universe where even atoms (and elementary particles, if they have any length at all) were one thousand times "longer"? Is this meaningless?

Do men need speech in order to think? In other words, can we do the act of thinking without "speaking" to ourselves consciously or unconsciously? For myself, I use colloquial English, the language I am most fluent in, when I think in my mind. Does it have to be the case that one would use his or her most developed language to think?

Why do people want to know so much about life if in the end we're all going to die anyways?