I'm a mathematician looking at some of the work of Leonhard Euler on the "pentagonal number theorem". My question is about how we can know some statement is true. Euler had found this theorem in the early 1740s, and said things like "I believed I have concluded it by a legitimate induction, but at the same time I haven't been able to find a demonstration" (my translation), and that it is "true even without being demonstrated" (vraies sans etre demontrees). This got me thinking that "knowing" something is not really a mathematical question. A proof lets us know a statement is true because we can work through the proof. But a mathematical statement is true whether we know it or not, and if you tell me you know that a statement is true, and then in fact someone later proves it, I can't show mathematically that you didn't know it all along. This isn't something I have thought about much before, and my question is are there any papers or books that give some ideas about this that would be approachable by...

hallo, I appreciate your homepage very much. I would like to ask you for opinion about a method of thinking. The idea is this one: If you have a question, and you think you cannot answer it, may you change your question to a similar/different one? For example: Does God exist? A similar question would be: How would it affect me if I knew that God does exist? (Example by: Bert Brecht- Stories of Mr. Keuner The question of whether there is a God A man asked Mr. K. whether there is a God. Mr. K. said: “I advise you to consider whether, depending on the answer, your behavior would change. If it would not change, then we can drop the question. If it would change, then I can at least be of help to the extent that I can say, you have already decided: you need a God.”) I think it means getting a different point of view or a different way to approach towards a question. What do you think about such a method of thinking? Is it legal or not? Do you think it is a serious way of thinking or is it a trap...

Over a year ago, I read Quine's Two Dogmas for a philosophy class. One part in it makes the step from talking about meanings to abolishing meanings and talking only about synonymy. I never quite got that. I mean, if there are two things similar (or the same) about something, don't they each have to have those things? If two pieces of string have the same length, they have each have a length, and they happen to be the same. Likewise for any other properties I could think of, such as color, volume, mass, etc. I don't see how sameness could not imply those "intermediary entities" which are the same. Thanks.

What happens to the souls of people who are in a coma?

My younger brother, who is 13, is arguing that he will not go through any drastic changes in personality and mannerisms from now until the future and therefore a child is no different from an adult. I argued in the contrary stating that he will go through a lot of changes that might radically alter his outlook on life and personality. Is this correct or does it vary from person to person?

Can you give me some good examples of things that philosophers have produced throughout history. The reason I'm asking this question is this: I can think of many things that scientists (including mathematicians) have produced but I cannot think of any thing that philosophers have produced. Ahmet Thanks

A close friend broke a very big promise to me, knowing just how upset it would make me. She did so because she has been having a hard time lately and decided that it would be the best thing for her to back out, which I completely understand. However, given the nature of the promise she broke, her actions also amount to a personal insult and a logistical mess that I may have to deal with continually for a year or more. She claims that I am still a very important friend to her. I thought friends were supposed to have an altruistic interest in each other's well-being, or at least a sense of obligation toward one another. While in the best case she'd have kept her promise out of inclination and not obligation, I wish she'd kept it for *whatever* reason. I don't know in what sense I can be a "very important friend" given her behavior. Is it possible that she is telling the truth? If so, how? What am I missing about what it means to be a friend?

Hi, I have an engineering background but I have been studying philosophy for a couple of years. The problem I have is this. When I read a scientific (that is, not philosophical) problem, I almost always easily understand what the problem is (of course, I do not mean that I can easily solve the problem). A good way to test understanding is to try to explain the problem to another person. And most of the time I can easily explain a scientific problem to another person. But, in philosophy this is not the case. Even I spend so much time trying to understand what a philosophical problem is, I almost always have the feeling that I do not understand the problem. And the test I told above confirms me. Most of the time it is very difficult for me to explain the problem to another person. I suspect that the reason for this situation is something related with the nature of philosophy. What do you think? and what should I do to remedy this situation? Thanks, Unakil

Dear Philosophers, Please don’t take offense at this question, but just what is philosophy? I go to Stanford Encyclopedia of Philosophy and the Routledge Encyclopedia of Philosophy and search “philosophy”, and there is no entry that helps me. I’ll be directed to particular types of philosophy, but nothing that tells me what makes philosophy philosophy. I would have thought that philosophers, who are always asking themselves what makes X an X, would have been able to answer this question concerning their own discipline. Is it simply a matter of semantics—of figuring out the meaning of our terms (like “knowledge”, or “freedom”)? Or is it a matter of metaphysics—of figuring out what knowledge and freedom really are, in the same way that scientists figure out what DNA really is? Is it a matter of figuring out what our concepts are, or what they should be? What are its questions, and what are its methods for discovering answers to these questions? And why should we think that these methods are reliable...

How does one go about becoming a philosopher?