I have a question about Whitehead and Russell "Principia Mathematica". Can mathematics be reduced to formal logic?

Is the following situation a logical and rational reason to believe in G-d?: Judaism, unlike any other known religion, claims that G-d gave the torah not to just one person but to an entire nation. The whole nation of Israel, which numbered over a million people witnessed Moses receiving the ten commandments and heard G-d tell them what the torah was. Unless the above really happened, there is no logical way to explain the tradition that over a million people heard G-d speak. The generation it was supposed to happen to would not be able to be convinced that they saw something they really didn't. And if the "lie" tried to be started a few generations later, the people would ask why they had never heard this claim before. Therefore, it must have really happened and the torah and all it contains is divine.

In a conversation with a teacher today I expressed that I thought that teachings from the Bible and any other “facts” or “information” gained through reading it are false. My teacher responded to this by saying, “you do realise I am a Christian, don’t you?” I did, in fact, know that she is a Christian but I do not see why, just because she is a Christian, I have to pay such high respect to what she believes to be “truth”. I believe that the Bible is neither truth nor fact, yet she would not have to pay respect to my opinion. This has lead me to ask why we should have to give so much respect to someone’s views when they are based on religion. Why does religion demand such high respect when it is simply an opinion?

Do you think it's possible, even theoretically, for there to exist a substantive belief (any kind, about anything) that is impervious to any argument, cannot be debunked, etc., and yet is false?

I was recently having a conversation with a friend about what should be the ultimate goal of life. I suggested that happiness (although this was not strictly defined) may be one of the most worthy goals to aim for in life since it is not a means to anything else but an end in itself. In response my friend argued that if happiness were to be the ultimate goal of someone's life then it would be best achieved by taking a 'happiness' drug or otherwise stimulating the brain in such a way as to induce a state of perpetual happiness. Although this seemed inherently wrong to me it nevertheless seemed to fulfill my criteria of the purpose of a life. It is an important point to bear in mind when answering this question that my friend tends to offer explanations in terms of reductionist science. He is an undergraduate biologist and for him even emotions, such as happiness, can be simply reduced down to chemical reactions and electrical impulses. As a result it seems to me that if happiness is seen in these...

Are necessary truths ultimately grounded in induction? For example truths of mathematics are said to be necessary, yet don't they make generalizations about an infinite set of numbers that are not verifiable; wouldn't this be considered induction? And if we ground our necessary truths on axioms, aren't these axioms theorems that a community has agreed to as being true and are not objectively true? Thanks for your answer, John

Does Rawls consider inborn abilities an important determinant of social status? I haven't read his entire text in A Theory of Justice, but when he mentions the veil of ignorance, is he considering social status more or less a matter of fate?

Why is it that whenever I write something philosophical, I hate it? Do any other philosophers feel this way about their own writing? How do philosophers write?

There have been many arguments that are offered in support of the proposition that God exists. So far, it seems that none of them have been compelling. Do you think that any possible argument offered as establishing a conclusion like 'God exists', could be compelling. That is, could there exist an argument such that it's conclusion is 'God exists' and the argument is compelling? If no such argument could possibly be compelling, can we not just infer that no argument offered as establishing the existence of God is compelling? Or, do you think one (an argument) exists that may be compelling when learned by us?

Notation: Q : formal system (logical & nonlogical axioms, etc.) of Robinson's arithmetic; wff : well formed formula; |- : proves. G1IT is always stated in the form: If Q is consistent then exists wff x: ¬(Q |- x) & ¬(Q |- ¬x) but we cannot prove it within Q (simply because there is no deduction rule to say "Q doesn't prove" (there is only modus ponens and generalization)), so it's incomplete statement, I don't see WHERE (in which formal system) IS IT STATED. (Math logic is a formal system too.) In my opinion, some correct answer is to state the theorem within a copy of Q: Q |- Con(O) |- exists x ((x is wff of O) & ¬(O |- x) & ¬(O |- ¬x)) where O is a copy of Q inside Q, e.g. ¬(O |- x) is an arithmetic formula of Q, Con(O) means contradiction isn't provable...such formulas can be constructed (see Godel's proof). But I'm confused because I haven't found such statement (or explanation) anywhere. Thank You Very Much