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Is the underlying mathematics of string theory both complete and consistent? If it is, then apparently Gödel was wrong; if it is not, then how can it be a theory of everything? Would not an endless string of metatheories be needed for sufficiency? If not, what did Gödel, Tarski, etc. miss. Dave

I don't know anything about string theory, but I assume that itemploys rich enough mathematics that, were we to articulate thatmathematics in a formal system, Gödel's 1931 Incompleteness Theoremwould apply to it to yield the result that, if the system isconsistent, then it is incomplete, that is, then there is somemathematical statement in the language of the system that is neitherprovable nor disprovable in that system.

You ask whether theconsistency and (hence) incompleteness of the system would conflictwith the claim that string theory is "a theory of everything". Itdepends on what "a theory of everything" means. If it means that thetheory can answer all questions about physical phenomena,then there need be no conflict: the undecidable statement of the formalsystem (the statement that can neither be proved nor disproved if thesystem is consistent) is one in the language of mathematics. It is notmaking a claim about the physical world. If, on the other hand, by "atheory of everything" one means something that can settle all questions about the physical and the mathematical worlds,then you're right that Gödel's theorem rules out such a theory: itshows that most any consistent mathematical theory will fail toanswer all mathematical questions (in particular, will fail to answervery basic mathematical questions about itself). But I suspect thatwhen people talk about string theory, it's the first sense of "theoryof everything" that they have in mind: that string theory can inprinciple settle all questions about the nature of the physical world.

As science progresses, it seems that it starts to infringe more deeply on philosophical questions - things like the anthropic principle in physics or neuroscience's discoveries about consciousness. What are things that scientists can take from philosophers? Also, do philosophers have an obligation to look into the science if it impacts their area of expertise?

Perhaps philosophers can offer the scientist clarification of some of the concepts or claims in play in his or her theories. For the most advanced sciences, like physics, such insight typically does not lead to any change in the practice of the working scientist. (That said, some philosophers believe that philosophical illumination of the foundations of mathematics, the most advanced exact science, might lead to a revision of our mathematical practice.) For less advanced sciences, like psychology, such clarification can have far greater impact on how the subject matter is understood and the research is pursued. Philosophers can also offer scientists help in thinking about issues that cut across particular sciences, for instance questions about how to understand claims about unobservable objects, the nature of explanation, the goals of science, the rationality of science, the nature of scientific laws, and so on.

I think most philosophers would agree with the conditional claim that if some empirical inquiry is relevant to their work then they should pay attention to it. Philosophers will divide about how often the "if" part of that conditional holds. Some philosophers are prepared to see much scientific work as relevant to what they do, while others believe that many philosophical concerns, properly understood, are quite independent of such empirical issues. The relevance and significance of empirical work to philosophical questions is itself sometimes a substantive philosophical issue.

How is it that such can be true, as in many historic philosophical works and their base, that all has been done... that nothing is to be seen as new... when quite factually (according to science) the relative age of our existence in regard to all else that is known and yet to be discovered in our perception and reality, is comparable to that of an infant at best? Perhaps even yet to have been "born" being still in a gestative state..... Is such opinion not simply from our confined and very limited perspective?

There are a few philosophical works that express the conviction that they have solved all the important problems and that nothing new of any interest should be expected. But these are in the minority. Most philosophical works on the contrary emphasize how much work is left to be done, how much we don't know, how much room and need there is for new ideas and approaches.

Hi, I am an aspiring philosopher and I would like to become a professor one of these days. But I don't know how to go about it. I am still an undergrad student and I don't what steps to take. The advice will be much appreciated. Thanx.

One good test of whether one ought to pursue philosophy is whether one finds oneself staying up at night worrying about philosophical questions.

In this vein, I was once told that if I read Thomas Nagel's Mortal Questions and found one essay that kept me up worrying, then I would know that I should go on to graduate school. (Nagel's book is a good test of one's interest because it includes essays on a wide variety of topics, from ethics to the philosophy of mind to free will to the meaning of life.)

It is important to try to figure out how much, and why, it matters to one to be a philosopher. After all, philosophy in particular, and academia in general, is not the easiest of professions, and one must be willing to make all sorts of sacrifices, both in graduate school and afterwards, in order to remain in the profession. So one should try to determine whether one is willing to make the sacrifices that may be necessary.

Why do I feel stupid when confronted with questions about Philosophy and yet, I'm strangely attracted to it? Am I a masochist or someone who doesn't know better? Cheers! Victor

Of course I can't say what's up with you, Victor, since I don't know you, but I can report that the questions in philosophy often have that dual effect on people. On the one hand, they are utterly seductive and mesmerizing. On the other hand, their elusiveness and apparent intractability can be painful at times. Some of the greatest of philosophers have felt the stupidity before philosophical problems that you report; for instance, the Austrian philosopher Ludwig Wittgenstein felt this very strongly and would frequently castigate himself — often before his dumbfounded students — for his stupidity. Perhaps you're right in your suggestion that these traits might be connected: for some people are most attracted by precisely that which remains out of their reach.

What is the difference between ethics and morality?

A distinction is sometimes drawn between ethics as concerning all the values or goods that might be instantiated in a person's life (well-being, friendship, virtue of character, aesthetic qualities, and so on), and morality as the narrower domain of moral obligation only (right and wrong, what's forbidden and permitted, etc.). Bernard Williams thought that one of the problems with modernity and modern philosophy is an excessive focus on morality as opposed to ethics, the former being what he called 'the peculiar institution' (see his *Ethics and the Limits of Philosophy*, ch. 10). The Greek philosophers, he thought, had a broader conception, one we should try to share.

Are there logic systems that are internally consistent that have a different makeup to the logic system that we use?

On Dan's comment. The distinction between so-called weak counterexamples and strong ones is, of course, important. But it really is possible to prove, in intuitionistic analysis, the negation of the claim that every real is either negative, zero, or positive. The argument uses the so-called continuity principles for choice sequences. I don't have my copy of Dummett's Elements of Intuitionism here at home, but the argument can be found there. A short form of the argument, appealing to the uniform continuity theorem—which says that every total function on [0,1] is uniformly continuous—can be found in the Stanford Encyclopedia note on strong counterexamples.

There is an important point here about the principle of bivalence, which says that every statement is either true or false. It's sometimes said that intuitionists do not, and cannot, deny the principle of bivalence but can only hold that we have no reason to affirm it. What's behind this claim is the fact that we can prove that we will not be able to find a statement P and show that it is neither true nor false. That is to say, we can prove that there is no statement that is neither true nor false. But that does not, by itself, show that it is incoherent to hold that not every statement is either true or false. The two claims are intuitionistically consistent.

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