If someone's belief about something turns out to be wrong, that doesn't show that his belief was "wasted". Perhaps it was his false belief that led others (or himself) later to arrive at a correct belief. True beliefs usually don't spring into being from nothing; they gradually emerge from a fertile soup of false beliefs. And this process is usually gradual enough that arriving at the truth doesn't have the dislocating consequences you mention.

Mathematics investigates number systems some of whose properties arecritical for measurement. And without measurement, we wouldn't be ableto provide our scientific theories with sharp reality checks.Furthermore, those theories are themselves shot through with extremelysophisticated mathematics; most central claims of the advanced sciencescannot even be stated without a generous helping of mathematics. Manyhave been amazed that mathematics, often developed independently ofempirical research, turns out to be so useful, indeed necessary, forscience. But whatever one's explanation, it's a fact that it has. Mathematics,by contrast, appears independent of science in important respects. It's true thatmathematical inquiry was often initially prompted by scientific inquiryinto the natural world. But what inspires mathematics is one thing, andwhat it owes its justification to is something else entirely. Mostmathematicians will tell you that the only ground for accepting amathematical claim is that someone has...

I thank the poster for this challenging question and Jyl especiallyfor her stimulating response. Her idea is a nice one: that we deemsomething to be supernatural just in case we take it to be foreverbeyond the limits of scientific understanding. I'm not sure though. Ifsomeone were like Jyl and didn't believe that there are anysupernatural objects, then it would follow that she didn't believe thatanything was in principle beyond the limits of scientificunderstanding. Now, many people do believe that it's likely that there aresome truths about the universe that are in principle beyond humanunderstanding (for instance, see here ).Does this belief commit them to the existence of the supernatural? Thatdoesn't seem right. If you want to make room for someone who believesthat, say because our minds have the particular structure they do,there are things about the world that we cannot in principle understandand yet who also holds that there are no supernatural phenomena, thenwe'll have to understand the...

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...

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...

The following comment has been kindly sent in by Professor Kannan Jagannathan (Department of Physics, Amherst College): "The best evidence we have for the isotropy andhomogeneity of space leads cosmologists to hold that the universe hasno center and no periphery. If the universe is infinite now, it was soat the Big Bang, and the bang occurred everywhere (in such a case, thedensity of the universe would have been infinite at BB); if theuniverse is finite (and unbounded) now, it was probably point-like atBB, but it is not to be thought of as embedded in some larger space. That was all there was as far as space was concerned; it was'everywhere' then, and is everywhere now. In the standard model of cosmology, as well as inmost variants of it, the initial rate of increase of the scaleparameter (crudely, the radius of the universe, or the rate ofexpansion of space) would have been bigger, perhaps much bigger, thanthe speed of light. The combination of these two points would suggestthat if...

Farther apart. And as Bob Dylan sang, you don't need a philosopher to know which way you travel.

I think most scientists would reject an assumption in your question — that they believe the Universe needs to be one way or the other. Theories in science do not say how matters must be, they describe how they are .As to why scientists think the Universe does have a beginning, well,presumably it's because that hypothesis best fits the availableastronomical data. If you want the details, talk to yourlocal physicist.