Does there need to be a single, particular contribution that philosophical research makes and other disciplines fail ito make? Of course, science and math clarify concepts and contribute to making empirical predictions. Philosophical research does all of that, too, from time to time. I don't think there needs to be an interesting answer to "What does philosophy do?" that distinguishes philosophy from science and math. All are in pursuit of truth. Philosophers, scientists, and mathematicians are trained somewhat differently, often have somewhat different tools in their toolkits, and come out of somewhat (though overlapping) traditions and so will generally be familiar with different argumentative moves. But these may be differences in degree, not in kind.

Sometimes, when we say things like "Jones died because the butler killed him with an ax", what we have said is false if the butler did not in fact kill Jones. After all, Jones' history of smoking cigarettes cannot have caused Jones to develop lung cancer if Jones did not have a history of smoking cigarettes. (By the same token, Jones' history of smoking cigarettes cannot ahve caused Jones to develop lung cancer if Jones did not, in fact, develop lung cancer!) Notice that I have cunningly shifted from explanation to causation. Clearly, for event C to cause event E, both C and E must have happened. On the other hand, there are times when we say that a scientific theory explains some fact even when that theory is false. For instance, if we are deliberating among several rival, mutually incompatible theories, we might say something like "Theory A explains fact E but doesn't explain fact F, whereas theory B explains both E and F, so (all other things being equal) theory B is more plausible than theory A...

I agree with you that observational evidence for the hypothesis that all processes conserve energy (or mass, or mass-energy) inevitably fails to prove that hypothesis (though succeeds in confirming the hypothesis strongly), just as our observational evidence for the hypothesis that (say) "All bolts of lightning are followed by claps of thunder" inevitably fails to prove that hypothesis. Even if every lightning bolt we have observed so far has been followed by a thunder clap, no contradiction would result from the next lightning bolt occurring without a thunder clap. So the "problem of induction" applies to both examples equally. Perhaps your science professors had something else in mind in emphasizing the "unprovability" of energy conservation. Suppose we observe a process that apparently fails to conserve energy. The system's energy before the process occurs seems to exceed the system's energy after the process occurs. Rather than rejecting the conservation of energy, couldn't we always respond by...

The notion of a "falsifiable" hypothesis is very difficult to make precise in a way that allows us to count as "falsifiable" all and only those hypotheses that we are inclined to regard as "scientific." Take the hypothesis that the total amount of energy in the universe is the same at every moment in the history of the universe ("energy conservation"). No observations would ever be enough, all by themselves, to demonstrate that the total amount of energy has changed. There would be no way to prove, on the basis of observations alone, that we have failed to take into account some previously hidden form of energy that would suffice to "balance the books." This is not a craftily chosen example. Typically, in mature sciences, when an individual hypothesis (such as energy conservation) is tested against observations, other hypothesis are needed in order to conduct the test. So if our observations fail to go as we expect, there is the possibility of putting the blame on those other hypotheses, rather than on...

Thank you for your interesting questions. The standard view is that space and time (or, more accurately, spacetime -- since space and time are not independent entities according to the theory of relativity) came into existence with the Big Bang. So there was no time before the Big Bang. So the laws of physics were not existing before the Big Bang, just waiting to come into force. However, there is a sense in which many laws of physics are waiting to come into force. Suppose it is a law of physics that two electrical point charges of 1.234 statcoulombs and 5.678 statcoulombs, at a distance of 1 centimeter, exert upon each other a mutually repulsive force of 10.234 dynes. There was presumably a first moment in the history of the universe when there were two point charges of those quantities, 1 centimeter apart. (Or perhaps there has never yet been such a moment. Perhaps there never ever will be two such point charges in the entire history of the universe.) The law governing two such point...

Whether the "law of parsimony" works depends on what it says. Broadly speaking, it says that we should prefer a simpler explanation over a complicated explanation of some phenomenon, all other things being equal. This leaves a lot unspecified: What makes one explanation simpler than another? What does it take for one fact to explain another? What are the "other things" and what does it take for them to be "equal"? What does "prefer" mean? (Believe? Believe more likely to be true? Adopt as a working hypothesis?) Leaving all of that to one side, there will certainly be cases where the simpler explanation turns out to be false. Suppose a patient has a large collection of symptoms. Perhaps there is one disease that often produces just that collection of symptoms. But there may also be a pair of diseases, the first of which often produces the first half of those symptoms and the second of which often produces the second half. Arguably, parsimony favors the first hypothesis: that all of the symptoms...

Generally, when philosophers write about scientific reasoning, they are interested in how scientists (or, more broadly, how anyone) ought to reason. For example, they might be interested in specifying what it takes for a piece of evidence to count in favor of a given hypothesis, and why certain pieces of evidence should count for more than others. They are generally not interested in explaining why scientists in fact regarded a given piece of evidence as counting for more (that's for historians to figure out) except insofar as this explanation goes via some account of why that piece of evidence *should* have counted for more. It is sometimes said that philosophers are trying to give a "rational reconstruction" of scientific reasoning. But the history of science is not at all irrelevant to this task. For example, any account of scientific reasoning that regards as unjustified some renowned episode of scientific reasoning has a great (though not impossible) hurdle to climb, just as any...

I have heard this said as well. In the history of science, there are many examples in which several researchers independently came up with the same new idea. Schrodinger and Heisenberg independently came up with the same theory (quantum mechanics) and presented it in such different forms that someone else (Born) had to figure out that they were equivalent. Darwin and Wallace (both from reading Malthus!) independently came up with the theory of natural selection. Adams and LeVerrier independently predicted the existence of the planet Neptune. Lavoisier and Priestley independently discovered oxygen. The examples are legion. These cases of simultaneous discovery are good evidence that once a problem reaches a certain point, it is widely recognized as a problem and the same solution would soon have been found even if the actual discoverer had not found it. Einstein's theories of special and general relativity are sometimes cited as exceptions to this general rule. One reason for this view is that the ...

An excellent question! Many of Einstein's most famous papers make shockingly few references to the details of previous empirical work by other scientists. To put the same point in another way, many of Einstein's most famous arguments arise largely from "philosophical" considerations. For instance, Einstein's 1905 special theory of relativity paper begins by noting a symmetry in electromagnetism: that the current induced by a magnet moving relative to a loop of conducting wire is the same, according to electromagnetic theory, whether the magnet is moving and the conductor is at rest, or vice versa, as long as their relative motion is the same in both cases. However, Maxwell's electromagnetic theory (as it was then understood) assigns the induced current different causes in the two cases. Einstein suggests that the current should be understood as having the same cause in the two cases, which leads him to suppose that there is no fact about whether a force is really electric or magnetic. Clearly, this...

Consider a match. It has the disposition -- the power, the capacity -- to produce fire. But suppose that as a matter of fact, the match is never struck. So it never, in fact, produces any fire. Yet it still had the power to produce fire. "This match produces fire" is false, yet "This match has the disposition to produce fire" is true. In your example, the thundercloud's disposition refers to (in Goodman's words) the "threats or promises" made by the thunderclouds , whereas a sentence like "Thunderclouds produce lightning" is true only if some thundercloud actually makes good on its threat.