It helps to begin by distinguishing laws of nature from our hypotheses about them. Then the first question is whether there really are laws of nature out there. I'm one of those philosophers who believes there are, though just what it takes to be a law is hard to say. For example, is a law just an objective pattern of properties, or does a law have a special kind of necessity? But some philosophers would deny that even the patterns are fully out there, because they hold that the structure of properties is something scientists impose on the world: the world does not come pre-carved into natural kinds. So the answer to your question is a little complicated. Even if the laws depend on our own scheme of classification, it would probably be misleading to say we invent them: it is not as if we can just make them any way we like. And even if the laws of nature are fully objective and out there independently of us, it is still up to us to think up the hypotheses that are supposed to describe them. In any...

Scientific theories cannot be proven or disproven. For one thing, some of the data on which the proof or disproof is supposed to be based may itself be incorrect. (Francis Crick, of double-helix fame, supposedly said that if you theory fits all your data then you know its false, because you know that some of your data is false.) But even if all your data are true, scientific theories go beyond those data (that's their point) and so cannot be proven from them. And theories can not in general be disproven by data either. Although a theory may be used to make a prediction that is then found to be false, the prediction almost never followed from the theory alone, but only from the theory along with various additional assumptions (the instruments are working properly, there are no disturbing forces acting on the experiment, etc.), so when the prediction fails, you do not know for sure whether to blame the theory or one of the other assumptions. Nevetheless, there is something to the idea that...

In philosophy it's often a good idea to begin with a clear case where we are particularly confident about what the right answer is, then move to subtler cases. If the question is whether water ever floats, the clear case is ice.

Scientists do seem to have a strong preference for simple theories, though the relevant concepts of simplicity are not at all easy to analyze. It is also very difficult fully to justify a simplicity preference, since scientists seem to prefer simpler hypotheses because they think them more likely to be correct, not just because they are more economical, and it is hard to see how we could justify the claim that the universe is more likely to simple without begging the question. But I don't think that a claim that assigns an infinite quantity is automatically simpler than one that assigns a finite quality. 'There are infinitely many rocks' mayh not be relevantly simpler than 'There are 437 rocks.' Of course there many more claims assigning specific finite numbers of rocks than there are claims assigning an infinite number of rocks (infinitely many more, in fact), but I think the relevant comparison is between specific claims.

I don't think scientific research is algorithmic, unless you use the term so broadly so that any non-random behavior counts. Research certainly doesn't follow rules that the scientists can articulate, and I think there are reasons to believe that they aren't following anything like a full set of tacit rules either. Thomas Kuhn mounts an extended case for an alternative to a rule-based account of research in his classic The Structure of Scientific Revolutions .

If indeterminism is true then, strictly speaking, nothing is determined no matter how big. Perhaps most larger scale systems behave as if they were governed by deterministic laws, but as I think the physicist Richard Feynman pointed out, all it takes to magnify atomic indeterministic effects is a geiger counter, which could serve as an indeterministic switch to turn on as large a system as you like.

I agree with Alex that our best hypotheses may well not capture the actual laws of nature, and that physicists strive for unification, and I think there is a third aspect to this question. In spite of what the 20th century philosopher of science Karl Popper maintained, science depends on induction, on making inferences about the unobserved on the basis of the observed. And as the great eighteenth century philosopher David Hume observed, this depends on some kind of assumption of the uniformity of nature. Hume notoriously argued that we can have no good reason for this assumption, and that is very close to the point that we have no good reason for assuming that the laws of physics are the same in those parts of the universe we have observed as they are in those parts we have not observed. But without making something like that assumption, science would be impossible. To put it differently, to leave open the possibility that laws might be different elsewhere is, if taken to an extreme, not just to...

In spite of the enormous interest in astrology over thousands of years and by some very bright people, there seems to be no good reason whatever to believe that the position of the planets when you are born affects your future.

Later scientific theories often contradict the theories they replace. Does this mean that science is not in the truth business? There is a simple and much discussed argument for this conclusion. The argument is known as the 'pessimistic induction': all scientific theories more than say two hundred years old are now known to be false, so it is likely that all present and future theories will eventually be found to be false as well. So much for truth. There are a number of responses those of us who do think science is in the truth business can give. We can quibble with the premise of the pessimistic induction: surely not all theories more that two hundred years old are now known to be false. For example, we still believe the theory that the blood circulates around the body, and that theory is much more than two hundred years old. But even if the premise is an exaggeration, lots of our best old theories are contradicted by what we now believe. For example, if Einstein is right, then...

This is a surprisingly difficult question to answer. There are a number of answers that seem to have something going for them, but also face various difficulties We might say that science is empirical, based on observation and experiment, whereas you can do philosophy with your eyes closed. But some parts of science are highly conceptual and far removed from the data, and on the other side a number of philosophers have denied that philosophy or any other form of inquiry could be entirely independent of empirical evidence. We might say that science concerns how things are while philosophy concerns how things ought to be. But although questions about how we ought to act and what we ought to believe are central to philosophy, there are also other, more descriptive aspects of philosophy, such as metaphysical questions about what sorts of things exist. We might say that science asks questions that we know in principle how to answer, whereas philosophy asks questions which, although they seem...