I don't think that there is or could be a general principle that says that a paradox arising from idealizations will inevitably carry over (much less become worse) when the idealizations are relaxed. In some cases, the paradox will disappear when the idealizations are removed. In other cases, the paradox will persist (or become worse). There is no general rule here. It depends entirely on the details of the case.

For example, various paradoxes result in classical electromagnetic theory when pointlike charged particles are used. Point charges are a convenient idealization for many purposes, but the energy in such a field is undefined (the integral blows up). However, if we go to charge densities and extended charged bodies rather than point charges, these problems disappear. Likewise, in cosmology, Newtonian gravitational theory is afflicted with various paradoxes if we assume an infinite universe with a homogeneous, isotopic distribution of matter. Remove these idealizations and the problems go away.

These are intended merely as examples to show that sometimes paradoxes arise because of the idealization. In other cases, they arise despite the idealization. The matter can only be resolved in a case-by-case way, given the details of the particular paradox.

Just a footnote to Marc Lange's response (which seems spot on to me). It is worth adding that in serious analytical philosophy there is actually a good deal more agreement on arguments than there might appear to be at first sight, and there is a good deal of pretty secure knowledge.

For what often emerges from the to and fro of debate is essentially something of the form "If you accept A, B and C, then you'd better accept D too". Then one party might endorse A, B and C and conclude that D; and another party might think D is unacceptable, and conclude that one of A, B, or C must be wrong. And another party again (me, often!) might not know how to respond. [A trite example. If you accept act utilitarianism plus some other things, it seems that you should sanction the sheriff hanging an innocent man if that is the way to stop a riot in which more innocent people are killed. Some bite the bullett, some think so much the worse for utilitarianism.]

Now, there may indeed be a loud disagreement between the first two parties. But a lot of hard thinking may have gone into working out what they agree on, namely that "If you accept A, B and C, then you'd better accept D too". [For example, initially people might have thought, wrongly, that accepting A and B alone forced conclusion D, and it took some subtle argument to show that C was playing a role too. Working out what act utilitarianism really does sanction is like this.] And finding that sort of connection can represent a solid achievement of which we can be tolerably certain, even while there remains vigorous disagreement about what to do with the discovery.

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.

The kinds of reasons that are given for favoring one scientific theory over its rivals are a good deal more subtle than "observation is king." To begin with, a theory need not be justly rejected merely because it conflicts with a given observation; sometimes, the observation is appropriately doubted, and sometimes, a given theory is rationally retained despite its failure to fit our observations because blame for the mismatch is placed on other theories ("auxiliary hypotheses") that were used to bring the theory to bear on those observations. (The Copernican model of the solar system, for instance, was retained despite 300 years of failure to observe the stellar parallax it apparently predicts.) By the same token, a theory that fits our observations very well may nevertheless be justly and emphatically rejected on the grounds that it is ad hoc, fails to fit nicely with our other theories, lacks unity or fruitfulness or explanatory power, etc.

Once these familiar features of scientific practice are recognized, then I think the choice among theories in philosophy seems not so dissimilar to the choice among competing scientific theories. Admittedly, much of philosophy is a priori, unlike science. However, the virtues of elegance, parsimony, unity, coherence, explanatory power, and so forth play significant roles in both scientific and philosophical theory-choice.

Finally, philosophy has long been and is increasingly brought into contact with empirical results. A philosophical analysis of causal relations, for instance, that fails to do justice to modern physics has a severe deficiency. Of course, philosophers will disagree about the extent to which modern physics (or even classical physics) discovers causal relations, as well as disagreeing about what physics has revealed about them. Nevertheless, philosophical theorizing hardly takes place in isolation from empirical results. Recent literature in the philosophy of mind and perception offers a host of tremendously potent examples of this.

A great deal has been written on that, and opinions vary. I will just give you mine. 'Science' and 'scientific' are not themselves terms of science. Some philosophers have attempted to give the terms a clear meaning (Karl Popper, for example). I think they have failed. And I don't think that the ordinary language terms 'science' or 'scientific' are very clear or useful. So I would suggest that your questions aren't good ones. Further, there are many branches of natural science and many branches of the social sciences and there is probably little to be learnt from carving the whole lot into two groups and trying to compare and contrast them. Better: look at each branch of study that interests you and see if the theoretical claims are properly justified.

Ian Hacking, in his very readable book Representing and Intervening, describes an experiment done by a friend which involved changing the electrical charge on a minuscule ball of niobium. And how was that done, he asked? His friend said "Well, we spray it with positrons to increase the charge or with electrons to decrease the charge". And Hacking comments "From that that day forth, I've been a scientific realist. So far as I'm concerned, if you can spray them then they are real."

Hacking's story reminds us that many of our best theories about "unobservables" enable us to do a lot more than reliably predict observable behaviour in a hands-off, watching-from-the-sidelines, sort of way. They do more than merely tell us a story about a supposed hidden substructure of the world, a story that we could perhaps treat as a "just so" story, a useful fiction, a "heuristic". Our theories guide us in causally manipulating unobservables, and in causally producing desired observable effects. We can reach in and tweak causal micro-processes, spraying electrons, cutting up DNA strands, and the like (or at least, that is how it is natural to describe what we are doing). How are we to understand what we are up if we suppose that such processes are actually mere fictions?

Indeed, do we even understand what such a supposition really means? Imagine that Jack and Jill are engaged in the experiment Hacking mentions. Day in, day out, they improve the design of their experimental apparatus, improve their techniques for spraying very sparse streams of electron onto the niobium ball, and so forth. They talk in the laboratory incessantly of electrons, positrons, molecules and other other unobservables, and cheerfully use the relevant parts of the best going theories about such things, with great success. And now let's ask: what would really be at stake if one night Jack were to say in the pub afterwards, "But for all that, you know, I think electrons don't really EXIST"? (Shouting or thumping the table as he says it doesn't make what is at stake any clearer!)

In the laboratory Jack cheerfully talks about electrons, and works out how to spray them around with ever increasing accuracy. It isn't, we are supposing, that he has common-or-garden scientific reservations about what he is up to, any more than Jill has. So what could his purported philosophical reservations about some idea of capital-E existence really amount to? It isn't, to say the least, entirely clear, until we get a lot more explanation.

Now, of course, these quick remarks can only be the beginnings of a long and complex set of arguments about scientific realism. But perhaps they are just enough to suggest that the common-sensical realist view of at least some theories about unobservables (the theories that guide micro-technologies, for a start) has something going for it -- at least as a default starting point, pending some strong counter-arguments. (Philosophy being philosophy, there are of course those who try to offer such counter-arguments!)

The question of the status of string theory, however, is a whole different can of worms!

At any one time, quite a bit of science is provisional, conjectural, and the subject of hot debate among scientists. So, rather boringly, science in general can't be said to be a system of "universally codified opinion".

I suspect, however, that the intended question is something more like this. Take a scientific claim that isn't any longer provisional, conjectural and contested -- e.g. take the claim that DNA has a double-helix structure. Then, the rephrased question goes, does this claim in any good sense tell us the fact of the matter, tell us how the world is independently of us? Or is it, in the end, merely that some bunch of people (the scientists) have come to a shared opinion about the world, in this case the opinion that DNA has a double-helix structure?

To which the common-sense realist answer is the first. After all, science tells us, it is the fact that DNA has a double-helix structure which causally explains the behaviour of DNA under X-ray diffraction etc.; it is not the opinions of scientists which do the causing! And science tells us too that the structure was there before we had any opinions about it (it hasn't developed only recently); and it will still be there in the dark ages to come, when scientific knowledge has been lost, and our shared opinions have evaporated.

And who are we to say that science has got it all wrong here? We'd certainly need some pretty strong arguments to usurp the common-sense answer to our rephrased question.

Now, maybe there are such arguments to be had. But I rather doubt that Paul Feyerabend, for one, has provided any. To be sure, in many of his later writings, he wanted to tease and torment mainstream philosophers of science of the day about how hopeless their accounts of scientific methodology supposedly were. Famously, he argued that "Anything goes!" was about as useful and accurate as the recommendations of some methodologists. But it is one thing to say that our philosophical stories about how scientists come to represent the world they are discovering are not very good; it is quite another thing to say that scientists aren't ever really discovering how the world is, but merely coming to agree on shared stories to indoctrinate their students with.

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." In that remark, we allowed a false theory to do some explanatiory work.

Of course, we might want to reinterpret that remark as follows: "If theory A is true, then it explains E but not F, whereas if theory B is true, then it explains both E and F..."

On the other hand, we do sometimes regard a theory as explaining some fact even when that theory is false -- as long as the theory is a good enough model for facts of that kind. For instance, a theory with idealizations (ideal gases, frictionless planes, perfectly smooth surfaces...) may explain some phenomenon even if the theory is, strictly speaking, false. It seems that an explanatory model does not need to be true. But then what must it be?

My brief reply would be that I don't "believe in science" either. But I do believe that for many questions, science provides our best way of getting at the likely answers. And I also believe that in any number of cases, the most reasonable belief by far is that science has gotten it right. Are some illnesses caused by viruses? The evidence seems pretty overwhelming. Are there electrons? As some people like to point out, we've even learned how to manipulate them. Are water molecules made of hydrogen and oxygen? What reason is there to think not? The list could go on and on.

Not everything that science says or has had to say is true. But then, I'm not aware of any infallible sources of knowledge, and science doesn't claim to be infallible. On the contrary, science takes much more seriously than people are usually inclined to that we are indeed fallible, and so we need to be careful when it comes to settling difficult empirical issues. But for a lareg range of questions, I can't even begin to imagine a better way of approaching them than the way that science does.

On the one hand... There's some controversy here, but a nice, readable paper by Bradley Monton argues that methodological naturalism neither is nor should be a presupposition of science. Monton provides further references to the literature. To see the paper, click here.

I think Monton makes a case that we can't use methodological naturalism as a criterion of demarcation between science and non-science. But then there may not be much we can say by way of offering strict criteria of demarcation between science and other activities. Even if science isn't, as it were ,"by definition" naturalistic [aside: when someone says that something is so "by definition, you should be suspicious] it's not an accident that across the sciences, researchers almost always start with and end up with naturalistic hypotheses. That includes researchers who count themselves as religious believers. There's no one simple reason for this; it's partly a matter of history, partly a matter of shared intellectual values, partly a matter of what makes for research programs that lead to good experimental questions, and a good deal else. This means that coming up with a good account of the more-than-coincidental connection between science and naturalism calls for reading around in lots of areas. Other panelists may have some more specific suggestions for further reading.