In biology, definitions tend to be approximate and fuzzy, since the phenomena biologists deal with are far more complex.
I would agree with this.
Precise definitions are much more important in physics than in biology.
But not this. In fact, it seems a bit backwards. I would say that definitions in biology are more approximate because you have no other choice - because no one has been able to get their hands around biology in a definitive way that allows them to announce the "laws" of biology the way physicists do. As such (though you're not going to like this), I would rate biology lower than quantitative sciences.
As a practical matter I can accept that biology must approximate because it deals with higher complexity (I would say the "ultimate" complexity of the physical universe). But at the same time, I maintain that this means confidence is lower in the methods of biology than in the methods of physics. Without producing something quantifiable, I don't know how one could say anything else. If biology wanted to do better, it would need to take the route I alluded to earlier, that of using physics to explain biology. Even though I say that, I don't believe that would really ever go anywhere. But, still, maybe it's worth someone giving it a try.
As a parallel, a quick search would yield you a smattering of papers with titles like "Is History a Science?" Around the turn of the 20th century there was a crisis of confidence in science that undermined the "method" work of people like C.S. Peirce and produced people like Duhem (and laid the groundwork for Einstein). Prior to that, historians expected history to become a science with as much rigor as physics. After that, there was a lot of hand-wringing about whether history had any value at all, which has progressed into much purple prose extolling its metaphysical benefits. Einstein et al lifted physics out of that swamp. So far, it seems to me physics is the
only science that has risen out of that swamp.
I'm willing to look at a particular passage if you have a citation, but I'm not willing to read an entire book to find an example to support your claim. That strikes me as your job, and I really don't have the time this month anyway.
Yes, reading books is hard, isn't it.
I don't read everything people link to on the Internet either. My level of interest and the credibility of the poster plays into whether I read it. But I have read books because they were recommended in forums like this. I'll take your reply as a polite euphimism. Regardless, I've thought of another example from physics that I can give - one that Wiccan suggested to me some time back.
Regardless, unresolved issues have little to do with incommensurability, since both sides in most scientific disputes agree on what kinds of data will settle the issue.
The example I could explain best is #12, to which you didn't respond. But, since you don't have time right now, I doubt we could reach the depth necessary for you to grasp it.
Also, we need to be careful not to confuse 2 topics here. Assumptions and incommensurability can be, but are not necessarily linked. They are 2 different topics.
More to the point, I don't see what unresolved issues and any assumptions underlying them have to do with disagreements between biologists and creationists. Creationists dispute things that have been resolved within science.
Uh huh. I appreciate your honesty in admitting the approximate nature of biology, but it leaves me baffled that you would then make statements like this. I have said before that this becomes an issue of evidence, and that I consider much of the evidence that evolution relies on (depending on how you define the scope of the conversation) to be historical, not scientific. However, every time I approach the issue of quantified/qualified with someone, that discussion seems to die out.
Since I don't know what a fixed point means in this context, I can't comment.
I didn't mean you had to answer every example. My point was that if you choose to play the ultimate skeptic, you'll always have a way to wiggle out. It's the nature of debate. If I'm going to pick one of these examples, it wouldn't be this one. But I'll explain further anyway. From there forward, since you seem to need an example from physics, let's focus on "force," as that is the one I can best explain.
Anyway, the "fixed point" example centers on the difference between a Cartesian approach that assumes a fixed frame of reference and the Einsteinian approach that assumes everything is relative.
Your concerns are well founded. You asked about assumptions in science, not in math.
Physics is heavily based on math. Changing the 5th postulate assumption had not only a major impact on math, but on physics as well.
As has already been said, you need to make assumptions in order to do or think anything interesting. As far as I am concerned, science is an enterprise that judges models, including their assumptions, on how well they permit us to explain, predict and manipulate natural phenomena. If two sets of assumptions are identically effective, then they are equivalent and there is no scientific reason for choosing one or the other. If they do not, then there are grounds, at least potentially, for choosing one.
The emphasis is mine, as it is the part I want to focus on. This is exactly what an assumption is. One is faced with a choice, but doesn't have an explicit method for choosing between the two. That doesn't mean the choice is arbitrary. Euclid chose his answer to the 5th postulate based on what his personal experience seemed to indicate. In truth, his choice remains much more intuitive to me that others. I'd have to question the honesty (and/or sanity) of anyone who says differently. Yet, even though he was convinced of the truth of his choice, he couldn't prove it using the method he had adopted. Therefore, the honest approach was to identify it as a postulate.
Within mathematics the 5th postulate remains (and will forever remain) an open question. The reason for rejecting Euclid and going with Riemann in modern physics is because of the explanatory power demonstrated by Einstein. But that doesn't make Einstein's choice "right." If Einstein demonstrated anything, it was that we may find in the future that we need to change that assumption yet again.
And that is the new example I was reminded of (#13 I suppose). The quote from Wiccan is this, "CM is good for low-speed, middle-sized things. QM is good for the very small, SR for the very fast, and GR for the very large and the very massive (and SR is a part of GR). Since QM and GR deal with different things, they rarely interact. But in the case of black holes, you have something very heavy (GR) and something very small (QM). They don't agree." IOW, whether one chooses GR or QM (and, implicitly, the relative assumptions of them) will determine what prediction is made. Assuming the logic of both is sound, what else can one conclude but that it is the assumptions that cause them to differ? Of course, if you have an insight into where the logic of one might be wrong, I'd very much like to hear that.
Anyway, let's move on to force. This is an example proposed by Ernest Nagel, and one that radically changed my view of mechanics. In fact, it led me to investigate some incommensurate ideas for my own work. The example is simply this: Newton's 2nd law can be stated as F = ma. This is not really a "law," but a postulate. It proposes an ideal that can never be perfectly tested. As you mentioned earlier, it assumes rigid bodies.
What is interesting, however, is that even though this law can never be demonstrated (it can only be approximated), no one questions it. When people found an obvious discrepancy regarding flexible bodies, they simply amended the ideal with Hooke's law. Later it was amended with Rayleigh's work on damping. And this will continue forever. There is
never a reason to question the ideal. Instead, people will simply continue to amend the ideal with new forces.
And yet there are alternatives to Newton's ideal. The example given by Nagel was one proposed by Jean Buridan that, rather than force being necessary to sustain acceleration, force is necessary to sustain velocity. It is an equally valid assumption, and one that could generate an equally valid mechanical model (even though it may not be as parsimonious - that I don't know since Buridan's proposal was never developed as far as Newton's).
The point is, that how one defines "force" can lead one to different conclusions about a system. As I said, I worked on some alternatives for my own work, so after you digest this I can give an example of what differences this can produce.
