3.  Here is the Incommensurability argument.  Incommensurability is a very complicated issue; I will give only an inadequate sketch.
    When we're deciding whether to accept a particular theory, we compare the theory to its competitors to see whether it outstrips them in explanatory goodness.  But what is it for theories to be mutual competitors or rivals in the first place?  Intuitively, it's for one of the theories to say something about X or about F's and the other theory to say something incompatible with what the first one says.  T₁ says that X is an F and that all F's are G's; T₂ says that X is not an F and that some F's are not G's.  T₁ and T₂ cannot both be correct.   Rival theories, we believe, have overlapping referents; they refer to, and are about, some of the same things and kinds of thing.
    Not so, say Feyerabend<1> and Kuhn<2>.  The theoretical terms of a theory get their meanings in a special way: not, as you might think, directly from what they refer to.  Rather, the terms are implicitly defined by their containing theories, according to the respective roles they play in those theories.  Since the theories say different things using the terms, it follows that the same terms don't mean the same things from theory to theory.  Therefore, when T₁ says that X is an F and T₂ says that X is not an F, they are not really disagreeing, but talking past each other; "X" and "F" do not mean the same as between the two theories.  For example, "mass" in Special Relativity does not mean the same as "mass" in Newtonian mechanics, so Special Relativity is not disagreeing with Newton and so is not a competitor or rival of Newtonian mechanics (at least on that point).  The theories are mutually incommensurable.  And if they are incommensurable, they cannot be compared.  In particular, we cannot say in any absolute sense that one is a better theory or explanation than the other.
    (Some critics of this argument have contested the incommensurability thesis; some have objected only to the move from incommensurability to incomparability.)

    4.  The Meta-Induction:  One thing that stands out about the history of science is that all previous theories have been false, mistaken, at least on some important points.  (Duhh; that's why we don't hold them any more.)  Now, remember the pattern of inference that I called "enumerative induction":  "N% of all the observed F's have been G's / So, roughly N% of all F's are G's."  Let N = 100, the F's be scientific theories, and the G's be false scientific theories!   Conclusion:  Roughly every single one of all scientific theories, including of course our present ones, is false.  (The sample seems of sufficient size, and there does not seem to be any bias in it.)
    The point is sometimes added that our current theories are actually known to be false even by the people who hold them.  There are always known exceptions, or deliberate idealizations.

    5.  Suppose you are a skeptic about the explanatory virtues, as is the neoPositivist Bas van Fraassen<3>.   Simplicity and neatness and conservativeness and the rest are nice, and it's natural and understandable that we like them, but they are just not marks of truth; their value is pragmatic and aesthetic only.  Now plug in a second premise, which I think is a nearly indisputable one (though van Fraassen disputes it):  One cannot choose a theory in any science without appealing to one or more of the explanatory virtues.  It follows that no scientific theory is one that we are justified in believing to be true.  From the point of view of evidence and nothing but, no theory is any more rationally justified than any other.

    There; I've finished yesterday's lecture.

    By the way, I will be making fairly constant additions to the "Documents" page of our web site.  Today I've added a couple of articles from the Stanford Encyclopedia of Philosophy (which work as a whole I recommend), and a Feyerabend site that I found.

 Now, about our three philosophies of science and the potential conflicts between science and religion:  The potential for bothersome conflict is obvious only if we are Scientific Realists.  (Philip Kitcher is, as you can guess from reading his book, a Scientific Realist.  So am I.)
    If we are Historicist Relativists, and we don't believe that scientific theories are rationally justified (except possibly relative to this or that), then it will not trouble us if our religious views come into conflict with a scientific theory, for there will be nothing irrational about simply rejecting the theory.
    If we are Positivists, the situation is a little more complicated, because the Positivist holds that the relevant scientific theories are true, denying only that they assert anything that outruns the observable.  For a Positivist, then, a conflict between a religious claim and science would have to be a conflict between the religious claim and an actual or hypothetical scientific observation.
    Another interesting complication is that the Positivists themselves thought that religious claims--at least theological ones--had been shown meaningless by the Verifiability Principle because they are unverifiable; what is meaningless cannot conflict with anything.  (However, I myself think it's fairly obvious that theological claims are verifiable in the Positivist sense.   I bet you can think of a possible set of experiences that would tend to confirm the existence of God; I certainly can.)
    A famous 19th-century English naturalist and divine named Philip Gosse experienced a very sharp conflict between his fundamentalist religious views and his firm belief in Darwinian evolution by natural selection.  He resolved that conflict, in his book Omphalos, by propounding a very prescient early version of instrumentalism.  I'll take a few minutes and tell you that story next Thursday.
 
 

1 Against Method (Schocken Books, 1977).

2 The Structure of Scientific Revolutions, 2nd edition (University of Chicago Press, 1971).

3 The Scientific Image (Oxford University Press, 1980).