I want to shift to the arena of testing the adequacy of
statistical models and misspecification testing (leading up to articles by Aris Spanos, Andrew Gelman, and David Hendry). But first, a couple of informal, philosophical mini-posts, if only to clarify terms we will need (each has a mini test at the end).
1. How do we obtain knowledge, and how can we get more of it?
Few people doubt that science
is successful and that it makes progress. This remains true for the philosopher
of science, despite her tendency to skepticism. By contrast, most of us think
we know a lot of things, and that science is one of our best ways of acquiring
knowledge. But how do we justify our lack
of skepticism? Any adequate account of the success of science has to square
with the fact of limited data, with unobserved and unobservable phenomena, with
theories underdetermined by data, and with the slings and arrows of the threat
of error. Intent on supplying such an account, I’m drawn not toward some ideal
form of knowledge “deep down,” nor toward some perfectly rational agent, but
simply toward illuminating how in fact we get the kinds of knowledge we manage to obtain—and
how to get more of it!
As such, the centrally relevant question is: How do we learn about
the world despite threats of error?
2. Inductive inference as “Evidence Transcending”
The risk of error enters because we want
to find things out—make claims or take action—based on limited
information. When we move beyond
the data to claims that are “evidence transcending,”
the argument, strictly speaking, is inductive. The premises can be true while
the conclusion inferred may be false—without a logical contradiction.
Conceiving of inductive inference, very generally, as “evidence-transcending”
or “ampliative” reasoning frees us to talk about induction without presupposing
certain special forms it can take.
Notably, while mathematical probability arises
in inductive inference, there are two rival positions on its role:
·
to quantify the degree of confidence, belief, or support to assign
to a hypothesis or claim (given data x); and
·
to quantify how reliably probed, well-tested, or corroborated a claim is (given data x).
This contrast is at the heart
of a philosophical scrutiny of statistical accounts.
Confusion about induction and
the threat of the so-called philosophical problem of induction have made some
people afraid to use the word—even statisticians, who could in fact be teaching
philosophers about it. Such fears,
however, are unwarranted, once it is properly understood. But more important, even those who
claim to restrict themselves to variations on “deductive” falsification must
warrant their premises empirically, as that arch falsificationist Karl Popper
knew only too well.
3. Popper, Probabilism and Severe Tests
Since Popper keeps popping up
in the statistical literature (e.g., in Stephen Senn, Andrew Gelman), let me try without philosophical fanfare to say something
about him. In one sense Popper was
a skeptic: he didn’t think we could justify hypotheses as either true or
probably true—he rejected “probabilism” (also called “inductivism,” which is
confusing). Yet he still thought
science was successful and that there were rational methods of science.
Consider the two views of
probability just given. The first view, that probability arises to assign
degrees of belief, truth, or support to hypotheses, goes hand in hand with the
conception that claims are warranted by being either true or probable. Popperians also call this probabilism or justificationism, and we can retain those terms. When it is said
that Popper was an anti-inductivist, what is really meant is that he rejected
probabilism. He did not reject the
idea that it was possible to warrant evidence-transcending claims. Instead, he required that
evidence-transcending claims be accepted (or preferred, or inferred) only if
they have been subjected to, and have passed, stringent tests. Probability,
accordingly, arose in the second sense.
Here, probability is best seen as
characterizing the properties of a method or rule, which we may call a method
of testing.
For example, a
good testing rule might be one that with high probability would falsify a
hypothesis H if false, but not
otherwise. For Popper, a hypothesis was well corroborated only to the extent
that it passed a severe attempt to falsify it.
4. The Wedge between Skepticism and Irrationalism
This focus on using probability to qualify testing methods
(rather than claims) is the key that allowed Popper to “drive a wedge between
skepticism and irrationalism”. (e.g. Musgrave 1999, p. 322).
We can be skeptics about inductively inferring that H is probable---we
can reject probabilism outright---while still allowing warranted inferences to
H. We need only have rational
testing methods or rules.
We can allow
It
is warranted to infer H
to be open to
including any number of epistemological stances: It is warranted to infer
(believe, accept, prefer, act in accordance with) H.
Popperians oust probabilism but retain
rationality by defining rationality as following a rational method. A
rational method is one that infers (or claims to have evidence for) H only to
the extent that H has passed a severe test---a test which would have, with
reasonably high probability, detected a flaw in H, were it present.[i]
Popper
often viewed hypotheses as “solving problems” –where the problem could be
construed very generally. So we
might say that an irrational method is one that would, with high probability,
declare our problem solved, when in fact it was not (or not solved to a degree
specified). Such a method would to readily declare the problem solved
erroneously.
Popperians
escape the need to come up with a logic of (or methods for) confirmation—but they
still need methods for severe tests, and ways to evaluate tests on their
error-probing ability. Can this be
achieved? Stay tuned.
_______________________________________________
Mini-Test:What are the two uses of probability in inference?How does Popper drive a “wedge” between skepticism and irrationality?What is probabilism (or justificationism)?What would be an irrational method for solving a problem?
____________________________________________
Lakatos, I. 1978. The Methodology of Scientific Research Programmes. Edited by J. Worrall and G. Currie. Vol. 1 of Philosophical Papers. CUP.
Mayo, D. 1996. Error and the Growth of Experimental Knowledge. Chicago: University
of Chicago Press.
Mayo, D. 2011. “Statistical Science
and Philosophy of Science: Where Do/Should They Meet in 2011 (and Beyond)?”
Rationality, Markets and Morals (RMM) Vol. 2: 79-109.
Musgrave, A. 1999. Essays in
Realism and Rationalism. Amsterdam: Rodopi; Atlanta, GA.
Popper,
K. 1959. The Logic of Scientific
Discovery. New York: Basic Books.
Popper,
K. 1983. Realism and the aim of Science. NJ: Rowman and Littlefield.
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