Those of you interested in complexes of deductive
and inductive warrant, and blends of linguistic
meaning, imaginary worlds, and causal
explanation, might have fun sorting out the following
classics:
"Treason doth never prosper: what's the
reason? For if it prosper, none dare call it
treason." Sir John Harington, Epigrams, bk. 4, no.
5 (1591).
"Changes are real. Now, changes are only
possible in time, and therefore time must be
something real." Immanuel Kant, Critique of Pure
Reason, "Transcendental Aesthetic," section II
(1781).
"Does the past exist? No. Does the future
exist? No. Then only the present exists. Yes. But
within the present there is no lapse of time? Quite
so. Then time does not exist? Oh, I wish you
wouldn't be so tiresome." Bertrand Russell, Human
Knowledge.
"Nothing is demonstrable unless the contrary
implies a contradiction. Nothing that is distinctly
conceivable implies a contradiction. Whatever we
conceive as existent, we can also conceive as
non-existent. There is no being, therefore, whose
nonexistence implies a contradiction.
Consequently there is no being whose existence is
demonstrable." David Hume, Dialogues
Concerning Natural Religion, part IX (1779).
"What is politically good, cannot be morally
bad, unless the rules of arithmetic, which are good
for a large number, are bad for a small one."
Jeremy Bentham, Principles of Legislation (1802).
Kant says nothing, but to join the rest of this vein, here's my favorite,
also from Hume (A Treatise of Human Nature, Book I, Section XII, 1739.
We may observe, that there is no probability so great as not to allow of a
contrary possibility; because otherwise 'twou'd cease to be a probability,
and wou'd become a certainty.
So what are we to make of such passages?
Are they not to be regarded as serious arguments,
or serious lines of reasoning? Even leaving aside
our poets and mystics, our novelists and
rhetoricians -- although I'm not sure why we should
leave them aside! -- our tradition is still filled with
what purports to be warranted inferences -- yet
inferences in forms not usually sported by our
scientists and lawyers (although the latter often
come closer). Vern.
I draw two conclusions:
1) Probability trees should be more often employed when presenting formal
arguments (and perhaps in UAI).
2) The 'logic' of induction must be normative rather tautological.
With regard to the first point, I highly recommend Hacking's discussion of
Pascal's Wager on the Existence of God in The Emergence of Probability
(1976). With regard to the second point, it's pretty hard to improve on
Locke and Hume.