Doubt itself rests only on what is beyond doubt… But
since a language-game is something that consists in the recurrent
procedures of the game in time, it seems impossible to say in any
individual case that such-and-such must be beyond doubt if
there is to be a language-game—though it is right enough to say
that as a rule some empirical judgment or other must be beyond
doubt.

3. Peter Unger's view is an
exception. He directs the attack on the psychological condition which
he takes to be required for knowledge, namely certainty. He thinks
very little, if anything, is such that we are certain of it since
“certainty” is an absolute term. Further, he claims that
since “certainty” is an absolute term, if we are more
(nearly) certain of x than we are of y, y
cannot be something about which we are certain. And virtually
everything is such that we are more (nearly) certain of something
else. See Unger 1975.

4.
There is no term
readily available. A natural one would be “cognitivist” but that term
already has a very specific application in ethics. “Cognitist” just
strikes my ears as cacophonic.

5. Sextus Empiricus,
Outlines of Pyrrhonism, I:226. Also see his discussion of
Carneades in Against the Logicians, I:159–190. The “logicians”
were considered to be dogmatists by Sextus. (In fact, the essays
against the logicians were part of his larger work called “Against the
Dogmatists.” See the preface by Bury, ibid., vii.)

7.
For a contrasting
discussion of the realm of the doubtful, see Stroud 1984, Chapter
1.

8. I say
“seriously” here because, in fact, the next ground for
doubt that he mentions is that perhaps he is mad (insane). He asks
whether he could be mad and like the people who imagine that they are
kings when they are in reality poor, or that they are clothed when
they are naked, or that they are pumpkins or made of glass. His answer
is “But they are mad, and I should not be any the less insane
were I to follow examples so extravagant” (Descartes 1931,
p. 145). This is somewhat puzzling because on the face of it, the evil
genius hypothesis seems no less “extravagant.” One way of
explaining this way of rejecting the possibility that he is insane as
a genuine basis for doubt is to embrace the minimal counter-evidence
account (discussed later) of what makes a proposition a genuine ground
for doubt. If a genuine ground for doubt must be a proposition for
which there is some evidence, however minimal, then the lack of any
evidence for the proposition that he is insane would disqualify that
proposition as a genuine ground for doubt. Perhaps Descartes means
that it would be mad for him to seriously entertain something for
which he has no evidence whatsoever.

9. Strictly speaking,
condition (1) entails (3), and hence, (3) is not needed. For if
S did have a way of neutralizing the effect of d,
then adding d to S's beliefs would not have the
effect of making assenting to p no longer adequately
justified. That is, ~(3) entails ~(1). (3) was included to make
clear the distinction between denying the potential ground for doubt
and neutralizing it.

10.
See, for example,
DeRose and Warfield 1999. In that volume most of the authors take the
CP-style argument to be the primary one. There is an excellent
discussion of Academic Skepticism in the Introduction to that
volume.

11. For the sake of
clarity, it is important to point out that the neutralizing
proposition, n, could itself have a genuine ground for
doubt, d1, so that even if (n
& d) did not reduce the warrant for
x, [(n & d) &
d1] could defeat the justification for x
because d1 would defeat the restoring effect of
n. But then, (d & d1) would
be a new grounds for doubt. So, we need not include this epicycle.

12. In other words, every
contrary is a potential genuine grounds for doubt but not every
genuine grounds for doubt is a defeater.

13. The probability could
be either subjective or objective. The reason for including
“non-overridden” in the supposition is that it would not
be sufficient for S to be entitled to believe something
if S only had good enough grounds to render a proposition
sufficiently likely to be true because S might also have
counter evidence that overrides those positive grounds.

20. The caricature is
mentioned by Diogenes Laertius, but is also somewhat mitigated by
pointing out that the suspension of assent was only “his
philosophy” and that Pyrrho lived to be nearly ninety. Here is
what he says:

He [Pyrrho] led a life consistent with his doctrine, going
out of his way for nothing, taking no precaution, but facing all risks
as they came, whether carts, precipices, dogs or what not, and,
generally leaving nothing to the arbitrament of the senses; but he was
kept out of harm's way by his friends who…used to follow close
after him. But Aenesidemus says that it was only his philosophy that
was based upon suspension of judgement, and that he did not lack
foresight in his everyday acts. He lived to be nearly
ninety. (Diogenes Laertius, Lives of Eminent Philosophers, Bk
IX, 62)

21. Strictly speaking,
there seem to be two other possibilities: 1) there are foundational
propositions and there is an infinite number of propositions
between the foundational proposition and the one for which reasons are
initially being sought; (2) the number of propositions in the circle
is infinite. Interestingly, such hybrid views might be
indistinguishable in practice from infinitism and, hence, for our
purposes we can treat both of these as forms of infinitism.

22. These are glosses on a
selection of the best arguments. No claim is made that the
Pyrrhonians gave these very arguments.

23. The matter is put that
way in order to make clear that foundationalism can embrace some
aspects of coherentism. Basic propositions with only minimal
justification, if coherent, could gain additional credibility. Thus,
this account of foundationalism includes both weak and strong
foundationalism as characterized in BonJour 1978.