A peculiar question that has divided philosophers since the Middle
Ages (and possibly earlier) concerns the status of Conditional
Excluded Middle. CEM says that for any propositions A and C, either
C would be the case if A were the case, or ¬C would be the case if A
were the case. Some accept CEM as valid, others reject it. In the last
few decades, the CEM supporters have been gaining ground, especially in
the field of semantics. See, for example, Williams 2010, Moss 2013,
Mandelkern
2018, Shaffer and Beebe 2019, Cariani and
Goldstein 2020, Marty, Romoli, and Santorio
2020, and Ramotowska et al.
2025.
There's a lively literature on how graded beliefs (credences) relate
to ungraded beliefs. Some hold that ungraded beliefs are reducible to
credences, others that credences are reducible to ungraded beliefs; yet
others hold that both are real and irreducible to one another. I find
this debate confusing. By which of course I mean: confused. I'll try to
explain why. I'll also comment on one particular proposal, that
credences are beliefs about probability; an interestingly new version of
this has just been defended in Buchanan and Dogramaci
2026.
First, why I find the debate confusing. Imagine a parallel debate
about desire. Desires patently vary in strength: we desire some things
more than others. In decision theory, an agent's desires are represented
by a utility (or "desirability") function that assigns numbers to
propositions; the higher the number, the stronger the desire. Now
imagine someone asks how these graded desires relate to ungraded
desires: are graded desires reducible to ungraded ones, or the other way
round?
"Neg-raising" occurs when a negation that appears to have wide scope
(over some operator) is interpreted as having narrow scope. For example,
(1) conveys not only the absence of a belief that pizza is available (as
one might expect), but also the presence of a belief that pizza is
unavailable.
(1)I don't think there's any pizza.
There is a large literature on this phenomenon, with many competing
explanations. Foolishly, I've tried to contribute to this literature
with a new proposal.
My proposal is that neg-raising is an instance of a more general
phenomenon whereby negative utterances are interpreted as conveying
positive information. (2), for example, tends to convey not only that
Jack didn't sing Hey Jude, but also that Jack sang something
else – especially if Hey Jude has intonational focus.
Gerritsen
2023 raises a good worry about revolutionary moral fictionalism,
as advocated in Joyce
2001.
The (revolutionary moral) fictionalist says that our naive moral
practice rests on the mistaken assumption that there are
mind-independent moral facts. There are no such facts. But this doesn't
mean that we should stop caring about morality. It is in our personal
interest, according to the fictionalist, to adopt a fiction of morality
and continue talking and acting much like before.
Standard Bayesianism assumes that agents are "logically omniscient":
they assign credence 1 to all necessary truths. This seems wrong.
But we need to be clear about the data (as Stalnaker has emphasized,
for example in 1991 and 1999). It's
not a datum that we don't give credence 1 to all necessary truths.
"Credence" is a theoretical term. The data that cast doubt on logical
omniscience are things like this:
Imagine a community of people who pass encrypted messages to one
another, without knowing what they mean. Agent X has encrypted a message
and handed it to messenger A, who passes it to messenger B, who passes
it to agent Y, who has the codebook to decrypt the message. When A
utters the message to B, she has no idea what it says; neither does
B.
Intuitively, the meaning or content of A's
utterance is the content of the decrypted message. That's why A and B
don't know what the utterance means.
I finally got around to adding the papers from Janssen-Lauret and Macbride
2023 to the search corpus at https://www.david-lewis.org. It's
a wonderful collection with lots of treasures. I want to comment on an
intriguing passage on pp.71f., from an abandoned 1969 textbook project
on confirmation theory.
First, some context. At this point in the manuscript, Lewis has
introduced \(\mathcal{M}\) as a
probability measure on the propositions expressible in a language \(\mathcal{L}\) with classical boolean
connectives; \(\mathcal{C}\) is the
associated conditional probability measure, defined by the ratio
formula. Lewis notes that conditional probabilities are often read as
"the probability of C if A", which suggests that \(\mathcal{C}(C/A)\) might equal \(\mathcal{M}(C\textit{ if }A)\), where
'\(C\textit{ if }A\)' is the material
conditional. But that's obviously false. Lewis continues: