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:
Here's an attractive picture. All there really is, at a fundamental
level, are fields in spacetime (or something like that). The world as we
know it, with its rocks and chairs and cats and people, somehow emerges
from this basis: all truths about rocks and chairs etc. are made true by
truths about fields in spacetime. But how? To explain this, it would
help if we could locate the familiar objects – rocks and chairs etc. –
in the physical description of reality. With the help of classical
mereology, which is plausibly analytic, this
seems possible: ordinary objects can be identified with aggregates of
spacetime points. They are regions in spacetime. With this, we can
explain how simple facts involving ordinary objects can emerge. For
example, what makes it true that my chair has steel legs is that its
region has a certain kind of subregion with high-amplitude excitations
of quark and electron fields in a certain arrangement.
I taught two courses this year that I haven't taught before. One of
them was our 4th-year undergraduate course on mathematical logic,
"Logic, Computability, and Incompleteness". As usual, I ended up writing
my own textbook. Here it
is as PDF and here as
HTML.
Why yet another textbook? Two reasons mainly. One is that many
existing textbooks are addressed at maths students. This shows up not
only in the examples and illustrations, but also in the fact that
comparatively little time is spent motivating, explaining, and
discussing definitions, proof ideas, or results. I wanted more of
that.