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.
A widely held view in philosophy is that ordinary information and
ordinary belief are concerned with "objective" propositions whose
truth-value doesn't vary between perspectives or locations within a
world.
Some hold that all genuine content is objective, and that the
appearance of counterexamples is an illusion that can somehow be
explained away. (See, e.g., Stalnaker 1981, Magidor 2015, or
Cappelen and
Dever 2013.) Even those who accept that there is genuinely
perspectival or self-locating information tend to treat it as a special
case that requires special rules for integration with ordinary,
non-perspectival information. (See, e.g., Bostrom 2002, Meacham 2008,
Moss 2012,
Titelbaum
2013, Builes 2020, or Isaacs, Hawthorne, and
Russell 2022).