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.
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).
I'm moderately confident that I don't live in a computer simulation.
My reasoning goes like this.
A priori, simulation scenarios are less probable than
non-simulation scenarios.
My evidence is more likely in non-simulation scenarios than in
simulation scenarios.
So: It is highly improbable, given my evidence, that I'm in a
simulation scenario.
By a "simulation scenario", I mean a scenario in which a subject's
experiences of themselves and their environment are generated by a
computer program that simulates an ordinary (non-simulated) subject and
their environment.
I assume that it is a priori possible for a computer program to
generate experiences (and a "subject") by simulating an ordinary subject
with experiences. I'm not 100% sure this is true. (If not, premise 1 can
be strengthened: simulation scenarios have probability 0.) But it seems
plausible, especially if we're liberal about what qualifies as a
computer program and as a simulation.
Sensory information is centred. Right now, for example, my visual
system conveys to me that there's a red wall about 1 metre
ahead (among much else); it does not convey that Wolfgang
Schwarz is about 1 metre away from a red wall on 22 January 2026 at
12:04 UTC.
We can quibble over what exactly is part of the sensory information.
We can also quibble over what "sensory information" is even meant to be.
But it should be uncontroversial that we gain information from our
senses. My point is that, on any plausible way of spelling this out, the
information we receive is centred: it doesn't have parameters that fix a
unique location in space and time. If I were unsure about what time it
is or who I am, looking at the wall in front of me wouldn't help. The
underlying reason, of course, is that photoreceptors are insensitive to
differences in spatiotemporal location: they don't produce different
outputs depending on where or when they are activated by photons.
I (somewhat randomly) picked up Kripke 2011 the other day. This
is Kripke's first engagement with the problem of empty names. What
struck me is the biased selection of examples. Most of the paper is
concerned with names of fictional characters like 'Sherlock Holmes', and
Kripke only seems to consider simple utterances in which they figure as
the subject, like (1).
A somewhat appealing (albeit, to me, also somewhat obscure) view of
mathematics is the pluralist doctrine that every consistent mathematical
theory is true, insofar as it accurately describes some mathematical
structure. I want to comment on a potential worry for this view,
mentioned in (Clarke-Doane 2020): that
it has implausible consequences for logic.