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.
A famous argument, first proposed in Lucas 1961, supposedly shows that the
human mind has capabilities that go beyond those of any Turing machine.
In its basic form, the argument goes like this.
Let S be the set of mathematical sentences that I accept as true. S
includes the axioms of Peano Arithmetic. Let S+ be the set of sentences
entailed by S. Suppose for reductio that my mind is equivalent to a
Turing machine. Then S is computably enumerable, and S+ is a computably
axiomatizable extension of Peano Arithmetic. So Gödel's First
Incompleteness Theorem applies: there is a true sentence G that is
unprovable in S+. By going through Gödel's reasoning, I can see that G
is true. So G is in S and thereby in S+. Contradiction!
I'm teaching an intermediate/advanced logic course this semester. So
I had to ask myself how to introduce the semantics of quantifiers, with
an eye on proving soundness and completeness. The standard approach,
going back to Tarski, defines a satisfaction relation between a formula,
a model, and an assignment function, and then defines truth by
supervaluating over all assignments. The main alternative, often found
in intro logic textbooks, is Mates' approach, where ∀xA(x) is defined as
true in a model M iff A(c) is true in every c-variant of M, where c is a
constant not occurring in A.