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  <title>wo's weblog</title>
  <link>https://www.umsu.de/blog/</link>
  <description>Musings in Analytic Philosophy</description>

  <item>
    <title>Comment by wo on 'Teaching mathematical logic'</title>
    <link>https://www.umsu.de/blog/2026/829#c2475</link>
    <guid>https://www.umsu.de/blog/2026/829#c2475</guid>
    <pubDate>Mon, 11 May 2026 14:54:54 +0000</pubDate>
    <description><![CDATA[No, sorry, I didn&#039;t write up the solutions.]]></description>
  </item>
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    <title>Comment by Harriet Baber on 'Teaching mathematical logic'</title>
    <link>https://www.umsu.de/blog/2026/829#c2474</link>
    <guid>https://www.umsu.de/blog/2026/829#c2474</guid>
    <pubDate>Sun, 10 May 2026 18:28:21 +0000</pubDate>
    <description><![CDATA[Are there solutions to the exercises? I looked through but couldn&#039;t find.]]></description>
  </item>
    <item>
    <title>Teaching mathematical logic</title>
    <link>https://www.umsu.de/blog/2026/829</link>
    <guid>https://www.umsu.de/blog/2026/829</guid>
    <pubDate>Thu, 30 Apr 2026 15:38:00 +0000</pubDate>
    <description><![CDATA[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 mot...]]></description>
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    <title>Comment by Alexander Pruss on 'Gödel, Mechanism, Paradox'</title>
    <link>https://www.umsu.de/blog/2025/823#c2473</link>
    <guid>https://www.umsu.de/blog/2025/823#c2473</guid>
    <pubDate>Mon, 20 Apr 2026 14:47:08 +0000</pubDate>
    <description><![CDATA[Here&#039;s a variant that uses a non-factive operator (inspired by Modal Liars). Let P be epistemic possibility, e.g., understood as consistency with what I know. Construct G such that PA proves: G iff ¬P(⌜G⌝). Suppose G. Then G is not consistent with what I know. But all truths are consistent with what I know. So, ¬G. So P(⌜G⌝). But now this looks paradoxical: surely I know ¬G, having seen the proof, so G isn&#039;t consistent with what I know. Fun!

I think it&#039;s a bit har...]]></description>
  </item>
    <item>
    <title>Comment by wo on 'Gödel, Mechanism, Paradox'</title>
    <link>https://www.umsu.de/blog/2025/823#c2472</link>
    <guid>https://www.umsu.de/blog/2025/823#c2472</guid>
    <pubDate>Mon, 20 Apr 2026 10:49:27 +0000</pubDate>
    <description><![CDATA[Nice! <br />
<br />
More generally, the fact that knowledge entails truth makes it not too surprising that sentential accounts of knowledge (knowledge predicates that apply to sentences, rather than e.g. sets of worlds) run into paradox. My interest in paradoxes for sentential belief stems partly from trying to show that the paradoxes for sentential attitudes don&#039;t simply piggy-back on the Liar.<br />
]]></description>
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    <title>Comment by Alexander Pruss on 'Gödel, Mechanism, Paradox'</title>
    <link>https://www.umsu.de/blog/2025/823#c2471</link>
    <guid>https://www.umsu.de/blog/2025/823#c2471</guid>
    <pubDate>Mon, 20 Apr 2026 01:01:05 +0000</pubDate>
    <description><![CDATA[Another thought on your formalized Knower. It feels very close to just a formalized contingent Liar. Here&#039;s why. Start by noting that K(p) is something like T(p)∧JBPlus(p) (knowledge is true justified belief plus). Let K*(p) be T(p)∧M(p) for any contingent M(p). The same argument gives ¬K*(⌜G⌝) and G for an analogous G to yours. But if G, then T(⌜G⌝). (This is the more controversial half of the T-schema, so one could push back, which is why I used the weasel phrase &quot;ver...]]></description>
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    <title>Comment by wo on 'Gödel, Mechanism, Paradox'</title>
    <link>https://www.umsu.de/blog/2025/823#c2470</link>
    <guid>https://www.umsu.de/blog/2025/823#c2470</guid>
    <pubDate>Sun, 19 Apr 2026 05:53:36 +0000</pubDate>
    <description><![CDATA[@Alexander: Thanks.

Maybe you&#039;re right that we can&#039;t fully grasp the meaning of G, although (1) by the MRDP theorem there&#039;s a version of G that&#039;s &quot;just&quot; a diophantine equation, and (2) I&#039;m not sure how much is required to grasp the meaning of a mathematical statement in general. But more importantly (as you mention) the paradox returns if we reason about the knowledge of smarter agents, so I still think it cautions against assuming that we have a clear gr...]]></description>
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    <title>Comment by Alexander Pruss on 'Gödel, Mechanism, Paradox'</title>
    <link>https://www.umsu.de/blog/2025/823#c2469</link>
    <guid>https://www.umsu.de/blog/2025/823#c2469</guid>
    <pubDate>Fri, 17 Apr 2026 17:48:03 +0000</pubDate>
    <description><![CDATA[What I just said stupidly missed what K(n) means. I now take it that K(n) means that n is the number of a sentence that expresses a proposition that I know, not that I know that a sentence with number n is true. So you don&#039;t have to believe any proposition about the big messy number ⌜G⌝ to have K(⌜G⌝). 

That said, I think a variant of my point still works. The sentence G is a very long nasty complicated sentence in the language of arithmetic (a concatenation-theoretic version ...]]></description>
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    <title>Comment by Alexander Pruss on 'Gödel, Mechanism, Paradox'</title>
    <link>https://www.umsu.de/blog/2025/823#c2468</link>
    <guid>https://www.umsu.de/blog/2025/823#c2468</guid>
    <pubDate>Fri, 17 Apr 2026 15:36:02 +0000</pubDate>
    <description><![CDATA[Here&#039;s a really naive thought. It&#039;s obvious that ¬K(⌜G⌝). Why? Well, it is well within human abilities to write out G and write out a proof that G ↔︎ ¬K(⌜G⌝), and so on. At the end you will write a gigantic numeral, which happens to equal ⌜G⌝, followed by the words &quot;is the Godel number of a true sentence.&quot; If you believed this final sentence, you would have K(⌜G⌝). But you don&#039;t believe this sentence, because the number referred to by the giganti...]]></description>
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    <item>
    <title>The tyranny of the objective</title>
    <link>https://www.umsu.de/blog/2026/828</link>
    <guid>https://www.umsu.de/blog/2026/828</guid>
    <pubDate>Fri, 20 Feb 2026 16:39:33 +0000</pubDate>
    <description><![CDATA[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 ...]]></description>
  </item>
    <item>
    <title>Are we living in a computer simulation?</title>
    <link>https://www.umsu.de/blog/2026/827</link>
    <guid>https://www.umsu.de/blog/2026/827</guid>
    <pubDate>Mon, 09 Feb 2026 16:10:17 +0000</pubDate>
    <description><![CDATA[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 progra...]]></description>
  </item>
    <item>
    <title>Integrating centred information</title>
    <link>https://www.umsu.de/blog/2026/826</link>
    <guid>https://www.umsu.de/blog/2026/826</guid>
    <pubDate>Thu, 22 Jan 2026 14:30:37 +0000</pubDate>
    <description><![CDATA[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, ...]]></description>
  </item>
    <item>
    <title>Kripke on empty names</title>
    <link>https://www.umsu.de/blog/2026/825</link>
    <guid>https://www.umsu.de/blog/2026/825</guid>
    <pubDate>Mon, 12 Jan 2026 10:27:25 +0000</pubDate>
    <description><![CDATA[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).
(1)Sherlock Holmes is a detective.
He argues, plausibly enough, that an apparent assertion of (1) should
be understood as a preten...]]></description>
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