Against Certainty, Pt. 2: Logic | Who Shaves the Barber? #13

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What about 2+2=4? Can we be 100% sure of that?

In this second part of my case against 100% certainty, I tackle claims to logical certainty. These include appeals to the three fundamental laws of logic: the Law of Excluded Middle, the Law of Non-Contradiction, and the Law of Identity. To call excluded middle into doubt, I discuss non-referring terms, vagueness, fuzzy logic, and Aristotle’s problem of future contingents. For contradiction, the topics are legal contradictions, the Liar paradox, and Zeno’s Arrow. To argue against certainty of the law of identity, I cover Theseus’s ship, problems with time, problems of mereology, and the universe of symmetrical spheres. I then argue that even claims like “2+2=4” and “bachelors are bachelors” can’t be fully foolproof. Finally, a quick barrage of skeptical concerns – concerns that, while they may not be enough to justify a self-defeating view like skepticism, are enough to block claims to 100% certainty.



Next week: The Case for Anarchism, Pt. 1: Social Ontology
Special thanks for Jackie Blum for the podcast art, and The Tin Box for the theme music.

Topics discussed:

0:20 – Quick pt. 1 recap
1:21 – Introducing claims to logical certainty
2:21 – Classical logic, syllogistic logic, and the 3 laws
5:48 – Law of Excluded Middle
6:45 – Non-referring terms: the present king of France
9:16 – Vagueness and fuzzy logic
12:11 – Future contingents
13:51 – Law of Non-Contradiction – DeMorgan’s Law
15:38 – The legal case
18:22 – Liar paradox
22:09 – Zeno’s arrow
26:45 – Law of Identity – Theseus’s ship
29:26 – Content of an instant
31:17 – Mereological – Tibbles
36:06 – Symmetrical spheres
37:47 – Do we understand identity?

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The Münchhausen Trilemma

There are many forms of radical skepticism: skepticism of the external world, skepticism of other minds, and skepticism of rationality, to name just a few. They arrive at skepticism via different channels, some more successful than others.

Agrippan skepticism is an ancient Greek variety. It is perhaps the hardest-hitting attack on the possibility of knowledge in the history of philosophy. I don’t know of any satisfactory solution.

Epistemologists agree on this much: in order for a belief to count as knowledge, it needs to be at least a justified true belief. What does it mean for a belief to be justified? It means we have a reason for believing it. If this reason will work as justification, it must be a reason that we know.

Of course, if we know this reason, it must be a justified true belief. So what is its justification? It has to be some other reason that we know. And we’re off on a regress.

The problem can be put this way: justification can only happen in three ways:

  • Regress argument: belief A is justified by belief B, which is justified by belief C, which is justified by belief D, and so on.
  • Circular argument: belief A is justified by belief B, which is justified by belief A.
  • Dogmatic argument: belief A is axiomatic. It requires no justification.

None of these options succeed in justifying a belief. Regress arguments fail to justify because they never bottom out at some belief that is already justified.…

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