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.
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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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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