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
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?
“This sentence is false.” More ink has been spilled over the meaning of these four words than almost any other paradox in the history of philosophy. Why? What makes the Liar’s loopy reasoning more than just a party trick? How does the Liar challenge basic laws of logic and the meaning of truth? To understand the problems the Liar poses, we need to dive into its structure. What makes the Liar tick? Is it self-reference? What does it share with related paradoxes, like Russell’s paradox and the truth-teller paradox? What do the phenomena of “strengthened liars” and “circular liars” tell us about what’s at stake with this family of paradoxes?
0:04 – Intro
1:37 – Liar reasoning
2:40 – History of the Liar (Epimenides, Eubulides, Russell)
7:27 – Why it matters: excluded middle, non-contradiction, t-schema, self-reference
11:56 – 3 ways out
13:39 – “I am hereby lying”
14:57 – Circular liar
16:30 – Strengthened (revenge) liars
20:33 – Structure of the Liar
24:21 – Set theory disclaimer
25:57 – Russell’s paradox
28:30 – Properties
29:40 – Truth teller paradox
31:54 – Principle of uniform solution
Next week: Intro to the Liar, Part 2: Structure
Special thanks for Jackie Blum for the podcast art, and The Tin Box for the theme music.…
Chances are, if you’re reading this, you’ve heard me go on about a philosophy podcast I’m launching any moment now. Well, today’s the day. Concurrent with this post, I’m officially releasing episode one of Who Shaves the Barber? I’ll pretend you have questions and answer them:
It’s a weekly podcast – new episodes every Tuesday. Episodes will range anywhere from 40 – 90 mins (I’ll try to keep ’em short, but I’m a naturally long-winded fella). For some episodes (I’m aiming for about half-ish), I’ll interview philosophers. For the others, I’ll do my own presentation on a topic.
Oh, cool. Is there a more specific focus than just all philosophy?
The tagline is “Exploring paradoxes, thought experiments, and other pointless problems.” That doesn’t really answer your question, but it’s kinda relevant and I wanted to share it. (By the way, I don’t really think philosophy is pointless, I just like piss off people who take it very seriously [unless they’re my guests].)
The useless but most accurate answer is that I’ll be talking about whatever topics interest me. The more useful answer is that I’m most interested in paradoxes, philosophy of logic, philosophy of language, epistemology, skepticism, ontology, and metaphilosophy. In terms of focus and style, my presentation will tend to mesh most with the “analytic” tradition (although, as the scare quotes indicate, I’m skeptical of the premise behind the “split.” But that’s a topic for another day).
I’m not super knowledgeable. How much background knowledge are you assuming?