Steve Patterson: Certainty and Logic | Who Shaves the Barber? #26

Download this episode / Watch on YouTube / RSS Feed / iTunes

Steve Patterson

Steve Patterson’s book Square One: The Foundations of Knowledge begins with the bold claim: “Truth is discoverable. I’m certain of it.” The rest of the book is an attempt to prove that there are certain truths for which there is not a sliver of doubt.

I am, to say the least, unconvinced. Universal fallibilism – the claim that all knowledge leaves room for doubt – is, ironically enough, a view I’m particularly confident of (though, obviously, not certain of). Indeed, I did a two-part podcast on this topic (Against Certainty: Knowledge and Experience and Against Certainty: Logic). In this interview, I challenge Steve’s claims to certainty with my skeptical doubts. The conversation takes us through the Münhhausen Trilemma, the nature of justification, subjective experience, and, of course, the ever-popular liar paradox.

Audio

Video

Next week: Catarina Dutilh Novaes: Logic as Social Practice

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.
Click here for the full list of episodes!

Topics discussed

0:41 – The goal of certainty
2:59 – Agrippan trilemma
6:37 – Certainty v. necessity (epistemology v. metaphysics)
19:08 – Justification (grounds for belief)
25:42 – Certainty about experience v. certainty about logical truths
29:03 – Meditating on experience
31:40 – Presuppositions of skepticism?
41:50 – Negation
43:32 – “Logic and existence are inseparable”
47:28 – Philosophy of language
49:50 – Liar paradox, negation, and the possibility of contradiction

Sources

Square One: The Foundations of Knowledge by Steve Patterson
How to Resolve the Liar’s Paradox” by Steve Patterson (video)…

Continue Reading →

Greg Restall: Logical Pluralism | WSB #16

Download this episode / Watch on YouTube / RSS Feed / iTunes

Greg Restall

What is logical pluralism? Greg Restall, logician and Professor of Philosophy from the University of Melbourne joins me to answer this question.

When we study logic, we’re concerned with consequence or entailment: what follows from what. But what are the criteria for being “consequence”? Professor Restall says there are three: necessity, formality, and normativity. Given these criteria, he argues there is more than one relation worthy of the name “consequence”. In other words, there is more than one system of logic that correctly represents our informal grasp of necessary entailment. This is because logical rules operate differently depending on the sort of “case” they’re functioning in. Among various, Professor Restall highlights two types of cases: “possible worlds” and “situations”. The first fit classical logic, the second paraconsistent logic. Though they differ on what kinds of arguments are valid, they both correctly represent deductive reasoning. Professor Restall explains why this makes perfect sense.

Audio

Video

Next week: Greg Restall: Objections to Logical Pluralism, and the Preface and Liar Paradoxes

Special thanks to Jackie Blum for the podcast art, and The Tin Box for the theme music.

Topics discussed

0:20 – Introduction to Greg Restall
1:49 – What is logic about?
12:41 – The metaphysics of logic
21:20 – What is logical pluralism?
22:52 – The criteria for consequence
24:32 – Necessity
25:37 – Formality
27:17 – Normativity
33:15 – The role of cases: classical v. paraconsistent logics
39:10 – Possible worlds v.…

Continue Reading →

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

Download this episode / Watch on YouTube / RSS Feed / iTunes

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.

Audio

Video

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?

Continue Reading →