Stephen Read: Bradwardine Solution to the Liar | Who Shaves the Barber? #42

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Bradwardine Liar
Thomas Bradwardine

For much of the 20th century, the Liar paradox has stood as an elusive and stubborn puzzle. The main solutions to it have significant drawbacks, such as blocking meaningful cases of self-reference or abandoning bivalence (the principle that all propositions are either true or false and not both). In recent decades, Stephen Read has rediscovered and defended a solution by the medieval thinker Thomas Bradwardine. If Bradwardine’s argument is correct, the liar sentence is simply false. When properly examined, its falsity does not imply its truth. Bradwardine shows this with a clever argument that does not require us to abandon classical logic or block self-reference. It does rely on a controversial principle, “closure”: any statement implicitly says (or means) everything that follows from what it says. Arguably, whether the Bradwardine solution succeeds or fails to conclusively solve the Liar depends on whether one accepts closure. In this interview, Stephen Read runs through Bradwardine’s argument in some detail, then defends it against a few objections.

Bradwardine’s argument is rather subtle and abstract and can be hard to follow verbally. Here’s a short written version of Bradwardine’s argument, with minimum symbolism, that shows each step and notes where logical principles are invoked.

Be sure to listen to the first half of this interview, where Stephen explains the Liar and its significance and solutions in the 20th century.

Next week: Jason Lee Byas: Against Criminal Justice



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

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Dialetheism: From Language to Reality

A physical contradiction?

I recently published a post in defense of dialetheism. I argued that in the case of statements about “man-made” states of affairs, it is obvious that some contradictions are true. For example, the law can easily contradict itself in such a way that a statement about what is legally mandated be a true contradiction. I invented “Timmy the Square Circle” to show that, similarly, there can be true contradictions about fictional characters. If this doesn’t seem intuitively obvious, read that post before this one.

The concluding paragraph included this teaser:

It is perhaps now tempting to draw a sharp line: the world of man-made ideas allows for true contradictions, reality doesn’t. However, this line is not so sharp.

If we grant that there are true contradictions about what is made up, does this tell us anything about whether there are true contradictions about objective reality? To say there are is a stronger, and intuitively harder to swallow, version of dialetheism. As we’ll see, however, there is no way to say anything about anything without talking, in part, about the man-made. This inescapable fact leaves open the possibility of true contradiction in claims about the physical world, even if it’s the case that the physical world itself, independent of our descriptions of it, cannot be contradictory.

Conceptual reality: Liar and Sorites paradoxes

We first need to establish that there are different “levels” of objective reality, and accepting a contradiction in one level may be much more counterintuitive than in another level.…

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Greg Restall: Objections to Logical Pluralism and the Preface and Liar Paradoxes | Who Shaves the Barber? #17

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Greg Restall

In the first half of my interview with Professor Greg Restall, he laid out logical pluralism: the view that there is more than one correct logical consequence relation. In this second half, he responds to objections. Specifically, he explains why it makes sense to admit inconsistent situations even if one believes, as he does, that all possible worlds are consistent. He also touches on the relationship between notions of deductive validity and reasoning norms. We then take an extended detour into the Preface paradox, the Liar paradox, dialetheism, and the relationship between proof theory and philosophy.



Next week: Tomasz Kaye, Pt. 1: Foundations for Political Philosophy

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

Topics discussed

0:38 – Logical pluralism recap
1:00 – Why admit inconsistent situations?
15:24 – Relationship between logic, reasoning, and normativity
21:50 – Preface paradox and normativity
34:10 – Dialetheism
38:15 – Bradwardine on the Liar
42:15 – Becoming a logician
44:30 – Proof theory and philosophy


Logical Pluralism by Jc Beall and Greg Restall – Greg Restall’s website
Proof Theory and Philosophy by Greg Restall (book manuscript in progress)
The Liar Paradox from John Buridan to Thomas Bradwardine” by Stephen Read
Models of Liars in Bradwardine’s Theory of Truth” by Greg Restall
Normativity of Logic and the Preface Paradox” by William Nava…

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