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

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

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Thomas Bradwardine’s Solution to the Liar

I recently interviewed Stephen Read on Thomas Bradwardine’s solution to the Liar and Read rehearsed Bradwardine’s argument step-by-step. Since the specifics of the argument can be hard to follow (but also rather ingenious), I decided to try writing out a simplified version of the argument. I kept in a tiny bit of symbolism, for ease of presentation, but am not assuming familiarity with formal logic. I include reference and links to logical principles where they are invoked unless they are fairly obvious and intuitive (eg, double negation elimination). My intention was to make the argument as short and accessible as possible without sacrificing accuracy.

You can, of course, also find more thorough reconstructions of the argument at the Stanford Encyclopedia of Philosophy, in Stephen Read’s paper, and in Bradwardine’s book itself.

It should be said: Bradwardine assumes that a statement is true if and only if everything it says is the case.

The crucial move uses Bradwardine’s principle of “closure”: that all statements implicitly say everything that follows from the supposition that what they say is the case.

~ means “not” and T<L> means “L is true”.

Case 1: Suppose the Liar (L) says only that it itself is not true.

says [~T<L>]
Suppose L is not true (as it says). Then not everything it says is the case:
~~T<L>
T<L>
says [T<L>] (closure)

It is therefore not the case that L says only that it itself is not true (because if that were so, it would also mean that it’s true, contradicting the premise that it only says that it’s not true).…

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Stephen Read: Liar Paradox | WSB #41

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Stephen Read

“This sentence is false”. Is that sentence true or false? If it’s true, then what it says must hold; but what it says is that it’s false, so it must be false. But if it’s false, then what it says must not hold; but what it says is that it’s false, so it must not be false. But if it’s not false, it must be true. So if the sentence is true, it is false, and if it is false, it is true. The sentence, therefore, seems to be both true and false, which seems absurd.

Philosopher and logician Stephen Read is one of the preeminent scholars on this “liar paradox”. He is known, in large part, for rediscovering and defending a long forgotten solution to the paradox first proposed by the medieval philosopher Thomas Bradwardine. In this first half of our conversation, Read covers the paradox’s rich and influential history. It was first discovered, in its full form, in the 4th century BCE by Eubulides (who also first set down the sorites paradox). It became a central problem in the 20th century via its association with Russell’s Paradox, a major problem in the foundations of mathematics. Later in the century, two thinkers – Alfred Tarski and Saul Kripke – proposed monumentally influential theories of language and truth motivated, largely, by the paradox. But even after their contributions, the consensus is that the paradox remains unsolved. …

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