Peter Klein: Infinitism and Pyrrhonism | Who Shaves the Barber? #36

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Suppose you know X. How do you know? Maybe you know because of Y. How do you know Y? Maybe the answer is Z. How do you know Z?

This is the regress problem of knowledge, also called the Agrippan trilemma and the Münchhausen trilemma. It is based on the supposition that if we claim to know something, we must have a reason for it and that reason must itself be something that we know. This leaves open four possible solutions. One is skepticism, the belief that we have no knowledge. The most common is foundationalism, which posits certain basic facts that require no external reasons to be justified. Another option is coherentism, which solves the problem via a kind of circular reasoning or justification loop. And finally, there is infinitism, the view that there is no end to the regress. For any chain of justification, the final member of the chain will always be unjustified, and it is always possible to go looking for further reasons of reasons of reasons. As infinitist Peter Klein puts it, knowledge is never “settled”. Even so, says Klein, it is still possible to have knowledge. In this interview, Klein first argues why he thinks coherentism, foundationalism, and a certain kind of skepticism all fail. He then explains his own account of justification, as “something that we do”, and how it makes the infinitist picture look more plausible than it first seems.…

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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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Timothy Williamson: Vagueness | Who Shaves the Barber? #33

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The problem of vagueness stems from the sorites paradox. A heap of sand cannot be turned into a non-heap by removing a single grain of sand. A short person cannot become tall by growing one millimeter. Someone who is sober cannot become drunk by ingesting one-tenth of a milliliter of alcohol. These conditionals hold regardless of what we take as our starting conditions. But if this is true, we can iterate the conditionals many times over, until we can prove that one grain of sand makes a heap, an 8-ft. tall man isn’t tall, and someone who’s just ingested a liter of alcohol is sober.

This ancient paradox has become one of the toughest puzzles in contemporary metaphysics and philosophical logic. During our conversation, Professor Timothy Williamson explains and rejects a few approaches, including supervaluationismfuzzy logic, nihilism, and contextualism. His preferred solution, known as epistemicism, is much simpler: all vague predicates have a precise cutoff point – we just can’t know where it is. Williamson supports this counterintuitive view with compelling accounts of meaning and knowledge. Meaning, he explains, is determined in part by aggregate use; since we cannot know all of the factors of aggregate use, we cannot know the exact meanings of vague terms. From this, we can infer that there are many cases in which we know something but do not know that we know it.

Interested in vagueness? Check out my interview with Graham Priest on the sorites paradox.…

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