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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Vagueness

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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The Easy Case for Dialetheism: Timmy the Square Circle and Divaltopian Law

Dialetheism is the view that some contradictions are true. Put another way, dialetheists claim that there are propositions that are both true and false at the same time and in the same respect.

For many people, this is plain crazy. Others find it extremely counterintuitive but will grant it because they’ve heard quantum mechanics proves it. Others still may suspect it is a desperate response to certain logical paradoxes, such as the Liar.

I wish to argue that all of this is quite beside the point. I don’t understand quantum mechanics (at all), but I would be surprised if there were really no way to account for experimental data without recourse to true contradictions. I’m (somewhat) better versed in debates about logic. I can tell you with confidence: the paradoxes have plenty of coherent solutions. Philosophers disagree primarily on the relative costs and benefits of these solutions. If dialetheism were truly incoherent and demonstrably impossible, we wouldn’t be backed into it: cheaper options than insanity are for sale.

There is a much simpler reason to be a dialetheist: despite initial appearances, it is intuitively compelling and even quite obviously true. We need no special training in physics or logic to see this.

Before getting on with the argument, a quick clarification about a misinterpretation of dialetheism that I encounter alarmingly often: dialetheism is the view that there is at least one true contradiction. It is not the view that all contradictions are true. That view is actually nuts. For example, that my name is William Nava is only true, it is not also false.…

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