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 anythingabout 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.…
Why do students go to school? The usual answer is to learn. But if this is true, why do students rejoice at canceled class? Why do they prefer an easy “A” instructor over a difficult one who has more to offer? Why don’t they just sit in on classes for free, which you can do at many of the best schools? And why is the final year of school so much more lucrative than other years, given that we don’t usually learn more that year?
These problems and others fall into place when we consider that we go to school more for the degree than for the education. The main purpose of education is to send a signal to employers, says economist Bryan Caplan. Employers pay more for college-educated employees not because what they learned in school was itself useful, but because the fact that they got the degree demonstrates that they must be generally smart, disciplined, and conformist. This makes little difference to the individual – you should still go to school and send that signal. But for society, this makes education a bad deal; status, unlike learning, is zero-sum, making much of the education system a waste of resources. In this interview, Caplan explains the signaling model in more detail, addresses objections, and predicts what would happen if his prescriptions were followed.
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 supervaluationism, fuzzy 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.