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.…
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.
Roderick Long’s essay “On Making Small Contributions to Evil” tackles a deep problem in ethics and rational actor theory. Suppose you, individually, decide to stop recycling – will that make any detectable difference for the environment? Suppose you stop eating meat for ethical reasons – will that result in the death of even one less animal? Suppose you vote in the general election – will that make any detectable difference to the election result? Most likely: no, no, no.
This seems like a problem. It feels like there are ethical imperatives involved here – certainly, we should recycle if it is good for the environment. At the same time, are there really ethical imperatives without consequences? Does that make sense?
Eradication of evil as a public good
Long’s essay conceptualizes this issue as one about the provision of public goods. Public goods are goods that are non-excludable (that is, it is very difficult to exclude someone from using them) and non-rivalrous (their utility isn’t diminished by one more person’s use). A beautiful sunset is an example: anyone can benefit and it doesn’t diminish anyone’s benefit if an additional person benefits. Same goes for lighthouses, national security, and asteroid defense.
Public goods tend to be underprovided by the market because of the “free-rider problem”: if the good is non-excludable, why would you ever pay for it? If you had the choice, would you pay in for national security? Why bother? Even if you don’t, so long as your neighbors do, you’ll still benefit.…