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.
Do we have any reason to doubt appearances? And does perception show us intermediary mental representations or real objects themselves?
Michael Huemer’s first book, Skepticism and the Veil of Perception, tackles both these questions at once. Huemer is a direct realist: he thinks that when we perceive, we’re perceiving reality directly. This contradicts the common philosophical position (“indirect realism”) that our perception is of mental objects which are images or representations of real objects to which we have no direct access. The usual challenges against direct realism involve an appeal to illusion and hallucination, though Huemer argues that these are less problematic than is often suggested. Huemer also argues that a direct realism (along with a correct general approach to epistemology) helps refute the famous skeptical arguments: the infinite regress of justification (the “Agrippan trilemma“), the “problem of the criterion“, the famous brain in the vat, and Hume’s argument against the possibility of induction.
Steve Patterson’s book Square One: The Foundations of Knowledge begins with the bold claim: “Truth is discoverable. I’m certain of it.” The rest of the book is an attempt to prove that there are certain truths for which there is not a sliver of doubt.
I am, to say the least, unconvinced. Universal fallibilism – the claim that all knowledge leaves room for doubt – is, ironically enough, a view I’m particularly confident of (though, obviously, not certain of). Indeed, I did a two-part podcast on this topic (Against Certainty: Knowledge and Experience and Against Certainty: Logic). In this interview, I challenge Steve’s claims to certainty with my skeptical doubts. The conversation takes us through the Münhhausen Trilemma, the nature of justification, subjective experience, and, of course, the ever-popular liar paradox.
0:41 – The goal of certainty
2:59 – Agrippan trilemma
6:37 – Certainty v. necessity (epistemology v. metaphysics)
19:08 – Justification (grounds for belief)
25:42 – Certainty about experience v. certainty about logical truths
29:03 – Meditating on experience
31:40 – Presuppositions of skepticism?
41:50 – Negation
43:32 – “Logic and existence are inseparable”
47:28 – Philosophy of language
49:50 – Liar paradox, negation, and the possibility of contradiction