The philosopher of linguistics and mathematics Stephen Yablo kindly granted me an interview earlier this year. Yablo’s work on fictionalism has been a huge inspiration to me in my recent work, and I greatly enjoyed the chance to question him about it.
Chris Bateman: You first gained attention for your short paper, Paradox without Self-Reference (published in 1993) which describes a version of the famous Liars Paradox (“This sentence is false”). You called your version the omega-liar, but it’s come to be called Yablo’s paradox. How does it feel to have a paradox named after you, and what do you think about this paper in retrospect?
Stephen Yablo: Right, it’s a variant of the Liar paradox that is not supposed to involve any circularity or self-reference. Instead of one sentence describing itself as false (which is what the Liar does), my paradox involves an infinite series of sentences each describing all its successors as false. I have a bit of an idiot savant feeling about that paradox, actually. I thought of it, all right, but it didn’t seem like a big deal to me. It took other people, mainly Saul Kripke and Thomas Forster, to explain its real significance to me.
Chris: I’m rather fond of Kripke’s philosophy. What’s his connection to your work?
Stephen: Funny story about that: the paradox originally appeared in a 1985 paper called “Truth and Reflection.” I was still in graduate school at UC Berkeley then. One day Kripke called from the east coast about it. I wasn’t home, however, so he got into a conversation with my housemate Kayley. I would’ve given anything to talk to the guy. But by the time I got home, he and Kayley were deep into the metaphysics of time zones and he’d forgotten all about me. I never did find out what he’d been wanting to say to me.
Chris: You make considerable use of Professor Walton’s make-believe theory of representation (also known as pretence theory, or prop theory) in your later work. When did you first come across Walton’s prop theory of representation, and what attracted you to his approach?
Stephen: I came across the theory in the late 80s or early 90s, which I think may been when he was working it out. We were colleagues at Michigan along with David Hills, now at Stanford, and we all spent a fair bit of time talking about “serious” uses of make-believe. I remember one camping trip in particular where he explained the way pretense could help us make sense of sentences like “Hamlet doesn’t really exist.” But I wasn’t all that interested in metaphor and the arts, which is what he was mostly trying to explicate with his stuff on prop-oriented make believe. I asked Ken one day whether he’d thought about applying his theory outside of aesthetics, to issues in heavy-duty metaphysics. He said, “No, why don’t you do it?” So with his permission, that’s what I did.
Chris: In 1998, you published a paper entitled “Does Ontology Rest on a Mistake”? that explores the classic debate between W.V. Quine and Rudolf Carnap over ontology – the question of what can be said to exist. Using prop theory, you conclude that the kind of ontology Quine hoped for – whereby we can know what kind of things exist by trusting in our most reliable models – was unworkable because of the sheer extent to which metaphor pervades our models. You wrote this paper as if you started out on Quine’s side, but then veered over into Carnap’s. How did this happen?
Stephen: I was on Quine’s side to the extent that I thought he had the best way of making ontology rigorous. I think I ended with something like this: “It is not out of any dislike for Quine’s method – on the contrary, it’s because I revere it as ontology’s last, best hope – that I conclude that philosophical existence-questions are moot. If they had answers, Quine’s method would turn them up. It doesn’t, so they don’t.” Quine lost the debate, in my mind, because he trusted science to drive out the metaphors, leaving behind the literal truth. I didn’t see why metaphorical entities couldn’t earn a permanent place in our theories.
Chris: Speaking of metaphorical entities, you mention in a footnote in the 1998 paper that mathematical entities lack “naturalistic connections” that “prevent reference relations and epistemic access”, and then add “I take it that mathematical objects exhibit these features to a higher degree than, say, God, or theoretical entities in physics.” What motivated you to include this aside?
Stephen: I think of some existence questions as sillier than others. Whether numbers are “really there,” for instance, is a sillier question than whether God exists, or electrons do. But it is not so easy to keep these issues apart. Numbers aren’t directly experienced. But it’s not as though we directly experience electrons, either. Both of them, one might think, are theoretical postulates of some sort. I was trying to find a way of being unserious about theoretical entities in math that didn’t force me to take a similar view of theoretical entities in physics.
Chris: Since the 1998 paper, you’ve expanded your ideas into a robust form of “hermeneutic fictionalism” – a term used pejoratively by Jason Stanley, but that you have taken over as your own. How would you summarise hermeneutic fictionalism in layman’s terms?
Stephen: John Burgess introduced a distinction between “revolutionary” nominalism, which says we should stop believing in mathematical objects, and “hermeneutic” nominalism, which says we never did believe in them, appearances to the contrary owing to a over-literalistic take on mathematical language. Stanley’s distinction is meant to be a generalization of that. The hermeneutic fictionalist is someone who thinks we tie ourselves in unnecessary knots by insisting that ordinary ways of talking are always to be taken literally. So, to use an old example of Wittgenstein’s, if someone says they “married money,” we do ourselves no favours by hunting around for the money they married. Likewise there’s no point in trying to make room in your world-view for the “hurdles they put in my path.” Wittgenstein thought a lot of philosophical problems were based in a kind of semantic over-scrupulosity, and he encouraged us to just get over it. The hermeneutic fictionalist takes in many cases a similar view.
Chris: You propose that numbers can be best understood in terms of Walton’s concept of prop-oriented make-believe, saying: “Rather as ‘smarts’ are conjured up as metaphorical carriers of intelligence, ‘numbers’ are conjured up as metaphorical measures of cardinality”. The idea of numbers as metaphors isn’t entirely new, but putting it in terms of prop-theory is an inspired twist, and one that pulls the rug out from under Platonic objects entirely. Since quite a few philosophers are rather attached to Plato’s version of realism, has your stance generated a lot of vocal opposition?
Stephen: Platonic realists say, “abstract objects are special and sublime; the bar is high, but they clear it.” Deflationary realists say, “the bar is so low that it would be hard for them not to clear it. If you doubt the number of planets exists, that just shows you have an exaggerated idea of what its existence would involve. Worrying that there are planets, but no such thing as ‘their number’, is like worrying that people are married, but that doesn’t make them a ‘married couple.’ What more could the existence of couples possibly involve?” I get more flak from deflationary realists than Platonic ones; the Platonic ones mostly ignore me. I like it that way, to be honest, because I feel some attraction to the deflationary view myself. The reason I’m not a deflationist is that I don’t see where to get off the train. If couples exist, why not lines of argument? If there are lines of argument, why not things I never got around to doing? If they exist, why not nonexistent planets like Vulcan? Now we’ve gone too far, though; if something is by hypothesis nonexistent, then I think we are entitled to assume it doesn’t exist.