Franz is Chair of Logic and Metaphysics at the University of St Andrews-Arché and at the Institute for Logic, Language and Computation (ILLC) at the University of Amsterdam. He works on non-classical and modal logics, ontology and its methodology, and the philosophy of computation.
This week at The Junkyard we’re hosting a symposium on Franz Berto’s recent book Topics of Thought: The logic of knowledge, belief, and imagination (OUP 2022). Today we begin with an introduction from Franz. Commentaries and replies will follow Wednesday through Friday.
Topics of Thought [ToT] features two co-authors across four of its eight chapters, Aybüke Özgün and Peter Hawke. It’s a contribution to epistemic logic, broadly taken as the logic of knowing, believing, supposing, being informed... It’s inspired by (1) a traditional view of what it means to think that something is the case; and (2) recent developments in formal semantics.
As for (1): a way of understanding ‘One thinks (supposes, believes, knows, etc.) that P’ is that one has a sentence, say, of mentalese, tokened in the head (perhaps in a belief box, a knowledge box, etc., whatever these metaphors may mean). We may call this a syntactic way. ToT pursues a semantic way: one has an attitude towards a propositional content, that P, directed (a venerable name for this directedness is ‘intentionality’) towards whatever that proposition is about. Aboutness, says Steve Yablo on p. 1 of a celebrated book bearing this title, is ‘the relation that meaningful items bear to whatever it is that they are on or of or that they address or concern’. This is their topic or subject matter.
Which brings us to (2): an explosion of research in topic-sensitive semantics, thanks to the works of Lewis, Yablo, Fine, Gemes, Osorio-Kupferblum, Humberstone, Moltmann, Plebani & Spolaore, and more. Such works understand the topics of sentences in different ways. Some map topics to questions the sentences can be taken, in context, as answering to. The seminal Lewisian example of conversational topic was the number of stars (hence the stars on the ToT cover). It comes with the question, ‘What’s the number of stars?’. That splits modal space: two worlds end up in the same cell when they agree on the answer. The splitting gives what ‘There are ten stars’ can be about. Others take topics as given by states or (exact) truthmakers: ‘There are ten stars’ is about a situation which makes it true and which, unlike an entire possible world, is wholly relevant and responsible for its truth.
Anyway, a common theme is the dissatisfaction with the standard view that propositional contents are (just) sets of worlds because it offends what Yablo called ‘our sense of when sentences say the same thing’ (p. 2 of Aboutness). ‘Equilateral triangles are equiangular’ and ‘2 + 2 = 4’ are true at the same worlds but don’t say the same: only one is about how equilateral triangles are like. Topic-sensitive semantics are generally hyperintensional: they tend to individuate contents in a more fine-grained way than standard intensions.
Much work has focused on those ‘meaningful items’ which are declarative sentences. But, on the semantic conception, thoughts are ‘meaningful items’, too, and so have topics: when one thinks that John is tall and thin, one’s thought is, say, about John’s height and looks; when one supposes that the Fed will increase the interest rates, one’s supposition is, say, about what the Fed will do with the rates; when one believes that Mary is a lawyer, one’s belief is, say, about Mary’s job. To the traditional view that such attitudes have propositions as contents, ToT adds the idea that propositions are individuated (also) by what they are about.
Technically, it’s simple. In standard epistemic logic, (conditional or plain) belief, knowledge, etc., are taken as modals: quantifications of various kinds over worlds. One’s knowing that P is understood as P holding throughout a set of worlds representing how things may be for all one knows. One’s believing that Q conditional on P is understood as Q holding throughout a set of worlds one finds most plausible among those where P is true. ToT takes on board the standard framework (and so, capitalizes on the remarkable contribution provided by post-Hintikkan modal-epistemic logic to our understanding of knowledge, belief, information, etc.); adds topic-sensitivity, thereby getting a range of topic-sensitive intentional modals (TSIMs); and experiments with the results.
There are different TSIMs in ToT: some are two-place, some are one-place operators; some represent knowability relative to information; others, imagination qua reality-oriented mental simulation; others yet, plain and conditional belief. They’re mostly in for all-or-nothing, not graded, attitudes, but the last chapter gets into the connections between topicality and probabilities. Chapter 1 includes an overview of the rest of the book. You may download the book here: it’s free!
But if you’re in a rush, here’s the gist. When the topic of P is x, and one thinks (supposes, believes, etc.) that P, one must think about x, and this delivers logical closure features for the TSIMs. Yablo has a label: ‘immanent closure’ – closure under standard entailment and topic. Even supposedly logically anarchic mental deeds, such as imagining that something is the case, seem to comply with immanent closure. Try and imagine that John is tall and thin without imagining that John is tall. That would be as difficult as imagining that John is tall without imagining that John is tall, wouldn’t it? That is so, TSIM theory says, because what P is about is (a proper) part of what P & Q is about. And by thinking about the whole, you have already thought about the parts: there’s nothing more for you to do, such that if you failed to do it you’d be thinking that P & Q without thinking that P.
(This may draw a wedge between the semantic and syntactic conceptions: if thinking that P & Q is having a sentence of mentalese, say, ‘P & Q’, tokened in the head, one may need to do something to move from thinking that P & Q to thinking that P; and if one gets distracted while applying, say, Mental Conjunction Elimination, one may have the item ‘P & Q’ tokened in the head without having the item ‘P’ there: one will think that P & Q without thinking that P.)
But immanent closure is weaker than full closure under (classical, modal) logical consequence: one may think that P without thinking that Q although the former entails the latter, because one is not thinking about what Q is about: mere logical consequence is not topic-preserving.
That can happen in different ways. One may, for instance, believe that P without believing that P v Q although the former easily entails the latter, because one lacks some concept needed to grasp what Q is about; and one cannot have attitudes such as believing, supposing, etc., towards contents one cannot grasp. (Adapting Stalnaker: William III believed that England could avoid war with France, without believing that either England could avoid war with France or France could develop a nuclear arsenal; he had no idea what nuclear weapons might be, and so could not entertain thoughts about them.) So the TSIMs are good for modelling agents who, like us all, are subject to certain conceptual limitations.
Or, one who thinks that P may not think an entailed Q because one shouldn’t; and one shouldn’t because Q is off-topic, thus irrelevant, while one has good reasons to keep one’s thought focused. When one supposes that one jumps the river, trying to predict whether one would make it to the other side, that either two is prime or two is composite is a silly thing to think although the latter proposition follows from the former by (classical) logic. Off-topic necessary truths and consequences are a distraction. As Gilbert Harman forcefully argued, rational thinkers with limited resources shouldn’t clutter their minds with irrelevant stuff.
Among the things TSIMs can deal with are, e.g., how to address the Kripke-Harman dogmatism paradox (ch. 4) whereby knowing agents seem to be immune to rational persuasion via information bringing in new evidence. Or, how reality-oriented mental simulation can have epistemic value (ch. 5). Or, what goes on when we believe exactly one of two necessarily equivalent claims due to differences in what they are about (ch. 6), e.g., when one believes that Socrates exists without believing that {Socrates} exists; or, for a less philosophical example, when one believes that one’s job application has 60% chances of success, not that it has 40% chances of failure (a typical framing effect: ch. 7). Or (ch. 8), how comes that we sometimes don’t accept a conditional although the consequent is very likely given the antecedent (‘If the Fed causes a recession, then there’ll be some heads in the first 100 tosses of this fair coin’); or, although we accept the corresponding conjunction (‘Raccoons have no wings and they cannot breathe under water’ vs ‘If raccoons have no wings, then they cannot breathe under water’).
Now you will have spotted that some TSIM closure and closure failures seem to have to do more with how we usually think, some more with how we should think; which may have triggered the question: is the TSIM setting descriptive or normative? I’ll get to this in the replies to the commentaries, but to give it a polemical start: for the purpose of understanding what epistemic logicians do when they model mental states, the descriptive/normative distinction is, I think, overrated. It doesn’t even overlap well with the distinction between realistic and idealized-as-simplified, which is the one we should focus on.