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). See here for an introduction from Franz. Commentaries and replies will follow Wednesday through Friday. Derek Lam’s commentary proceeds in two parts; see yesterday’s post for Part 1.

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Modeling the Internal Chaos (II)

Picking back up from where I left off in yesterday’s commentary, if Berto’s logic describes an idealized scientific model of human thoughts, whether it is good partly depends on how well it allows us to represent the crucial aspects of the target phenomena, the same way any other empirical psychological models are evaluated. Berto has shown his formal language’s promise in handling a wide range of observation in human psychology. In this part of my commentary, I examine how well it represents two phenomena in belief-revision: (1) a-ha moments and (2) cross-attitude thoughts.

A-HA MOMENTS. Let me focus on the conditional version of his logic. Berto’s logic doesn’t only model conditional relations among beliefs within a time-slice; he also intends it to model the dynamics of belief-revision. As much as our trains of thought often stay on topic, we don’t always do so. By that, I don’t just mean the occasional slip-ups and loss of focus, which can reasonably be omitted in an idealized model. Wandering off-topic seems to be a crucial and positive part of human thought process. Among other things, it produces the eureka moments that we tend to celebrate.

Associationist thoughts are a big part of creativity. A creative thought process involves people jumping from one thought to another, bringing them together, even if they seem irrelevant to each other. This can happen when people break through a creative block while doing and thinking about something irrelevant. We even try to consciously exploit this feature of human thought sometimes. When we are stuck with a problem, we take a break to do and think about something else, hoping that this can trigger our creativity and new insights about the problem. Kekulé (allegedly) saw a snake in his dream and his belief about the snake led to his belief about the structure of a benzene ring: Bqp so that q = “a snake bites its own tail” and p = “benzene has a ring molecular structure”. (Recall from yesterday’s post that Bqp represents conditional belief, “a belief that p given a belief that q.”) Or, someone may go through a thought process while baking cookies that stimulates them to an a-ha moment of a creative solution to a maths problem they were working on before. In all these cases, a person comes to believe one thing because they hold belief about another thing, yet the two things are not related in topic.

This presents a prima facie difficulty for the formal languages based on TSIMs. Focusing on their application to belief-revision, the semantics of Bqp requires that for Bqp to be true, the topic of q wholly contains the topic of p; Berto labeled this SX (p.65). If q’s topic does not engulf p’s topic, Bqp is false in all TSIMs — not just that it isn’t valid. As flexible TSIMs are in letting Berto’s logic represent our thought processes, they don’t let us describe models of human thoughts that represent doxastic jumps across topics no matter how we tweak the accessibility relation among possible worlds in the TSIMs. As long as SX is in place, Berto’s logic describes models that forbid creative thoughts.

I’m aware of a potential response. Given how little specifics we have about topic individuation,[1] perhaps there is a way to interpret our associationist thoughts so that not a single instance of them truly involves jumping from one topic to another distinct topic. I suppose this isn’t a good way out though. Perhaps I have read carelessly and missed something because saying so seems to imply that our thoughts are doomed to be forever trapped in the same topics as we move from one thought to the next (since we had our first thoughts?!), which seems plainly false even if we set a-ha moments aside. Prima facie, people go from one happy/depressive thought to another happy/depressive thought even if the two are not related in topic. (I take it that being a depressive thought doesn’t need to be part of the content and topic of the thought.)

(My comment so far has focused on belief-revisions, but perhaps the phenomenon of associationism is most pronounced in imagination. When we imagine things, a part of it is cohesive suppositional thinking as Berto’s ROMS suggests; but perhaps an even bigger part of it is our minds’ wandering from topic to topic: from the rain drops running down the bus window to an ugly breakup to Taylor Swift’s upcoming album. It seems the constraint of topics, despite the work it may do for us, makes it impossible to model not just some marginal aspects of imagination that can be idealized away, but what seems like an essential wandering aspect of imagination?)

An idealized model may omit and remain silent on things. But there still needs to be an answer to the question: under what context would it be an acceptable feature of a scientific model of human thoughts that it models cross-topic thinking as impossible? What can reasonably be idealized away in a model depends on the scientific purpose of the model. Perhaps Berto could say he isn’t modeling a person’s thought per se but a train of thought. When a person switches topics in their thoughts, that person starts a new train of thought. Berto’s logic isn’t meant for modeling our transitions from one train of thought to another. What this means is we need much more clarity on what we are trying to model so that we can see in a more principled manner what can be idealized away and what can’t. For example, what is a train of thought exactly so that we are supposed to agree that switching topics within a train of thought is impossible, which seems to happen in associationist thoughts? What’s the scientific rationale for choosing trains of thought as the unit of modeling? If narrowing the target of model is the answer, I’m curious to hear more what can be said about these questions.

CROSS-ATTITUDE THOUGHTS. Given that many of Berto’s formal languages’ fundamental building blocks are formulae in conditional form Xqp (again, not all), it seems that they can only represent connections among thoughts that involve only one kind of propositional attitude: a belief conditional on another belief, a piece of knowledge conditional on another piece of knowledge, one imagining conditional on another imagining.

It seems natural to wonder, to me at least, what we are supposed to make of the fact that human thoughts always involve a web of multiple propositional attitudes. For example, one can form a belief in light of an imagining. An athlete who imagines themselves winning a competition can lead them to believe that they are going to win it. And for some philosophers, imagination can justify forming beliefs, either about the actual world (Kind 2018), or about other possible worlds. Or the reverse: a paranoid person’s belief that someone has been conspiring against them behind their back can psychologically prime them into imagining things in a certain way. Such cross-attitude thinking is no less sensitive to the topics of thoughts. If a formal language based on TSIMs is designed to describe models specifically to represent how the topics of propositions shape human thoughts, it seems a big miss if the models cannot represent how the mereology of topics plays a role in cross-attitude thoughts. From the perspective of scientific modeling, what is the rationale behind having a model that compartmentalizes conditional connection within each type of propositional attitude when human thinking is never restricted this way?

Certainly, ideal models are meant to be somewhat detached from reality. But first, usually idealization in a scientific model is there to enhance our understanding of the explanatory structure of the modeled phenomenon. Secondly, de-idealization of an idealized model is typically possible. In this case, I need some help to see the explanatory purpose of this idealization. Stripping out cross-attitude interactions seems to create an alien psychology that matches our psychology only in very artificially limited scenarios. Realistically, for every single thought that we have, it is formed on the basis of so many other thoughts, so many other kinds of thoughts together. And I’m not sure I see how to de-idealize this aspect of Berto’s model to recover a fuller range of human thoughts with all the interactions among different kinds of thoughts. I wonder if Berto can say a bit more to help me better understand the considerations behind the idealization.

Notes

[1] That it seems we have so little specifics about topic individuation may be my small hesitation about having topics play an irreducible role: we seem to be replacing one obscure thing with another. I suppose that was one motivation that philosophers tried to reduce talk of content to the more tangible extensional notions. Although the reduction project definitely failed, the motivation to reduce remains. But I don’t want to dwell on this concern here.

REFERENCES

Berto, Franz. Forthcoming. Topics of Thought. Oxford University Press.

Kind, Amy. 2018. “How Imagination Gives Rise to Knowledge”. In Fiona Macpherson & Fabian Dorsch (ed.), Perceptual Imagination and Perceptual Memory. Oxford University Press: 227-246.

Reply to Derek’s commentary, Part 2

Derek is right that the topic-sensitive setting does not capture ‘a-ha moments’ – cognitively valuable associations of ideas not bound by any connection of topicality. It does not ‘describe models that forbid creative thoughts’ though: models don’t automatically forbid what they don’t capture! Surely our thought processes are not ‘doomed to be forever trapped in the same topics as we move from one thought to the next’. I only think that, at times, they are; and that, at times, they’d better be.

However, I suspect there’s a more specific worry to Derek’s a-ha moments point. It’s that demanding, as I do in ToT, that, e.g., for ‘Supposing P, one imagines that Q’ to be true, Q be fully on-topic with respect to P, is too draconian a requirement. I have something to say on this at the end of chapter 5, where, following ideas by Aybüke and Aaron Cotnoir, I propose to weaken topic-inclusion between P and Q into a topological connection; remark that this may look intuitively better, but doesn’t change the logic one bit; and take comfort from this.

Now I admit I’m less than perfectly happy with that reply already. Someone who has done better is Aybüke (again) and Tom Schoonen, who here introduce a distinction between the topic of the initial supposition and that of a whole exercise of mental simulation: in episodes of mental simulation unfolding in time, one can step completely outside of the initial suppositional topic, provided one stays within the boundaries of the overall topic of the imaginative exercise.

Derek’s final point has to do with cross-attitude thoughts: ‘human thoughts always involve a web of multiple propositional attitudes’, and so it’s a ‘big miss if the models cannot represent how the mereology of topics plays a role in cross-attitude thoughts.’ He is right that ToT has little to say on this. The way to go would be by having a multi-modal language and semantics combining various TSIMs, and checking for hopefully illuminating (in)validities. I didn’t do it in ToT for the addition of topics to modal-epistemic logic is relatively new, and the results may be surprising – in a good, but also in a bad way.

[That one can run into trouble by combining epistemic modals is no news to logicians. E.g., if one takes an S5 logic for knowledge, K; a KD45 logic (which is essentially S5 minus factivity) for belief, B; and combines the two via the plausible-looking bridge principles ‘If KP, then BP’ (knowledge implies belief), ‘If BP, then KBP’ (one knows what one believes), and ‘If BP, then BKP’ (one treats what one believes as if one knows it) – one can derive that BP iff KP: belief and knowledge collapse into one, which we certainly wouldn’t want.]

Now there have been surprising results with the TSIMs already (e.g., one I won’t explain, for it’s rather techy, has to do with the irreducibility of a dynamic topic-sensitive epistemic operator to static ones via standard reduction axioms in the style of Dynamic Epistemic Logic: see Section 4 of this). Overall, investigating the interactions between different topic-sensitive attitudes requires care and logical skills going beyond what I managed to do in ToT, which, as I explained in ch. 1, is a mere initial exploration of an idea.