Chris obtained his PhD from Ruhr University Bochum, Germany on “Logic(s) of Imagination” in 2021. He has posted on this blog before, one time together with Tom Schoonen. Disclaimer: Chris has co-authored an article with Franz and Franz co-supervised Chris’ PhD. Nevertheless, Chris has tried his best to put on his critical glasses for this post.
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 follow Wednesday through Friday.
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What do logics of imagination give to philosophy?
Introduction
The major aim of Topics of Thought by Franz Berto is to provide formal models of our thoughts (for the sake of this entry, simply, “logics”). It is primarily concerned with logics for the mental states knowledge, belief, and imagination. In developing the respective logics, the book explores a new approach to the logic of thought – a new, unified way of answering the question: given that one thinks (believes, knows, etc.) that P, what other Qs does one think (believe, know, etc.) by the logic of one's thought? Under which logical operations is one's thought closed? (p. 2, notation adjusted)
Here is a general question: why do we need formal logics to answer this question? Doesn’t cognitive psychology provide us with the respective answers? What does the investigation of formal logics of mental states add to answering this question? I think these questions are especially pressing, given Franz’s methodology in the book seems to be – besides taking into account intuitions concerning certain validities – to heavily rely on results from cognitive psychology (and philosophy of mind) and then build logics that satisfy exactly the logically relevant features that cognitive psychology ascribes to the respective mental state.
Here is a non-comprehensive list of what I take logics could add to philosophy, other humanities, and the sciences, especially classical propositional logics and modal logics based on it:[1]
1. provide new insights and raise new, interesting questions about the concepts they aim to model (e.g. negation, the conditional, knowledge),
2. provide precise definition of “valid/sound argument” and typically at least one way of determining whether an argument is valid or not (e.g. truth-tables),
3. address and resolve paradoxes (e.g. liar-paradox),
4. disambiguate via formalization of natural language,
5. provide a means to formulate precise questions qua formalization.
For reasons of brevity, I’ll only talk about the logic of imagination from Chapter 5: Imagination and Suppositional Thought. I’ll briefly talk about Chapter 4: Epistemic Closure, Dogmatism, Scepticism, Fallibilism.
New insights and questions
To answer my question, let me first highlight what I consider to be the biggest achievement of the book with respect to the quote above: Franz offers a rather simple and elegant framework, which allows to treat all the aforementioned mental states, which he assumes are conditional, i.e. we always believe, know, imagine given some further information, some supposition, etc. The distinction between the logics of the mental states then relies solely on which logical rules they satisfy, which makes his approach quite modular, similar to standard modal logic. By offering this unified treatment, I think that Franz is living up to the aim of providing a logic of thought in general. Of course, the mental states might differ in their phenomenology and other aspects, but from a semantic perspective, according to Franz’s approach, they all work similarly and only differ in how strictly they constrain our going from one thought to another. Of course, one might want to debate that there is a class of such conditional mental states that behave similarly semantically in the way Franz describes. I think all this is clearly contributing to 1. from the list above.
Franz’s investigation of imagination as reality-oriented mental simulation covers a great deal of “typical” inferences from conditional logic. One such inference, which comes out as valid, is “Special Transitivity”: I(A, B), I(B, C) entails I(A, C).[2] That is, if in supposing A one imagines B, and in supposing B one imagines C, then in supposing A, one imagines C. I am not going to enter the battle of the counterexamples at this point. What I want to highlight is this: first, this is an inference, of which we can test whether people accept it or not, just as there is a huge literature on which types of conditionals people (don’t) accept. I am not aware of any research concerning this. Now, while there might be counterexamples to this inference, it is also worth testing, how convincing people find these counterexamples. Second, as this is an inference we can test of whether people reason according to it, the formal approach has actually now helped us formulate a research question for cognitive psychology. This might not come as a surprise for you but I think it is worth emphasising that trying to build a formal logic might in fact help us put certain inferences on the map, which we might not have thought of if we were doing “pure philosophy” or “pure cognitive psychology”. Finally, supposing the result of the experiments have been found, there is always the question, why do people attest to the inference or why do they not. Again, this is an interesting question to ask from the standpoint of cognitive psychology, or so I think. Again, all this suggests that Franz’s approach satisfies 1.
Missing application
While Franz’s logic of imagination comes with a definition of validity, what the chapter on imagination is missing, in my opinion, is an application of the logic to arguments in the debate about imagination, or debates close to it. That the general framework has the potential for this, we can see in Chapter 4, where Franz and Peter Hawke formalize the Kripke-Harman Dogmatism Paradox and show how it fails for, according to them, the right reasons. The right reasons have to do with the fact that we do not know all logical consequences of what we already know (no full closure) and that new information can affect what we know (non-monotonicity), both features that can be expressed precisely in the formal logic and which their logic of knowledge relative to information (KRI) satisfies.
In chapter 5, Franz briefly mentions the case of imaginative resistance when discussing his Success-principle, namely that I(A,A) is a theorem. (Which, by the way, reads “in supposing A, one imagines A” and would seem to imply that all supposition occurring in a reality-oriented mental simulation is imagination.) I would like to see how one of the stories from the philosophical literature describing a situation which prompts imaginative resistance would be formalized aand whether it really hangs on this principle whether we have a case of imaginative resistance at hand or not. I think that here we have the potential for disambiguation and precisification of what makes a little story a story prompting imaginative resistance in the imaginer, and, possibly, to more precisely state what imaginative resistance is (so, 3., 4., 5.). More generally, if we think of our engagement in thought-experiments as a case of reality-oriented mental simulation, then they seem to be promising candidates for being formalized and judged valid or not by Franz’s logic of imagination as well.
Conclusion
In conclusion, I think that the formal treatment of imagination in the book is an inspirational hub for logicians, philosophers of imagination, and cognitive psychologists to come up with interesting research questions about imagination. Other chapters, like chapter 4, of the book show the potential of the overall framework to formalize arguments and resolve/address paradoxes. However, in the case of the logic for imagination, this application is yet to be provided. I invite you to post in the comments examples of arguments, which you think could be fruitfully formalized by Franz’s logic.
Reply to Chris’ commentary
In spite of having ‘tried his best to put on his critical glasses’ for his former PhD supervisor, Chris has been too kind. As for his ‘New Insights and Questions’ section, one minor point there is that there’s no inferential schema named ‘Special Transitivity’ in ToT. There’s one called ‘Cautious Transitivity’ (maybe this is the one Chris has in mind, for, confusingly, I called it ‘Special Transitivity’ in some other work); but it doesn’t go as (in Chris’ notation): I(P, Q) and I(Q, R) entail I(P, R). That’s (General) Transitivity, which fails for the imagination operator of ch. 5 Chris is focusing on. (It holds for another operator, Knowability Relative to Information, from ch. 4.)
As for Special-Cautious Transitivity, it goes: I(P, Q) and I(P&Q, R) entail I(P, R): when supposing P one imagines Q, and supposing both P and Q one imagines R, then supposing P one imagines R. This only holds for the imagination operator if one buys a certain condition on the semantics, which I call ‘Equivalence in Imagination’ and discuss in section 5.4 of that chapter. It's an interesting story, for Equivalence in Imagination sounds plausible and gives a reasonably strong logic for suppositional thought; but it delivers Special-Cautious Transitivity, whose status is, I think, dubious. This said, I agree with all the rest Chris says in the ‘New Insight and Questions’ part of his commentary (unsurprisingly, since he only says good things about ToT ).
It’s more painful to agree with what he says in the ‘Missing Application’ part, but I’m afraid I have to: there is no application of the logic of imagination of ch. 5 to debates in the philosophy of imagination, comparable to the application of the logic of knowability of ch. 4 to the debate in mainstream epistemology triggered by the Kripke-Harman paradox. One case in which I merely hint at one debate, picked up by Chris, has to do with a very basic validity holding in the logic of imagination of ch. 5: when one starts by supposing P, e.g., because one is reading a fiction where it’s explicitly said that P, one imagines that P. On a natural reading, the logic seems to rule out cases of imaginative resistance, as famously studied by Gendler, where we’re prompted to imagine something by a work of fiction, but we resist doing so in spite of being perfectly on top of what the input is about.
Is the natural reading justified? Well, to begin with, it's easy to invalidate ‘Supposing P, one imagines that P’ in the TSIM setting anyway: one just drops a little constraint in the semantics of ch. 5 (which is not even in the basic TSIM setting of ch. 3), whereby the set of worlds the agent looks at supposing P only includes ones where P is true. Then the debate on imaginative resistance can be phrased as something like this: under which conditions, if any, does one who starts by supposing P, e.g., because one reads a story in which it’s said that P, fail to imagine a scenario where P? I just leave the question hanging in section 5.3. The missing application is simply due to the fact that I’m too ignorant on the debate around imaginative resistance to even start thinking how my TSIM logic of imagination might be applied to it in detail.