Logic and Experimental Data
In the presence of lots of philosophers of methods, it's hard not to spend some time thinking about formal methods in philosophy. For a long time I've wanted to write something about what formal methods in philosophy are, and why we should keep on using them. But, since I've yet to formulate my thoughts on this, I'll compromise and give you some related thoughts about logic and experimental data. More precisely, experimental data and the model- vs proof-theory divide.
Although frequently labelled as one, I'm not at all the sort of hardline proof-theorist who finds no room in his philosophy of logic for model-theoretic techniques. (Does the hardliner exist? Yes - check out this paper by Tennant.) Quite the contrary, I believe the two approaches complement each other, both being equally valuable in formal methods broadly construed. Nevertheless, for particular purposes in one's philosophy of logic, preferring one over the other is sometimes right. Lots of philosophers share the suspicion that inference rules are somehow integral to acquiring and possessing logical concepts. And, accordingly, a lot of energy has been put into exploring the link between this idea and entitlement to infer. (Examples are Christopher Peacocke, Paul Boghossian, and Crispin Wright.)
Yet, in the spirit of experimental philosophy one might wonder whether or not the critical claim about concept-aquisition is empirical (and, further, experiment-susceptible). I started thinking harder about this issue after an introductory talk by Ruth Byrne, a leading expert on the mental model theory in psychology. The mental model theory is a theory of reasoning in psychology which is accompanied by numerous experimental results. Roughly, the theory says that human capacity to imagine mental scenarios or possibilities is what engenders basic inferences. The experimental work involves Wason task studies, studies on counterfactual reasoning, and on how children develop mental models. For some information about the programme, see the Mental Models Website. Actually, I noticed that the psychological theory is not entirely unconnected to its formal counterpart, model theory: In the SEP entry for model theory, Wilfrid Hodgson mentions mental models as cognitive theory support for the importance of model theory in logic.
Correspondingly, proof-theory has its own psychological counterpart. In fact, the mental model theory is a response to the idea that inference is a result of a rule-based mental capacity which relates to formal calculi. Byrne calls it the formal rule theory. As its model-theoretic rival, the formal rule theory offers experimental support for why reasoning as a psychological process is a largely rule-based affair. One source for this view is The Psychology of Proof (1994) by L. J. Rips.
You don't have to subscribe to experimental philosophy in its most rampant forms in order to see the value of connecting the above experimental work with the philosophy of logic. In fact, my hunch is that philosophers - although experimentally crippled (aka "don't try this at home") - can contribute to the experimental work with logical expertise. Actually, philosophers of logic have hypotheses about actual human reasoning that are primed for testing, and which aren't likely to be tested by psychologists who don't know discussions about, say, vagueness and semantic paradoxes. Earlier I've mentioned one admirable adventure into experimental research by Dave Ripley, and another by Jeff Pelletier.
My plan is to start out by checking out The Rational Imagination (2005, MIT Press) by Ruth Byrne.
Correspondingly, proof-theory has its own psychological counterpart. In fact, the mental model theory is a response to the idea that inference is a result of a rule-based mental capacity which relates to formal calculi. Byrne calls it the formal rule theory. As its model-theoretic rival, the formal rule theory offers experimental support for why reasoning as a psychological process is a largely rule-based affair. One source for this view is The Psychology of Proof (1994) by L. J. Rips.
You don't have to subscribe to experimental philosophy in its most rampant forms in order to see the value of connecting the above experimental work with the philosophy of logic. In fact, my hunch is that philosophers - although experimentally crippled (aka "don't try this at home") - can contribute to the experimental work with logical expertise. Actually, philosophers of logic have hypotheses about actual human reasoning that are primed for testing, and which aren't likely to be tested by psychologists who don't know discussions about, say, vagueness and semantic paradoxes. Earlier I've mentioned one admirable adventure into experimental research by Dave Ripley, and another by Jeff Pelletier.
My plan is to start out by checking out The Rational Imagination (2005, MIT Press) by Ruth Byrne.
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5 comments:
I forgot to mention that Keith Stenning works in Edinburgh, so it shouldn't be too complicated to bring him over to St. Andrews...
Hey, what happened to my previous comment? Here it is again:
I think the most interesting recent work combining psychology and cognitive science with (philosophy of) logic is done by Keith Stenning and my colleague Michiel van Lambalgen:
http://www.amazon.com/Human-Reasoning-Cognitive-Science-Bradford/dp/0262195836/ref=sr_1_1?ie=UTF8&s=books&qid=1264612561&sr=8-1
Stenning is a cognitive scientist and van Lambalgen is a logician, and the combination yields very interesting results. One of their points is precisely that a better knowledge of logic as it is actually done can contribute to experimental research. They correctly point out in the book that the notion of 'logic' underlying most of the work in the psychology of reasoning tradition is much too narrow.
Also relevant for the interface between philosophy and cognitive science and psychology is the following recent volume:
http://www.amazon.com/Reasoning-Studies-Human-Inference-Foundations/dp/0521612748/ref=pd_sim_b_2
Very interesting post! And I've been thinking about similar things lately.
A couple of weeks ago, Florian was talking about separability, and Stewart Shapiro asked: Are claims about the justification of logical inferences empirical or normative?
Florian's answer was: normative. However we actually come to learn/acquire logic rules and reasoning techniques, the question is whether there is a reconstruction of them which shows that they preserve warrant.
Florian's answer seems right to me. But it raises the further question. How closely must your reconstructions track actual cognitive processes?
Certain kinds of reconstruction may look nothing like the actual processes of concept acquisition (whatever they look like). The question is, why we should think that this matters. If all we wanted to know was whether our practices are justifiable?
In fact, I think there is a risk here. Certain kinds of traditional interests interests for proof theorists seem to depend upon quasi-empirical claims. For example: it is not immediately clear why we should care about issues like separability. The justification often given for separability is that that, in the reconstruction, we'd want to acquire concepts one-by-one. But why must reconstructions have that form?
We might try to justify an interest in separability on other grounds. In particular, it tends to be easier to prove nice results about separable than logics than about non-separable logics. So, in Popperian spirit, we should start with the separable logics, and see how far we can get with them; if we don't get very far, then we should start investigating non-separable logics. (Michael Potter suggested something a little like this, without mentioning Popper.)
The problem with this line of justification is the following. If you want to justify classical logic, and you find that separability is an impediment to that, you can simply (again, in Popperian spirit) drop the requirement of separability.
All of which makes me think a few things.
(1) How many other issues are affected in the same way as separability? For example, why should we insist that our reconstructions must be harmonious, once we've dropped separability?
(2) I think that neither Stewart's question, nor Florian's answer, depend specifically on any stance in the proof v. model theory debate. (As it happens, I think that Florian, you and I all reckon that proof theory and model theory are complementary, but tend to have a softer spot for proof theory.) So there ought to be similar issues for people who favour model theory over proof theory. I'm not yet exactly sure what they would be, but here's one thought. When we ask about truth (in the light of the Liar) and offer a Field-style model-theoretic story, we ought to ask why we should care about that kind of a reconstruction.
(3) Did Florian give the right answer to Stewart's question? I'm pretty sure he did. But I'm wondering if we might be able to find some cunning way to reject Stewart's question.
I'd be very interested to hear your thoughts!
Tim,
These are indeed the crucial issues to be raised. Data from experimental psychology have something to say about disputes in philosophy of logic only insofar as the latter is at least to some extent a descriptive enterprise. But it is not obvious that it is, or that it should be (but it is also not obvious that it shouldn’t be), so the bearing that experimental data can have on these discussions is not a straightforward matter.
This being said, I absolutely agree with you that, while most people would endorse the kind of claim made by Florian (i.e. that it is a strictly normative matter), in practice people often appeal to what *is* the case in our cognition of logic (instead of what *ought* to be the case) as an argument to defend a particular position. (In your words: “Certain kinds of traditional interests for proof theorists seem to depend upon quasi-empirical claims.”) Two cases that spring to mind. (i) The claim often put forward by proponents of the proof-theoretical approach to logical consequence to the effect that their approach does better justice to (gives better insight into) the epistemic aspects of logical cognition. But this is clearly a quasi-empirical claim: do we really process logical cognition in a way that is more similar to the proof-theoretical, rule-based approach? (ii) The debate on single vs. multiple conclusions. Opponents of the multiple-conclusion approach (Rumfitt, Tennant) often appeal to the ‘unnaturalness’ of handling multiple conclusions from a cognitive point of view---again, an empirical claim, but one which is not given empirical corroboration in these discussions.
The real problem for the kind of reply given by Florian (which I do endorse, at least to some extent) is that the obvious question to be asked next is: on the basis of *what* are we to judge whether certain inferential practices are justifiable? What are the criteria? Where do they come from? In other words, it is of course fine to maintain that the justification of inferential practices is a purely normative affair, but we still need a story concerning the source of this normativity---that is, if it is not adequacy to how we actually draw inferences.
My own view on these matters, which still needs to be substantially developed, is that it is going to be a normative story, but one that takes into account the kind of agents we actually are. Something like: this is how our inferential practices should be, but given our actual cognitive make-up and epistemic mechanisms. So empirical data will be relevant for the formulation of the full story, but it will not be a purely descriptive story either. (There is a nice paper by Pelletier et al. on psychologism and the is/ought divide for logic, I think it is called ‘Is logic all in our heads?’) As it turns out, our actual patters of reasoning appear to differ significantly from the canons of logic (as suggested by the experiments in the ‘heuristics and biases’ tradition, and as extensively discussed by e.g. G. Harman, among others), so the is/ought dichotomy is particularly delicate in this case.
Tim: Thanks for good questions. Sorry that this got a bit long. I agree that the theoretical nature of the proof-theoretist's constraints is an interesting one. I'll try to say something about that below.
'Are claims about the justification of logical inferences empirical or normative?' Stewart has been pressing us on this question for some time already. I think that the answer is a negotiation between the two. I'll try to explain why.
First, it makes little sense, I think, to let experimental data alone dictate when we are entitled to make certain inferences. We know from extensive testing that people are terrible at abstract reasoning, even when they do (generally) infer correctly in particular instances. I wouldn't let data like that undermine modelling reasoning with general (abstract) laws. In other words, there is a normative issue of correct inference that is independent of the data. (Unless you want to let people's response to, say, the Monty Hall Problem be indicative of correct probabilistic reasoning.)
However, an epistemological story about justification of deduction is something more complicated. I guess this is what Stewart is asking about. The orthodox inferentialist, for example, thinks that there is a connection between separability and our acquisition of logical concepts. This connection in turn underlies the understanding-entitlement link that is crucial to their epistemological story. (This is one of the things Williamson attacks in his book.)
Should our reconstruction of logical reasoning reflect this by including separability (or, say, harmony/conservativeness/cut elimination, or whatever else you think is a crucial formal constraint)? Yes - if you think that it is integral to the justificatory story (like the inferentialist often does). Is that theory then hostage to empirical considerations? Yes, I think so. If it happens to be the case that the connection between separability and concept-acquisition (or between the latter and the understanding-entitlement link) is undermined by experimental psychology or cognitive science, that is pertinent to the credibility of the theory.
Yet, it also appears clear to me that there is more to this type of theorizing than the data. Like in other fields, considerations that are non-empirical might count in favour of a theory as well. Negotiating that boundary is hard, as we know.
I hope this is not simply a way of rejecting Stewart's question. I am, ultimately, tempted to answer it by saying 'empirical', but with the proviso stated above. The critical part is that it being empirical doesn't mean that it answers (only) to data about reasoning patterns, but about a bigger picture about language- and reasoning-modules.
Finally, I absolutely agree that the issue cuts across the two camps. Of course, this is precisely why Stewart asks the question: As a model-theoretician he has struggled with which parts of his models are 'modelling' something, and which are mere artefacts of the formal theory. (See his Vagueness in Context, for example.)
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