There are three recent books on my desk which I’m looking forward to tackling. Two are Joan Weiner’s Taking Frege at his Word (OUP) and Juliette Kennedy’s Gödel, Tarski and the Lure of Natural Language (CUP). But I’m going to start by reading, and blogging about, a third:
Catarina Dutilh Novaes’s The Dialogical Roots of Deduction was published last month by (CUP). Your library could already have e-access via the Cambridge Core system.
CDN aims, says the blurb, ‘to bring together perspectives from philosophy, history, psychology and cognitive science, and mathematical practice … to argue for an overarching conceptualization of deduction as a dialogical practice’. We’ll have to see what this amounts to, and what new light gets thrown on old puzzles about the nature of deductive reason by this approach. So let’s dive in (and it is good to report that the book is engagingly readable).
Chapter 1 is titled ‘The Trouble with Deduction’. There’s a throat-clearing Introduction, and then §1.2 asks ‘What is a Deductive Argument?’. CDN highlights three features: (a) necessary truth-preservation, (b) stepwise structure and perspicuity, and (c) what she calls the bracketing belief requirement.
The first idea is a familiar enough theme: deductive validity is defined as requiring necessary truth-preservation. The question arising is going to be the nature of the necessity here; we’ll return to this.
The second idea is that ‘something else is required of a good deductive argument other than necessary truth-preservation: it must somehow make clear what the connection is between premises and conclusion such that the truth of the premise(s) guarantees the truth of the conclusion(s).’ So, to meet this requirement ‘a deductive argument … will typically contain numerous steps, each of which may be individually simple and thus individually not very informative, but by chaining such steps in a suitable way we may derive non-trivial conclusions from the given premises’.
The third idea is that ‘In its basic form, the game of deduction requires the reasoner to take the premises at face value, no questions asked: the focus is exclusively on the connection between premises and conclusions, not on the nature or plausibility
of the premises or conclusions.’ After remarking on some psychological research, CDN suggests ‘it seems that inferring conclusions from premises while disregarding one’s own doxastic attitudes toward premises and conclusions may require specific training. Yet, it is an integral component of deductive reasoning.’
Now I rather doubt that the third idea of belief bracketing tells us something special about deductive arguments. For isn’t this a feature of lots of (all?) kinds of argumentation? The law student faced with a description of an engagingly complex case, and asked to argue whether e.g. John Doe still has a contract with Jane Roe, entirely disregards whether ‘John Doe’ and ‘Jane Roe’ are pseudonyms for real people, and even disregards the likehood of the two parties getting themselves into the tangle described. The vaccine designer, reasoning about how to modify her vaccine in response to a range of different types of possible future virus mutation; her abductive reasoning brackets at least some questions about the relative plausibility of the scenarios (as she prepares for the worst while hoping for the best).
Perhaps there could be reasoners who can only reason from beliefs. But famously, it grants us an evolutionary advantage to be able to take our reasonings ‘offline’, argue from mere suppositions, and so we are able to send our suppositional hypotheses out to die in our stead. And that’s a general point about reasonings not about deductive reasoning in particular.
What about the second idea, that an epistemically useful deductive argument will typically chain together a number of individually not-very-informative steps? Well, again, isn’t this a point about argumentation more generally? The law student’s expansive legal argument for John Doe’s continuing contractual obligation, the vaccine-designer’s step-by-step argument for tweaking her vaccine design just so, again build up a case (perhaps for a surprising conclusion) by putting together simpler bits of reasoning. What is distinctive about the deductive case is not that there may be numerous steps leading to non-trivial conclusions, but (surely) that each step is necessarily truth-preserving (a property not lost by adding new steps to the argument).
So, until I hear more, I’m inclined to think that what is going to really matter for an account of distinctively deductive argumentation is going to be (as usually supposed, perhaps) the story about necessary truth-preservation (or warrant-preservation if you are constructively minded). Though this is consistent, of course, with that story being best told within a wider account of dialogical procedures of joint reasoning: we’ll see.
In §1.3, ‘The Issues’, CDN presents three philosophical questions about deductive
reasoning. One of them we have already noted, the nature of the necessity supposedly involved in deduction. Can we cash out the notion of necessity here in terms e.g. of a quantification over models? Is a proof-theoretic approach viable? There is a familiar bunch of questions here, and CDN notes some of the inconclusive recent debates in the literature.
But a prior issue is ‘Where Is Deduction to Be Found?’ — just what role does deductive reasoning play in our conceptual economy? CDN leans to the view that ‘deductive
reasoning is predominantly instantiated in mathematics and in some other regimented contexts of argumentation, such as philosophy’. Really? Maybe extended stretches of deductive reasoning are principally to be found there. But what about one-step syllogisms in Barbara? What about the instant one-step inference from a background general belief that No As are Bs and the new discovery that Jo is A to the conclusion Jo is not B? What about the jump from the background beliefs that ‘John is taller than Jo’ and ‘Jo is taller than Jane’ to the conclusion that ‘John is taller than Jane’? I’d have thought that such bits of local mini-inference were pretty common outside our mathematical activities! CDN’s view seems, then, to apply not to deductive reasoning in general but rather to extended passages of deductive argumentation in particular.
The third issue CDN raises is ‘What Is the Point of Deduction?’. The worry here is the old one — how to resolve the supposed inherent tension between the justification of deduction (the conclusion is already somehow there in the premisses) and the utility of deduction (we can get new knowledge by deductive reasoning). I confess I’ve always found this difficult to get excited about once we’ve noted that, while ‘entails’ may be transitive, ‘obviously entails’ certainly isn’t. Still, CDN remarks that ‘Deduction does not seem to be a particularly suitable way to produce new information … and it does not seem to be a reasonable guide for managing our beliefs and thoughts either’ (after all, it can’t be a sensible instruction to adopt every deductive consequence of our beliefs). So, she asks, ‘What, then, if anything, is the ‘point’ of deduction?’ And the promissory note is that her dialogic approach will give us a grip on this.
To be continued.