The Dialogical Roots of Deduction, 1

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.

10 thoughts on “The Dialogical Roots of Deduction, 1”

  1. Back in the days when I would pick up a book like this in a bookstore, sigh, the second or third thing I’d do after sampling a bit would be to check the index. Is there any mention of Peirce, his take on demonstrative reasoning, which is expliative or information preserving, versus non-demonstrative reasoning, which is ampliative or information altering, or the relation deductive inference bears to abductive and inductive inference?

    1. Thanks for the pointers to Peirce (who is someone I want to know more about).

      The book seems to have some discussion of whether deductive reasoning is non-ampliative, but there doesn’t seem to be any reference to Peirce.

  2. 1. I see we have the usual absurd prices:

    Taking Frege at his Word — £65
    Gödel, Tarski and the Lure of Natural Language — £75
    The Dialogical Roots of Deduction — at least £71 and not available except on Kindle (£48) from Amazon UK (what has CUP done with this book?)
    (Conceptions of Set and the Foundations of Mathematics — £75)

    Can anything be done? I suspect there’s an economic argument from a publisher’s POV that attaches such prices to academic books that are unlikely to sell many copies. However, they don’t do it to all academic books that might appear near those on a bookshop’s shelves, so I have to wonder why those particular books were especially thought to be in need of a high price.

    2. I think CDN may be right ‘that inferring conclusions from premises while disregarding one’s own doxastic attitudes toward premises and conclusions may require specific training.’ (And I don’t think that saying ‘it is an integral component of deductive reasoning’ has to mean it doesn’t happen elsewhere too.)

    Your two examples — a law student and a scientist — would at least have had some relevant training.

    And the bracketing they do seems quite limited. With deductive reasoning, we’re supposed to completely disregard the truth, plausibility, and even much of the ordinary meaning of premises and conclusions. (All lions are fruits. No fruits are self-reversing. …) I think there’s quite a difference between that and making realistic suppositional hypotheses.

    Besides, reasoning with suppositions can be deductive. And what says the law student isn’t doing deductive reasoning anyway? It’s also not clear what abductive reasoning — inference to the best explanation? — the vaccine designer is meant to be doing when “reasoning about how to modify her vaccine in response to a range of different types of virus mutation”. And abductive reasoning often would, it seems to me, consider relative plausibility.

    1. On book prices: a resounding “hell, yes, this is all getting out of hand”. One upshot, of course, is that it evidently makes people pretty conscience-less about uploading to The Stunningly Useful PDF Repository of Which We Do Not Speak. Including the last two books of those four … And even though my own books have ended up there, it would have been hypocritical to protest too much!

    2. We can agree that reasoners need to learn to sharply distinguish the questions “is the data you are starting from actually correct?” and “is your reasoning from that data reliably enough truth-conducive?”. That’s a distinction that matters for various kinds of enquiry, involving various kinds of reasoning. And we train up reasoners (including lawyers and scientists) to work from practice data and from suppositions made “just for the sake of argument”, so learning to infer conclusions “while disregarding one’s own doxastic attitudes toward premises”. So the question is whether the situation with deductive reasoning is in a different ballpark from the other sorts of reasoning.

      We could argue more about that. But the point for the moment is that CDN doesn’t say enough (yet): we’ll have to wait to see whether it is an important, theory-driving, theme for her that belief-bracketing in deductive reasoning has a quite distinctive character.

      1. (a) If deduction has the key features CDN lists, that can be interesting and significant in itself even if they don’t distinguish deduction from other sorts of reasoning.

        (b) I don’t think CDN is saying that belief-bracketing occurs only with deductive reasoning, or that it distinguishes deductive reason from other sorts. Instead, it seems to be just necessary truth-preservation that she says has the distinguishing role.

        For instance, in the Preface, pp x-xi, she writes:

        Chapter 1 starts by defining the explanandum of the whole book, i.e. the phenomenon (or phenomena) that it is about. There, I introduce deduction as having three main characteristics: necessary truth-preservation (which is perhaps the most central one, distinguishing deduction from other forms of inference and argument such as induction and abduction), perspicuity, and belief-bracketing.

        And in §1.2.1, Necessary Truth-Preservation, p 5:

        Indeed, this is what distinguishes deductive reasoning from other modes of reasoning – a necessary, constitutive property for any argument to count as deductively valid (though it may not be sufficient for deductive validity).

        Instead, she just says belief-bracketing is one of the ‘main features’, ‘key features’, ‘key components’, or ‘main characteristics’ of deduction, and ‘an integral component’ and fundamental aspect’. That can all be true without belief-bracketing having to be unique to deduction.

        (c) And even if belief-bracketing isn’t completely absent from other forms of reasoning, it might take a more extreme form, or play a more central role, in deduction. (I don’t think it has to, though, for CDN’s account to of interest.)

        (d) I don’t understand your law student and vaccine designer examples. I’m guessing it’s meant to be obvious that they’re not doing deductive reasoning, and what sort of reasoning they are doing instead. It’s not obvious to me. Why wouldn’t a 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’ reason deductively? You say the vaccine designer is doing ‘abductive reasoning’, but what about ‘reasoning about how to modify her vaccine in response to a range of different types of possible future virus mutation’ would have to be abductive?

        (e) In any case, the vaccine designer’s bracketing seems extremely limited (‘relative plausibility’), as does the law student’s (whether names are pseudonyms, likelihood of such tangles).

        1. I didn’t mean to imply that CDN is committed to thinking that belief bracketing is quite unique to deductive arguments. But I did read ‘key components’, ‘main characteristic’, ‘an integral component’ and ‘fundamental aspect’ as implying that CDN thinks that a story about belief bracketing is going to show us something important about (not just reasoning in general) but about deductive reasoning in particular. We’ll see.

          A propos legal reasoning, it is an old and familiar view (one I’m sympathetic with but am not positively arguing for here) that legal reasoning in the English case law system depends on considerations of precedence and analogy that can’t (except in the most procrustean and misleading way) be forced into a deductive model.

          As for our vaccine scientist, I confess I was just using “abductive” as a probably misleading placeholder for “some mix of the usual styles of scientific reasoning”! Which was slapdash.

        2. Catarina Dutilh Novaes

          Thanks for this Rowsety Moid, you do a better job at responding to Peter’s worry than I would have done myself, haha… (My reply can be found in this twitter thread: https://twitter.com/cdutilhnovaes/status/1350375926748602371 )
          The thought is exactly that what is unique to deductive reasoning is necessary truth-preservation, but the other two features need to be taken into account if we are to understand practices of deduction in, e.g., mathematical proof. In the philosophical literature there is much focus on necessary truth-preservation, which is of course perfectly reasonable, but it seemed to me that the other two aspects were under-appreciated and thus deserved a more detailed treatment than they usually get (even if they may be present, albeit perhaps in different forms/to different degrees, in other forms of reasoning/argumentation).

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