Saturday, June 20, 2009

All reasoning is deductive

Brian recently wondered whether philosophy is deductive or somehow ampliative. I don't think I believe in ampliative inference. I think that all reasoning is deductive.

By 'deductive inference,' I mean inferences where the premises entail the conclusion, and one is led to accept the conclusion on the basis of the believed premises. (I'll limit this to inference in belief, although I think there's a broader important notion that is neutral on the attitude in question.) I'll use 'ampliative reasoning' to refer to reasoning that is not deductive; where one concludes something that goes 'above and beyond' what was given in the premises.

Suppose I see that Herman has an iPhone, and come to believe on this basis that Herman has an object. It is very natural in this instance to represent my reasoning deductively:
Herman has an iPhone.
Therefore, Herman has an object.

(I don't much mind if you want to include a tacit premise to the effect that iPhones are objects. Put it in or leave it out, as you like.)

Some reasoning, however, is commonly thought to be ampliative. Just which cases are like this is a matter of some controversy. One might think that ordinary perceptual judgments are like that:
It appears to me as if I have pocket kings.
Therefore, I have pocket kings.

Or maybe standard cases of induction are like that:
Torfinn got angry the last twenty times someone mentioned two-dimensionalism.
Therefore, Torfinn will get angry the next time someone mentions two-dimensionalism.

I think there's generally thought to be a strong intuitive sense in which it is correct to formalize these arguments as ampliative, rather than deductive. But I just don't see it. These ampliative bits of reasoning are easily recast as deductive ones. One way to do this is to add to each a tacit premise at least as strong as the material conditional from original premise to conclusion. Another way is to take the inferences as being run against the background assumption that such a bridging principle holds. (I'm not sure how different these two ways are.) Either way, I'm trying to make sense of the intuitive idea that, in inferring Q from P, one demonstrates one's commitment to the material conditional P > Q. One cannot conclude that Q on the basis of P while regarding it as an open question whether it might be the case that P and ~Q.

Insisting that all reasoning is deductive will, I think, get us out of some messy problems. (Without going into detail here, I'm thinking about closure iterations, easy knowledge, and bootstrapping.) There must be some reason it's not the obvious choice, but I don't see what it is. What reason do we have to avoid positing tacit premises like these?


  1. I am sympathetic to this line of thought. I thought a lot about this, so I apologize in advance for the lenght of this comment.
    There are different ways in which one can question the basic idea. I suppose the most important is the following. It's true that you can always add the material conditional (or something stronger) as a tacit premise to the reasoning in question (although there is a worry about how psychologically plausible this is); but it's not clear how the reasoner is justified in believing the material conditional. We cannot answer that the material conditional is a logical consequence of the conclusion, because the story you are suggesting holds that the belief in the material conditional comes before the belief in the conclusion both in the structure of justification and, presumably, in the chronological sense. Nor can we answer that the material conditional is justified by the first premise, because that does not entail it. A better thing you could say is that your background evidence plus the first premise entail the material conditional. But that just means that your background evidence plus the premise entails the conclusion as well, and the defender of inductive reasoning of course is going to deny that this is plausible. What could that additional background evidence be? certainly nothing about Torfinn follows deductively from the uniformity of nature, or even from more specific principles about the uniformity of people's behaviour. If Torfinn were to surprise us, we would not give up inductive methods altogether, or even change the way we reason about people's behaviour.
    One idea I toyed with at some point (actually, strictly speaking I defended it in print; but I'm quite ashamed of that) was to say that you just have to believe the addtional premise, and it does not matter whether it is justified. But that of course would be radically revisionary, since we normally assume that reasoning from unjustified premises cannot produce justification. I now think Bayesianism is a better way to go here. It allows us to capture something of the initial intuition, that is, that you are committed to the truth of the material conditional (since its probability cannot be lower than the conditional probability of the conclusion on the premises), while saving some intuitions about inductive reasoning, such as its fallibility (for the probability of the conclusion may be less than one). And the questions about the background evidence are more tractable, because the model does not require that background evidence plus premises entail the conclusion, but only that they assign it a high probability. It's a further question whether the Bayesian model can treat all forms of non-deductive reasoning (such as abduction), but I am not pessimistic about that.

  2. This seems pretty internalist of you, Daniele. There seem to me to be a number of attractive externalist options. I think I'm most attracted to something like this one: the tacit assumption is justified to the extent that it is a product of a reliable disposition to take the right things for granted; it's knowledgable to the extent that it's a successful such product. Some things, it's appropriate to take for granted, and some things, it's not. If you have a competence in this arena, they you are disposed to ignore the irrelevant possibilities, and focus on the ones that are relevant.

    Actually, now that I've said it, one could say all that much and still be an internalist, giving internalistic characterizations of relevance. I'm not inclined to do that; I think that the truth is always relevant, worlds very nearby in some sense are always relevant, etc.

    A pretty different way to go is Crispin's -- we're just automatically justified in accepting some things: those, maybe, for which accepting is a necessary condition of future inquiry.

  3. You might want to consider my argument that there is no such thing as deductive reasoning (e.g., Change in View, first chapter). This is available online at

  4. Thanks! I noticed a little while ago that your book is online; I downloaded it eagerly, and mean to spend a lot of quality time with it soon.

  5. Jonathan
    just talking about a reliable disposition to take for granted says next to nothing. What is the process of method involved?
    I'll put you a dilemma; either say your disposition to take fro granted the conditional is grounded in deductively conclusive evidence, and then you have to tell us what it is, or you say it is not, but then why not just say that the conclusion of the reasoning is justified becasue it is the product of a reliable disposition to infer from the premises to the conclusion.

  6. That's helpful, Daniele. I'll think a bit about just how I want to respond. Thanks.

  7. Is it a separate question as to whether people actually go through such simplistic reasoning processes on a day-to-day basis? I just can't imagine people have such simplistic "beliefs" about practical things like iPhones. It would probably look something like this:

    Herman has an iphone
    Therefore, my emotional state is that of jealously and this is biasing my perception and communication with Herman. He is so damn spoiled!

    Even this is an extreme simplification of what is actually happening on the psychological level. So my question then becomes, if these types of logic-games are not meant to accurately model the psychological processes of real human interaction, what is their purpose? To better understand the unique human capacity of logic although such skills are underemployed by the average person?

    "Belief-desire" psychology is so quaint and comes directly out of 17th century philosophy, so I would not be surprised if psychological theory eventually improved upon such vocabulary.

  8. Do you count any part of the sort of inference that goes on when a person conditionalizes or Jeffrey conditionalizes as an ampliative inference? I think it might not be clear how to classify some of that stuff.

  9. Nick, what parts of the relevant inferences are you worried about?