Monday, 10 October 2011

Deduction and the Necessary A Posteriori

Consider: There is a cat here, therefore there is an animal here.

Assuming we want to say that this inference is valid in some sense, here are three things we might say about it:

1) It is an elliptical argument, involving an unarticulated premise, namely that cats are animals.

2) It is an enthymematic or gappy argument, involving unarticulated reasoning.

3) It is a complete argument in itself - neither (1) nor (2) is the case.

On the first approach, the deduction is clearly a priori. But this is not the only possible attitude. While the belief that cats are animals could conceivably be overturned by experience, it is arguably not a contingent fact that all the cats around are animals (cf. Kripke 1980). So rather than regarding this as part of the matter being reasoned from, we might regard it as part of the deductive apparatus.

Thus, on the second interpretation, we might regard the move from 'cat' to 'animal' as being licensed by an unarticulated principle of reasoning (which may be expressed in the form of an inference rule, or an axiom such as 'All cats are animals'). Or we might resist even this, and say that nothing is unarticulated - perhaps still allowing that the argument can be justified by the principles of reasoning which are held to be unarticulated on the second interpretation.

Note how natural these latter two approaches are; there does seem to be some sense in which the conclusion follows from the single articulated premise. Note also that the argument by itself satisfies the natural (admittedly problematic) modal characterization of validity, if we take the relevant modality to be subjunctive or metaphysical modality ("what could have been the case") rather than a priori possibility or epistemic modality ("what could be the case"): it could not have been the case that there was a cat here yesterday but no animal here yesterday.

This may suggest that, according to some intuitive and central concept of deduction, some facts about what can be deduced from what are empirical (i.e. not knowable a priori).

However, this flies rather completely in the face of previous philosophical thinking about deduction. It also raises the following puzzle: on one way of thinking about necessity, our holding it to be necessary that all cats are animals means that we have made a certain kind of connection between our cat-concept and our animal-concept (an empirically defeasible connection, held constant when describing counterfactual scenarios). But it is natural to think of this conceptual connection as partly constitutive of the content of thoughts involving these concepts - thoughts such as 'There is a cat here' and 'There is an animal here'. Thus, someone who doesn't have such a connection arguably isn't in a position to have those two thoughts at all: there would appear to be little room for them to have those exact thoughts and yet not be able to work out a priori that one implies the other.

My suggestion is that, when faced with this sort of puzzle, one should try to distinguish different ways of individuating content, some more fine-grained than others. When talking about thoughts in, e.g., the context of communication, a relatively course-grained individuation scheme is often most appropriate. When talking about the epistemology of deduction - and not just the epistemology - a more fine-grained approach is called for. (That is, an approach where what are for many purposes two instances of the same thought get treated as distinct structures.)

Insofar as this is right, the more general moral is perhaps something like: when doing philosophy, be willing to put multiple modes of content-individuation on the table - don't let one obsess you to the exclusion of all others.

Tristan Haze

Reference

Saul A. Kripke (1980). Naming and Necessity. Harvard University Press.

4 comments:

  1. I'm not quite sure I get the puzzle -- maybe you sympathise here anyway. Why not take a "therapeutic" route and say that the question posed isn't really asking anything unless, say, a token of the given argument is paired with enough information (e.g. contextual) to push towards an answer like (1), (2), (3), etc. It seems that the nature of the question simply underdetermines warrant in answering it.

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  2. I guess it's not so much about saying whether the argument should be interpreted according to (1), (2) or (3), but more that (2)- and (3)-like interpretations of this and other arguments seem natural enough (as *possible* interpretations, if you like), and this may give rise to the puzzle outlined in the third last paragraph.

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  3. I like the idea that (2) and (3)-like interpretations are ‘natural enough’. Although I don’t myself think (3)-like interpretations are all that natural, I do think (2)-like interpretations are plausible, especially if your particular therapeutic wants lead you to consider whatever seems unarticulated in the original inference as “part of the deductive apparatus”.

    But I cannot see how:

    “This may suggest that, according to some intuitive and central concept of deduction, some facts about what can be deduced from what are empirical (i.e. not knowable a priori).”

    follows. I’ve read the lead up to it a few times over, but I cap out at the very point where I should be seeing what you mean. Some more explanation on this point would be helpful (to me).

    As for the puzzle, suppose the ‘unarticulated principle of reasoning’ to be ‘determination’: where p determines q iff for p to occur is for q to occur not simpliciter, but in some particular way. I’m sure this could be worked out more exactly (my rendering is ‘clunky’, we might say), but I am trying to suggest that we can come up with some general principle of reasoning that lets us know that whenever a determinate occurs (i.e. something is scarlet) then a determinable occurs (i.e. something is red) and that this is purely a logical matter.

    To my mind this explains why “the argument by itself satisfies the natural (admittedly problematic) modal characterization of validity”” because for p to occur (at some possible world) is for q to occur (there) not simpliciter, but in some particular way.

    With this in place the puzzle doesn’t seem so puzzling. I can 1) keep an empirically defeasible conceptual connection between my ‘cat-concept’ and my ‘animal-concept’ (i.e. determination) and I can 2) “think of this conceptual connection as partly constitutive of the content of thoughts involving these concepts - thoughts such as 'There is a cat here' and 'There is an animal here'.”

    But neither 1) nor 2) forces me to hold that my ‘animal-concept’ implies my ‘cat-concept’ a priori, because determination, no matter how clunkily defined, is a one-way necessitation relation. My ‘animal-concept’ implies my ‘living organism-concept’ but not vice versa, and my ‘cat-concept’ implies my ‘animal-concept’ but not vice versa.

    So yes, while the conceptual connection of determination is partly constitutive of the content of thoughts such as ‘There is a cat here’ and ‘There is an animal here’ I don’t see that the thought ‘There is an animal here’ conceptually includes the thought ‘There is a cat here’. It seems more correct to hold that the part of the content of the thought ‘There is an animal here’ which we attribute to the conceptual connection (determination) is that ‘an animal is occurring, not simpliciter, but in a certain way’.

    And surely that doesn’t make any particular animal (here) a cat.

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  4. Hi Gabe, thanks for the feedback.

    'I cannot see how:

    “This may suggest that, according to some intuitive and central concept of deduction, some facts about what can be deduced from what are empirical (i.e. not knowable a priori).”

    follows.'

    Maybe this will help: I did not mean to suggest that the mere (2)-likeness or (3)-likeness of the argument all by itself might suggest the above. It's that, together with Kripke's idea that it is not a priori that cats are animals.

    The line of thought could be crudely reconstructed this way: 'If it's valid to go straight from "There's a cat here" to "There's an animal here", because cats are necessarily animals, and if I know this only empirically, then I cannot know a priori that the argument is valid.'

    * * *

    The below is perhaps a bit less likely to be helpful, but it might be:

    Your way of not seeing a puzzle, if I can put it that way, seems to involve the sort of fine-grained way of thinking about content I alluded to.

    The reason why this may be puzzling if one isn't ready to switch between different granularities is the following: in other contexts we treat, e.g., a pair of people one of whom thinks cats are animals, another of whom thinks they are not, as differing over a single proposition - and yet one may have a cat-animal connection, another not. Here we need to go more coarse-grained (if we want to avoid saying that it's simply wrong in every sense that these two people disagree about some single proposition or content).

    * * *

    I didn't really understand the directionality point.

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