How do you know that your premises support your conclusion?

I suggested in an earlier post that any theory of inference needs to be able to distinguish between inferences of the following two forms:

(1) qr; therefore, p

(2) qr; <q> and <r> support <p>; therefore, p.

Intuitively, the difference is that, in order to perform an inference of form (1), you need yourself to be able to “see” that <q> and <r> support <p>. To perform an inference of form (2), however, you needn’t yourself be able to “see” this. So you can perform an inference of form (2), but not of form (1), when, for example, your grounds for thinking that <q> and <r> support <p> are merely testimonial, i.e., when someone told you, say, that the former together entail the latter, but you don’t yourself “see” the entailment relation.

The need to distinguish these two forms of inference poses a prima facie problem for defenders of the Taking Condition. For, according to the Taking Condition, it’s a necessary condition on inferring <p> from <q> and <r> that you (in some sense) “take” <q> and <r> to support <p>. The defender of the Taking Condition thus needs to explain why the Taking Condition doesn’t entail that there are no inferences of form (1), because all inferences that are apparently of that form are really of form (2).

Arguably, the view that all inferences are of form (2) generates a regress of the sort made famous by Lewis Carroll. My point here, though, is that, even if that regress were somehow shown to be non-vicious, we’d still have a problem. (Of course, that’s not to say that the solution to the regress and the solution to the current problem won’t be one and the same. But it opens up the possibility that some ways of solving the regress problem won’t solve the current problem, and perhaps vice-versa.)

A common move here is to suggest that the Taking Condition has no problem distinguishing inferences of forms (1) and (2), because the “takings” it introduces aren’t premise-beliefs. Inferences of form (2) are three-premise arguments, while inferences of form (1) are two-premise arguments. (And then it can be added that, in order to perform an inference of form (2), you need to “take” <q>, <r>, and <<q> and <r> support <p>> to support <p>––but, because this “taking” isn’t a premise-belief, there’s no threat of regress.)

It’s at this point that things get really messy. What’s clear is that the defender of the Taking Condition needs to provide an account of “takings,” one on which they aren’t premise-beliefs. But there are many ways to do this.  To take just the two most obvious of them: you might say that “takings” are beliefs, but that they don’t play the role of premise-beliefs; or you might say that they aren’t beliefs at all, but some other kind of attitude. (There are also other, less obvious, possibilities.)

I want to ignore that particular mess for now, because thinking about inferences of forms (1) and (2) suggests to me that the Taking Condition gets things the wrong way around. We can see this especially if we note (as I did in the earlier post linked above) that, whatever else we say about the “takings” involved in inferences, it’s plausible that they need to amount to knowledge (or to be in some sense relevantly knowledge-like). And then we can ask: how do you know that your premises support your conclusion? And our answer seems to affect––in fact, it seems to me to determine––whether your inference is of form (1) or of form (2). In short: in order for your inference to be of form (1), you need to know that your premises support your conclusion in a special way. What way? Well, we can begin by ruling some ways out. For example, you can’t know it merely by testimony.

More generally, though, it seems to me that, however you know that your premises support your conclusion, if that knowledge is prior to your act of inferring itself––prior, that is, to your drawing your conclusion––then your inference will be of form (2), rather than of form (1).

Consider an inference like <is taller than bis taller than c; therefore; is taller than c>. You might claim that your knowledge of the relevant support relation (or, perhaps equivalently, your knowledge that ‘taller than’ is transitive) is prior to your drawing the conclusion. But how plausible is this, really? How did you come to know the relevant support relation? Admittedly, you might have known it, in some sense, long before drawing this particular inference––it was years ago that you first learned that ‘taller than’ is transitive, and only recently that you met ab, and c, say. But did you learn it before drawing any such inference? How did you learn that ‘taller than’ is transitive?

You might have done this: you imagined one person (call them a), imagined them as being taller than a second person (call them b), imagined this second person as being taller than a third person (call them c), and then just realized that would also have to be  taller than cBut then it seems that your knowledge that <is taller than b> and <b is taller than c> support <is taller than c> is at best coeval with your knowledge that (under the imagined conditions) is (would be) taller than c (because is taller than b and b is taller than c).

So it seems that, when you perform an inference of form (1)––and assuming that you must, in performing that inference, manifest knowledge that your premises support your conclusion––your knowledge that your premises support your conclusion is not epistemically prior to your knowledge of your conclusion, and hence is not epistemically prior to your inference itself (since it’s through that inference that you know the conclusion).

Now, the Taking Condition doesn’t explicitly say that your knowledge that your premises support your conclusion needs to be epistemically prior to your inference. But it does say that your knowledge (or, more generally, your “taking” it) that your premises support your conclusion is causally prior to your inference. And it’s far from clear how that knowledge could be causally but not epistemically prior to your inference.

My own view goes even further: I think that, in the case of an inference of form (1), your knowledge that your premises support your conclusion is going to be both causally and epistemically posterior to your inference itself (hence to your knowledge of your conclusion). The argument I’ve given here doesn’t quite get us that far. For that, I need to make it plausible that you can come to know that your premises support your conclusion  by coming to know your conclusion on the basis of your premises.

But this doesn’t strike me as wildly implausible. Remember the question I raised earlier: how do you know that ‘taller than’ is transitive? My suggestion is that you know this by performing (perhaps merely in imagination––i.e., you needn’t actually be “reasoning with beliefs”) a relevant inference, e.g., <is taller than bis taller than c; therefore, is taller than c>. This might take explicitly suppositional form: “suppose that is taller than b and that is taller c; then will be taller than c.” Even here, though, the “then” is essentially inferential. And so it’s by drawing that conclusion (here, merely in imagination, as I’ve put it)––and by recognizing that it generalizes, i.e., that you weren’t relying on features peculiar to ab, and c––that you come to know that ‘taller than’ is transitive.

At any rate, it seems that there are at most two options here: either (i) your knowledge that your premises support your conclusion is both causally and epistemically posterior to your knowledge of your conclusion or (ii) your knowledge that your premises support your conclusion is both causally and epistemically coeval with your knowledge of your conclusion. And it seems to me that option (i) is significantly more plausible than option (ii).

(The latter view becomes significantly more plausible if we take the causation in question to be formal causation, in something like Aristotle’s sense, rather than efficient causation. This sort of view has been suggested by Ulf Hlobil, in some work in progress. But that view represents a significant departure from standard understandings of the Taking Condition, on which the causation involved is assumed to be efficient causation. More importantly, though, it’s not obvious that, on that understanding, option (ii) is even incompatible with option (i), since it isn’t obvious that your knowledge that your premises support your conclusion couldn’t be the formal cause of your conclusion/inference while at the same time being the efficient effect of it.)


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