Tuesday, March 18, 2014

The a priori and the a posteriori

I've been thinking about Chalmers' Constructing the World. It is absolutely crucial for Chalmers to have a distinction between what is a priori knowable and what is a posteriori knowable.

Now, imagine that we have evolved to believe that the number one has a successor (call this proposition "Two") as well as that many snakes are dangerous ("Snake"). In both cases, let us suppose, we evolved to believe the true claim because believing it conduced to our survival. (We may add that the reason belief in the claim conduced to our survival was explained by the truth of the claim, if we are worried about debunking arguments.) It now looks like Two and Snake are on par: either both beliefs are a priori or both beliefs are a posteriori. However, Chalmers cannot afford to say that Snake could be a priori—that will destroy much of his story.

So it seems that if Chalmers' story is to work, we will have to say that Snake and Two are a posteriori. However, it is also important for Chalmers to say that fundamental principles like Two are knowable a priori. The story doesn't destroy this: after all, something can be both a posteriori known and a priori knowable (say, a result of a calculation done with a calculator). Nonetheless, there is a problem here. It may well be that all fundamental principles like Two are known by us through something like this evolutionary mechanism (and "something like" includes the theistic variant where God instills this belief in us on account of its truth). And if so, then what reason do we have to think that they are a priori knowable, given that we don't know them a priori? One might have some conviction that some hypothetical or actual non-human reasoner knows them a priori, but it is difficult to see that conviction as justified.

However, I think there is a speculative non-naturalist story one could give that would help make the distinction. Suppose that all our knowledge is at base perceptual. However, sometimes what we perceive are abstracta and sometimes what we perceive are concreta. Knowledge that is grounded only in perception of abstracta is a priori, while knowledge that is grounded at least in part in perception of concreta is a posteriori. It may be that we can just see the number two as the successor of the number one. There is some phenomenological plausibility to this.

This would be really nice for Chalmers. For it is plausible that if any abstracta and their abstract relations are observable, they all are. If so, then all facts about the realm of abstracta are a priori knowable.

Granted, on this story knowledge of abstracta is observational and hence empirical. But while this does mean that the above use of "a priori" and "a posteriori" is idiosyncratic, the above use nonetheless may help recover at least some of Chalmers' story.

Some, but perhaps not the two-dimensionalism? For the account above is apt to make it a priori that wateriness is H2O-ness, since that seems to just be a fact about abstracta.


Mike Almeida said...

It now looks like Two and Snake are on par: either both beliefs are a priori or both beliefs are a posteriori.

It's really hard to see why. The fact that there is an a posteriori reason to believe p does not make p a posteriori. We all have some a posteriori reasons to believe mathematical propositions (our teachers told us they're true, for instance), but that does nothing to show that the propositions are a posteriori true. What makes them a priori is that there is evidence (not necessarily all evidence) justifying the propositions that is (in some sense) not derived from experience. So the fact that I have some reason from evolutionary history to believe p does not make p a posteriori.

Brian Cutter said...

These are great points. I might raise a small quibble about the word "perception" in the proposal, though. Suppose we say instead that there is a fairly natural epistemic relation, to which we might give the neutral label "apprehension" (or "quasi-perception"-- Russell uses "intuition"), which we bear to objects and states of affairs on both sides of the concrete/abstract divide. When we bear this relation to a concrete object or state of affairs, we call this "perception," and we call the knowledge based on it "a posteriori," "empirical," or "observational." When we bear it to an abstract object or state of affairs, we typically use a different word, e.g. "rational intuition," and we call the knowledge that results from it "a priori." This is mostly a verbal change, but when we make it, we will not be tempted to worry that "on this story knowledge of abstracta is observational and hence empirical," because "observational" and "empirical," like "perception" and "a posteriori" are, on this proposal, only to be applied when the objects in question are concrete.

(An alternative way to draw the distinction is in terms of the distinction between necessary and contingent beings/state of affairs rather than concrete and abstract beings/states of affairs. This would result in similar classifications, with one major exception: Direct apprehension of God would count as perceptual/observational/a posteriori on the former proposal, and intuitive/a priori on the latter. I'm inclined to think that the question of which of these is correct is, in Sider's sense, not a substantive question, because this whole way of looking at things makes the a priori/a posteriori distinction shallower, less "joint-carving" than one might have thought. The more important distinction, I think, is probably that between knowledge directly based in apprehension and inferential knowledge.)

Lastly: It's not clear that your proposal would make trouble for two-dimensionalism. Chalmers agrees that we know facts about abstracta a priori, but only provided we have non-twin-earthable terms/concepts for the abstracta, which we don't in the example "wateriness = H2O-ness." (I suppose he would insist on qualifying your proposal, saying that a priori knowledge is [quasi]perceptual knowledge of abstracta grasped under non-twin-earthable concepts.) An analogous case: Suppose I introduce the name "A," stipulating that it is to rigidly designate the Tim's favorite number, whatever it is. Supposing that number is 12, then "A = 12" is a fact about abstracta, but it's not a problem for 2D because "A" is twin-earthable and so "A = 12" is not a strong necessity.

Alexander R Pruss said...


One can call this perception with a weasel-term like "apprehension" or "rational intuition", but it is just perception by another name. :-) Which is basically what you say. But I'll adopt the wording for convenience.

Regarding your last point, it seems that once we draw the line between the necessary and the contingent as you suggest, then presumably any necessary state of affairs that can be apprehended will count as a priori. But, plausibly, every necessary state of affairs, or at least every necessary state of affairs solely about necessary entities, can be apprehended. But it seems that wateriness = H2O-ness seems a necessary state of affairs solely about necessary entities.

And on the abstract/contingent approach, again identity between two abstract entities seems something apprehendable.

(One might try to restrict apprehension to a priori states of affairs, but of course then we get circularity.)

Maybe one could say that "H2O-ness = wateriness" is partly about the water in our lakes and rivers, and not just about abstracta / necessary beings, since the sense of "wateriness" includes something about lakes and rivers. But this explains aprioricity in terms of senses, and that's the opposite direction of the one Chalmers wants to take. Still, maybe there is something to it.

Alexander R Pruss said...


Sure, but do I have any other kind reason to think these things? For all we know, all our mathematical knowledge ultimately depends on principles we know only in this kind of way.

Mike Almeida said...

I think knowledge of the a priori do have something like a perceptual basis. I don't know how 'rational intuition' became a weasel word, but it is roughly what I'd suggest is the basis. But it's too much to ask (isn't it?) that anyone offer an account of how exactly we know a priori truths? That's too hard. There's a lot of empirical evidence that we do not know them merely empirically. For instance, you would be unwilling to reject that p --> p no matter what empirical difficulties would be thereby solved (pace Quine).

Mike Almeida said...
This comment has been removed by the author.
Alexander R Pruss said...

It's plausible that empirical knowledge is knowledge by observation. If rational intuition is a kind of observation, then knowledge by rational intuition is empirical knowledge.

Now, I suppose, one can distinguish the modes of observation. We have the usual eight senses: sight, hearing, smell, taste, pressure, temperature, proprioception and introspection, and then we have rational intuition. But why should the first eight all go in one category while the last goes in a separate category? One might think that the difference between rational intuition and sight is like the difference between sight and introspection, or between smell and proprioception. If so, then instead of dividing knowledge into the a priori and a posteriori, we should divide knowledge into the rationally intuitive, proprioceptive, olfactory, visual, etc.

I certainly don't think we should align the a priori with the unrevisable. It's not clear to me that my knowledge that I think is a priori (it seems to depend on introspection), but I see no way to giving it up. So there may well be unrevisable a posteriori claims. And there are plenty of very revisable claims from rational intuition.

Mike Almeida said...

I think rational intuition is a sort of perception. I think it is fallible. But I'd deny that all perceptual/quasi-perceptual knowledge is thereby a posteriori. Why would anyone think that? Is it apriori true?

On your unwillingness to revise your beliefs concerning the validity of p --> p, I was not suggesting that you identify the unrevisable with the a priori. I was suggesting that the fact that you won't revise is evidence (under any evidential conditions) is evidence that you do not know p --> p a posteriori.

Alexander R Pruss said...

I don't see why unwillingness to revise is evidence of aprioricity. There are a handful of propositions I am unwilling to revise:
- some basic tautologies
- that I think
- the truths of the Catholic faith.

Since the last category is full of a posteriori truths, I don't see how my unwillingness to revise is evidence of aprioricity.

Mike Almeida said...

Suppose I learn that the card drawn from a fair deck is even, E. The probability that it's a deuce given E is greater than the probability it's a deuce. But E is evidence for lots of other things. It's evidence that it's a 4 of spades or 6 of diamonds, for instance. So what if R is evidence for a proposition p being other things (like a proposition in the Magisterium, for instance), it might also be evidence that p is a priori.

For what its worth, I had in mind propositions which we hold on the basis of evidence. I don't think you hold the propositions in the Magisterium on the basis of evidence. Further, I think it would be rational to hold that some propositions in the Magisterium are false, at least in their details. Probably, the fullness of divine truth is not quite, not exactly, what you find there, even if it approximates it.

Alexander R Pruss said...

Right: I am willing to say that unrevisability is incremental evidence of apriority. But I do not see that it raises the probability of apriority over 1/2.

I think the propositions taught by the Magisterium have sufficient evidence to hold them, but holding them irrevisably might be thought to go beyond the evidence. (Or not. For there is the testimony of the Holy Spirit to be considered.)