I’m not a lover of dichotomies and unnecessary philosophical distinctions. But I can’t see the motivation for abandoning the a priori/a posteriori distinction (or something in the vicinity of it).
It seems to me obvious that there is a difference between understanding and mere knowledge. There is difference between me understanding Pythagorean theorem (that is, understanding the relations depicted by it, and why those relations hold), and mere learning it by heart.
Maybe there is something about the terminology and its historical burden that alienates some people from a priori/a posteriori distinction. Would they accept the distinction between understanding and mere knowledge on another hand? If they do, what would they make of that distinction? Is it of qualitative or just a quantitative nature?
A brood comb 
I think the puzzle about apriori knowledge has more to do with ontology than anything else, but I could be quite wrong about this. As I see it, we have a very plausible folk theory of aposteriori perceptual knowledge: we posit the existence of objects and events that stand in causal relations to our perceptual mechanisms, giving us reliable beliefs about the physical world. The parallel story in the case of apriori knowledge looks pretty fishy: are we to believe that there is a realm of Platonic mathematical facts which we somehow contact through a mechanism of intuition? Now, that’s not much of an argument, but it is enough to see why the apriori is puzzling.
Hi Colin,
That makes lot of sense. I wonder though if abandoning the distinction also implies lack of any qualitative distinction between understanding and knowledge (like in the example of Pythagorean theorem). To me, it seems that it is a fact that there is difference between understanding the theorem (i.e the relations, and why they hold) and mere learning it (being able to say that a^2=b^2+c^2). Or, that it is a fact that there is a difference between believing Pythagorean theorem based on measurements of, i don’t know, hundreds of right-angle triangles, vs. believing it because we are understanding the proof.
What I want to say is that, while I agree it is puzzling, if the current theories don’t allow that we can be aware of necessary relations and being aware of them as necessary, then there is something missing from those views, as we in fact are. I mean, whenever there are two things, there has to be one and one more thing. It is something that I know for sure, without need to check the nature. This is a fact, and theories should explain it (or at least accept it).
This seems to me same as if in physics they would deny existence of some apparent phenomenon, just because it goes against the current paradigm.
I don’t mind it as a loose distinction but when it is a formal distinction I just don’t buy it. For pretty much the reasons Quine gives.
Hi Clark, can you point to some of those reasons? I will be interested to hear it, because the only reason I can see for someone to suspect (what seems to be an obvious) difference between knowing and understanding, is what Colin mentioned – that we just don’t have good (psychological?) story to support a priori knowledge.
As a person that doesn’t accept a priori, can you also please comment on the other question – do you take it that to mean that there is no (qualitative/essential) difference between understanding and mere knowledge (as in the example with Pythagorean theorem)? If you think that there is no such difference, what would you make of the commonsense distinction between understanding and mere knowledge (without understanding)?
Have you read his two dogmas?
http://www.ditext.com/quine/quine.html
Yes, some time ago, but I thought that 1.it is mostly attacking the analytic/synthetic distinction (which though in the positivists tradition is maybe seen as similar to a priori/posteriori distinction, seems as different to me), especially when 2.analytic in that tradition is closely related to the language/meaning, and I don’t think a priori truths (well, those which I think are a priori truths) like in math, have anything to do with language – e.g. it has nothing to do with language if triangles in euclidean geometry have a sum of their angles = 180 degrees.
But, might be that my comments here are off the mark, I probably need to reread the paper.
The point about the analytic/synthetic versus a-priori/posteriori distinction is a good one. I suppose it ends up being tied to how one views what the a priori is. If one is a constructionist about math one might say that it still exists as an a priori possibility given certain axioms. I’m certainly open to that kind of view. However it would seem we know them not in terms of the a priori but through experience. Of course a Platonist would demand something stronger. But I suspect one could be a kind of Platonist who thinks we still know through experience if reasoning is a kind of experience.
To be honest the only kind of a priori knowledge I could probably accept would be truths given us by the genetics and brain development we have. The question then becomes when they are knowledge. Are they knowledge innate? (An externalist might say this since we know them through a reliable method) Or are they only knowledge when we reflect on them.
It seems that there are all sorts of side issues one has to think through. I admit I just find the way Kant thought about them entirely implausible.
I am really unsure of the a priori. Freakly, i am bit skeptical of the very possibility. I have epistemic concern for how we come to have knoweldge of a claim that is supposed to be a priori.
In my mind, the distinction between a priori and a posteriori needs to be appreciated because they are both symbolic of two often-conflicting (though not so much now) inclinations – rationalism and empiricism. I believe that philosophers now choose to dilute this distinction between a priori and a posteriori as a means of mitigating rationalism – like Mr. Phillip Wong here suggested, nothing so far in reality that we have knowledge about was known solely and absolutely through the a priori method. When we gain knowledge a priori we use some base ideas to start out with. That knowledge itself is derived a posteriori. In practical terms, all instnces of a priori we know of are mitigated a priori. This is perfectly true for physics, but in a manner also for mathematics, for even mathematical logic needs the existence of the concept of numbers, which is in tun an allegorical derivation of real world quantities and the causal realism of rationality – both themselves being a posteriori.
Whether the distinction between a priori and a posteriori is justified, could only be known when there are no more uestions to be asked in physics – when we have a rationality explaining ALL. THEN, the distinction would be justiied.
I think too often we mistake certainty with knowledge. Also, you can know something without knowing that you know it and you can know something without knowing how you know it. There are three kinds of knowledge: knowledge by acquaintance, propositional knowledge, and skill/understanding/wisdom based on knowledge. When a child learns to identify objects he/she does learn a posteriori but there are instances where the child sees the picture of an apple for what it is, hears the word “apple” for the soundburst that it is and then learns to associate ( a posteriori) the apples picture with the soundburst “apple”. This is knowledge by acquaintance.
If you doubt that existence is apart from sensory perception then there really is nothing I can say to you. Good luck living out your egocentric life. How can I convince you that really exist apart from your perceptions if you aren’t even convinced that either of us exist.