This is an e-mail I have just sent.
Hello, xxx! It’s yyy here. Greetings!

I’ve been thinking about our discussion at zzz’s coffee room. I may have come to some interesting (tentative) conclusions! I think it will be best to separate the discussion in two kinds of scenario. This will be a long-ish e-mail, and I apologize in advance for any elliptic remarks or unnecessary long-windedness.

I. The first scenario is: real-life disagreement between philosophers. I think it is never the case that two humans wholly disagree on their intuitions. I am aware that you’re more interested in idealized cases of total “intuitive disagreement”, and I will consider this in section two (which I think is the more interesting part of this e-mail!).

Point one. In a nutshell: disagreement is usually about general or derivative statements, and less about the intuitive judgment of individual cases. — While it may seem to one philosopher that «Actions with the best consequences are always good», where to the other it seems that «Actions done in conformity to the Categorical Imperative are the only good actions», these two philosophers probably will not disagree in their intuitions of individual cases. This is where the concept of “biting the bullet” comes from: people accepting nigh-universally-recognized counter-intuitive judgments to preserve their general theory. The utilitarian does think it counter-intuitive that the doctor should kill his healthy patient in order to save the other five patients with his organs! Perhaps we can put it like this: (moral) reasoning can occur, and has occurred in the past centuries, precisely because people share many basic intuitions.

Point two. In a nutshell: intuitions about individual cases are usually negotiable, which makes inter-personal philosophical reasoning possible. — Intuition is not an infallible source of judgment, and one can have one’s intuitions mixed-up by confusion, misunderstanding, and lack of perspective. This is to be expected when we’re dealing with subtle, abstract, and complex questions, which are usually the turf of philosophy. For example, thinkers can learn that they weren’t considering all relevant factors of an individual case, and thereby change their intuitive judgment about it; or, they can learn of individual cases which provoke strong intuitions against their former general or derivative conclusions. (It is very common to have an “unbalanced diet of examples”!) Perhaps we can identify at least two sources of disagreement: (i) Oversight: intuitions are a vast pool of resources we rarely take into account all at once, such as when the utilitarian ignores counter-intuitive scenarios, and (ii) Misunderstanding: intuitions start uncultivated, but they can be refined to reflect a better understanding of the concepts, scenarios, arguments, and problems in question and their multiple interconnections.

Would there be disagreement between two humans capable of having a complete perspective on their pool of intuitions, and capable of perfectly understanding what’s at stake? Would there be irresolvable disagreement between humans at the end of their personal reflective equilibria? — The answer may lie in the next section.

II. The second scenario is: two entities understand perfectly what’s at stake, and disagree permanently on all their intuitive judgments (aliens vs. humans).

Now we are before a discussion whose two parties are (by stipulation!) permanently unwilling to accept any premise the other may offer in their reasoning. I want to avoid this possibility. I want to find out whether this scenario is even «possible»: whether there could be permanent disagreement between two agents who fully understand what’s under discussion.

Here’s a possibility of avoiding it. Perhaps some propositions are undeniable by any entity that fully grasps what the proposition means. Perhaps it is unthinkable to suppose two entities could be «intelligent» — to suppose that two entities could «understand completely what the ideas under discussion» — and still disagree whether 1+1=2, whether it is wrong to gratuitously throw an innocent person in a pool of acid, whether an entirely yellow surface can be also entirely purple, whether ex nihilo nihil fit, whether modus tollens is a valid argument, and whether a priori knowledge is possible!

(Please do not confuse me with saying such undeniable, necessary moral, metaphysical, epistemological, logical, and mathematical truths are analytic truths! That’s not the idea at all.)

If they could disagree, on the one hand, then I fail to see how there could be a “higher court” than that, if you understand what I mean. Once one abandons basic intuitions and allows for complete intelligent disagreement, I don’t think there’s anything left to grasp for. Reflect upon it: we cannot get any reasoning (or meta-reasoning, or meta-meta-reasoning, etc.) started if it possible to intelligently disagree (that is, disagree with full understanding of what’s under discussion) about any premise or principle that could be invoked to settle anything. In this case, I find it unsurprising that there’d be irresolvable disagreements.

If they couldn’t disagree, on the other hand, then the imagined scenario we were discussing is impossible. This could be the case if intuitions worked in the way I speculated above: we grasp concepts (or whatever they may be) and we just see (an intellectual kind of seeing) that they have certain features and relations. That’s the source of a priori knowledge. A cultivated intuition is just the intellectual understanding that every natural number has a successor, that A & A→B entails B, or that causing great unnecessary woe to innocent persons is wrong — if that turns out to be true. (An uncultivated intuition is, contrariwise, the appearance that something must be the case when it really mustn’t; an appearance due to intellectual oversight or misunderstanding.)

III. Conclusions. Thus, the claim that the adoption of an intuitionistic epistemology (and I currently doubt there’s any other possible epistemology!) opens up the possibility of permanent, complete, intelligent disagreement, is either (i) inevitable and unsurprising — because how could there be any further resources for solving disagreements, if all premises and principles of inference are always denied? — or (ii) false, due to the existence of a priori knowledge!

I want to re-state my conclusions, just to make them clearer. (a) Either a priori knowledge is possible, or there could be irresolvable disagreements. (b) Either a priori knowledge occurs automatically once one understands perfectly the ideas (scenarios, arguments, concepts, etc.) involved in the discussion, or there could be irresolvable disagreements between intelligent and fully-understanding agents.

Based on conclusion “(b)”, I say we must always begin arguments and reasonings with premises and principles of inference that “seem to be true” — that is, that are intuitive. There’s no other place to start, and along the whole process of cultivating our intuitions and performing reflective equilibrium we are supporting ourselves in intuitions.

Perhaps we can only «hope» that (1) intuitions do reflect intellectual understandings, and that (2) there is a priori knowledge to be had through intellectual understanding — OR, perhaps, we can find intuitive grounds for concluding “(1)” and “(2)”, needing thus no hope. If my account is correct, these intuitive grounds would spring from an understanding of why “(1)” and “(2)” must be the case.

(Perhaps it seems unsatisfactory that we need to use cultivated intuitive judgments to justify our belief in the truth-conduciveness of cultivated intuitive judgments. But such (hopefully benign) circularity cannot be avoided. We should shed our desire to find a “highest ground” upon which we wouldn’t need to justify our reliance on it using itself. There never could be such a thing!)

I hope you have found my hypotheses plausible (that is, intuitive) and my conclusions tenable (that is, supported by intuition)! Thank you for your sustained attention,