Methodists Vs. Particularists

In Intuition in Philosophy, I suggested that one difference between, say, mathematicians and philosophers is that philosophers will willingly privilege an intuition over a derived result whereas the mathematician will reject the intuition in favor of the derived result. To some extent I think this characterization may not have been entirely accurate. At the very least some clarification needs to be made.

I here will argue that many philosophers are particularists whereas mathematicians tend to be methodists. "Intuition" plays a role in what particulars the philosopher claims to have knowledge. This allows for there to be something along the line of "mathematical intuition" of which I think is believed to be present by many mathematicians. I will briefly sketch out the issue here.

I borrow the terms "particularist" and "methodist" from Roderick Chisholm with respect to The Problem of the Criterion. Chisholm paraphrases Montaigne as saying:

To know whether things really are as they seem to be, we must have a procedure for distinguishing appearances that are true from appearances that are false. But to know whether our procedure is a good procedure, we have to know whether it really succeeds in distinguishing appearances that are true from appearances that are false. And we cannot know whether it does really succeed unless we already know which appearances are true and which ones are false. And so we are caught in a circle.

Methodists are then those who hold that we have a procedure for making the relevant identifications. Then we can apply that procedure to particular cases. We know the particulars in virtue of application of the procedure.

Particularists, on the other hand, are those who believe we know particular things. We then attempt to formulate more general techniques and procedures but ultimately we will test these procedures against the particulars we already know.

To use the mathematical example I used in the prior post, the particularist would say that we already know that "all curves have a tangent" so if our definitions (criteria, procedures, etc) fail to derive that result, then we ought to reject those definitions.

Mathematicians tend to be methodists. They accept the definitions as given and then accept the particular results which follow.

Many philosophers appear to be particularists. The intuitionist sort of particularists believe that "intuition" or "common sense" grounds the "knowledge" of those particular beliefs.

Later I plan to take a closer look at particularism. I believe it's possible that particularists are not really particularists.