Taxonomising subsumptive justification, let's call it 'derivationalism'.

The two paradigms of justification are foundationalism and coherentism; where does subsumptive justification fit in with that?

Foundationalism is the method of justification whereby derived claims are justified in terms of fundamental claims. Coherentism is justification whereby claims are justified in terms of how well they cohere with other claims.

Well, it clearly doesn't seem to fit in with either of those, although it can be seen to be the reverse of foundationalism. So really, are we not talking about a kind of reverse foundationalism? 'Subsumptive justification' is a bit of a mouthful, so let's just call it 'derivationalism' instead, since I think that a clear case can be made for it as its own kind of justification.

Note that one advantage of derivationalism is that it can be fruitfully combined with foundationalism while moderated by coherentism. Both kinds of justification rely on a conceptual hierarchy of claims, with higher claims deriving logically from lower ones--I shall here call them "claim chains". It is reasonable that in a large enough desirable claim chain, not all the chains will necessarily depend on intuitively compelling foundations. With derivationalism included in the mix, however, not all of them have to do so. Sometimes, uncompelling foundations can entail attractive derivations, and when this happens, it seems reasonable to hold those foundations on the grounds of the 'fruit' that they have born. That's derivationalism! The point is that both foundationalist and derivationalist claim chains can coexist in the same conceptual hierarchy just as long as they cohere with each other--which is where the 'moderation by coherentism' comes into it.

Note, however, that I really do think that this is just a moderation by coherentism. It is definitely far different from the prototypical coherentist belief system, which does not depend on conceptual hierarchies at all. In a pure coherentist system, each belief would in some way reinforce every other belief, in a fairly democratic way. Of course, some beliefs would justify more beliefs more strongly than other beliefs would, but in general, there would be nothing like the rigorous conceptual hierarchy that foundationalism demands. Whereas, in the abovementioned foundationalist/derivationalist structure, no democracy of justification would exist at all. Every belief would exist in a strict hierarchy with every other belief.

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