Finished the section on the Regress Problem.

According to foundationalism, the regress is found by finding a stopping point for the regress in terms of foundational beliefs that are justified but not wholly justified by some relationship to further beliefs. (My emphasis.)

This is a turning point. According to this claim, some foundational beliefs could therefore be justified but not wholly justified by some relationship to beliefs derived from them. This sounds like subsumptive justification is more compatible with foundationalism than I thought.

Coherentists deny the need and the possibility of finding such stopping points for the regress.

In that case, the specific use for subsumptive justification that I have in mind is definitely foundationalist. I really don't think that science progresses if it isn't supported by some kind of foundationalism, as paradigmatic assumptions. This is what allows scientific debate to end, and be resolved one way or the other in order to move onwards from there.

Sometimes coherentism is described as the view that allows that justification can proceed in a circle (as long as the circle is large enough), and that is one logically possible version of the view (though it is very hard to find a defender of this version of coherentism).

Subsumptive justification is therefore compatible with either foundationalism or coherentism. Foundationalism can use it as a partial justification for its stopping points. Coherentism can use it as one of the techniques for bypassing stopping points, by linking a bottom-level claim to a top-level claim in a circle of justification, as described above.

Neurath's boat metaphor — according to which our ship of beliefs is at sea, requiring the ongoing replacement of whatever parts are defective in order to remain seaworthy–and Quine's web of belief metaphor–according to which our beliefs form an interconnected web in which the structure hangs or falls as a whole — both convey the idea that justification is a feature of a system of beliefs.

This is here presented as the more standard version of coherentism. I have already argued in Hierarchical versus Network Coherentism that I regard this view as fundamentally flawed, at least as it applies to level 2 claims in science. It removes the sharp distinction between confirmation and refutation of a hypothesis that science must make.

However, if only applied to the level 1, paradigmatic claims, it seems fair. It explains why paradigms succeed or fail as a whole, and survive anomalies in the interim with workarounds. The ship, in that case, finally sinks when too many workarounds become necessary and another paradigm becomes more attractive, solves more problems, or so on.

The classic example that Kuhn provides of this is the problems with Ptolemy's system of the planets. The assumptions became unnecessarily complex the more 'epicycles' needed to be added to explain the orbits of the planets. When Copernicus's pardigm came along, it was seen to fit the facts more elegantly, and scientists switched to it instead.

This negative point can be maintained either by denying that the chain has a stopping point, thereby endorsing a linear version of coherentism, or by denying the assumption that justification requires the existence of an inferential chain of reasons, thereby endorsing a holistic viewpoint.

This will be a useful dichotomy within coherentism. In fact, I can see from this section a very elegant taxonomy of epistemology. This taxonomy will help to provide a roadmap to enable the budding epistemologist better to decide where his own beliefs fall in the epistemological spectrum.

The regress problem can be seen as the point of departure. The beginning of philosophy is always a problem that admits of more than one self-consistent solution. That is what makes the problem of philosophical interest, that it allows philosophers to carve out different areas of the noosphere around it and defend their turf with reason and argument.

The first fork in the taxnomy is between skepticism and non-skepticism. Skepticism takes the regress problem seriously, and therefore denies the possibility that anything can be justified. Non-skepticism does not take the regress problem seriously, and therefore seeks means of either preventing it or denying that it is vicious.

The first fork in the tine of non-skepticism is between what I term finitism, and infinitism. Finitism denies the inevitability of a regress, and looks for ways of avoiding such as the means to justification. Infinitism, on the other hand, asserts the inevitability of a regress, but claims that an infinite regress of nonrepeating beliefs does constitute justification.

On the finitist tine of the fork lies foundationalism and coherentism. Foundationalism asserts that there are foundational stopping points in the regression that form the basis of justification. Coherentism asserts that no stopping points are possible, and that justification of beliefs does not rely on such stopping points in the first place.

Finally, on the coherentist tine of the fork, comes the fork of linear coherentism versus holistic coherentism. Linear coherentism states that justification comes from a circular chain of beliefs. Holistic coherentism states that the entire web of belief stands or falls as a whole, replacing individual parts as needed without damaging the integrity of the entire web.

I do not here attempt to taxonomise the various kinds of skepticism about justification. The project is not particularly interesting, because the tree of skepticism is just the converse of the tree of non-skepticism. Hence, the counterpart to infinitism is skepticism about infinitism, the counterpart to finitism is skepticism about finitism, and so on.