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Tuesday, January 19, 2010

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About vicious, virtuous and benign regress, my opinion is the following:
First we should distinguish between the ontological level (the facts) and the epistemic one (descriptions, beliefs, explanations, definitions, verifications, identifications), and then between vicious regress, virtuous and benign (or harmless). A regress arises when a given concept is applied iteratively to the result of its application. If the notion is epistemic, we are talking about epistemic regress otherwise not. Vicious and virtuous (vicious when one is unsatisfactory, virtuous if it's satisfactory) regresses are epistemic regresses, otherwise the regress is benign.
The vicious regress is unsatisfactory because the application conditions of the epistemic concept are:
1) A transitive system of dependencies which induces us to require a completion of an infinite series of applications of the epistemic notion (which looks incompatible with the human capacity). E.g.:
- Since B causes A then I would say "I'm explaining A by B"
- But I can't say this until B is explained
- Since C causes B then I would say "I'm explaining B by C"
- But I can't say this until C is explained
The transitivity implies that if I didn't explain C then I didn't explain A. So at each actual application of the epistemic notion of "explanation" there is something which is still to be explained. I can't never say at a given time I've explained something.
2) A contradictory system of dependencies: by automatically iterating the application of an epistemic concept we posit the successive terms of the regress; but then we are demanding that the success of the preceding application of the epistemic concept depends on a successful application of the epistemic notion to the subsequent term, postponing the success of the first application endlessly, but in a completely fictitious, precisely because the successive terms in the regress would not have obtained if the first application had not been effective. In short, the contradiction in which we incur is that on the one hand the first application of the epistemic notion must be successful to generate the next term of the regress, but on the other hand it CAN NOT BE SUCCESSFUL until the application of the epistemic concept to the next term succeeds. E.g.:
- Since B causes A then I would say "I'm explaining A by B"
- But I can't say this until B is explained
The question is: how could I possibly think that mentioning B could be an appropriate answer to the question "what explains A?" if I don't think that B does explain A? But then why am I calling into doubt the validity of that answer about A by raising the same question about B, and claiming that till I don't explain B I can't say I've explained A? To raise question about B must mean that I'm assuming that B is effectively a term of the regress; otherwise if B was a fictitious term, I wouldn't even bother ask explanation for B, and the regress would simply stop, because it NEVER started!

Other examples:
Example 1:
- We do not know that p until we know all the implications of p
- The implications of p are themselves propositions
The epistemic notion to apply is "to know that p"
Example 2:
- I didn't explain an effect X causally until I explained all its causes
- The cause of y is itself an effect
The epistemic notion to be applied is "to causally explain the effect x"
Example 3:
- I have not defined a word X until I have defined all the terms that belong to the definiens
- The terms belonging to the definiens are words
The epistemic notion to apply is "to define the word X"
Example 4:
- I have not verified that S has moved over the continuous path AB, until I verify that S has moved over all the intermediate stretches of AB
- An intermediate stretch of AB is a continuous path AB' < AB
The notion is epistemic "to verify that S has traveled the continuous line AB"
Example 5:
- I have not described (or analyzed) a complex X until I have named all its constituents
- each constituent is itself a complex
The notion is epistemic "to describe (or analyze) a complex X"
One can provide another version of the same regress by using the notion of "explaining the unity of the fact X" or "identify the fact X" and similar. Bradley's regress is vicious

Once again: the epistemic concepts involved in these regress become inapplicable due to flawed conditions of applicability. The reason of their failure is not only because the validity of a single application of the notion requires the actual completion of an infinite series of valid applications, but also because there is a contradiction between two requirements: on one side the need to derive a successive term of the regress by applying the epistemic concept to the preceding term in the series; on the other side the validation of the application to the previous term by means of the application to the derived term, although it is clear that if the derivation wasn't valid, the successive term wouldn't obtain.

The notion of "cause", the logical notions of "implication" and "truth", and the mathematic notion of "continuity" allow endless iteration of their application but this regress is harmless in epistemic terms, precisely because they themselves do not imply as such vicious application of epistemic notions. And whenever one considers an iterative application of a notion as a vicious regress, it means that either the notion is espistemic and its application conditions are flawed or it implies an epistemic notion whose application conditions are flawed.

As the first Wittgenstein has already pointed out in his Tractatus, the viciousness of a vicious regress rests on a fundamental misunderstanding about the relation between world (facts or state of affaires) and the representation of the world (thoughts, beliefs and propositions)

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