Friday, May 08, 2009

Logicality & paradoxicality

Christian theologians often invoke the category of “paradox” in Christian theology. Unbelievers regard that appeal as special pleading. From their standpoint, certain Christian doctrines are contradictory, and any appeal to paradox to justify such doctrines can only be ad hoc.

However, there’s an obvious problem with that objection. It’s not as if Christian theology has a monopoly on paradox. Paradox crops up in logic, science, philosophy, and mathematics. That being the case, why would Christian theology be any exception?

In addition, Gordon Clark and his followers reject theological paradox because, according to them, once we make allowance for paradox, we can no longer distinguish an actual contradiction from a merely apparent contradiction.

However, there are a couple of problems with that objection. One problem is that it’s a purely pragmatic objection. It substitutes hand-waving for a principled resolution to the widespread phenomenon of paradox in various fields of knowledge. A rationalist can’t very well content himself with a purely pragmatic objection to a logical paradox.

And even at a pragmatic level, the allegation is dubious, as James Anderson has attempted to demonstrate.

A preliminary question we need to ask ourselves is whether humanly insoluble paradoxes are antecedently impossible or even improbable. With that question in mind, I’d like to quote from two standard monographs on paradox.

“Paradoxes are serious. Unlike party puzzles and teasers, which are also fun, paradoxes raise serious problems. Historically, they are associated with crises in thought and with revolutionary advances. To grapple with them is not merely to engage in an intellectual game, but is to come to grips with key issues. In this book, I report some famous paradoxes and indicate how one might respond to them. These responses lead into some rather deep waters,” R. M. Sainsbury, Paradoxes (Cambridge, 2nd. ed., 2002), 1.

“This is what I understand by a paradox: an apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises. Appearances have to deceive, since the acceptable cannot lead by acceptable steps to the unacceptable. So, generally, we have a choice: either the conclusion is not really unacceptable, or else the starting point, or the reasoning, has some non-obvious flaw. Paradoxes come in degrees, depending on how well appearance camouflages reality,” ibid. 1.

“The deeper the paradox, the more controversial is the question of how one should respond to it…This means that there is severe and unresolved disagreement about how one should deal with them. In many cases, though certainly not all (not, for example, in the case of the Liar), I have a definite view; but I must emphasize that, although I naturally think my own view is correct, other and greater men have held views that are diametrically opposed. To get a feel for how controversial some of the issues are, I suggest examining the bibliographical notes at the ends of chapters,” ibid. 2.

“However, logic alone will not help us to choose how a conflict of inconsistency should be resolved. It does no more than tell us that we must forego one of the claims, but affords no hint as to which one…Which route shall we choose? Here we are simply at sea–unless and until we have some further guidance,” N. Rescher, Paradoxes (Open Court 2001), 11.

“Unfortunately, life being what it is, we cannot always get away with accepting the plausible outright because actual truth is something more selective and demanding than mere plausibility, seeing that plausibilities–unlike truths–can conflict both with truths and with one another,” ibid. 17.

“’Paradoxes,’ one student of the subject writes, ‘are self-enclosed statements with no external reference point from which to take a bearing upon the paradox itself.’ And this is true enough. For those paradoxical inconsistencies themselves afford no resources for their resolution–mere logical analysis of their assertoric content is no way out. To resolve paradoxes we need an external vantage point–a means of assessing the cognitive viability of the mutually incompatible theses that are involved, something about which those propositions themselves do not inform us,” ibid. 30.

“A fundamental fact of paradox theory–of aporetics–is that every paradox is resolvable in principle by abandoning commitments. For if we dismiss (and thus withhold endorsement from) sufficiently many of the theses that constitute the aporetic cluster at issue there will no longer be an inconsistency among our actual commitments. However, even the best available resolution may well be an indecisive one that leaves us confronting a disjunctive plurality of alternatives no particular one of which can be preferentially justified in the circumstances,” ibid. 37.

“Some paradoxes do not admit of a decisive resolution…It is clear, however, that ‘undecidable’ paradoxes of such a sort–where no particular resolution can be privileged on the basis of general principles–are distinctly more deeply paradoxical than their simpler compeers where a decisive resolution can be achieve,” ibid. 65-70.

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