No more reductiones!

Brown's second argument is essentially an "all hell will break loose" argument: if mathematics needn't be accountable to philosophical standards of rationality, then it might as well be speculative theology! At this point, Brown assumes that theology obviously doesn't get hold of the truth, and so any philosophical account of math that makes it seem like theology must be absurd. Not only is this argument an insult to the careful thinking of theology-friendly philosophers such as Robert Adams and Alvin Plantinga...--Hans Halvorson reviewing James Robert Brown, Platonism, Naturalism, and Mathematical Knowledge.

I have been hesitant to write about this because "speculative theology" and the name "Plantinga" are so polarising at the moment. Yet, Halvorson's rhetoric here strikes me as dangerous for our community. For, (a) if there are careful thinkers defending or working on, say, X, Halverson's position seems to imply that any reductio toward X becomes insulting to these particular careful thinkers defending or working on X. (Or something like that.) Call (a) the "Halvorson move." The whole glory -- maybe it is a problem? -- of analytical philosophy is that our methods and tools can be used to do careful and serious work on just about any X. The reason it is dangerous is not (although it may occur) that the Halvorson move will have a chilling effect on philosophical exploration--no more reductio! (I am not unsympathetic to the abolishment of reductios.)

Rather, the Halvorson move turns what seemed like a philosophical dispute into what will be perceived as a personal insult henceforth. Now, I am not against using the desire to prevent injustice(s) as an epistemic means toward philosophical truth. Yet, Brown's reductio is not causing an injustice toward Adams or Plantinga -- who are, by stipulation, careful and serious thinkers -- in any ordinary sense,  unless not taking their work seriously at all ought to count as an injustice. But then, let him (or her, or s/he) who is without such sin (i.e., always having an open mind about serious work on any X), cast the first stone.