07 February 2006

Rigor Mortis

Commentators compare Aristotle, Metaphysics II.3, in its discussion of limits of accuracy, to Nicomachean Ethic I.3. But I find it interesting that the former contains a 'moral' reason for lack of accuracy, not mentioned by the latter:

Again, some require exactness in everything, while others are annoyed by it, either because they cannot follow the reasoning or because of its pettiness; for there is something about exactness which seems to some people to be mean, no less in an argument than in a business transaction. Hence one must have been already trained how to take each kind of argument, because it is absurd to seek simultaneously for knowledge and for the method of obtaining it; and neither is easy to acquire. Mathematical accuracy is not to be demanded in everything, but only in things which do not contain matter. Hence this method is not that of natural science, because presumably all nature is concerned with matter (Ross, 995a7-16)

kai\ oi( me\n pa/nta a)kribw=j, tou\j de\ lupei= to\ a)kribe\j h)\ dia\ to\ mh\ du/nasqai sunei/rein h)\ dia\ th\n mikrologi/an: e)/xei ga/r ti to\ a)kribe\j toiou=ton, w(/ste, kaqa/per e)pi\ tw=n sumbolai/wn, kai\ e)pi\ tw=n lo/gwn a)neleu/qeron ei)=nai/ tisi dokei=. dio\ dei= pepaideu=sqai pw=j e(/kasta a)podekte/on, w(j a)/topon a(/ma zhtei=n e)pisth/mhn kai\ tro/pon e)pisth/mhj: e)/sti d' ou)de\ qa/teron r(a/|dion labei=n. th\n d' a)kribologi/an th\n maqhmatikh\n ou)k e)n a(/pasin a)paithte/on, a)ll' e)n toi=j mh\ e)/xousin u(/lhn. dio/per ou) fusiko\j o( tro/poj: a(/pasa ga\r i)/swj h( fu/sij e)/xei u(/lhn.

I think sumbolaion here is 'contract', and Aristotle's point, quite perceptive, is that attempts to put too much detail into contracts can seem to display, and perhaps typically do (echei ti to akribes toiouton), an absence of trust and friendliness. (We presume: it is impossible for contracts not to be open-ended; it is impossible to make fully explicit all of the terms of a contract.)

This would seem to imply a reason why rigor beyond a certain extent can be excessive in ethics as well: it would not allow sufficient scope for the good judgment of one's hearer. And yet (I think) that reason seems unstated in Nic. Eth., where we might most expect to find it.

A common view of the search for an ideal of rigor, in Frege and writers who follow him, is that complete rigor eliminates the need for intuition: in fact you can show that nothing like 'intuition' is needed for mathematical reasoning, if you can give a proof with complete rigor. But then presumably in fields in which the elimination of 'intuition' is impossible, or undesirable even if possible--limits to rigor are set primarily on moral grounds, and one offends (lupei) by inappropriate and excessive rigor.