Dried Roses

Two new theorems in number theory

In grade school we learn how to divide one whole number by another. Sometimes nothing is left over, but often the division leaves a “remainder”. One learns to say “Eleven divided by five is two remainder one”. Numbers that always leave a remainder when divided by another number other than themselves or 1 are called prime. All other numbers are called composite (except 1, which is neither prime nor composite).


LinkMay 21, 2013 in History of Science · Philosophy of Mathematics | Comments (0)

The soul of man pictured

Source: Jan Comenius, Orbis pictus
(Syracuse, NY: C. W. Bardeen, 1887).
The illustration above is from Jan Comenius’ celebrated, oft-reprinted school-book. The Orbis sensualium pictus presents, in words and in pictures, “all the fundamental things in the world and all the acts of life”. In pictures (an expensive novelty at the time) because, after all, “in Intellectu autem nihil est, nisi priùs fuerit in Sensu” (a famous Aristotelian slogan), and so one must exercise the senses, perceiving by their means the differences of things, so as to lay the foundations of wisdom and right action.


LinkMay 21, 2013 in History of Science · Psychology

Adversaries and disputants, gender and argument

Inspired by some comments of Jennifer Saul on Rebecca Kukla’s remarks concerning the “aggressive, argumentative” style in philosophy, Eric Schliesser and Catarina Dutilh Novaes here at NewAPPS have taken up the question of what I would call the character of philosophy. Does it consist in contests in which adversaries, having occupied positions, not only defend them vigorously but also attack those positions which, being contrary to their own, they take to be opposed to their own? Readers of Lakoff and Johnson’s Metaphors we live by will recognize here a familiar conceit: argument is war. How warlike should philosophy be?
Consider an ideal type: the (pure) adversary intends that his or her position should prevail. To be an adversary is, by presumption, to be engaged in a contest, that is, in a collective endeavor in which it makes sense to occupy a position.
It is clear from the discussion that no-one really thinks that philosophers should be pure adversaries. We don’t intend that our position should prevail come what may, but that our position should prevail, given that it is (as we think) true, or given that it has (as we think) the balance of reasons in its favor (a condition for which I will use the word “probable” in its older, scholastic sense). We aren’t pure adversaries, but rather adversaries in good faith. (For completeness’ sake I should have an account of devil’s advocacy, i.e. of arguing for positions that one does not in fact regard as true or probable. That would be either a mere exhibition of skill or else a component of some larger act of advocacy in good faith.)
So: a second ideal type. The (pure) disputant intends that his or her position should prevail, provided that it is true (or probable). The scholastic conception of philosophy was of a disputational, not an adversarial, endeavor whose end is the discovery of the true or the probable. In the American court system, on the other hand, because the legal question of guilt or innocence is decided (ceteris paribus) by a jury’s or a judge’s verdict, the proceedings are not, in an immediate way, disputational; instead there is a strong tendency for lawyers to become pure adversaries, their proximate end being not truth but persuasion. (On a distinction between “negotiation” and “scholarly communication” which is analogous to the distinction made here, see Andrew Gelman on “Different modes of discourse”.)
In philosophical discussion (as always, I presuppose good faith) it is understood that assertions must either be defended if questioned or explicitly taken as assumed (locally if not globally) for the sake of argument. A philosopher writing in an aphoristic mode may proceed as if that requirement had been suspended: but it is only suspended, not removed. To remove it would be to shift the aims of philosophy, e.g. toward spiritual exercise (historically, a character of philosophy no less prominent than truth-seeking: see Pierre Hadot’s Exercices spirituels et philosophie antique, Matt Jones on Descartes, Pierre Force on Montaigne and Pascal, and John Sellars on Justus Lipsius).
Philosophical discourse is in that respect always disputational. At minimum to offer reasons for p is also to offer reasons against not-p, and thus to implicate a sort of contest between the proposition asserted and its negation. (On the agonistic origins of Western philosophy see G. E. R. Lloyd’s Revolutions of wisdom and Demystifying mentalities and Marcel Detienne’s Maîtres de vérité; on scholastic disputation, see John Marenbon’s Later medieval philosophy, and on disputation as ritual spectacle see Enders 1993 in the bibliography below; Catarina Dutilh Novaes has written here on argument as dialogue). Kukla is right in exhibiting contempt for anyone who is put off by mere disagreement among philosophers (see also her further remarks at Facebook). But I see no reason to suppose that philosophy must be aggressively disputational. Must an objection be cast as an attack? Disputation needn’t be agonistic, in my view; on the contrary, if the collective aim is to conduct an inquiry into truth, cooperation may be just as productive. Placing a “high premium on verbal sparring and cleverness” (where cleverness denotes something other than or in addition to skill in argument) is at best an imperfect means to that aim; and it exacts a significant social cost insofar as it amplifies disparities of power which have nothing to do with the capacities needed to conduct inquiry.
An intense aggressive style can be used as an instrument of oppression: on that point I suppose there will be agreement. “Your objection has no merit” can be a way of saying “Shut up”, an exercise of power. But I take it that Kukla would include browbeating among the activities she agrees should be discouraged. So the question resolves itself to this: does the intense aggressive style itself (if indeed we can detach the exercise of that style from the social meanings of aggressiveness in particular social contexts) function as a filter in academic philosophy in ways that we would reject, once it became apparent that it was functioning thus? Kukla tries to arrange it so that the burden of proof is on the person who says yes, demanding evidence for that position while offering (so far as I can tell) only her own experience on behalf of her own. If you are antecedently persuaded of the benefits of the intense aggressive style, that may be enough. (I am not so persuaded. Perhaps that is because I am not solely concerned with who should be a philosopher, but with the social profile of philosophy generally.)
Kukla holds that, as far as she can tell, the intense aggressive style puts off people of all sorts equally, and so no social harm will result from its being a common or the prevalent style in philosophy. That, of course, is an empirical claim. Evaluating it would require an intimacy with the literature on small-group dynamics and on negotiation (since I think it reasonable to regard the activity of a seminar, e.g., as consisting partly in negotiations about group beliefs) that I lack. Perhaps others more qualified can comment on that point. I will conclude with some impressions.
In a quick review of studies of negotiation, the firmest general conclusion I can draw is that small differences in setting and expectation can generate significant differences in the importance of gender to influencing behavior. There is no easy answer to the question raised above. For example, if an activity is framed as a winner-take-all competition, women, even those who do well, are less likely to choose to take part than men (Bertrand 2010:1555), which suggests that we not frame discussion in such a way that only one person can be right. Or again: “women’s performance in negotiation improves significantly when negotiating for someone else as opposed to for themselves” (Bertrand 2010:1557), which suggests that we frame the task of discussion not as that of defending my opinion as against yours, but rather as that of determining which of the alternatives we should maintain.
It would seem that the trend of the later literature points to two major conclusions: (i) the differences are usually not large, and are exhibited only when conditioned on other features of the situation; (ii) other relations, notably power relations, with which gender relations are correlated may have a greater role in social interaction. In short: under favorable circumstances, prevalence of the intense aggressive style need not, perhaps, aggravate inequality, in particular gender inequality. But it is up to us to ensure that circumstances are favorable.
    Marianne Bertrand. “New perspectives on gender”. In: Handbook of labor economics 4b: 1545–1592.
    Linda L. Carli. “Gender, language, and influence”. Journal of personality and social psychology 59.5 (1990) 941–951.
    Renee Edwards, Mark A. Hamilton. “You need to understand my gender role: an empirical test of Tannen’s model of gender and communication”. Sex roles 50.7/8 (2004) 491–504. (Also a nice example of modelling complex causal relations.)
    Jody Enders. “The theater of scholastic erudition”. Comparative Drama 27.3 (1993) 341–363.
    Annette Hannah, Tamar Murachver. “Gender and conversational style as predictors of conversational behavior.” Journal of language and social psychology 18.2 (1999) 153–174.
    Michael A. Gilbert. “Feminism, argumentation and coalescence.” Informal logic 16.2 (1994) 95–133 (with bibliography of earlier literature).
    Deborah M. Kolb. “Too bad for the women or does it have to be? Gender and negotiation research over the past twenty-five years”. Negotiation journal Oct 2009:515–531.
    Laura J. Kray, Leigh Thompson, Adam Galinsky. “Battle of the sexes: gender stereotype confirmation and reactance in negotiations.” Journal of personality and social psychology 80.6 (2001) 942–958.
    Alex J. Novikoff. “Toward a cultural history of scholastic disputation”. The American historical review 117.2 (2012) 331–364.
    Amy E. Walters, Alice F. Stuhlmacher, and Lia L. Meyer. “Gender and negotiator competitiveness: a meta-analysis”. Organizational behavior and human decision processes 76.1 (1998) 1–29.
    Janice D. Yoder, Arnold S. Kahn. “Toward a feminist understanding of women and power”. Psychology of women quarterly 16 (1992) 381–388.

LinkMay 30, 2013 in NewAPPS · Philosophy of Philosophy · Society | Comments (0)