There are empirical indications that various skills and maybe even virtues are pretty domain specific. It seems that being good at reasoning about one thing need not make one good at reasoning about another, even if the reasoning is formally equivalent.
I do have a piece of anecdotal data, though. I’ve been doing some endurance-ish sports. Nothing nearly like a marathon, but things like swimming 2-3 km, or climbing for an hour, typically (but not always) competing against myself.
And I have noticed some transfer of skills and maybe even of the virtue of patience both between the various sports and between the sports and other repetitive activities, such as grading. There is a distinctive feeling I have when I am half-way through something, and where I am fairly confident I can finish it, and a kind of relaxation past the half-way point where I become more patient, and time seems to flow “better”. For instance, I can compare how tired I feel half-way through a long set of climbs and how tired I feel half-way through a 2 km swim, and the comparison can give me some strength. Similar positive thinking can happen while grading, things like “I can do it” or “There isn’t all that much left.” Though there are also differences between the sports and the grading, because in grading the quality of the work matters a lot more, and since I am not racing against myself so there is no point of a burst of speed at the end if I find myself with an excess of energy. Pacing is also much less important for grading.
I have no idea if anything like this transfer works for other people.
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This is akin to the 'positive transfer' of skills, as discussed with the sport science. So-called 'negative transfer', its opposite, is to be avoided at all costs. For example, if I try to play squash to improve my racket skills, I will ruin my tennis game. The racket skills are subtly different, due to the 'wrist flick' in the squash technique.
BTW, it may depend on how much one keeps to proper form in the different racquet sports. Someone like me who plays lots of different racquet sports (regularly: badminton; semi-regularly: tennis, racquetball, table tennis, pickleball; used to do occasional squash until our university's one court closed as nobody but my son and I played; used to do crossminton during Covid), maybe at an upper beginner level, perhaps does not have enough good form in any one of the sports for it to matter. I hadn't played much tennis this fall, but I played a fair amount of badminton, and seemed to find my tennis improved when I got back to it, maybe due to transfer of thinking about things like "how do I hit the shuttle away from where my opponents are", or maybe just due to general fitness improvement.
I think that's correct. The more one concentrates on good form, the more detrimental negative transfer becomes. This also applies in martial arts like Tae Kwon Do, on the self-defense side, whereby training to 'pull' kicks and punches (i.e. to safeguard your training partner), negatively transfers to real-life situations.
I've wondered about such incompossible goods myself. Weightlifting can reduce agility, for example, and while being tall is great for basketball, it is not good for weightlifting. Various niches seem to exist. It does raise the question of what a perfect human being consists of, however. Are some of these "perfections" merely accidental in the sense that they exploit what are normatively speaking (in relation to human nature) flaws? We know some sports are actually bad for the human body, or neglect the overall health of the body. Certain perfections seem to be perfections only in an analogical sense, perhaps something along the lines of being a "good thief" or an "effective deceiver".
Where intelligence is concerned, I am tempted to argue against incompossible goods either because intelligence isn't like that or for similar natural law reasons, but even more strongly, especially on account of the centrality of intelligence to humanity.
Consider your favorite déformation professionnelle, which, I submit, is more of a result of imprudence, habit, ignorance, lack of practice using other methods, and even effeminacy and arrogance. Someone with a rigorous philosophical education is less likely to try to pigeonhole reality into the reductive and simplified straitjacket of our physical models in the manner of at least some physicists who generally lack serious exposure to philosophy and may even hold it in contempt out of ignorance. A physicist may also be tempted to pigeonhole simply because of pride; if he isn't any good at metaphysics, then his thoughts on a metaphysical subject matter aren't likely to be very valuable or interesting, and that stings the prideful man accustomed to feeling like a hotshot. There is also the threat of seeing one's own field put in its methodological place, so to speak, deflating any pretensions to the kind of ultimacy that metaphysics lays claim to. A competent physics may also derive greater pleasure from exercising his specialized competence and choose his methods simply on the basis of what feels good and now what is called for by a problem. So here the question resurfaces: is there an incompossibility between being a good physicist and a good metaphysician? I suspect there isn't intrinsically, even if that is often the case which I suspect is rather a result of how one's time is spent. But even if it is the case, because general knowledge is superior and more worthy of human attention than specialized knowledge, we could argue that competence in physics that occurs at the expense of philosophical depth is, in fact, a kind of failure to attain human excellence by failing to devote proportional attention and effort to the kinds of knowledge that are most essential, and in doing so, risking intellectual deformation in important and even necessary matters.
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