With the exception of people on Less Wrong and people in the mathematical community, I’ve almost never seen high functioning people use the “relatively one strong argument” approach.
I think it’s more general than that (depending in your definition of the ‘mathematical community’). For example, I rarely see physicists attempt to argue something based on many weak arguments, and I think you would find the same to be true of engineers. More generally, I think that anyone who’s used to formalism is used to being presented with extremely strong arguments, and ending the search for arguments there. Consider a Bayesian actor who happens to be in a quantitative field of study:
I decide proposition A is true, and sketch out a proof on some scratch paper. The probability that I made a mistake is significantly smaller than the probability that I didn’t. I go home and write the proof out formally and carefully, and the probability of me being wrong drops further. I ask a peer to look over it and the probability that I make a mistake is vanishingly small. If prop A is important, then I may publish it, and after peer review, I can say that I have a strong argument for A: I have a proof P, and if P is correct, then so is A, with probability 1. The probability that P is incorrect is small, thanks to the formalism and many levels of peer review.
Since most of the arguments we believe are thus strong arguments, this trains our intuition with a heuristic to not bother looking for arguments that aren’t extremely strong. This effect would probably scale with the rigor of the field (eg be much stronger in mathematicians, where proofs are essentially the only form of argument written down)
The best physicists use the “many weak arguments” approach at least sometimes. See my post on Euler and the Basel Problem for an example of this sort of thing. (Nowadays, physicists fall into the Eulerian tradition more than mathematicians do.)
A close friend who’s a general relativity theorist has told me that the best physicists rely primarily on many weak arguments.
Hmm, I think I may be misunderstanding what you mean by “many weak arguments.” As in, I don’t think it’s uncommon for physicists to make multiple arguments in support of a proposition, but even each of those arguments, IME, are strong enough to bet at least a year of one’s career on (eg the old arguments for renormalization), by contrast with, say, continental drift, where you probably wouldn’t be taken seriously if you’d produced merely one or two lines of evidence. What this shares with the “one strong argument” position is that we’re initially looking for a sufficiently convincing argument, discarding lines of though that would lead to insufficiently strong arguments. It’s different mostly in that we go back and find more arguments “to be extra sure,” but you’re still screening your arguments for sufficient strongness as you make them.
Though admittedly, as a student, I may be biased towards finding my professors’ arguments more convincing than they ought to be.
I think it’s more general than that (depending in your definition of the ‘mathematical community’). For example, I rarely see physicists attempt to argue something based on many weak arguments, and I think you would find the same to be true of engineers. More generally, I think that anyone who’s used to formalism is used to being presented with extremely strong arguments, and ending the search for arguments there. Consider a Bayesian actor who happens to be in a quantitative field of study:
I decide proposition A is true, and sketch out a proof on some scratch paper. The probability that I made a mistake is significantly smaller than the probability that I didn’t. I go home and write the proof out formally and carefully, and the probability of me being wrong drops further. I ask a peer to look over it and the probability that I make a mistake is vanishingly small. If prop A is important, then I may publish it, and after peer review, I can say that I have a strong argument for A: I have a proof P, and if P is correct, then so is A, with probability 1. The probability that P is incorrect is small, thanks to the formalism and many levels of peer review.
Since most of the arguments we believe are thus strong arguments, this trains our intuition with a heuristic to not bother looking for arguments that aren’t extremely strong. This effect would probably scale with the rigor of the field (eg be much stronger in mathematicians, where proofs are essentially the only form of argument written down)
The best physicists use the “many weak arguments” approach at least sometimes. See my post on Euler and the Basel Problem for an example of this sort of thing. (Nowadays, physicists fall into the Eulerian tradition more than mathematicians do.)
A close friend who’s a general relativity theorist has told me that the best physicists rely primarily on many weak arguments.
Hmm, I think I may be misunderstanding what you mean by “many weak arguments.” As in, I don’t think it’s uncommon for physicists to make multiple arguments in support of a proposition, but even each of those arguments, IME, are strong enough to bet at least a year of one’s career on (eg the old arguments for renormalization), by contrast with, say, continental drift, where you probably wouldn’t be taken seriously if you’d produced merely one or two lines of evidence. What this shares with the “one strong argument” position is that we’re initially looking for a sufficiently convincing argument, discarding lines of though that would lead to insufficiently strong arguments. It’s different mostly in that we go back and find more arguments “to be extra sure,” but you’re still screening your arguments for sufficient strongness as you make them.
Though admittedly, as a student, I may be biased towards finding my professors’ arguments more convincing than they ought to be.