CJ: Unlike the essay, in my closing remarks in the video I compare Pólya to Bucky. In regards to the Inductive Attitude: should we be more like Bucky or more like Pólya?
Any other thoughts on either the video or the essay it riffed off of? https://www.cjfearnley.com/.../the-inductive-attitude-a.../
Me: I’ll take a look.
You earlier opened my eyes to Pólya’s intuitionism, another way of saying inductionism.
Mathematics can’t start out by simply proving stuff, as first we need to figure out what’s even worth proving i.e. where to invest our time. Heuristics matter.
Intuition gives us glimpses of an attractive whole (a destination), long before our deductive apparatus gets us there (if it ever does).
Per our last meetup together, I put emphasis on “gestalt switch” in my latest reiteration of my slide show. Meeting with Wisconsin TrimTab group this Saturday if all goes according to plan.
A couple things.
(1) since Pólya, inductive language games have evolved to include more of the so-called Bayesian perspective, such that one now commonly hears phrases like “based on my priors” or “given his priors”… all of which is to say I think the public is becoming increasingly fluent regarding the inductive / predictive / belief-tuning mindset.
Here’s a sample (chosen for brevity):
(2) regarding “illusion” and Pólya’s willingness to let us cling to them, I think you should make a lot of room for the closely related concept of “fantasy” or (better) “fiction”.
The fact is, many Trekkies and Star Wars fans, or people into LARPing and gaming (Pokemon…), are not seeking any “truths” behind their fictional worlds and know in advance that they’re synthesized “illusions” (dreams), more or less “believable” in the sense that we’re able to suspend disbelief and inhabit those worlds (e.g. Narnia, Middle Earth… at least temporarily). Consistency with human psychology matters i.e. we have trouble relating to fictional worlds wherein we don’t see our humanity (our experience being human) reflected.
Or take shows like Breaking Bad, The Simpsons, Nip ‘n Tuck… viewers know these edgy shows mirror aspects of reality (illegal drugs, middle class family living, plastic surgery world) without being built out of literally true facts (we know the characters are fictional).
Lets admit there’s a fine line between obvious fantasy fiction, and role playing.
People spend a lot of their lives fantasizing (as well they should), about the future especially, which, by definition, isn’t “true” yet i.e. there’s no way to think about the future at all, if confined to thinking purely in terms of what’s currently true.
Also, when we say the knight moves like this, the queen like that, in the game of chess, we call these rules, but we could say “axioms” instead. These rules are not “self evident” so much as “arbitrary” but we embrace them anyway, because “they make for a playable game”. Extrapolate from there to much of human society (rule based, not “truth” based).
My point: much of human reality, such as government, companies, militaries, courts… institutions of all kinds… are not founded on “true facts of the matter”. Instead, we’re talking about social agreements or imposed rules that help to organize human affairs. We are not thinking about “what’s true” so much as we are inventing playable games (cite World Game).
Put another way: the imaginative inner life of a person consists not solely of “truths” but of “dreams” which we agree are dreams. Literal truths drastically under-determine how we’re supposed to operate on Spaceship Earth. When it comes to ethics, or having a moral compass, it’s unnecessary to assume “facts” or “truths” are the foundation. On the contrary, our judgements do not come down to facts, but to ways of life (Wittgenstein).
None of which is to contradict Fuller putting all that emphasis on experience. He also wove dreamy tapestries based on intuitions he was having. Speculations are part of Universe. He was not opposed to speculating and he did so, quite a lot.
CJ: I like your observation that Pólya’s guessing or induction is intuition. Intuition is an imaginative guess. It might be a bad guess. But we are led to it. We are compelled to test it out.
Whether it is our intuition, our memory, our imagination, or some other faculty of guessing, the fact is that we have ideas. Intuition tends to privilege its ideas. Induction is more reluctant to accept its guesses. But otherwise, yes, inductionism and intuitionism are nearly synonymous: they both generate beliefs that we need to adapt to experience.