There will always be those more or less smart than you.
Subject to the (entirely reasonable, I believe) presumption that humanity is finite, a lack of maximal and minimal elements implies that "is smarter than" is not a strict partial ordering. (All finite partially-ordered sets have maximal and minimal elements.)
This seems profoundly counterintuitive to me; both the asymmetry and transitivity of the "is smarter than" relation seem almost axiomatic (and the irreflexivity is indisputable).
It seems to me that there must be thousands of individuals who are maximally smart -- each of them, naturally, incomparable to the others.
both the asymmetry and transitivity of the "is smarter than" relation seem almost axiomatic
Hah, you can't be serious! Look around you - asymmetry is so painfully obvious that even pop theories propose to split intelligence into "book smarts", "street smarts", "social smarts", etc.
In reality, I don't think "smart" is a word that makes much sense, outside of the context of signaling social status (pIQ).
It makes a ton of sense when if you concede that every single time you say it (well, really, say anything) it's done in context. You rarely say someone is "smart, without qualification" and even if you did it really absolutely means something more like "smart in most of the ways I admire and have observed that person performing".
Which is really total agreement with your point. "Smart" is as much a partial ordering as "friendly" is, for a lot of the same reasons.
Look around you - asymmetry is so painfully obvious that even pop theories propose to split intelligence into "book smarts", "street smarts", "social smarts", etc.
I don't see the connection. Asymmetry in the relation "is smarter than" simply means that it is impossible to have both "X is smarter than Y" and "Y is smarter than X" (for X != Y).
In the context of individuals of incomparable intellect, it is inappropriate to say that either is smarter than the other -- never mind that they are both smarter than each other.
I think I was considering a looser meaning of "smart", in the common language sense of "I'm smarter than you regarding dating, you're smarter than me regrading math". That pop theory removes the intuitive asymmetry by partitioning "smart" into supposedly asymmetric subrelations - "books smarts", etc. Each part of this partition is asymmetric.
Can you elaborate about intelligence in the context of signaling social status please? And provide links to books/reading? I am very interested in this
"...there must be thousands of individuals who are maximally smart..."
I think that's the core truth of "genius". Melville put it, "Genius all over the world stands hand in hand, and one shock of recognition runs the whole circle round".
Joseph Campbell, Isamu Noguchi, Martha Graham, and Rudy Arnheim were all geniuses in very different fields, but they were also drawn to each other in friendship & collaboration. They can't compare to each other on any scale, but somehow shared something in common.
Is modeling humanity as finite really the right way to go? There's always a stream of new humanity coming in, and old humanity dying off. Not to mention the way you change as you age- even if you're maximally smart at 16 (which everyone is, of course) eventually you won't be.
First of all... thats not the point. That statement wasn't meant as an absolute truism as much as something most people should keep in mind lest they get too cocky.
Secondly, even for someone X who is maximally smart, the statement "Y is smarter than X" can be true if its in a particular context. E.g. take two people who are maximally smart... there no one smarter than X in math (or whatever) and no one smarter than Y in history. Then X is smarter than Y and Y is smarter than X... depending on how you use the word.
Smarts, even in one subject, are multi-dimensional. High-school seniors that play football can test-score the same after a season of head-bashing as before, but they take longer to complete the test. Just as smart, but changed too.
Timed intelligence tests look for only fast-smart for instance.
Surely there is only a single individual who is maximally smart - I'd imagine you'd need an identical brain to be identically smart; assuming that (as is normal) even speed of application of knowledge is measured as part of smartness.
Subject to the (entirely reasonable, I believe) presumption that humanity is finite, a lack of maximal and minimal elements implies that "is smarter than" is not a strict partial ordering. (All finite partially-ordered sets have maximal and minimal elements.)
This seems profoundly counterintuitive to me; both the asymmetry and transitivity of the "is smarter than" relation seem almost axiomatic (and the irreflexivity is indisputable).
It seems to me that there must be thousands of individuals who are maximally smart -- each of them, naturally, incomparable to the others.