An idea-image that was bubbling in my mind while I was reading Note 1.
One naive definition of an infinite endeavor would be something like “a combinatorially exploded space of possible constructions/[phenomena to investigate]” where the explosion can stem from some finite set of axioms and inference rules or whatever.
I don’t think this is endeavor-infinity in the sense you’re talking about here. There’s probably a reason you called (were tempted to call?) it an “infinite endeavor”, not an “infinite domain”. A domain is “just out there”. An endeavor is both “out there” and in the agent doing/[participating in] the endeavor. That agent (thinker?) has a taste and applying that taste to that infinite but [possibly in a certain sense finitely specifiable/constrainable] thing is what makes it an endeavor and grants it its infinite character.
Taste creates little pockets of interestingness in combinatorially exploded stuff and those pockets have smaller pockets still; or perhaps a better metaphor would be an infinite landscape, certain parts of which the thinker’s taste lights up with salience and once you “conquer” one salient location, you realize salience of other locations because you learned something in that location. Or perhaps you updated your taste, to the extent that these two are distinguishable. Or perhaps the landscape itself updated because you realized that you “just can” not assume Euclid’s fifth postulate or tertium non datur or ex contradictione quodlibet and consequently discover a new way to do math: non-Euclidean geometries or new kinds of logic.
If I were to summarize my ad-hoc-y image of endeavor-infinity at the moment, it would be something like:
An infinite endeavor emerges from a thinker imposing/applying some (very likely proleptic) taste/criterion to a domain and then exploring (and continuing to construct?) that domain according to that taste/criterion’s guidance; where all three of {thinker, criterion, domain} (have the potential to) grow in the process.
(which contains a lot of ad-hoc-y load-bearing concepts to be elucidated for sure)
I only read the first note and loved it. Will surely read the rest.
An idea-image that was bubbling in my mind while I was reading Note 1.
One naive definition of an infinite endeavor would be something like “a combinatorially exploded space of possible constructions/[phenomena to investigate]” where the explosion can stem from some finite set of axioms and inference rules or whatever.
I don’t think this is endeavor-infinity in the sense you’re talking about here. There’s probably a reason you called (were tempted to call?) it an “infinite endeavor”, not an “infinite domain”. A domain is “just out there”. An endeavor is both “out there” and in the agent doing/[participating in] the endeavor. That agent (thinker?) has a taste and applying that taste to that infinite but [possibly in a certain sense finitely specifiable/constrainable] thing is what makes it an endeavor and grants it its infinite character.
Taste creates little pockets of interestingness in combinatorially exploded stuff and those pockets have smaller pockets still; or perhaps a better metaphor would be an infinite landscape, certain parts of which the thinker’s taste lights up with salience and once you “conquer” one salient location, you realize salience of other locations because you learned something in that location. Or perhaps you updated your taste, to the extent that these two are distinguishable. Or perhaps the landscape itself updated because you realized that you “just can” not assume Euclid’s fifth postulate or tertium non datur or ex contradictione quodlibet and consequently discover a new way to do math: non-Euclidean geometries or new kinds of logic.
If I were to summarize my ad-hoc-y image of endeavor-infinity at the moment, it would be something like:
(which contains a lot of ad-hoc-y load-bearing concepts to be elucidated for sure)
I only read the first note and loved it. Will surely read the rest.