Three Concepts of Commensurability and Comparability: Having a common cardinal measure, trichotomy, and the Archimedean Principle. @PhiloofAlexandria
I use the concept of value equation and look at monetary cost as a weak assessment tool. Still, value is based on beliefs, and it seems we are very factually superstitious. This superstition seem to be a property of knowledge itself, given that one can only know so much and that knowledge, or our abstraction of a subject, evolves over time.
Reminds me of math. The difference between rational and irrational numbers: between fractions and square roots. In math there is a always an additional fact: a context. The square root of two is an irrational number, but using geometry one can place it "somewhere" on the number line between 1 and 2. Using, in fact, Pythagoras' theorem on right triangles. In math the word incommensurability is tied, for me, to pi: the division of the circumference of a circle to its diameter. What "Pythagorean theorem" (context) allows us to compare curves to lines. Euclid asserted that lines were made out of points, did he have a further axiom on the building blocks of curves? The person who uncovered an answer to Fermat's last theorem, didn't he piggyback on additional material provided by a Japanese mathematician? He used an additional "fact" (context) to reason out an answer. Is there always an "additional fact" ready to come to our rescue when we have a conundrum? Sort of a pun or play on words that solves a riddle? In modern science time is the savior, the "additional fact", that always seems to come to the rescue. Just as time travel stories in science fiction can get you out of a jam, are they worth more than all the trouble they cause? After all Heinlein had a bizarre story called "All you Zombies", which diagrammed how the protagonist became his own grandfather - and grandmother for that matter. All you need is a time machine. I suppose that's what the intellect can be. Finding relationships in seemingly unrelated matters.
I never understood that saying. To me apples and oranges ARE comparable. They’re both fruit. One’s maybe more acidic, one’s maybe juicier, one’s maybe sweeter, one is more to my taste. But it’s the same in comparing oranges to oranges. An orange from one grove is more acidic, juicier, sweeter than than the other. Or is commensurability limited to what can be quantified/measured?
Great video. This question reminds me of Marx’s first chapter of Kapital where he dealt with this very issue of comparability; In which he tried to discover how qualitatively distinct commodities can be commensurable in the market. He concludes that socially necessary labor is the quantitative scale which sublates and negates their differences and hence makes them commensurable on the market. This makes me think that Hegel can potentially give us the proper tools to answer this question of commensurability.
