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In category theory, why do we meet more left adjoints than right adjoints
Yes, philosophy has an answer. Our universe is contingent. There are many possible ways it could have operated, in principle. What math, or logic applies to it in practice, cannot be predicted from logic principles, or math theory.
This point was articulated with great force by Kant in The Critique of Pure Reason. Kant however, did not go as far as philosophy has today. Kant held there were at least a few math relations we could know a priori that were true, and his go-to example was Euclidean geometry. Subsequently, non-Euclidean geometries were discovered in potential math space, and they actually turn out to be how our universe behaves! The desire to believe in the a priori "truth" of Euclidean geometry turned out to be a fallacy, of failure of imagination on Kant's part (the informal fallacy is generally called argument from ignorance)!! Apply this lesson to our world, and we cannot predict a priori (from logic or math principles) what math will apply to any physical aspect of our universe .
Subsequently, Godel discovered that one cannot even derive logic or math principles with confidence even within math-space, much less whether they apply to our world. And logic pluralism shows that there are infinite logics, and we cannot know if any of them even apply to our world. https://math.vanderbilt.edu/schectex/logics/
So -- the answer philosophy has, is that the lack of symmetry that mathematicians have found in applying math to our world, just happens to be the way our contingent world worked out.
This was not a comment, it was an answer, which is noted in the opening and closing sentence.
The answer does not seem to satisfy any of the criteria for deletion:
- commentary on the question or other answers
- asking another, different question
- “thanks!” or “me too!” responses
- exact duplicates of other answers
- barely more than a link to an external site
- not even a partial answer to the actual question
This was a 4 paragraph answer, which cited three different philosophers over 4 centuries. While the question asker does not consider any of the answers to actually answer the question, all three answers basically offer a similar message, that what the asker wants philosophy to provide, is not possible, at least in our world.
The policy of the site, to my knowledge, is that it is desirable to convert comments with content into answers. Not the other way around.