Timeline for Structure/object versus material/aggregate in category theory?
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
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| May 10, 2021 at 19:21 | comment | added | Tom Copeland | For more data, see linguistics.stackexchange.com/questions/224/… | |
| May 5, 2021 at 14:12 | comment | added | Tom Copeland | There's massaging the data to fit fhe theory, and there's massaging the theory to fit the data. | |
| May 4, 2021 at 4:17 | comment | added | Alec Rhea | I have voted to close as unclear after the edit -- I am not a downvoter and I think this is an interesting question, but the answer by Tim is more than I'd imagined would exist on this topic. If it isn't what you're looking for, I think it would be appropriate to narrow this down to a more precise, clearer mathematical objection -- 'if we apply the adjunction to [situation X], we get something that doesn't match natural semantics; here are the computations and their interpretations'. So far you've claimed a few specific circumstances, but I think working out the details of them would help. | |
| May 4, 2021 at 4:07 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Repy to replies
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| May 4, 2021 at 3:46 | comment | added | Tom Copeland | @ZhenLin, I suspected as much. | |
| May 4, 2021 at 3:35 | comment | added | Zhen Lin | My view is that it does not. Then again, I tend to be a sceptic regarding applications of deductive mathematics to semantics of natural languages. | |
| May 4, 2021 at 1:34 | comment | added | Tom Copeland | @ZhenLin, Like most people I have no problem intuitively distinguishing between substances and objects in the everyday world without the use of mathematics or even language. The question is really whether CT can inform on these topics significantly. | |
| May 3, 2021 at 18:08 | comment | added | Tom Copeland | There are many claims about the utility of category theory. This question is about a specific use and whether it is enlightening or not. | |
| May 3, 2021 at 18:02 | comment | added | Tom Copeland | Actually, about ten years ago when I first started asking questions on MO, I used the term 'polytope' and was immediately asked by a user with a very high rep count what that term meant, so I had to include a link. (The comment has since been removed.) Consequently, when I ask my questions, I keep my expectations minimal and let the conversation play out according to the temperaments of those engaged, pretty much as in any field of thought. | |
| May 3, 2021 at 17:48 | review | Close votes | |||
| May 13, 2021 at 3:02 | |||||
| May 3, 2021 at 6:30 | answer | added | Tim Campion | timeline score: 1 | |
| May 3, 2021 at 6:15 | comment | added | Tim Campion | @TomCopeland If your strategy for getting an answer to your philosophy / linguistics question is to ask it on a math forum, and if you expect the mathematicians you're talking to to read up on the non-mathematical background themselves, then it's understandable that you would not find your question to be answered to your satisfaction... | |
| May 3, 2021 at 0:58 | comment | added | Tom Copeland | Well, since you are a little shy about clicking links, it's understandable that you would not find my statements understandable. | |
| May 3, 2021 at 0:47 | comment | added | Tim Campion | I don't understand the connection between metaphor and count vs. mass nouns, but do note that the ability to treat either "masses" or "countable things" as objects of (different) categories is central to the approach of Reyes et al, because they can set up adjunctions between these categories to compare them systematically. So I don't see it as a drawback that the distinction between masses and coutable things is not something built into category-theoretic language at a fundamental level. | |
| May 2, 2021 at 22:59 | comment | added | Tom Copeland | A rough analogy: In topoloy in 3-D, a flat, bounded, compact, simply-connected 2-D surface with no holes is rubberlike. It is given no particular boundary structure. It is the material from which you can construct a torus, an object with two holes. | |
| May 2, 2021 at 22:35 | comment | added | Zhen Lin | Surely if there is a place to look for an analogue of the count/non-count distinction it must be measure theory, not category theory? | |
| May 2, 2021 at 22:21 | comment | added | Tom Copeland | Btw, Japanese have no trouble distinguishing between materials and objects. They just don't flag it in their grammar. | |
| May 2, 2021 at 22:15 | comment | added | Tom Copeland | If so, seems category theory would have serious limitations in elucidating the use of metaphor in cognition. | |
| May 2, 2021 at 22:05 | comment | added | Tim Campion | Haha! I had not clicked your link, but who knew that I'd be pointing out the same literature on this topic 8 years later! At any rate, it sounds like you have something more specific in mind than I'm able to pick up on from the question as you've stated it. Tentatively, I might suggest that category theory tends to treat these things on an equal footing. Compare, for instance the fundamental groupoid of a space $X$ -- a category whose objects are points of $X$ -- with the frame open sets of $X$ -- a category whose objects are in some sense the "parts" of $X$. | |
| May 2, 2021 at 22:04 | history | edited | Tom Copeland | CC BY-SA 4.0 |
Added ref
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| May 2, 2021 at 21:49 | comment | added | Tom Copeland | Yes, that ref is in the post (in your comments there?). Not sure whether it emphasizes the distinction between objects and materials or just the linguistic machinery that flags the distinction in English. | |
| May 2, 2021 at 21:43 | comment | added | Tim Campion | I'm not sure if this is what you're after, but for a category-theoretic analysis of count nouns versus mass nouns, you might be interested in Count nouns, mass nouns and their transformations: a category-theoretic unified semantics by Reyes, Reyes, and Zolfaghari. | |
| May 2, 2021 at 21:25 | history | asked | Tom Copeland | CC BY-SA 4.0 |