Ci talk:1004269130

GF says it's a noun: (名) 不需要任何證明就可以判斷為真實的假設。如不在一條直線上的三個點可以確定一個平面。 So does New Century. Example from Wikipedia: 平行公設（英語：Parallel postulate），也稱為歐幾里得第五公設， https://zh.wikipedia.org/wiki/%E5%B9%B3%E8%A1%8C%E5%85%AC%E8%A8%AD

So I have edited the POS from verb to noun. If it can be a verb as well as a noun, I apologize. In that case, perhaps the POS should be n./v. But so far I have seen only noun usage. Richwarm (talk) 12:53, 1 June 2018 (UTC)

--- 假設 can be a n./v., maybe this is similar, or 假設 is the source of the problem. Since GFC specifies n., I'm inclined to follow that, lacking other evidence. But I do see one example of 公设 as v., 设 is short for 设置 (in the "Cross-Straits" MOE dictionary), though this is not in a math context, but suggests n./v. might be OK. (BTW there's another n. usage syn. with 公共设施 given in that same source, and also in CC-EDICT.) We should look for clear examples of v. usage, but for now I'm leaning toward n./v. as an interim step, with a rem about the question. Rscook ---

REPLY:

Because of the 公 in 公设, I would expect that 公设 can not refer to a notion in the mind of just a single mathematician. Rather, it would be an assumption that is used as the basis for reasoning by an entire community of mathematicians, as is the case with 平行公設.

In mathematics, the subject of the verb "postulate" is usually a single person, as in the following examples:

1) "While at Gottingen, Gauss postulated the idea that there is a root to every algebraic equation." 2) "Gauss postulated that such variations are as equally likely to be above the mean as below it."

Again, because of the first character 公, I think it is hard to imagine that the verb "postulate" as used in the above examples could be translated using 公设.

On the other hand, by searching for the phrase 被公设, I have found evidence that 公设 is used as a verb outside of mathematics, in the domains of religion and philosophy.

- 也就是说，在对至善的必然探讨中，这样一种联系却被公设为必然的：

- 因此，整个自然的一个与自然有别的原因的存在也就被公设了，

- 比如意志自由、灵魂不死和上帝存在,其中被公设的“意志自由”可以为 ...

In this sense ("to be postulated by the community" as opposed to "postulated by an individual"), it is apparently also used in mathematics: 在數學上也允許用 已經被公設公理簡單證明到的定理 去證明更複雜的定理 http://www.phy.ntnu.edu.tw/demolab/phpBB/viewtopic.php?topic=23758

Richwarm (talk) 00:07, 2 June 2018 (UTC)

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2018-06-09T08:27:09PDT: I tried to address some of these issues in the entry.

Rscook

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