Day 9, Mat385

• ChatGPT: five priorities for research.

  "We think that the use of this technology is inevitable, therefore, banning it will not work. It is imperative that the research community engage in a debate about the implications of this potentially disruptive technology. Here, we outline five key issues and suggest where to start."

• At This School, Computer Science Class Now Includes Critiquing Chatbots: Move over, coding. Some schools are asking student programmers to think critically about rapid advances in artificial intelligence.

• From Think yourself better: 10 rules of philosophy to live by

  'In the Analects, Kongzi (also known as Confucius) says that the first thing he would do if he were to administer the government would be to "rectify names". He explains: "If names be not correct, language is not in accordance with the truth of things. If language be not in accordance with the truth of things, affairs cannot be carried on to success."'

  (It's interesting that the "hypothetical syllogism" is left to your imagination: what's the obvious conclusion?)

1. The negation of "for some" is "for all"; and the negation of "for all" is "for some". Words and "names" cause us trouble; we want to accurately name things.
2. The biggest error I'm seeing is mixing up quantifiers, and their usual connectives: usually we see that the following go together:
   • \(\forall\) and \(\rightarrow\)
   • \(\exists\) and \(\land\)

   Amusing observation on part a: to the text "Nothing is both a Corvette and a Ferrari", I wrote \[ \left(\forall x\right) \left[(C(x) \rightarrow F(x)') \land (F(x) \rightarrow C(x)') \right] \]

   (and I noticed that several of you did the same). While it works, it is a little "wasteful" -- why?

3. Since you're trying to prove an implication, the deduction method works well. But a temporary hypothesis also works (and one person went that route).

(and talk about the logical equivalent of induction, well-ordering).