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ויהי מבדיל בין מים למים
You are not serious.
Mithical: If it takes 5 machines 5 minutes to make 5 devices, how long would it take 100 machines to make 100 devices?
ChatGPT: If it takes 5 machines 5 minutes to make 5 devices, then it would take 100 machines 100 minutes to make 100 devices.
Why is ChatGPT bad at math?
As opposed to How does ChatGPT know math?, I've been seeing some things floating around the Twitterverse about how ChatGPT can actually be very bad at math. For instance, I asked it "If it tak...ai.stackexchange.com
Sure, and what it said is true. It takes 1 minute for 1 machine to make 1 device. 100 machines = 100 minutes. It was not told whether or not the machines were working in teams, or if they were working simultaneously. These details matter.
The benefit of working with the AI, is that it mimics the so-called logic you are using. It has been trained to use that form of primitive logic. That's what it defaults to, just as you are defaulting to this primitive so-called logic. Understanding this primitive programming, helps me understand your primitive programming.
But what's nice about the AI, is that it will correct itself once new facts are presented. And it is able to assess different methods for flaws. You seem to lack both of these capabilities.
Congratulations, you found your match. No surprise you generate all that nonsense.
Sure, it will default to the non-logic you are using. But I was able to correct it.
No. That is only true if the definitions are not defined. The ONLY reason that the empty set is considered a subset of all sets is because the subset is defined to permit it. But anytime a person tries to "look for elements" that proof fails.
No, it can be proven in classical logic that you are wrong. The same vacuous truth that shows the property is obtained can also be used to show that the property is not obtained.
Sure, but that's not what you're saying. You are saying "I don't know any Jews" AND "All the Jews I know are atheists" is vacuously true without including the necessary defintion of atheist or jew. It's just like the AI. You are behaving the same way. Lacking precision, results in a false conclusion.
Nonsense. Here is a formal proof using classical logic proving that "All the Jews I know are atheists" AND "I don't know any Jews" is always false. It works because I have properly defined the terms and included the necessary condition that a Jew cannot be both a theist and an atheist simultaneously.
1. Let A(x) represent "x is an atheist". Let T(x) represent "x is a theist". Let J(x) represent "x is a known Jew".
2. No person can be both a theist and an atheist simultaneously. J(x): { A(x) ⊻ T(x) }
3. Assume for contradiction: I don't know any Jews AND All the Jews I know are atheists.
4. Including the necessary conditions in step 1 & 2, the assumtion is: ¬(∃x)(J(x)) and J(x): { A(x) is true and T(x) is false }.
5. Now, under this assumption, we can deduce that J(x) implies both A(x) and T(x).
6. Since ¬(∃x)(J(x)) is assumed, it implies that J(x) is false for all x.
7. From step 6, J(x) → A(x) is vacuously true, as J(x) is false for all x.
8. Similarly, J(x) → T(x) is vacuously true, as J(x) is false for all x.
9. However, by the definition of J(x) in step 2, J(x) cannot simultaneously imply both A(x) and T(x).
10. Hence, the assumption in step 3 leads to a contradiction.
11. Therefore, the assumption ¬(∃x)(J(x)) and J(x): { A(x) is true and T(x) is false } is false.
12. The assertion "All the Jews I know are atheists" is always false, if "I don't know any Jews" with the necessary definition of Jews, Atheists, and Theists.
Now. THAT ^^ is inescable logic. The vacuous truth produces Q is true and ~Q is true if the set is empty. The same proof can be generalized for any set P and any property Q.
1. Let P(x) represent any set, and let Q(x) represent any property.
2. Per the law of non-contradiction, P(x): { Q(x) ⊻ ~Q(x) }, even if P(x) is empty.
3. Assume for contradiction the special case where P(x) is empty and a positive assertion is made about P(x) and Q(x): ¬(∃x)(P(x)) and P(x): { Q(x) is true and ~Q(x) is false }.
4. Under this assumption, P(x) implies both Q(x) and ~Q(x) vacuously.
5. Since ¬(∃x)(P(x)) is assumed, it implies that P(x) is false for all x.
6. From step 5, P(x) → Q(x) is vacuously true, as P(x) is false for all x.
7. Similarly, P(x) → ~Q(x) is vacuously true, as P(x) is false for all x.
8. However, by the law of non-contradiction, P(x) cannot simultaneously imply both Q(x) and ~Q(x).
9. Hence, the assumption in step 3 leads to a contradiction.
10. Therefore, the assumption ¬(∃x)(P(x)) and P(x): { Q(x) is true and ~Q(x) is false } is false.
11. In the case where P(x) is empty, any assertion P(x) → Q(x) is false because the assertion simultaeously implies P(x) → ~Q(x). This violates the law of non-contradiction.
12. For any set P(x), if it is empty, any positive assertion about a property Q(x) is always false.
13. Consequently the empty-set does not obtain any properties vacuously.
Nope, it is weak and ignorant of the obvious contradictory nature of using a vacuous truth to assert any property of an empty set. It only works if contradictions are accepted as true.
You have lost again.
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