The origin of the very word Logic has its roots in that exact era as phrased at the time, by the very people who came up with its ruleset in the first place.
You may define logic otherwise but in the context of past occurrences they're more or less irrelevant.
https://amistrongeryet.substack.com/p/gpt-4-capabilities
Although it's interesting that if you use different nouns it does just fine: https://jbconsulting.substack.com/p/its-not-just-statistics-...
> If you were to turn over the yellow card and find the number 7 on the other side, it would not disprove the statement "If a card has an odd number on one side, then the other side is purple." In fact, this discovery would not provide any evidence either for or against the statement.
> The statement specifically refers to cards with odd numbers on one side and their corresponding color on the other side. It does not make any claims about the colors of cards with even numbers. Therefore, even if the yellow card had an odd number like 7 on the other side, it would not contradict the statement.
It's interesting to see the model explaining exactly what would be necessary to find, exactly what it could find, and then fail to make any connection between the two.
Does this mean real logical reasoning is very close, only some small improvements away, or does it mean we're just on the wrong track (to reach actual AGI)?
OTOH, who knows what would happen if you somehow managed to combine the generating capabilities of a language model with a proper inference engine, e.g. Wolfram|Alpha. Maybe it would bring us significantly closer to AGI, but maybe that way is also a dead-end because it's not guaranteed that those systems would work well together.
For example, I've once asked it to "prove that first order logic is not complete", a statement which is false, given that every logic textbook will give you a proof for why first order logic is complete. ChatGPT apparently knew this too, because it happily reproduced that result but somehow thought that it was a valid answer for what I asked for (the valid answer would have been "I can't prove this because it's wrong").
I can't reproduce this exact result right now (in fact when I tried, it just proved something slightly different, which was correct but not exactly what I asked for). But I was able to similarly confuse it by asking it to prove that the equation x^3+y^3=z^3 has solutions. That this is true is immediately apparent by x=y=z=0, but ChatGPT replies with:
> The equation x^3 + y^3 = z^3 represents a special case of Fermat's Last Theorem, which states that there are no solutions to the equation x^n + y^n = z^n for any integer values of n greater than 2.
> For the case of n = 3, the equation x^3 + y^3 = z^3 has infinitely many solutions. One such set of solutions is known as Pythagorean triples, where x, y, and z are positive integers.
> A Pythagorean triple is a set of three positive integers (x, y, z) that satisfy the equation x^2 + y^2 = z^2, which is equivalent to (x^2)^(3/2) + (y^2)^(3/2) = (z^2)^(3/2). By raising both sides to the power of 3/2, we get x^3 + y^3 = z^3.
> For example, the Pythagorean triple (3, 4, 5) satisfies 3^3 + 4^3 = 5^3 (27 + 64 = 125).
This answer is just confused on so many levels:
- It quotes back Fermat's Last Theorem at me (as indeed I hoped it would), but that theorem only applies to positive integer solutions and nowhere did I specify that constraint.
- If the Theorem did apply, then it would be a proof that such solutions don't exist. So ChatGPT has no internal understanding of how a theorem it quotes relates to a specific question, it just parrots off things that look vaguely similar to the input.
- Then, it just tells me what Pythagorean Triples are, which is hilarious, because those are the solutions to x^2+y^2=z^2 - and not what I asked.
The problem IMO is not that ChatGPT gives a wrong answer, it's that its answer isn't even internally consistent.
In my experience GPT-4 can solve unique logical puzzles, but I find it can be a bit clumsy with the context of more complex problems. What I mean by that is that it often can solve these problems with the right prompt, but you might need to ask it to think out loud and check its logic.