Thinking a bit about the informal behavior argument: taking "rule-follower" to mean something that always follows a definite set of rules of conduct, it looks like Turing is imagining a syllogism roughly like [1] All rule-followers are machines; [2] No people are rule-followers; so [3] No people are machines. That syllogism has an undistributed middle term (as he says) and is invalid, which is easy to see from a diagram. But if the argument had been that all machines are rule-followers, then the syllogism would be valid. What Turing goes on to say seems to me to suggest that he thinks there are really two arguments here with different premisses to reject. The first goes like [1*] All machines are rule-followers; [2*] No people are rule-followers; so [3] No people are machines. Turing objects that we have no reason to think that [2*] is true. There might be a physical (?) law of behavior covering all people. The second goes like [1**] All machines are rule-followers; [2**] No people are rule-followers; so [3] No people are machines. I suppose that Turing rejects [1**]. But he's not super-clear about that as far as I can tell. Am I missing something? Does my reconstruction look right?
I definitely see the single-* version of your reconstruction as one thing going on in this paper. Several of Turing's discussions seem aimed at convincing us that there could be behavior that is in fact governed by a rule, even though it's practically impossible for anyone not involved in the design of that system to know what the rule is. I hadn't specifically thought about the double-** version of your reconstruction before. I'll have to look for signs of that next time I re-read this paper. I don't recall Turing talking much about machines that follow rules without explicitly doing so - but it does seem relevant to standard responses to the Lucas-Penrose argument, and might be relevant to Dreyfus's arguments about AI (that I haven't actually read the primary sources for yet).
At 0:27, you say that the machine described in Turing's 1936 work was the first abstract idea of a general purpose computer. But isn't Babbage's analytical engine (described in 1837) Turing-complete and hence general purpose in the same sense?
Probably the more precise thing I can say is that Turing's 1936 paper is the first one that explicitly considers the question of universality, and shows that there is a universal computer. I've heard that there might be some controversy about some details of the analytical engine, regarding whether it is truly universal as described, or if a slight modification is needed. But I'm fairly sure that one or more of Post, Gödel, or Church gave their definitions before Turing, which do turn out to be universal, so that Turing's innovation is stating and proving universality, rather than defining a universal system.
Thank you for explaining after each paragraph, you made it very easy to understand!
you really helped explain a few of the confusing bits thanks
appreciate this very good introduction to Turing's work ty
thank you for your dedication
Thanks so much awesome format for a video! 😁
Thinking a bit about the informal behavior argument: taking "rule-follower" to mean something that always follows a definite set of rules of conduct, it looks like Turing is imagining a syllogism roughly like [1] All rule-followers are machines; [2] No people are rule-followers; so [3] No people are machines. That syllogism has an undistributed middle term (as he says) and is invalid, which is easy to see from a diagram. But if the argument had been that all machines are rule-followers, then the syllogism would be valid. What Turing goes on to say seems to me to suggest that he thinks there are really two arguments here with different premisses to reject. The first goes like [1*] All machines are rule-followers; [2*] No people are rule-followers; so [3] No people are machines. Turing objects that we have no reason to think that [2*] is true. There might be a physical (?) law of behavior covering all people. The second goes like [1**] All machines are rule-followers; [2**] No people are rule-followers; so [3] No people are machines. I suppose that Turing rejects [1**]. But he's not super-clear about that as far as I can tell. Am I missing something? Does my reconstruction look right?
I definitely see the single-* version of your reconstruction as one thing going on in this paper. Several of Turing's discussions seem aimed at convincing us that there could be behavior that is in fact governed by a rule, even though it's practically impossible for anyone not involved in the design of that system to know what the rule is.
I hadn't specifically thought about the double-** version of your reconstruction before. I'll have to look for signs of that next time I re-read this paper. I don't recall Turing talking much about machines that follow rules without explicitly doing so - but it does seem relevant to standard responses to the Lucas-Penrose argument, and might be relevant to Dreyfus's arguments about AI (that I haven't actually read the primary sources for yet).
At 0:27, you say that the machine described in Turing's 1936 work was the first abstract idea of a general purpose computer. But isn't Babbage's analytical engine (described in 1837) Turing-complete and hence general purpose in the same sense?
Probably the more precise thing I can say is that Turing's 1936 paper is the first one that explicitly considers the question of universality, and shows that there is a universal computer.
I've heard that there might be some controversy about some details of the analytical engine, regarding whether it is truly universal as described, or if a slight modification is needed. But I'm fairly sure that one or more of Post, Gödel, or Church gave their definitions before Turing, which do turn out to be universal, so that Turing's innovation is stating and proving universality, rather than defining a universal system.
@@keaswaran0 That's helpful, thanks!
Really enjoyed they thank you
Very helpful. Thanks a lot!
Thank you. Flow 444