User:More Than Magnetic Ink/Sandbox

Serene, thanks for the helpful feedack. I recommend that RW edit the article as follows: Delete the existing ref. 5 and immediately following the present superscript link to ref. 5, quote the Stanford Encyclopedia of Philosophy (SEP) article's "brief summarized form of the standard counterargument," perhaps as follows:

Raatikainen summarizes the consensus on the Penrose-Lucas argument as follows:

"These Gödelian anti-mechanist arguments are, however, problematic, and there is wide consensus that they fail. The standard response to this argument goes along the following lines ...: The argument assumes that for any formalized system, or a finite machine, there exists the Gödel sentence which is unprovable in that system, but which the human mind can see to be true. Yet Gödel’s theorem has in reality a conditional form, and the alleged truth of the Gödel sentence of a system depends on the assumption of the consistency of the system. The anti-mechanist’s argument thus also requires that the human mind can always see whether or not a given formalized theory is consistent. However, this is highly implausible."

The sources deleted with reference 5 are restored as part of the three new references 5, 6, and 7 added by the above text. What's not restored is the statement, "Works with counterarguments are too numerous to list here." The quotation from and reference to the SEP article are much more helpful to those on both sides of the argument.

It appears that Lucas has controverted "the standard counterargument" in Minds, Machines and Gödel: a Retrospect. In the same article, Lucas wrote, "I have been much attacked. Although I argued with what I hope was becoming modesty and a certain degree of tentativeness, many of the replies have been lacking in either courtesy or caution. I must have touched a raw nerve. That, of course, does not prove that I was right. Indeed, I should at once concede that I am very likely not to be entirely right, and that others will be able to articulate the arguments more clearly, and thus more cogently, than I did. But I am increasingly persuaded that I was not entirely wrong, by reason of the very wide disagreement among my critics about where exactly my arguments fail. Each picks on a different point, allowing that the points objected to by other critics, are in fact all right, but hoping that his one point will prove fatal. None has, so far as I can see. I used to try and answer each point fairly and fully, but the flesh has grown weak. Often I was simply pointing out that the critic was not criticizing any argument I had put forward but one which he would have liked me to put forward even though I had been at pains to discount it. In recent years I have been less zealous to defend myself, and often miss articles altogether. There may be some new decisive objection I have altogether overlooked. But the objections I have come across so far seem far from decisive." The Wikipedia article concurs on the criticisms' lack of consistency, stating, "The Penrose–Lucas argument about the implications of Gödel's incompleteness theorem for computational theories of human intelligence was criticized by mathematicians,[11][12][13] computer scientists,[14] and philosophers,[15][16][17][18][19] and the consensus among experts[20] in these fields is that the argument fails,[21][22][23] with different authors attacking different aspects of the argument." (Emphasis added.) In ref. 23 of that article, a hostile witness concurs: "There is at least this much to be said for Lucas and Penrose, that logicians are not unanimously agreed as to where precisely the fallacy in their argument lies On the Outside Looking In: A Caution about Conservativeness (Burgess, John).