Science Forums 2

[Kriminal99]

So, the depcition I have created is one frequently used to describe the Halting undecidability proof in more detail. At first glance one might come to the mistaken conclusion that the strict diagonalization proof might be different from this depiction. Actually the depiction is a more explicit demonstration of what is happening in the diagonalizatiton proof. For instance, if you say machine G takes Machine H on input encoding of Machine H as input, then you have implicitly created the copy Machine referenced in the above depiction.

Furthermore, your claim regarding program tracing is incorrect. For a Halting (or even Universal Turing Machine) that partially traces the computations of it's input encoding, it is not necessary that the machine completely trace the computations. It could for example stop when any loop has occured by comparing the current state with any previously obtained state. Perhaps if you had more experience working with theoretical touring machines, you would know this.

However attempting to trace it at all is enough to create the infinite regress in the setup Touring has implicitly provided.

I find it amusing that you attempt to attribute the blind obedience that is a direct result of social pressures to the working of simple problems in a university setting. If a student in a "introductory computer science class" objected in any way to the presented proof, the professor would just declare by fiat his grade to be an F either directly or through concealed logic errors in grading. This not only means that the student would keep quiet if something did appear to be off, it also means he would not bother to think about it to the degree required to notice anything "fishy".

You then want to look at this abuse of power as some sort of evidence that the proof is widely accepted. This is bandwagon fallacy of the simplest form. If everyone agrees solely because everyone agrees, then nobody really knows.

Thus he who finally has an objection is truly dealing only with the person in ancient histotry who originally presented the idea, and maybe some peers of that time who could see no error with it. Thre is no reason to believe anyone after that who is under social pressure to conform has subjected it to an appropriate amount of skepticism.