> On 24 Feb 2020, at 21:19, John Clark <johnkcl...@gmail.com> wrote: > > On Mon, Feb 24, 2020 at 8:40 AM Bruno Marchal <marc...@ulb.ac.be > <mailto:marc...@ulb.ac.be>> wrote: > > >> a Halting oracle produces paradoxes, > > > I don’t see why you say this. > > I have a halting oracle machine and it has 2 input slots, one slot for the > logical blueprints of a computer in digital form and the other slot for a > program, also in digital form, to run on that computer. The oracle machine > will then output either the words "Halt" or "Not Halt" depending on what a > program running on that computer will do. I decide to use the oracle machine > as one part of a new 3 part machine I will call machine X. The first part of > machine X is just a photocopier that makes two copies of its input and then > feeds them into the 2 input slots of the oracle machine. The last part of > machine X is the negator, if it receives a "Not Halt" input from the oracle > machine then the negator will output "Halt" and then stop, if the negator > receives a "Halt" input from the oracle the negator will go into an infinite > loop and never stop. The entire X machine as constructed has one input slot > and one output slot. > > I will now input machine X with machine X's own blueprints, so after the > photocopier has done its work the oracle machine will receive identical > inputs in both slots and the oracle machine will have to figure out what will > happen to the X machine when the X machine is fed it's own blueprint as > input. If the oracle says under those circumstances the X machine will halt > then the X machine will never halt, and if the oracle says the X machine will > not halt then the X machine will print "Halt" and stop. So the halting oracle > machine always makes predictions that are wrong. So there is no such thing as > a halting oracle machine. QED.
This shows that the machine+halting-oracle cannot solve the halting (machine+halting-oracle) problem, but the halting-oracle is supposed fro be concerned only for the machine halting problem, i.e. the machine without oracle. Bruno > > John K Clark > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAJPayv2kWy03pZRds8M1tsqAPjfmvOU3t__dy0Hoaqa2hgQ%2Byg%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv2kWy03pZRds8M1tsqAPjfmvOU3t__dy0Hoaqa2hgQ%2Byg%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/519850B2-F650-43B9-BFF4-FD74BF7E7568%40ulb.ac.be.
