ProfHewitt

10 ms·

61.
by ProfHewitt 5y ago
Problem with 1st-order PRA is that it is too weak to serve as foundation of mathematics.
62.
by ProfHewitt 5y ago
The logical contradiction is that allowing the [Gödel 1931] proposition I'mUnprovable into foundations makes the foundations inconsistent.
63.
by ProfHewitt 5y ago
Results in [Gödel 1931] depend on existence of proposition I'mUnprovable . Since, the proposition doesn't exist in foundations, the results in [Gödel 1931] do not hold for foundations.
64.
by ProfHewitt 5y ago
Yes, it is very easy to check that [Gödel 1931] was for a system for the foundation of mathematics.
65.
by ProfHewitt 5y ago
The reason that [Gödel 1931] was influential was that it claimed to prove incompleteness for a system for the foundations of mathematics. 1st-order systems such a PA were introduced later and quickly shown to be inadequate for the foundatio
66.
by ProfHewitt 5y ago
As explicitly stated in the title [Gödel 1931] for a system for the foundation of mathematics.
67.
by ProfHewitt 5y ago
[Church 1935] proved the computational undecidability of the halting problem before [Turing 1936], which was written up in a hurry after [Church 1935]. The Y-combinator does not work for strongly-typed systems. Instead recursion must be e
68.
by ProfHewitt 5y ago
Thanks for your perceptive remarks! The following article has more information: https://papers.ssrn.com/abstract=3603021 Also, there are further articles linked here: https://professorhewitt.blogspot.com/ I
69.
by ProfHewitt 5y ago
Thank you very much sillysaurusx!
70.
by ProfHewitt 5y ago
Contra Schmidhuber's article, [Turing 1936] was correct in its statement that the proof of computational undecidability of the halting problem is very different from [Gödel 1931] attempted proof of inferential undecidability using the
71.
by ProfHewitt 5y ago
Veritasium missed that existence of the [Gödel 1931] proposition I'mUnprovable leads to inconsistency in foundations by the following simple proof: Ever since Euclid, it has been a fundamental principle that a theorem ca
72.
by ProfHewitt 5y ago
See the following article: https://papers.ssrn.com/abstract=3603021
73.
by ProfHewitt 5y ago
Indeterminacy is crucial for next generation Intelligent System. See https://papers.ssrn.com/abstract=3581859
74.
by ProfHewitt 5y ago
There might be two propositions of different orders that have the same characters in the same order.
75.
by ProfHewitt 5y ago
[Gödel 1931] was for a system for the foundations of mathematics with orders on propositions. The [Gödel 1931] proposition I'mUnprovable is certainly of historical interest and may perhaps be of philosophical interest. However, inclu
76.
by ProfHewitt 5y ago
Orders on propositions were introduced by Bertrand Russell to prevent inconsistencies in foundations of mathematics. Strong types prevent construction of I’mUnprovable using the following recursive definition: I’mUnprovable:Propositi
77.
by ProfHewitt 5y ago
A proof is only as good as definitions and axioms used in the proof. All of the computer-verified proofs of existence of [Gödel 1931] proposition I'mUnprovable left out the order of proposition in its Gödel number :-(
78.
by ProfHewitt 5y ago
If two propositions have the same characters in the same order, then they have the same Gödel numbers. Unfortunately, Gödel number of a proposition leaves out the order of the proposition :-(
79.
by ProfHewitt 5y ago
Did you not get the point? If [Gödel 1931] proposition I'mUnprovable exists in foundations, then foundations are inconsistent. See https://papers.ssrn.com/abstract=3603021
80.
by ProfHewitt 5y ago
If proposition I'mUnprovable exists in foundations, then the foundations are inconsistent, which was proved in the article linked elsewhere in this discussion.
81.
by ProfHewitt 5y ago
Hilarious means "extremely amusing", which is your position on censorship?
82.
by ProfHewitt 5y ago
Indeterminacy using many=cores speeds up processing . Enforced determinacy slows down processing .
83.
by ProfHewitt 5y ago
Coq, Isabelle, and HOL-light are inadequate for the foundations of mathematics. See discussion in related work section of the following: https://papers.ssrn.com/abstract=3603021
84.
by ProfHewitt 5y ago
Work on the incompleteness theorem is valuable in preventing successful next generation cyberattacks. See the following: https://papers.ssrn.com/abstract=3603021 PS. This link has been posted to this discussion several time
85.
by ProfHewitt 5y ago
The [Gödel 1931] proposition I'mUnprovable does not exist because the fixed-point on which it is based does not exist since it violates restrictions on orders of propositions.
86.
by ProfHewitt 5y ago
Computer systems make extensive use of arbiters in addition to Boolean circuits. See the following: https://papers.ssrn.com/abstract=3459566
87.
by ProfHewitt 5y ago
Before McCarthy, Turing called the developing field "Machine Intelligence", which is a much less misleading name for the field. To develop and deploy Universal Intelligent System in this decade will require considerable developmen
88.
by ProfHewitt 5y ago
Why do you find Wikipedia censorship hilarious?
89.
by ProfHewitt 5y ago
Bounded nondeterminism means that there is a bound determined by initial input for the number of possibilities that a system can explore given that it must always come back with an answer. A Nondeterministic Turing Machine has the property
90.
by ProfHewitt 5y ago
Have you read the article? Can you suggest any improvements?

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