On Mon, May 6, 2019 at 4:41 PM Jason Resch <jasonre...@gmail.com> wrote:
> On Mon, May 6, 2019 at 1:19 AM Bruce Kellett <bhkellet...@gmail.com> > wrote: > >> >> This is essentially the point that both Turing and Goedel made when they >> pointed out that human consciousness is not Turing emulable -- it involves >> intuitive leaps that are not algorithmic, presumable coming from an >> uncodable environment. >> > > Could you provide citations to Turing and Godel's thoughts on this? In my > view Turing was the founder of functionalism/computationalism, when in his > 1950 paper "Computing Machinery and Intelligence" he wrote: > > > “The fact that Babbage's Analytical Engine > was to be entirely mechanical will help us rid ourselves of a > superstition. Importance is often > attached to the fact that modern digital computers are electrical, and the > nervous system is also > electrical. Since Babbage's machine was not electrical, and since all > digital computers are in a sense > equivalent, we see that this use of electricity cannot be of theoretical > importance. [...] If we wish to > find such similarities we should look rather for mathematical analogies of > function.” > > > As for Godel, while I am aware of instances where his ideas have been > misapplied by some philosophers to argue that human consciousness is not > Turing emulable, I am not aware of any writings of Godel where he expressed > such ideas. It is hard for me to believe Godel himself misunderstood his > own ideas to the extent necessary to believe human mathematicians somehow > immune to its implications. According to Godel's 14 points (his own > personal philosophy) it suggests he sees nothing special about the material > composition, and he also believes all problems (including art) can be > addressed through systematic methods. This suggests to me he would be a > proponent of at least "weak AI", which again is sufficient for my thought > experiment. > > 1. The world is rational. > 2. Human reason can, in principle, be developed more highly (through > certain techniques). > *3. There are systematic methods for the solution of all problems (also > art, etc.).* > *4. There are other worlds and rational beings of a different and higher > kind.* > 5. The world in which we live is not the only one in which we shall live > or have lived. > 6. There is incomparably more knowable a priori than is currently known. > 7. The development of human thought since the Renaissance is thoroughly > intelligible (durchaus einsichtige). > 8. Reason in mankind will be developed in every direction. > 9. Formal rights comprise a real science. > *10. Materialism is false.* > *11. The higher beings are connected to the others by analogy, not by > composition.* > 12. Concepts have an objective existence. > 13. There is a scientific (exact) philosophy and theology, which deals > with concepts of the highest abstractness; and this is also most highly > fruitful for science. > 14. Religions are, for the most part, bad– but religion is not. > > > (Emphasis mine) > > Jason > I base these comments on an analysis in a paper by Copeland and Shagrir, in the book "Computability: Turing, Goedel, Church, and Beyond" (MIT Press, 2015). The main argument is that "In about 1970, Goedel wrote a brief note entitled 'A Philosophical Error in Turing's Work' (1972; in Goedel's Collected Works)." "In the postscript, Goedel also raised the intriguing 'question of whether there exist finite non-mechanical procedures'; and he observed that the generalised incompleteness results 'do not establish any bounds for the powers of human reason, but rather for the potentialities of pure formalism in mathematics." "A philosophical error in Turing's work. Turing in [section 9 of "On Computable Numbers" (1936, 75-76)} gives an argument which is supposed to show that mental procedures cannot go beyond mechanical procedures. However ... what Turing disregards completely is the fact that mind, in its use, is not static, but constantly developing ... Although at each stage the number and precision of the abstract terms at our disposal may be finite, both (and, therefore, also Turing's number of distinguishable states of mind) may converge toward infinity in the course of the application of the procedure. (Geode 1972, 306)." Further: "What Turing disregards completely is the fact that mind, in its use, is not static, but constantly developing. This is seen, e.g., from the infinite series of ever stronger axioms of infinity in set theory, each of which expresses a new idea or insight ... Therefore, although at each stage of the mind's development the number of possible states is finite, there is no reason why this number should not converge to infinity in the course of its development. (Godel in Wang 1974, 325)." The article by Copeland and Shagrir then goes on to defend Turing against Goedel's criticism, by pointing out that Turing actually says "Having defined a certain infinite binary sequence \delta, which he shows to be uncomputable, Turing says: "It is (so far as we know at present) possible that any assigned number of figures of \delta can be calculated, but not by a uniform process. When sufficiently many figures of \delta have been calculated, an essentially new method is necessary in order to obtain more figures". This sequence of essentially new methods is, itself, uncomputable. In Turing's view, the activity of what he called the faculty of intuition brings it about that mathematical judgments exceed what can be expressed by means of a single formal system. I recommend going to the original Copeland and Shagrir paper for more detail. Bruce -- 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 post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
