It’s bad form to say this up front, but I don’t think you actually have terribly deep understanding of the phenomena you glibly reference. (You could, of course, prove me wrong; it’s just that an inductive inference from the history of the Internet suggests that most people making similar references don’t really know what they’re talking about). All the same, I’m going to discuss them as if you have more than a passing acquaintance.
The Halting Problem, for those who don’t know, is the general question of determining which computer programs halt and which don’t. It’s fairly easy to show that no computer program can solve this. (Indeed, this generalizes; for reasonable classes of processes P, it’s easy to show that no P-process can determine which P-processes halt). But there’s nothing preventing physical processes from solving the general Halting Problem for computer programs. It is an open question whether any physical processes, or for that matter the human brain, can solve the general Halting Problem for computer programs, though most believe they cannot. But it is pretty much a mathematical certainty that there is no describable physical machine which takes in descriptions of other physical machines, goes into motion for a bit, and then either flashes a “Yes, that machine eventually comes to a halt” light or a “No, that machine never halts” light, immediately afterwards “halting” itself.
Well, subject to certain conditions, this is fair enough, but more general than you imply. I would reword it as the fact that no system at all, whether mind, machine, or mathematical construct, “formalizable” or not, can be both sound and complete (i.e., always give correct answers) with respect to a language with the ability to speak about the system itself, in an appropriate sense.
But what’s essentially going on with both the Halting Problem and Goedel’s Incompleteness Theorem is that you go to some system S and mention a statement something like “S doesn’t think this statement is true” (worded in such a way that one doesn’t need explicit self-reference to pull off the same effect). Clearly, whatever S thinks about such a statement, it’s fucked (no matter what kind of thing S is). It’s unclear what genuine relevance any of this has to the current discussion, though. But perhaps you can make the point more strongly.
I’m quite sure you are making an assumption. You know what happens when you assume. As far as the longest time I can imagine, well, that’s imaginary isn’t it ? Are we having a real discussion or are we drifting into the imaginary ? If you would like to tell me how long “forever” is, for the purpose of your inquiry, please do so. It’s not my question.
Good then. Everything seems to be working out just fine.
Duck and weave all you want. If I imagine a cow, are cows imaginary? Does that make any subsequent discussion about cows imaginary? You know good and well what I am asking, and to pretend otherwise does not speak well of you.
I have already amended the “question,” as you refer to it. To pretend that you have not seen it does not speak well of you. It is in the paragraph directly below the one you just quoted. Here it is again.
**
*
Or, to restate the problem, prove that the current “limits” to the human mind cannot be surpassed.***
I guess. Do you feel these are substantive, relevant limits, in the context of the discussion of science, psychics, ghosts, etc.?
At any rate, consider:
“, when appended to its own quotation, forms a sentence Iknewit does not consider true.”, when appended to its own quotation, forms a sentence Iknewit does not consider true.
There. That is a sentence in the exact same spirit as all the Goedelian constructions, which you personally, Iknewit, simply cannot correctly come to a consistent position on. (I can, though. Everyone can, except you. Sorry, it’s just the nature of the construction.)
Would you say, as a result, that you don’t understand that construction? That you cannot explain what’s going on there? Have I given you serious reason to doubt your ability to understand other phenomena?
Would you say this has any relevance to a discussion of science, psychics, ghosts, electricity, black holes, dark matter, whatever?
Forever ? What the heck do you mean ? The rest of my life ? The rest of your life ? The rest of human existence ? The rest of the Earth’s existence ? Universal “forever” ? Conceptual “forever” ? God like “forever” ? Just a very long time that is definable as “forever” ? Like love notes that say “together forever” and then it’s over in two weeks ?
What do mean by forever ? Do you know ? Ducking and weaving won’t get any meaningful answer to your question.
That actually gave me a bit of a chuckle. More at myself than at you. I actually thought you were being serious. Congratulations for stringing me along in such a manner. Well played.
I’m not sure what it is you want for backing it up. The only argument for the theorum not applying to human logic is that humans make mistakes and therefore are not consistant. Even when accepting this as true, is does not show that human logic can solve redundancies, only that we are capable of making a mistake thus presenting a psuedo solution.
Well, for example, with the sentence:
“, when appended to its own quotation, forms a sentence Iknewit does not consider true.”, when appended to its own quotation, forms a sentence Iknewit does not consider true.
Do you think this sentence’s existence demonstrates substantive limits in your own explanatory abilities or powers of understanding? Because these are the only kinds of limits imposed by the Goedelian results.
[Also, just as a minor technical point, one can make mistakes, in the sense of accepting things which are untrue, and still be consistent; just, also wrong. In this area of mathematical logic, consistency refers to avoiding contradiction, while soundness refers to avoiding incorrectness]
he must be using a different definition of intelligence from the rest of us. Machines can augment our reasoning power in many ways, as I mentioned in my post, but not our raw intelligence.
Yes I do. It demonstrates that the statement can not be proved true or false. Hence the back and forth demands for proof in this argument. The analogy to the theorum illustrates that no definite number of principles exist.
Reasoning is a part of raw intelligence. Indeed we are using different meanings of intelligence. Can you demonmstrate where reasoning is not a part of intelligence ?
By this logic, Caterpillar and Case and Back & Decker have been extending the manner in which human strength has evolved.
That humans have a tool-making ability says nothing about actual intelligence. Just as sharp sticks and flattened sticks extended the human hand and later developments of metal-working, the employment of beasts, the development and employment of wedges, inclined places, pulleys, etc. continually extended the ability to apply that strength while developments in alternative power sources eventually led to the ability to apply strength without even employing more than negligible effort, so the scratchings of sticks in mud, the development of paper (or similar surfaces), the development of written languages, eventually moving into the realm of printing and, later, electronic storage and manipulation merely demonstrates the effects of humanity’s capacity for tool-making. It says nothing about actual intelligence which is biologically based and for which there is no evidence that it has actually increased in any recorded time period.
Black and Decker and Caterpillar are testamnets to human intelligence, not strength. They in fact demonstrate the evolution of intelligence to mitigate the primal importance of strength. The industrialization of the human race has abstracted us from our more primitive ancestors. Greater importance of cognative ability along with the circumvention of natural selection in modern man has freed areas of the brain to tackle other thoughts in lieu of constant primal means of survival. Intelligence has increased.
“Newborn chicks which have small brains are able to correctly perceive partially occluded objects as one object. However, human babies were likely to perceive it as two separate objects (Langer, 2004). This study demonstrates that intelligence develops over time, and if intelligence can develop over time in one individual, it is possible for intelligence to develop over time for an entire population. Since intelligence can develop and because popular views on intelligence and types of intelligence are changing, there has also been increased pressure to revise methods of testing intelligence; for which the most common measure is currently modifications of the Wechsler intelligence test (Esters, 1999).”