13

I'm very familiar with the argument John makes with his Chinese Room argument, and he's extremely consistent about what he means it to portray: that our concept of what it means to understand language is mistaken when we try to apply the term to any machine which operates only syntactically. It's primarily a refutation of the notion that a Turing Test is ...


12

All mathematical formalizations of (intuitive) computability are known to be equivalent, in particular they are all equivalent to computability on the universal Turing machine. So technological implementation is irrelevant. The Church–Turing thesis states that this coincides in scope with what is "computable by a human being" unconstrained by limitations of ...


11

What the result means, essentially, is that in certain toy models there can be no algorithm deriving some macroscopic characteristics (spectral gap) from microscopic parameters of the models. The main import is that we get a Gödel sentence that unlike the original has some explicit mathematical meaning. Let's be generous and assume that the situation extends ...


11

If philosophy is mathematics and mathematics is computation, can I conclude that philosophy is computation? Yes. So is philosophy merely computation? No because philosophy isn't mathematics and mathematics isn't computation. Can we axiomatize philosophy? If you want. Getting philosophers to agree on a set of axioms should be amusing. Can a ...


8

Douglas Hofstadter would call this a strange loop. If one believes mathematics can "fully describe" reality, one can make a pitch to claim that reality is a subset of mathematics. Empirically, these two would look identical. Tegmark is arguing that you can choose to put reality inside mathematics instead of putting mathematics inside reality. Like all ...


8

I think you are right to be impressed with the Curry-Howard correspondence. It is a detailed and extensive rule-by-rule and feature-by-feature isomorphism. This strongly suggests that proof and computability are closely related. I also agree that it is under-appreciated within the philosophy of logic and that we can and should allow it to inform our ...


7

Summary Information distinguishes between multiple states of affairs; which indicates at the very least a bias in the likelihood that some state of affairs is realized, and ideally which indicates that some single state of affairs is realized while a number of alternatives have not been. In order to have a unit of information, you must have at least two ...


7

What you indicate is that the tome which allows John to simulate communication in Chinese is a rather tremendous computational resource: one which is very close in complexity — assuming that its rules are complex enough to successfully years of conversation in the same way that a Chinese essayist might — to simply conferring with a Chinese person. And I ...


7

About Gödel's incompleteness theorem, we need first to understand with reasonable precision what it states; see Torkel Franzén, Gödel's theorem An incomplete guide to its use and abuse (2005) : First incompleteness theorem (Gödel-Rosser). Any consistent formal system S within which a certain amount of elementary arithmetic can be carried out is ...


6

Abstract mathematics doesn't have to be related to physics. There are many things that mathematicians routinely consider (such as non-measurable sets, etc) that cannot possibly exist in the physical world. In particular, the laws of the physical world have no bearing on the P=NP problem.


6

The answer is going to greatly depend on what you think creativity means. If creativity is taken to mean "able to create something we find pleasant to experience", then the answer is clearly yes. If creativity is taken to mean "able to engage in a creative process" that yields a novel creation, then much will hinge on what we think such a process is. ...


6

The OP proposal is similar in spirit to the one in Farkas's paper Belief May Not Be a Necessary Condition for Knowledge. His primary example is Otto, a guy with severe memory loss, who keeps all important information in a notebook which he carries with him at all times, and which "extends" his mind: "There are parts of knowledge that are too tedious to ...


5

1: In what way do they exceed the expressive power of first-order logic? I don't know whether the untyped lambda calculus and first-order logic can be compared directly, but the Simple Type Theory is a typed lambda calculus and at the same time a formalization of higher-order logic. According to wikipedia: The lambda calculus was introduced by ...


5

So far considerations based on computational resources are consequential only to a small group of philosophers known as radical anti-realists, who extend strict finitism to epistemology. Unlike constructivists and moderate anti-realists (intuitionists) like Dummett, who are usually satisfied with computability in principle radical anti-realists insist on ...


5

The linked IEP article seems to me to be accurately summarized in the OP:"the argument about quantum processes in the brain falls short if we reject the original Gödelian argument... Penrose goes on to suggest that even if we deny the Gödelian argument we will still come to the same conclusion". But on my reading "the same conclusion" of Penrose is not that ...


5

This is intended as a complement to Conifold's and Jobermark' answers Penrose's argument can be broken down to two parts: Based on Lucas's Gödelian argument against mechanism, he argues that the human mind is more than just a Turing machine. The part of the human mind that is more than Turing machines can be explained by quantum phenomena in the brain. ...


5

Even if the man inside the Chinese room memorised every single translation instance (theoretically every possible combination which is impossible given our limited memory, but it's a thought experiment, so this constraint doesn't matter), would he understand Chinese, since he doesn't understand the meaning of any of the cards he has been presented with? ...


5

Nobody has ever found any credible evidence that the human brain is anything besides a very complicated computer running strange software. Nobody has ever found any credible evidence that humans are not the same thing as p-zombies. In particular, you don't have any credible evidence that you're not a p-zombie. "But that's ridiculous," you may say. &...


4

Although I believe Searle is mistaken, I don't think you have found the problem. You are postulating that the input contains the content not just knowledge of Chinese in distilled form, especially with the walking-across-the-room example. But many machine learning algorithms simply take lots of examples and can then generate appropriate behavior (within ...


4

I think you're right that computation is not fundamental, but to me the point of using computation is that universal computation lets you compute anything including any metric of information that you might like. Therefore, measuring information in terms of computation is merely availing yourself of infinite expressive capability. It's not a statement that ...


4

This line of thought has a rich tradition in philosophy. One potential way to gain empirical evidence one way or another is through the famous Turing Test, which challenges a computer to successfully imitate the perceptible output of human thought processes effectively enough that a human being would be unable to tell the difference. To the extent that a ...


4

It is logically possible that you can in fact calculate that fast but you need the ritual of submitting the problem to a computer in order to be able to consciously access the answer. You can take this to ridiculous extremes by having mathematics formulas generated from block-codes from Bitcoin mining, with the calculation done without you observing, and ...


4

The laws of physics, in particular quantum physics, seem to imply that it is possible to construct a universal computer that could simulate any physical system with arbitrary accuracy, this is called the Turing Principle, see http://www.daviddeutsch.org.uk/wp-content/deutsch85.pdf and "The Fabric of Reality" by David Deutsch. The relevant kind of computer ...


4

In a sense, computers are already capable of a degree of creativity. However it has always been humans who have been urging the computers to become creative - it has not been the computer that has engaged in the act of creativity for its own explorative or expressive requirements. Creativity in computers has normally been based upon one or more elements of ...


4

Interestingly enough we have an answer: The Blue Gene/Q has a 5D torus interconnect, meaning any software or logic developed for it would STRONGLY resemble the structure you are looking for. Developers are encouraged to think in terms which leverage this 5D structure. This is efficient in 3D space because much of the propagation time between nodes is in ...


4

In reverse order: "What on Earth does or did it mean that “the brain is a digital computer”. Literally it's just nonsense": Obviously the brain doesn't use binary code or run assembler, it uses neurons and analogue signals. The use of the word digital here is very misleading. What is meant here is that the brain is functionally equivalent to a digital ...


4

Minimal logic is intuitionistic logic without ex falso quodlibet. One way to understand the difference in interpretation between minimal (ML), intuitionistic (IL) and classical logic (CL) is by considering the different way they treat the implication operator →. In ML, A → B can be interpreted as "I can show that a proof of A can be manipulated into a proof ...


4

Penrose believes that quantum mechanics is incomplete. So even if it is true that all quantum processes as they are currently known are computational, Penrose would argue there's something missing and that missing part is non-computational. Reference video: https://www.youtube.com/watch?v=3WXTX0IUaOg At 2:44, he explains his argument about why he thinks ...


Only top voted, non community-wiki answers of a minimum length are eligible