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[Dacke]

BTW I ultimately belive in logic that can handle a=!a

That's not logic. Per definition, "a" and "not a" cannot be true at the same time. If you want that expression to mean something else, you have to redefine it.

The brain can handle this case.

The brain is unable to consider all it's beliefs at the same time. It's just not powerful enough to stay consistent. It's a sign of (necessary) weakness, not a sign of strength.

Proof? The only thing that does not change is changement.

That's just wordplay.

[Gimym JIMBERT]

Not
Because if the brain could not handle it it would be bring down easily, Gôdel already made the demonstration that all logic system have contradiction and paradox, and they can only be solve by creating a higher order logic system, ad infinitum.

The way a=!a works is that it's genrally a signal to check a given belief system, the brain can actually rework a new logic system from that point. But it's a proof that the internal brain logic is a super system that can manipulate all kind of logic.

But eastern logic (from hindu to chineese) and mathematics are based on that kind of logic and were miles ahead western logic (before being ripped off).

[Pineapple]

@_madK
Blind horse are rare
Rare things are valuable (see gold)
Therefore Blind horse = valuable

Cold, hard, irrefutable simple basic logic.

"Rare things are valuable" as a universal statement is false. "Some rare things are valuable" is a true statement. Extrapolating from one example that all rare things are valuable is faulty logic. The worlds "valuable" and "rare" are also highly relative and imprecise. What characteristic of something makes it rare? Gold is not rare inside a room full of gold. "Rare" is not applicable to any particular substance in all situations. Water is highly "valuable" to the existence of human life inside a desert, but it is not "valuable" to the existence of sand inside a desert. "Valuable" is highly dependent on both circumstance and who or what the object is "valuable" to.

I hope you're being completely sarcastic and not trying to make a point.

[Gimym JIMBERT]

Sarcasm indeed but you pretty much made the point
I think there is a line in the bible that say "law of human are not law of god" which pretty much defeat your demonstration, it's all about the axiom, logic isn't that prefect tool we are sometimes lead to believe.

[Dacke]

Because if the brain could not handle it it would be bring down easily

It would prevent us from believing with absolute certainty that two contradicting things were true. But that would only be a good thing. We would still be able to assigning probabilities to different possibilities, which is much better.

Gôdel already made the demonstration that all logic system have contradiction and paradox, and they can only be solve by creating a higher order logic system, ad infinitum.

No, that's not what Gödel proved. Gödel's theorems show that a complex logic systems are either self-contradictory or incomplete. They are called the incompleteness theorems for a reason. They show that a given system will always be incomplete, not that logic systems have to be self-contradicting.

The way a=!a works is that it's genrally a signal to check a given belief system, the brain can actually rework a new logic system from that point. But it's a proof that the internal brain logic is a super system that can manipulate all kind of logic.

No, the brain uses approximations to figure things out. The same goes for man-created neural networks. The brain is not exact and unable to cleanly handle big, complex systems. Instead it makes a qualified guess and hopes for the best. Which means it is able to process large amounts of data and get stuff right most of the time, but also messes up quite often.

Things like fuzzy logic, neural networks and evolution-based solution finding are all great. They allow us to find approximative solutions to problems that are too hard to find exact solutions to (like Backgammon or Go). But an exact solution, when available, is always preferable.

[Gimym JIMBERT]

If the brain could only handle fuzzy logic it would not be able to handle logic and mathematics to the level human can (and animal can't).

I don't believe the brain only use one kind of system but it can summon and emulate all kind of logic. I think it have a very deep logic system (a logic langage) that can be use to reconstruct any logic (a=!a too). Btw NN are just function aproximation, I'm not sure you can reduce the brain to current articficial NN system, and even that way, it's a very heterogenous NN that does not work everywhere in the same maneer. There is a hi level of abstraction that is left unexplore in AI or mathematics (hinted by Hofstader I think).

The brain is build for survival, it have some greedy system for fast decision and some deep system when danger is down. Classic Logic is only one way to handle information and process it, I believe it's a certainty check system more than a truth check (it check !a instead of a), which is pass to decision system that weight the logic against experience (using a more fuzzy logic set).

But obviously, if classic logic was so strong, computer would have been not prone to error, there not. It's the current crisis in AI that have led to exotic logic to solve problem that can not be solve with classic logic. One thing that strike me is how classic logic fail to handle exception. No fuzzy logic does not help either, that mean there is still something missing.

BTW I have certainly misquote godel, but eastern tradition was already doing that before godel, godel simply put it in a less mystically charge fashion (god are mathematical concept in old hi level mysticism).

[Pineapple]

Your claims regarding AI are absurd.

There is no computation without classic logic - in fact, the second most basic computational unit (above transistors) are termed "logic gates" because they operate exclusively on the basic logical principles of AND, OR, EXCLUSIVE OR, and NOT. (NAND, NOR, and XNOR are simply a combination of NOT and another logic function.) All other forms of conceivable logical can be simplified and translated into this system of classical logic. This is demonstrated by the fact that a computer operating on these four binary logical principles is capable of simulating the same logical process used by the human brain in a system called artificial neural networking. If you demand evidence, see programs that use this system to recognize speech and handwriting.

A computer operating on AND, OR, XOR, and NOT, with enough computational speed and memory is capable of performing the same thought processes as a biological (human) brain.
Therefore, if a human brain can think it, a computer can, too.

[_Tommo_]

Oh noes Godel's Incompleteness spawned again, at least it took a dozen of pages!

why, WHY it has to be thrown into any metaphysical discussion when it just talks about DAMNED AXIOM SYSTEMS.

It will not prove that humans have a soul or that computers can't emulate brain or that brain can't comprhend itself, it actually "only" proves that for any given algebra, there have to be some postulates undemostrable by the same algebra that they define. That's it  

@_madk: in fact a computer is able to simulate the reality in which the brain operates, so it should be able to simulate a brain. However I don't really see neural networking as more than an academic toy, it is just TOO different from real neurons.
And besides that, a brain has its function in its connections, it isn't a buch of neurons tossed together.

[Gimym JIMBERT]

@MadK
yep all you need is NAND (the universal logic gate), or all you need is a basic lambda calculus (in the form of f(x) )

But it still don't have the "auto wiring" that human have, it cannot create system that have not been thought yet and it cannot imagine exotic logic. And we still don't know how to do that! (but we are capable to go there). We don't have the AI set that allow the ai to "self build" itself, up to a general logic generation.

It lack the "emergent" (disclaimer, it's an overused overcharged world) property of the brain.

[Dacke]

If the brain could only handle fuzzy logic it would not be able to handle logic and mathematics to the level human can (and animal can't).

I don't believe the brain only use one kind of system but it can summon and emulate all kind of logic. I think it have a very deep logic system (a logic langage) that can be use to reconstruct any logic (a=!a too). Btw NN are just function aproximation, I'm not sure you can reduce the brain to current articficial NN system, and even that way, it's a very heterogenous NN that does not work everywhere in the same maneer. There is a hi level of abstraction that is left unexplore in AI or mathematics (hinted by Hofstader I think).

The brain is build for survival, it have some greedy system for fast decision and some deep system when danger is down. Classic Logic is only one way to handle information and process it, I believe it's a certainty check system more than a truth check (it check !a instead of a), which is pass to decision system that weight the logic against experience (using a more fuzzy logic set).

But obviously, if classic logic was so strong, computer would have been not prone to error, there not. It's the current crisis in AI that have led to exotic logic to solve problem that can not be solve with classic logic. One thing that strike me is how classic logic fail to handle exception. No fuzzy logic does not help either, that mean there is still something missing.

BTW I have certainly misquote godel, but eastern tradition was already doing that before godel, godel simply put it in a less mystically charge fashion (god are mathematical concept in old hi level mysticism).

Some animals can do some math. Many humans can't do basic math.

The brain uses a neural network to figure things out. It is not exact and does not contain the foundation for formal languages.

According to one approximation, a human brain has the computational power of all the general-purpose computers that existed in 2007. The human brain is very powerful. So it is indeed able to handle math correctly, but only if things are separated into tiny pieces that are small enough for the brain to handle.

Yes, the brain is built for survival. For survival, it is more important to be able to quickly compute lots and lots of approximative solutions. The need for absolutely correct solutions isn't something we needed until a few thousand years ago. Having a brain that is bad at proper logic is a good trade-off for survival reasons, but proper logic is still more correct.

Computers are not prone to error, not in the slightest. The logic in a computer is flawless, as long as there are no hardware errors (which are quite unusual). The problem lies in the human brain's inability to give correct instructions to computers and to interpret the answers correctly.

The eastern tradition did not do advanced math and logic that could compete with western math in the 1930s. What understanding do you have of modern math?

Edit: Wait.. am I being math-trolled?

[Gimym JIMBERT]

@Tommo
I believe it's inevitable, because it deal about how we are programmed to act within reality, religion give a set of belief (a programmation), people check this belief against logic to "check" if it's working. And metaphysics is another set of check, it check if the current programation have some value, it actually reevaluate value.

If you thinks about it, question like "who am I, why i'm here" is a process of reprogrammation to better fit the world, the reevaluate purpose. Computer can't reevaluate their purpose. It's also a short term survival mechanism, it makes a force check of situation (hence trigger logic).

I can see metaphysics happen in two general situation, when everything is bad enough and people are caught in bad strike, dissatisfaction lead to a check of what's wrong and reevaluate the programation. Second case is when everything is right,  it force a check to see if things could be better, longer or if there isn't flaws.

There is an assumption that humanity can't reach true happiness because human are forever dissatisfied, you can see this root into that survival check. It's also countless movie and story, see plato's cave.

[Gimym JIMBERT]

Yes computer are prone to error because they are discrete machine. Actually most engineer I know need to anticipate the error margin to write their program. There is floating point error, rounding error, out of bound error, etc...
Computer are very precise (more than human) they have some limits too

edit: it's not because many human can't that the brain cannot, animal don't demonstrate conjoncture.

edit2:
This discussion is not about math, it's about FAITH in math and logic.
When I discuss old mathematics, it's obvious that the modern world have catching up since. We are using their concept!

edit 3:
Raw power is also a fallacy, good structure trumps raw power most of the time (especially if it is scaling with raw power, see search algorythm)

edit 4:
And all the brain power is not dedicacate to math or logic too, it deal with a lot of homeostatic regulatory problem and lot of signal preprocessing, it also handle memory retrieval etc... It can't use all that raw power for one task, it does it for million of small specific task, which lead to a comparison fallacy with computer.

[Pineapple]

Computers are infinitely precise; mathematical errors are not caused by imperfections in logic, it's because arbitrary precision is inefficient by today's computing standards, not because it can't be done.

[Gimym JIMBERT]

But you therefore need infinite precision which made a perfect computer a theorical beast by definition, doesn't it? I don't believe computer to be infinitely precise!

[---]

But you therefore need infinite precision which made a perfect computer a theorical beast by definition, doesn't it? I don't believe computer to be infinitely precise!

Pi is never constant because of pixels. It is only estimated.

>_> This guy has no clue what he's talking about.

[Pineapple]

But you therefore need infinite precision which made a perfect computer a theorical beast by definition, doesn't it? I don't believe computer to be infinitely precise!

The purpose of mathematical approximation using computational logic (which results in floating point errors, rounding errors, etcetera) is because it takes more time for electricity to pass through a larger quantity of logic gates than a smaller quantity, and it takes fewer logic functions to approximate arithmetic than it does to consider it arbitrarily. Since we like our computers fast and generally only scientific applications require perfect precision, the consumer gets a computer whose default systems use approximation. It is entirely possible to create a program whose mathematical accuracy is bounded only by the amount of memory able to be lent by the machine on which the program is running.

Please educate yourself.

[Reefpirate]

Baptist, Pentecostal, etc. are "denominations" of Protestantism. Catholicism, Protestantism, and Mormonism are grouped together only because the Bible is significant to all of them. They are very different otherwise.

Rastafarianism, listed here as 'Rasta' is also Christian.

[Gimym JIMBERT]

But you therefore need infinite precision which made a perfect computer a theorical beast by definition, doesn't it? I don't believe computer to be infinitely precise!

Pi is never constant because of pixels. It is only estimated.

>_> This guy has no clue what he's talking about.

Symbolic computation does not make the computer infinitely precise, it only dodge the problem with another representation, one where precision is not a problem at all.

@Madk
It is still bound to memory, infinite memory is not happening, it is still theorical and not "real" (which is the root of our discord), by the way it have nothing to do with the original discussion.
Arbitrary != infinite

Let's admit I made a little mistake, it does not invalidate my main point, which is classic logic is limited and computer does not have the structure to support and process "a generic logic system" like the brain can (with the power to self emulate, self generate and run exotic logic).

We don't have the "logic" of logics.

Human have it and can program a computer for any logic he can think of, the computer don't think, he does not have this hi order processing, even if we have all the raw power possible, he just can't actually, not until we crack that code.

And to crack that code I propose that we can create a logic system which can handle a=!a as a principle. It should be able to check that and recreate a logic when it deal with that. a=!a is the process of which most mathematical invention have been made, it's the moment of leap of faith, that's how we had imagined non euclidian space and how he had discovered imaginary number, which solve entire new case of problems, is the brain wired to deal with those extreme abstraction? certainly not directly, but through a deep logic system that allow to go against "classical logic" and not terminate the problem handling as impossible (at least not always). It have the logics of logic!

  I guess I cannot make my point ever, it's too exotic

[Guillaume]

I guess I cannot make my point ever, it's too indie

Fixed that for you.

[Gimym JIMBERT]

 

By the way, my point line up approximately with Hofstader:
http://en.wikipedia.org/wiki/Fluid_Concepts_and_Creative_Analogies

edit:
A logic that can reflect on his own structure. Classic logic does not handle "what if"