Souron said:
trueknowledge.com is an attempt at a universal expert system.
I find that funny. I mean under mathematics for "the square root of 501" it lists 22.3830292856 which works as wrong at two levels.
1. The machine doesn't spot the contradiction in terms by talking about "the square root of 501", since the definite article "the" means exactly
one and only one. 501 has TWO square roots in the reals, so "the square root of 501" ends up a contradiction in terms. Or it arbitrarily favors positive roots over negative roots. The machine doesn't spot this as an arbitrary assumption about roots.
The cube root example works out worse, since you can't as easily produce complex roots from a positive real root.
2. It produces a rational number, while a square root of 501 comes as an irrational number. So, the machine should write 22.3830292856..., but it doesn't.
This one I also find kind of funny. If you trusted that machine and had no knowledge of American presidents, you would think it gave you a complete list of the presidents for the years during which Barrack Obama's age lay in {13, ..., 19} where the members of that set only take on the values of natural numbers. But, of course, the machine ONLY gives you the first and last presidents in that time period.
Souron said:
I mean that the field of logic is well understood.
I certainly dispute this. Look, here's one possible propositional logic which I doubt you'll find any logician talking much about, and I doubt they know how to "understand" it. Let 1 denote truth in the classical sense. Let 0 denote falsity in the classical sense. Numbers in (0, 1) will denote degrees of truth between 0 and 1. Let u stand for disjunction of propositions, i for intersection, -> for implication, ~ for negation, and <-> for equivalence. Then, one possible extension of the classical logic connectives which can serve for as a propositional logic comes as:
i(a, b)=.4 if a=.2
.1 if a=.3
min(a, b) otherwise
u(a, b)=pi-3 if a=e-2, where pi indicates the transcendental number pi, and e indicates the exact value of the exponentional function at 1.
max(a, b) otherwise.
~(a)=1 if a=0, 0 if a=1, a otherwise.
a->b=.4 if a=.5 or b=.5
min(1, 1-a+b) otherwise
a<->b=+sqrt(2)-1 if a=.4 or if b=+sqrt(3)-1, where +sqrt(n) indicates the positive square root of n.
1-abs(a-b) otherwise.
Who has studied and understood such a propositonal logic? Thing comes as one can produce as many propositional logics like the above as there exist real numbers.
Souron said:
What do you mean by "commonsense reasoning", and what is not completely understood about it?
It may not quite work, but I'll assume "commonsense reasoning" as synonymous with dispositional logic. In other words, we have propositions which
usually hold true, but not always. What doesn't come as completely understood comes as what "usually" means within a context. It doesn't just mean "most" or greater than or equal to 50%. The problem comes as that "usually" varies very, very widely across contexts. It might mean between 65% and 75% of the time (with say 70% as the best fit) in one context, while it might mean above 90% and below 93% in another context.
Souron said:
Anything in the field of logic or math can be.
Then completely describe a single irrational number. If you write ... or etc. or some similar phrase in your description I don't see the description as complete, I see it as only describing part of the entity in question, and then us inferring from that pattern how such a complete description
would work given that we had infinite time and resources to go on with the description. But, of course, we never have such time and resources.
As another challenge, describe all ways of describing "usually" as a
fuzzy number of type-1. Or a type-2 fuzzy number.
Souron said:
Anything that can be approximated by a mathematical framework can be mimicked to the extent that that framework is accurate.
This means we do NOT have a
total description. We have an approximation which, by definition, misses some part of the entity in question.
Souron said:
I'm not sure what you're trying to say here. The human brain is a computer that can reason in real time.
Alright, say I grant that. Then, what kind of circuits does it have? What sort of logic gates in the "human brain" allow some electrical signals to pass through and others not to pass through? There exist more problems than just fitting logical neurons onto a chip. Computers only work with electrical signals. Neurons work with both electrical and chemical signals. Can we really imitate such a system just by electrical signals? I doubt it.
Neurons don't work as the only carriers of information.
Glial cells also do such. There exists a lot more going on in the brain than just neurons communicating. See the video "networks in the brain"
here.
(i am Automaton)
