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Logic and deductions and proofs are a part of mathematics
Of course chess and maths are related. A computer wouldn't be able to play chess otherwise.
Don't confuse logic with mathematics. As the failure of Russell's Principia demonstrated, logic is not the basis of mathematics, nor is there an inherent relationship between one and the other.
Boolean algebra IS logic.
Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847)
Maybe you should read the book. You are very confused about the words you are using, and you certainly haven't a clue about Russell's attempt and the outcome.
No. You don't have a clue. You're a naive philosopher.
Yeah Russell's attempt blah blah.
What do you know about Boolean algebra?
Jack sh*t I presume?
Ok but, AFAIK, you can make a chess playing input-output device using only logic gates (not, and, or, etc).
I mean, humans don't play this way of course, so it doesn't completely define chess, but I don't think computers are a bad link between logic and chess.
Also I don't know why, e.g. Godel's incompleteness theorem, means Boolean algebra is not symbolic logic. IOW I don't know why both you and amilton542 aren't both right.
You're a philosopher.
Correction: math-trained and physics-trained philosopher... and trained at top universities, and I've served on conference panels in instances where discussion crossed boundaries between math and formal logic. It was long a project of mathematics-trained logicians (Whitehead and Russell, who also doubled as "naive philosophers, as you say) to demonstrate that formal logic is the foundation of mathematics, and it failed. What you are referring to with your little wikipedia page, which I doubt you much understand, is work that was produced long, long before 20th century realities set in. But you're right, I'm wrong.
For bb_gum234: Boolean algebra is a concoction of logic and mathematics. (The function of "concocted in that sentence is pointed, as I am referring to the inclusiong of members from two different sets of objects, namely, operations, etc.) The work of George Boole was one of the key researches that led to the optimism of trying to reduce all mathematics to formal logic. I think the biggest thing that non-initiates are missing here is that they are taking it that symbols from two systems are somehow the same, constituting, collectively "symbolic logic," which happens because the symbols are alien to them. It is equivalent to showing someone, who only speaks English, Serbian words in cyrillic and Russian words in cyrillic: they all look the same, because they seem to be of a similar sort, but nothing could be further from the truth, i.e., Serbian words are not Russian words. (Maybe Japanese Kanji and Chinese pictograms would have been a better example.) The long and the short is that the reference I made to Russell (and Alfred North Whitehead), and the outcome of their project, is relevant because they tried to demonstrate that mathematics could be reduced to formal logic, i.e., that mathematics springs from a foundation, called "formal logic." Hope that helps.
yes.. because "mathematics "is a problem solving analysis so as the "chess"..
Going off topic a bit here, it's interesting that if math isn't a subset of logic (I guess that's an ok way to say it) then what exactly is it? Or rather, how is it thought of today?
A math-trained philosopher is probably a good person to ask
Math is applied logic. You set axioms and derive logically conclusions. What a lot of people seem unaware of is that Russell/Whitehead etc work ARE NOT what nowadays people use as foundations of mathematics. Most of the criticism of nowadays mathematics based on works from pre-1930 era is irrelevant.These works were useful to fix all the paradoxes that occured in the "naive" set theory introduced by Cantor.
Nowadays maths uses :-Turing machines related concepts to explain what mathematical logic and calculation really are and what can you expect from them (or what is impossible). These are explained in computer science (imho the best way to understand all this fuss is to be familiar with those topics)
-Zermelo-Fraenkel set of axioms (including the axiom of choice although there's some debate): math theorems are derived from them using first order logic. Everything can be made 100 % formal if we really want. It is possible to build a computer software which test consistently whether a given string is a legit math statement or not (written in a proper formalized language). It is also possible to build a computer software which test whether, given a string and a legit math statement, if the former is a legit proof of the latter.
About the Gödel theorems: they actually claim you cannot find a proof that the theory above is consistent by using ZFC itself (assuming it is actually consistent, otherwise every statement becomes provable). But that doesn't prevent any of what is described above (some people believe Gödel proved that formalized math was bull*** but that's not true). In computer science standard lectures you'll find proper explanations and proof of Gödel theorem.
while math is just the same numbers over again.
You're probably confusing math with that anzan training they do in Japan. This is not what we were talking about. Math (understood at studying and proving theorems) is highly creative.
Does the horse move two squares or three? Is that a question of math(s)?
Yes! Count: one, two, bend!
The horse doesn't moves to squares: it magically teleports on them :p
The last time my horsey was in trouble, I pulled out my calculator.
He still died.
chess and math are 2nd cousins.
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