Paul Erdős (Hungarian: Erdős Pál [ˈɛrdøːʃ ˈpaːl]; 26 March 1913 – 20 September 1996) was a renowned Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. He was known both for his social practice of mathematics (he engaged more than 500 collaborators) and for his eccentric lifestyle (Time magazine called him The Oddball's Oddball). He devoted his waking hours to mathematics, even into his later years—indeed, his death came only hours after he solved a geometry problem at a conference in Warsaw. — Wikipedia
He had his own idiosyncratic vocabulary; although an agnostic atheist, he spoke of "The Book", a visualization of a book in which God had written down the best and most elegant proofs for mathematical theorems. Lecturing in 1985 he said, "You don't have to believe in God, but you should believe in The Book." He himself doubted the existence of God, whom he called the "Supreme Fascist" (SF). — Wikipedia
The rationale is simple: no proof at all for G is indistinguishable from there is proof of G but you haven't discovered it yet) — Agent Smith
The Argumentum ad ignorantiam fallacy states that just because G hasn't been proved, we can't then conclude ~G. The rationale is simple: no proof at all for G is indistinguishable from there is proof of G but you haven't discovered it yet). — Agent Smith
No proof for G is found. Can I then conclude that ~G = God doesn't exist, is true? — Agent Smith
Just asking for a bit of clarification. According to what you quoted, The Book involves only proofs of mathematical theorems. But you say that it includes proofs of every proposition, "mathematical or otherwise." Are you referring to an imaginary different book? — Ciceronianus
Ah, I see. The fact that there's no proof at all of your version of The Book, that doesn't mean there is no proof of your version of The Book, right? Or the fact there is no proof at all of your version of The Book is indistinguishable from there is proof of your version of The Book but we haven't discovered it yet. — Ciceronianus
Digression: The time to believe in something is when there is sufficient evidence. Sure, lack of evidence is not proof against a proportion, however that does not imply 'believe it anyway'. A responsible atheist would not say there is no god, they would say there is no good reason to believe in god. Just as there is no good reason to believe in goblins - even though goblins also can't be disproved. That said, reason is largely bypassed on this question anyway. Most tend to choose beliefs like these based on emotional grounds and dress them up with reasons. — Tom Storm
Have fun with The Book. — jgill
"God exists" is not a well-formed formula in mathematics. Hence it cannot be a theorem. The book contains only proofs of theorems. SO "God exists" could not be int he book.
So it's a muddled question.
More interesting is Gödel's work, which shows that the book can never be complete. There will always be missing theorems. — Banno
No. Absence of proof is not proof of absence. — Book273
To go from "there is no good reason to believe in god" and "there is no good reason to believe in goblins" to there is no god and there are no goblins is to commit the argumentum ad ignorantiam fallacy (vide infra). — Agent Smith
You've missed the point. You keep skipping ahead. A responsible atheist does not say there is no god. S/he says there is no good reason to believe in god - the case has not been made. It's like a murder case in law. A person found not guilty is not innocent. They simply have not met the legal criteria for guilt. — Tom Storm
Have fun with The Book. — jgill
:up: So your Erdős number is low. I think someone with a mathematical background can shed light on what I'm trying to say. — Agent Smith
Yes, proud to say it's 0. I'm happy to shed no light on what you are trying to say. :cool:
nowReplyOptions — jgill
Wrong. He would not be seen dead in my image. — jgill
Gödel claims that given an axiom set A, there are true propositions (say p) that are true but not provable in A. — Agent Smith
Are you sure about that? :chin: — jgill
This statement does not appear in the book.
Ah! So, "there is no good reason to believe in god" implies atheism but it doesn't imply "there is no god"? :chin: There are brands of atheism consistent with this line of reasoning. Could you elaborate on that. Thanks. — Agent Smith
Consider:
This statement does not appear in the book.
It is either false or not in the book, and hence the book is incomplete.
The book is either inconsistent or incomplete.
If it is inconsistent then one cannot rely on any proof that god exists.
If it is incomplete then one cannot conclude from god's not being mentioned that god exists or does not exist.
So the book is irrelevant. — Banno
What about undecidability? — Agent Smith
But, importantly, one can't prove a negative. — Tom Storm
Why is the default truth value for a proposition false? Is it though? Atheism? — Agent Smith
So, there's The Book, generalizing Erdős' idea, which contains all the proofs, elegant or inelegant (I'm not as demanding as Erdős), for each and every true proposition, mathematical or otherwise. — Agent Smith
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