Originally posted by NotAllThere
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Antisemitism in Christianity
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Sorry: typo. I meant 1+1=2 is defined as a part of integer arithmetic. You don't need to prove it or use statistics etc. It is by definition true."Don't part with your illusions; when they are gone you may still exist, but you have ceased to live" Mark Twain -
For a start, even if it is a tautology, it in no way invalidates the contention that for a given x, 1+1=x has an infinitesimal probability of being true.Originally posted by Cirrus View PostSorry: typo. I meant 1+1=2 is defined as a part of integer arithmetic. You don't need to prove it or use statistics etc. It is by definition true.
But it isn't a tautology. It's a proposition.
Alfred North Whitehead and Bertrand Russell spent a couple of hundred pages proving it in Principia Arithmetica. The Peano arithmetic proof of 1+1=2 arises from these axioms:
0 is a natural number.
The next four axioms describe the equality relation. Since they are logically valid in first-order logic with equality, they are not considered to be part of "the Peano axioms" in modern treatments.[5]
- For every natural number x, x = x. That is, equality is reflexive.
- For all natural numbers x and y, if x = y, then y = x. That is, equality is symmetric.
- For all natural numbers x, y and z, if x = y and y = z, then x = z. That is, equality is transitive.
- For all a and b, if b is a natural number and a = b, then a is also a natural number. That is, the natural numbers are closed under equality.
- For every natural number n, S(n) is a natural number.
- For all natural numbers m and n, m = n if and only if S(m) = S(n). That is, S is an injection.
- For every natural number n, S(n) = 0 is false. That is, there is no natural number whose successor is 0.
Note: 1+1=2 is not an axiom. But it is provably true from these axioms. Of course, if you choose to define 2 as 1+1, then 1+1=2 is a tautology. But mathematicians don't define numbers like that.
It is a logical fallacy to say that because the probability of a proposition being true is infinitesimal, then the proposition isn't true.Originally posted by TheGreenBastard View PostIn a different category of mathematics (statistics) what he's saying is true.
Another interesting problem, discussed by minds greater than ours over the centuries. More interesting are these 2 questions.Originally posted by xoggoth View PostQuite. And if god is both good and almighty where did evil come from?
1. Why God (if existing) allows purposeless (non teleological) evil to exist?
2. Where does the notion of evil arise?
I got a 1st on my essay regarding the 1st in Philosophy at university.
Though my main subject was maths. If you like we could argue about the number of angels who'll fit on the head of a pin.
Down with racism. Long live miscegenation!Comment
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consider this -Originally posted by NotAllThere View PostFor a start, even if it is a tautology, it in no way invalidates the contention that for a given x, 1+1=x has an infinitesimal probability of being true.
But it isn't a tautology. It's a proposition.
Alfred North Whitehead and Bertrand Russell spent a couple of hundred pages proving it in Principia Arithmetica. The Peano arithmetic proof of 1+1=2 arises from these axioms:
0 is a natural number.
The next four axioms describe the equality relation. Since they are logically valid in first-order logic with equality, they are not considered to be part of "the Peano axioms" in modern treatments.[5]
- For every natural number x, x = x. That is, equality is reflexive.
- For all natural numbers x and y, if x = y, then y = x. That is, equality is symmetric.
- For all natural numbers x, y and z, if x = y and y = z, then x = z. That is, equality is transitive.
- For all a and b, if b is a natural number and a = b, then a is also a natural number. That is, the natural numbers are closed under equality.
- For every natural number n, S(n) is a natural number.
- For all natural numbers m and n, m = n if and only if S(m) = S(n). That is, S is an injection.
- For every natural number n, S(n) = 0 is false. That is, there is no natural number whose successor is 0.
Note: 1+1=2 is not an axiom. But it is provably true from these axioms. Of course, if you choose to define 2 as 1+1, then 1+1=2 is a tautology. But mathematicians don't define numbers like that.
It is a logical fallacy to say that because the probability of a proposition being true is infinitesimal, then the proposition isn't true.
Another interesting problem, discussed by minds greater than ours over the centuries. More interesting are these 2 questions.
1. Why God (if existing) allows purposeless (non teleological) evil to exist?
2. Where does the notion of evil arise?
I got a 1st on my essay regarding the 1st in Philosophy at university.
Though my main subject was maths. If you like we could argue about the number of angels who'll fit on the head of a pin.
1 + 1 = II
1 + 1 + 1 + 1 = IV
1 + 1 + 1 + 1 + 1 = V
and V + V = X
and don't forget hexadecimal where A + B = 21
so, 2,3 4, etc are only character indicators which we find convenient and are taught to do maths in.Comment
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42Originally posted by NotAllThere View PostFor a start, even if it is a tautology, it in no way invalidates the contention that for a given x, 1+1=x has an infinitesimal probability of being true.
But it isn't a tautology. It's a proposition.
Alfred North Whitehead and Bertrand Russell spent a couple of hundred pages proving it in Principia Arithmetica. The Peano arithmetic proof of 1+1=2 arises from these axioms:
0 is a natural number.
The next four axioms describe the equality relation. Since they are logically valid in first-order logic with equality, they are not considered to be part of "the Peano axioms" in modern treatments.[5]
- For every natural number x, x = x. That is, equality is reflexive.
- For all natural numbers x and y, if x = y, then y = x. That is, equality is symmetric.
- For all natural numbers x, y and z, if x = y and y = z, then x = z. That is, equality is transitive.
- For all a and b, if b is a natural number and a = b, then a is also a natural number. That is, the natural numbers are closed under equality.
- For every natural number n, S(n) is a natural number.
- For all natural numbers m and n, m = n if and only if S(m) = S(n). That is, S is an injection.
- For every natural number n, S(n) = 0 is false. That is, there is no natural number whose successor is 0.
Note: 1+1=2 is not an axiom. But it is provably true from these axioms. Of course, if you choose to define 2 as 1+1, then 1+1=2 is a tautology. But mathematicians don't define numbers like that.
It is a logical fallacy to say that because the probability of a proposition being true is infinitesimal, then the proposition isn't true.
Another interesting problem, discussed by minds greater than ours over the centuries. More interesting are these 2 questions.
1. Why God (if existing) allows purposeless (non teleological) evil to exist?
2. Where does the notion of evil arise?
I got a 1st on my essay regarding the 1st in Philosophy at university.
Though my main subject was maths. If you like we could argue about the number of angels who'll fit on the head of a pin.Comment
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There’s no point in having that number without knowing how you got it.Originally posted by BR14 View Post42
Having brought Millie in from a muddy walk earlier, I gave her a shower. As I towelled her off, I was thinking to myself: What do you get if you multiply six by nine?
...and that’s how you get 42.…Maybe we ain’t that young anymoreComment
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nah, that's 25 or 6 to 4Originally posted by WTFH View PostThere’s no point in having that number without knowing how you got it.
Having brought Millie in from a muddy walk earlier, I gave her a shower. As I towelled her off, I was thinking to myself: What do you get if you multiply six by nine?
...and that’s how you get 42.
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Originally posted by BR14 View Postnah, that's 25 or 6 to 4

how many roads must a mouse travel?Comment
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In hexadecimal A + B = 15.....Originally posted by JohntheBike View Post
and don't forget hexadecimal where A + B = 21Comment
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