"If we define a religion to be a system of thought that contains unprovable statements, so it contains an element of faith, then Gödel has taught us that not only is mathematics a religion but it is the only religion able to prove itself to be one."
John Barrow, Pi in the Sky, 1992
Actual humans are afraid of being considered obnoxious, stupid or antisocial. Karma loss is just an indication that perception may be heading in that direction.
This is how lost purposes form. Once you’ve figured out that karma loss is a sign of something bad, you start avoiding it even when it’s not a sign of that bad thing.
The quote, phrased in a less tortuous way, says that mathematics contains true statements that cannot be proven, and is unique in being able to demonstrate that it does. So far, so good, although the uniqueness part can be debated.
But the quote also states that mathematics therefore contains an element of faith, that is, that there exist statements that have to be assumed to be true. This is not the case.
Mathematics only compels you to believe that certain things follow from certain axioms. That is all. While these axioms sometimes imply that there exist statements whose truth will never be determined, they do not imply that we should then assume that such-and-such a statement is true or false.
That is why it should be downvoted. Because not knowing something doesn’t mean having to pretend that you do.
It sounds to me like a goofy language game, akin to “How many legs does a dog have if we call a tail a leg?”
That conundrum, to which the correct answer is “four”, is not a goofy language game. It is making the point that you cannot change the truth of a proposition by changing the meanings of the words in it. When you change the meanings of the words, you are creating a different proposition. It looks like the original one, because it consists of the same string of words, but it is not. Its truth need have nothing to do with the truth of the original one.
Would you still be able to see these words if we called black white?
I always hated that question due to its ambiguity. Those who state the answer is four legs seem to interpret the question as asking: “Labeling our current language as Language-A, and mentioning a different language Language-B in which ‘leg’ also refers to tails, and keeping in mind that we do not speak Language-B, how many legs does a dog have?”
However, for some reason I first interpreted the question as asking: “Labeling our current language as Language-A, and mentioning a different language Language-B in which ‘leg’ also refers to tails, what is the answer to ‘how many legs does a dog have?’ in Language-B?”
I apologies for both the brevity and ambiguity of these interpretations. However, I doubt that I am the only person who interprets the question in something along the lines of my fashion.
Definition is the basis of language. Without a common understanding of terms, there can be no discussion. Anything that has not been falsified is theory unless it is proven to be true. Without a common understanding of terms, how can we know that a statement has been proven false? Mathematics is the most rigorous language in the sense that there is nearly universal understanding of terms among professional mathematicians, but it is still a language. The answer to your question is unambiguous; if a dog has a set of appendages that we will call “Legs” that consists of four of what we commonly call legs plus one tail, then the number of elements in the set of “Legs” is equal to 5. We could say that the set L = {a,a,a,a,b). Either way, it is simply a matter of definition—not really a ‘goofy game’.
I think you have it the other way around. Definitions are based on language. Language is based on meaning. I knew the meaning of the word “red” before I had any definition for it, and I’d guess that so did you.
(with a smile) Perhaps we need to define definition. True that definitions are based on language. Also true, I believe, that if language is to communicate effectively, it will need commonly understood meanings for specific sounds/symbols. I may “see as red” what you “see as orange”. My guess is that we both saw and could differentiate between colors before we knew the commonly accepted terms for them.
It vaguely associates math with religion in the sort of mind that is in the human that reads LessWrong. In such minds that means it is both saying something positive about religion and negative about math. That means it deserves twice the downvotes obviously. Let’s downvote it, Nominull! I’ll downvote it if you do. Let’s start a circle-jerking session, Nominull. I will if you do. Agreed?
You might want to remove the space at the beginning of the line. It’s distracting to have to use the scrollbar to read the full quote.
also, how is math the only system able to prove that it has unproveable truths? that was missing from my copy of Godel’s theorems.
Did you mean to reply to kateblue rather than me? (Or did you want to evade the karma fee?)
I don’t understand—what fee? Would Jonathan_Graehl get more downvotes if he replied directly to kateblu? Why?
There’s a new “feature” that replies to sufficiently negative karma posts instantly lose 5 karma.
i was hoping you’d let my cowardice pass unnoted.
Wait actual humans are afraid of losing karma?
...i dont even
Actual humans are afraid of being considered obnoxious, stupid or antisocial. Karma loss is just an indication that perception may be heading in that direction.
Attempts to avoid karma loss by procedural hacks are a stronger indication...
This is how lost purposes form. Once you’ve figured out that karma loss is a sign of something bad, you start avoiding it even when it’s not a sign of that bad thing.
Maybe wedrifid is taking that into account and renormalizing. It’s hard to tell.
Of something different.
Of people assigning excessive weight to very small changes in signaling?
#noshitsherlock
Yes.
I don’t think it’s any weirder than viewing losing karma as an entertaining game.
Only on LessWrong would a statement with that much insight be downvoted because it could be taken to signal something vaguely positive about religion.
The quote, phrased in a less tortuous way, says that mathematics contains true statements that cannot be proven, and is unique in being able to demonstrate that it does. So far, so good, although the uniqueness part can be debated.
But the quote also states that mathematics therefore contains an element of faith, that is, that there exist statements that have to be assumed to be true. This is not the case.
Mathematics only compels you to believe that certain things follow from certain axioms. That is all. While these axioms sometimes imply that there exist statements whose truth will never be determined, they do not imply that we should then assume that such-and-such a statement is true or false.
That is why it should be downvoted. Because not knowing something doesn’t mean having to pretend that you do.
I was tempted to downvote it because it could be taken to be negative about math.
It sounds to me like a goofy language game, akin to “How many legs does a dog have if we call a tail a leg?”
That conundrum, to which the correct answer is “four”, is not a goofy language game. It is making the point that you cannot change the truth of a proposition by changing the meanings of the words in it. When you change the meanings of the words, you are creating a different proposition. It looks like the original one, because it consists of the same string of words, but it is not. Its truth need have nothing to do with the truth of the original one.
Would you still be able to see these words if we called black white?
I always hated that question due to its ambiguity. Those who state the answer is four legs seem to interpret the question as asking: “Labeling our current language as Language-A, and mentioning a different language Language-B in which ‘leg’ also refers to tails, and keeping in mind that we do not speak Language-B, how many legs does a dog have?”
However, for some reason I first interpreted the question as asking: “Labeling our current language as Language-A, and mentioning a different language Language-B in which ‘leg’ also refers to tails, what is the answer to ‘how many legs does a dog have?’ in Language-B?”
I apologies for both the brevity and ambiguity of these interpretations. However, I doubt that I am the only person who interprets the question in something along the lines of my fashion.
Definition is the basis of language. Without a common understanding of terms, there can be no discussion. Anything that has not been falsified is theory unless it is proven to be true. Without a common understanding of terms, how can we know that a statement has been proven false? Mathematics is the most rigorous language in the sense that there is nearly universal understanding of terms among professional mathematicians, but it is still a language. The answer to your question is unambiguous; if a dog has a set of appendages that we will call “Legs” that consists of four of what we commonly call legs plus one tail, then the number of elements in the set of “Legs” is equal to 5. We could say that the set L = {a,a,a,a,b). Either way, it is simply a matter of definition—not really a ‘goofy game’.
Be wary when issuing grand proclamations about language, lest you wind up looking silly to the linguistically-knowledgeable.
I think you have it the other way around. Definitions are based on language. Language is based on meaning. I knew the meaning of the word “red” before I had any definition for it, and I’d guess that so did you.
(with a smile) Perhaps we need to define definition. True that definitions are based on language. Also true, I believe, that if language is to communicate effectively, it will need commonly understood meanings for specific sounds/symbols. I may “see as red” what you “see as orange”. My guess is that we both saw and could differentiate between colors before we knew the commonly accepted terms for them.
I had assumed the audience had heard the joke before. The punch line: “Four. Calling a tail a leg doesn’t make it one.”
Which is the sort of thing that could be called “problematic on so many levels” — or just “goofy”.
Modus pwnens, modus trollens.
That sounds positive about religion to you?
It vaguely associates math with religion in the sort of mind that is in the human that reads LessWrong. In such minds that means it is both saying something positive about religion and negative about math. That means it deserves twice the downvotes obviously. Let’s downvote it, Nominull! I’ll downvote it if you do. Let’s start a circle-jerking session, Nominull. I will if you do. Agreed?
Circle-jerkIng is like more like a stag hunt; only implicit cooperation and an explicit lack of shame are required.