Not disagreeing, but fleshing out part of what it seems you’re trying to say:
Numbers don’t exist, that much ought to be clear. I think Eliezer says that numbers are in our minds, and our minds exist, but this is not the case: it’s not numbers that are in our minds but representations of numbers.
Mathematical Platonism is, to me, religion for intellectuals. Mathematicians as esteemed at Kurt Goedel have even gone so far as to postulate that mathematics exists in an alternate universe. This is a basic error or at least wildly unparsimonious, akin to saying that modus ponens exists in an alternate universe.
To see how silly this is, it helps to realize that a sufficiently intelligent being would find all our mathematical theorems just alternative ways of stating the axioms, and all our mathematics just axioms and definitions with a bunch of obvious rephrases of the same. It would find our most advanced theorems as simple and obvious as modus ponens is to us—as just rewordings of the axioms and definitions.
From the perspective of a sufficiently intelligent being, mathematics is just a set of initial statements (axioms and definitions), along with humans’ silly little demonstrations to help each other realize that a bunch rewordings of those statements (theorems) all mean the same thing.
From the perspective of a sufficiently intelligent being, mathematics is just a set of initial statements (axioms and definitions), along with humans’ silly little demonstrations to help each other realize that a bunch rewordings of those statements (theorems) all mean the same thing.
From the perspective of a sufficiently intelligent being, physics is just a set of initial statements, along with a silly demonstration that history is what you get when you apply those statements over and over. How dull!
Hi. I agree with you completely and like the phrase "religion for intellectuals". I just don't see the difference in saying that numbers and mathematics exist somewhere but we can never show you where and saying that other things exist somewhere but we can't show you where. But, trying to get even very intelligent people (ie, your example of Goedel) to see this or even listen to this type of reasoning seems almost impossible. Oh, well! Thanks!
Roger
One thing I’ve noticed that is probably covered somewhere in LW archive (I hope!) is that really smart and rational people can sometimes just be really good at hiding the truth from themselves. In other words, the smarter you are, the better you are at Dark Arts, and the easiest person to trick with Dark Arts is sometimes yourself.
[Heads up: your comments are displaying as one long line requiring side-scrolling instead of with natural line breaks.]
Not disagreeing, but fleshing out part of what it seems you’re trying to say:
Numbers don’t exist, that much ought to be clear. I think Eliezer says that numbers are in our minds, and our minds exist, but this is not the case: it’s not numbers that are in our minds but representations of numbers.
Mathematical Platonism is, to me, religion for intellectuals. Mathematicians as esteemed at Kurt Goedel have even gone so far as to postulate that mathematics exists in an alternate universe. This is a basic error or at least wildly unparsimonious, akin to saying that modus ponens exists in an alternate universe.
To see how silly this is, it helps to realize that a sufficiently intelligent being would find all our mathematical theorems just alternative ways of stating the axioms, and all our mathematics just axioms and definitions with a bunch of obvious rephrases of the same. It would find our most advanced theorems as simple and obvious as modus ponens is to us—as just rewordings of the axioms and definitions.
From the perspective of a sufficiently intelligent being, mathematics is just a set of initial statements (axioms and definitions), along with humans’ silly little demonstrations to help each other realize that a bunch rewordings of those statements (theorems) all mean the same thing.
From the perspective of a sufficiently intelligent being, physics is just a set of initial statements, along with a silly demonstration that history is what you get when you apply those statements over and over. How dull!
Amanojack,
One thing I’ve noticed that is probably covered somewhere in LW archive (I hope!) is that really smart and rational people can sometimes just be really good at hiding the truth from themselves. In other words, the smarter you are, the better you are at Dark Arts, and the easiest person to trick with Dark Arts is sometimes yourself.
[Heads up: your comments are displaying as one long line requiring side-scrolling instead of with natural line breaks.]