Shouldn’t this be physics as a lossy compression algorithm? A lot of math has nothing to do with anything in the real world. I guess I agree, the mathematical nature of physical laws is simply an expression of the predictability of the universe.
I can certainly imagine a universe where none of these concepts would be useful in predicting anything, and so they would never evolve in the “mind” of whatever entity inhabits it. To me mathematical concepts are no more universal than moral concepts
While numbers might not be useful in some universes, they would nevertheless be correct. 1 + 1 would still equal 2 because they are defined that way. Whether the universe contains an entity capable of expressing that fact doesn’t matter.
Shouldn’t this be physics as a lossy compression algorithm?
Think of math as the JPEG compression algorithm, and physics as cat pictures (not “real cats”). And some other science as, say, pictures of the sunset. JPEG works on both kinds of pictures, even if there is not much in common between cats and sunsets.
While numbers might not be useful in some universes, they would nevertheless be correct. 1 + 1 would still equal 2 because they are defined that way. Whether the universe contains an entity capable of expressing that fact doesn’t matter.
That’s the Platonic view. I am suggesting that in a universe without cats and pictures no one would invent JPEG, just like in some other (or even this) universe no one would invent human morality, even though one can state that “morality exists” as an abstract concept.
I’m not sure that this is a useful disagreement. But anyway: the JPEG comparison is interesting because JPEG is an algorithm, it doesn’t “exist” but it isn’t contingent on anything physical. Its just an algorithm. Does Hamlet “exist” in an alternate universe where Shakespeare was never born. The question doesn’t really mean anything.
I’m not a Platonist, if anything I would lean to towards formalism but I am very wary of taking a firm position on a philosophical issue that I am not intimately familiar with. And I think that Formalists and Platonists would answer yes to the question of whether 1+ 1 = 2 in an alternate chaotic universe (The logicists and intuitionists are rare). You can read about this here.
The Platonist view is that 1 + 1 = 2 expresses some truth about the entities “1”, “+”, “2” and “=”
The formalist view is that 1 + 1 = 2 follows from the axioms, its isn’t a truth but rather the predicate of a system of rules. If “mathematical axioms are granted” then “1 + 1 = 2″
But pretty much no philosopher thinks that mathematical statements are contingent on something. And I’m not sure if you’re saying that. Mathematical statements would not be generated in some universes yes, but that’s not relevant to whether the statements themselves are true. The statements are not contingent on the nature of the universe.
If you think that they are contingent, how far does this go? Is the law of non-contradiction contingent because in a sufficiently weird universe, no one would discover it?What about the statement “If X then X”?
Is the virtue of mercy contingent because in a sufficiently weird universe, no one would discover it?
I don’t know if I’m a moral realist. But assuming I were for a second: mercy essentially means “be nice to people even if they are bad/ do bad things”. Its not a statement about the world. Its not a truth claim. Its not a definition. Its not an algorithm. Its an imperative, an instruction. As such it is not subject to being contingent or necessary. Is the statement “Eat your vegetables” true? Well no it doesn’t have a truth value. Likewise with ethical statements.
Which isn’t remotely similar to mathematical statements which most philosophers either think express truths (Platonists) or formalisms—sequences of symbols that are generable from simple rules. But no philosophers that I know of think that mathematical statements require referents in the real world. There are some very strange mathematical fields that have nothing to do with this universe. My take on this is that it doesn’t really matter all that matters is that mathematics is useful.
Shouldn’t this be physics as a lossy compression algorithm? A lot of math has nothing to do with anything in the real world. I guess I agree, the mathematical nature of physical laws is simply an expression of the predictability of the universe.
While numbers might not be useful in some universes, they would nevertheless be correct. 1 + 1 would still equal 2 because they are defined that way. Whether the universe contains an entity capable of expressing that fact doesn’t matter.
Think of math as the JPEG compression algorithm, and physics as cat pictures (not “real cats”). And some other science as, say, pictures of the sunset. JPEG works on both kinds of pictures, even if there is not much in common between cats and sunsets.
That’s the Platonic view. I am suggesting that in a universe without cats and pictures no one would invent JPEG, just like in some other (or even this) universe no one would invent human morality, even though one can state that “morality exists” as an abstract concept.
I’m not sure that this is a useful disagreement. But anyway: the JPEG comparison is interesting because JPEG is an algorithm, it doesn’t “exist” but it isn’t contingent on anything physical. Its just an algorithm. Does Hamlet “exist” in an alternate universe where Shakespeare was never born. The question doesn’t really mean anything.
I’m not a Platonist, if anything I would lean to towards formalism but I am very wary of taking a firm position on a philosophical issue that I am not intimately familiar with. And I think that Formalists and Platonists would answer yes to the question of whether 1+ 1 = 2 in an alternate chaotic universe (The logicists and intuitionists are rare). You can read about this here.
The Platonist view is that 1 + 1 = 2 expresses some truth about the entities “1”, “+”, “2” and “=”
The formalist view is that 1 + 1 = 2 follows from the axioms, its isn’t a truth but rather the predicate of a system of rules. If “mathematical axioms are granted” then “1 + 1 = 2″
But pretty much no philosopher thinks that mathematical statements are contingent on something. And I’m not sure if you’re saying that. Mathematical statements would not be generated in some universes yes, but that’s not relevant to whether the statements themselves are true. The statements are not contingent on the nature of the universe.
If you think that they are contingent, how far does this go? Is the law of non-contradiction contingent because in a sufficiently weird universe, no one would discover it?What about the statement “If X then X”?
I guess I failed to present my view clearly enough. See if this works better:
Is the virtue of mercy contingent because in a sufficiently weird universe, no one would discover it?
I don’t know if I’m a moral realist. But assuming I were for a second: mercy essentially means “be nice to people even if they are bad/ do bad things”. Its not a statement about the world. Its not a truth claim. Its not a definition. Its not an algorithm. Its an imperative, an instruction. As such it is not subject to being contingent or necessary. Is the statement “Eat your vegetables” true? Well no it doesn’t have a truth value. Likewise with ethical statements.
Which isn’t remotely similar to mathematical statements which most philosophers either think express truths (Platonists) or formalisms—sequences of symbols that are generable from simple rules. But no philosophers that I know of think that mathematical statements require referents in the real world. There are some very strange mathematical fields that have nothing to do with this universe. My take on this is that it doesn’t really matter all that matters is that mathematics is useful.