I’d argue not. Even though Eliezer and Scott brought the gods in for the theatrical and rhetorical impact, evolution is the same old evolution and competition is the same old competition. Describing the idea differently does not automatically make it a different idea—just like describing f(x)=(x+1)2 as g(x)=x2+2x+1 does not make it a different function.
In case of mathematic functions we have a simple equivalence law: f≡g⟺∀xf(x)=g(x). I’d argue we can have a similar equivalence law for beliefs - A≡B⟺∀XP(X∣A)=P(X∣B) where A and B are beliefs and X is an observation.
This condition is obviously necessary because if A≡B even though ∃YP(Y∣A)≠P(Y∣B) and we find that P(Y)=P(Y∣A), that would support A and therefore also B (because they are equivalent) which means an observation that does not match the belief’s predictions supports it.
Is it sufficient? My argument for its sufficiency is not as analytical as the one for its necessity, so this may be the weak point of my claim, but here it goes: If A≢B, even though they give the same predictions, then something other than the state and laws of the universe is deciding whether a belief is true or false (actually—how much accurate is it). This undermines the core idea of both science and Bayesianism that beliefs should be judged by empirical evidences. Now, maybe this concept is wrong—but if it is, Occam’s Razor itself becomes meaningless because if the explanation does not need to match the evidences, then the simplest explanation can always be “Magic!”.
The Quotation is not the Referent. Just because the text describing them is different doesn’t mean the assertions themselves are different.
..because exact synonymy is possible. Exact synonymy is also rare, and it gets less probable the longer the text is.
You need to be clear whether you are claiming that two theories are the same because their empirical content is the same, or because their semantic content is the same.
just like describing f(x)=(x+1)2 as g(x)=x2+2x+1 does not make it a different function.
Those are different...computationally. They would take a different amount of time to execute.
Pure maths is exceptional in its lack of semantics.
f=ma
and
P=IV
..are identical mathematically, but have different semantics in physics.
If A≢B, even though they give the same predictions, then something other than the state and laws of the universe is deciding whether a belief is true or false (actually—how much accurate is it)
If two theories are identical empirically and ontologically, then some mysterious third thing would be needed to explain any difference. But that is not what we are talking about. What we are discussing is your claim that empirical difference is the only possible difference , equivalently that the empirical content of a theory is all its content.
Then the answer to “what further difference could there be” is “what the theories say about reality”.
The Quotation is not the Referent. Just because the text describing them is different doesn’t mean the assertions themselves are different.
Eliezer identified evolution with the blind idiot god Azathoth. Does this make evolution a religious Lovecraftian concept?
Scott Alexander identified the Canaanite god Moloch with the principle that forces you to sacrifice your values for the competition. Does this make that principle an actual god? Should we pray to it?
I’d argue not. Even though Eliezer and Scott brought the gods in for the theatrical and rhetorical impact, evolution is the same old evolution and competition is the same old competition. Describing the idea differently does not automatically make it a different idea—just like describing f(x)=(x+1)2 as g(x)=x2+2x+1 does not make it a different function.
In case of mathematic functions we have a simple equivalence law: f≡g⟺∀xf(x)=g(x). I’d argue we can have a similar equivalence law for beliefs - A≡B⟺∀XP(X∣A)=P(X∣B) where A and B are beliefs and X is an observation.
This condition is obviously necessary because if A≡B even though ∃YP(Y∣A)≠P(Y∣B) and we find that P(Y)=P(Y∣A), that would support A and therefore also B (because they are equivalent) which means an observation that does not match the belief’s predictions supports it.
Is it sufficient? My argument for its sufficiency is not as analytical as the one for its necessity, so this may be the weak point of my claim, but here it goes: If A≢B, even though they give the same predictions, then something other than the state and laws of the universe is deciding whether a belief is true or false (actually—how much accurate is it). This undermines the core idea of both science and Bayesianism that beliefs should be judged by empirical evidences. Now, maybe this concept is wrong—but if it is, Occam’s Razor itself becomes meaningless because if the explanation does not need to match the evidences, then the simplest explanation can always be “Magic!”.
..because exact synonymy is possible. Exact synonymy is also rare, and it gets less probable the longer the text is.
You need to be clear whether you are claiming that two theories are the same because their empirical content is the same, or because their semantic content is the same.
Those are different...computationally. They would take a different amount of time to execute.
Pure maths is exceptional in its lack of semantics.
f=ma
and
P=IV
..are identical mathematically, but have different semantics in physics.
If two theories are identical empirically and ontologically, then some mysterious third thing would be needed to explain any difference. But that is not what we are talking about. What we are discussing is your claim that empirical difference is the only possible difference , equivalently that the empirical content of a theory is all its content.
Then the answer to “what further difference could there be” is “what the theories say about reality”.