The debate is apparently about the meaning of ‘different’. Someone might define different as, ‘predicting different observations’ and another as ‘different ontological content’.
If there is a box in front of you, which either contains as $20 or $100 note. However, you have very strong reasons to believe that the content of the box shall be unknown to you, forever. Is the question, “Is there a $20 or $100 note in the box?” meaningful. Is the belief in the presence of a $20 note different from the belief in the presence of a $100 note? That is essentially, similar to the problem of identical models.
Whether something is empiricly unknowable forever is itself unknowable … it’s an acute form of the problem of induction.
it doesn’t matter what’s inside it
But that isn’t quite the same as say ing that statements about what’s inside are meaningless. A statement can be meaningful without mattering. And you have to be able to interpret the meaning, in the ordinary sense, in order to be able to notice that it doesn’t matter.
If a universe where the statement is true is indistinguishable from a universe where the statement is false, then the statement is meaningless. And if the set of universes where statement A is true is identical to the set of universes where statement B is true, then statement A and statement B have the same meaning whether or not you can “algebraically” convert one to the other.
If A and B assert different things, we can test for these differences. Maybe not with current technology, but in principle. They yield different predictions and are therefore different beliefs.
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”.
In the thought experiment we are considering , the contents of the box can be er be tested. Nonetheless $10 and $100 mean different things.
I’m not sure you realize how strong a statement “the contents of the box can be never be tested” is. It means even if we crack open the box we won’t be able to read the writing on the bill. It means that even if we somehow tracked all the $20 and all the $100 bills that were ever printed, their current location, and whether or not they were destroyed, we won’t be able to find one which is missing and deduce that it is inside the box. It means that even if we had a powerful atom-level scanner that can accurately map all the atoms in a given volume and put the box inside it, it won’t be able to detect if the atoms are arranged like a $20 bill or like a $100 bill. It means that even if a superinteligent AI capable of time reversal calculations tried to simulate a time reversal it wouldn’t be able to determine the bill’s value.
It means, that the amount printed on that bill has no effect on the universe, and was never affected by the universe.
Can you think of a scenario where that happens, but the value of dollar bill is still meaningful? Because I can easily describe a scenario where it isn’t:
Dollar bills were originally “promises” for gold. They were signed by the Treasurer and the secretary of the Treasury because the Treasury is the one responsible for fulfilling that promise. Even after the gold standard was abandoned, the principle that the Treasury is the one casting the value into the dollar bills remains. This is why the bills are still signed by the Treasury’s representatives.
So, the scenario I have in mind is that the bill inside the box is a special bill—instead of a fixed amount, it says the Treasurer will decide if it is worth 20 or 100 dollars. The bill is still signed by the Treasurer and the secretary of the Treasury, and thus has the same authority as regular bills. And, in order to fulfill the condition that the value of the bill is never known—the Treasurer is committed to never decide the worth of that bill.
Is it still meaningful to ask, in this scenario, if the bill is worth $20 or $100?
I can understand that your revised scenario is unverifiable, by understanding the words you wrote, ie. by grasping their meaning. As usual, the claim that some things are unverifiable is parasitic on the existence of a kind of meaning that has nothing to do with verifiability.
The debate is apparently about the meaning of ‘different’. Someone might define different as, ‘predicting different observations’ and another as ‘different ontological content’.
If there is a box in front of you, which either contains as $20 or $100 note. However, you have very strong reasons to believe that the content of the box shall be unknown to you, forever. Is the question, “Is there a $20 or $100 note in the box?” meaningful. Is the belief in the presence of a $20 note different from the belief in the presence of a $100 note? That is essentially, similar to the problem of identical models.
If the content of the box is unknown forever, that means that it doesn’t matter what’s inside it because we can’t get it out.
Whether something is empiricly unknowable forever is itself unknowable … it’s an acute form of the problem of induction.
But that isn’t quite the same as say ing that statements about what’s inside are meaningless. A statement can be meaningful without mattering. And you have to be able to interpret the meaning, in the ordinary sense, in order to be able to notice that it doesn’t matter.
If a universe where the statement is true is indistinguishable from a universe where the statement is false, then the statement is meaningless. And if the set of universes where statement A is true is identical to the set of universes where statement B is true, then statement A and statement B have the same meaning whether or not you can “algebraically” convert one to the other.
They’re not, because A and B assert different things.
If A and B assert different things, we can test for these differences. Maybe not with current technology, but in principle. They yield different predictions and are therefore different beliefs.
You keep assuming verificationism in order to prove verificationism.
They assert different things because they mean different things, because the dictionary meanings are different.
In the thought experiment we are considering , the contents of the box can be er be tested. Nonetheless $10 and $100 mean different things.
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”.
I’m not sure you realize how strong a statement “the contents of the box can be never be tested” is. It means even if we crack open the box we won’t be able to read the writing on the bill. It means that even if we somehow tracked all the $20 and all the $100 bills that were ever printed, their current location, and whether or not they were destroyed, we won’t be able to find one which is missing and deduce that it is inside the box. It means that even if we had a powerful atom-level scanner that can accurately map all the atoms in a given volume and put the box inside it, it won’t be able to detect if the atoms are arranged like a $20 bill or like a $100 bill. It means that even if a superinteligent AI capable of time reversal calculations tried to simulate a time reversal it wouldn’t be able to determine the bill’s value.
It means, that the amount printed on that bill has no effect on the universe, and was never affected by the universe.
Can you think of a scenario where that happens, but the value of dollar bill is still meaningful? Because I can easily describe a scenario where it isn’t:
Dollar bills were originally “promises” for gold. They were signed by the Treasurer and the secretary of the Treasury because the Treasury is the one responsible for fulfilling that promise. Even after the gold standard was abandoned, the principle that the Treasury is the one casting the value into the dollar bills remains. This is why the bills are still signed by the Treasury’s representatives.
So, the scenario I have in mind is that the bill inside the box is a special bill—instead of a fixed amount, it says the Treasurer will decide if it is worth 20 or 100 dollars. The bill is still signed by the Treasurer and the secretary of the Treasury, and thus has the same authority as regular bills. And, in order to fulfill the condition that the value of the bill is never known—the Treasurer is committed to never decide the worth of that bill.
Is it still meaningful to ask, in this scenario, if the bill is worth $20 or $100?
I can understand that your revised scenario is unverifiable, by understanding the words you wrote, ie. by grasping their meaning. As usual, the claim that some things are unverifiable is parasitic on the existence of a kind of meaning that has nothing to do with verifiability.