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I have heard a Strong Reductionist theory, which goes as follows: History is Psychology. Psychology is Biology. Biology is Chemistry. Chemistry is Physics. Physics is Math. In other words, you can (in principle) derive the higher order theory from the more fundamental theory.

For any deterministic interpretation of quantum mechanics, it seems that this would necessarily have to hold (though for MWI, it would not tell you which universe you happen to be in).

As a completely irrelevant aside, the first link is tenuous - it's awfully hard to explain Pompeii in terms of just psychology - but it would still be true that you could derive all of history from sufficient knowledge of starting conditions, and could possibly work backwards from sufficient knowledge of the present (which, for MWI, would include sufficient knowledge of the state of all worlds).

If for no other reason, I reject that theory because Physics is not Math. Physics is inherently about making statements that have empirical content. Math is inherently about making statements that lack empirical content.

Would you say that you are expressing a difference in the territories covered by physics and math, in our existing maps of physics and math, in any potential map of physics and math, or in our methods of constructing the maps?

TimS14y00

Would you say that you are expressing a difference in the territories covered by physics and math, in our existing maps of physics and math, in any potential map of physics and math, or in our methods of constructing the maps?

I think the answer to your question is "method of construction."

In principle, a Cartesian skeptic should be able generate the same map of "Math" that we use. In contrast, there is no reason that a Cartesian skeptic's map of Physics would have any resemblance to the territory at all. (I accept that it is hard t... (read more)

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Is math subjective?

by [anonymous]

25th Oct 2011

1 min read

-7

I was arguing with a friend over whether reality is objective or subjective. He says subjective, because of the double-slit experiment, and that reality changes depending on whether we observe it or not, so it only exists in our minds.

I know this is right.. But something still seems off to me.

I said, well math is objective. But then he said that no, math is relative depending to where we are. In a black hole, math is different from on earth.

So reality changes... depending on our location... Yes? No?

I'm confused. I'm trying to write an essay on objective versus subjective reality, but I just keep getting mind-fucked.

And yes, I've read some articles on LessWrong on this topic, but I couldn't exactly find one that fit my question completely. :/

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[-]dlthomas14y130

I was arguing with a friend over whether reality is objective or subjective. He says subjective, because of the double-slit experiment, and that reality changes depending on whether we observe it or not, so it only exists in our minds.

I know this is right.. But something still seems off to me.

This isn't right.

[-]Jack14y120

Your friend is wrong about the double-slit experiment and math in black holes. The answer to your question depends entirely on what you mean by "subjective" and "objective" and I'm not sure you know what you mean. So try to tell us what you mean by these terms.

[-]RobinZ14y10

Better still, try to tell us what you mean without using those terms.

[-]drethelin14y90

Math is entirely conceptual. What's different in a black hole is PHYSICS, so the math used to describe physics is different, but 2+2 is entirely unaffected by gravitation, however mighty.

In terms of quantum physics I'm a layman so forgive me if this is too simplistic or wrong, but I think I see a couple problems with the way you state it. 1) Once the situation is observed and the state is determined, it doesn't get redetermined differently for different observers. Having an effect on reality is not the same as reality being subjective. 2) Quantum physics doesn't actually care about intelligent "observers". The reason "observing" something influences the state it is in is because at the quantum level you get information about things by how they interact with other things bounced off them, and those things effect the thing being observed. A way of thinking about is if there are a bunch of bottles in a dark room and you can only figure out where they are by throwing a baseball into the room. Each time you hit a bottle, you find out WHERE it was, but it's no longer there because you just shattered it. Until you hit it, you only have a rough idea of its probability of being in any given spot. When you "Observe" it the state of the bottle changes, but it's not something that you did by observing it but by the method you used to gain information about it.

[-]pragmatist14y50

I would not even say that physics is different in a black hole. In fact, I would strongly bet against it. What is true is that our best physical theories fail to give coherent results at the center of a black hole, but of course this does not mean the actual physics is different. One must not confuse the map and the territory.

[-]dlthomas14y20

The bottle shattering is unnecessary and possibly distracting. It seems to be enough that it is moved (ETA: unpredictably), for the relation you are trying to draw. (I think that may still be incomplete, but I will let someone wiser in the ways of QM weigh in there).

[-][anonymous]14y00

[-][anonymous]14y60

reality changes depending on whether we observe it or not

no. reality changes depending on interactions that happen within reality.

so it only exists in our minds.

even worse. see map and territory. Even if it's in your mind, there is a system that generates predictions and a system that generates observations. They are different.

math is relative depending to where we are. In a black hole, math is different from on earth.

Math is same everywhere. Physics may break down in black holes. Math is constant and objective. Even God can't touch math.

So reality changes... depending on our location

but I couldn't exactly find one that fit my question completely.

map and territory (the simple truth). beyond the reach of god. quantum physics sequence.

[-]lavalamp14y50

He says subjective, because of the double-slit experiment, and that reality changes depending on whether we observe it or not, so it only exists in our minds.

Even if that were true, it wouldn't really be a kind of subjectivity that matters. It doesn't give you superpowers, you can't close your eyes and jump off a cliff. If reality actually were subjective, it'd show up in more places than subatomic particles, and he'd have much better evidence.

Suggested reading: the quantum mechanics sequence, and the simple truth.

http://lesswrong.com/lw/r5/the_quantum_physics_sequence/

http://yudkowsky.net/rational/the-simple-truth

[-]KPier14y20

Try math is subjectively objective., which explores the issue I think you're trying to raise.

As other commenters have said, with regards to the double-slit experiment and black holes your friend is just wrong.

[-]RobertLumley14y20

This sounds like a case of Disputing Definitions to me. Is there anything different about your and your friends model of reality inside a black hole, or your understanding of quantum physics? If not, then there is no dispute, and you're just calling reality different words.

[-]TimS14y20

I totally disagree with his conclusion, but here is Eliezer on possible proofs that 2 + 2 doesn't equal 4

[-]TimS14y-20

In a distinct post to distinguish my view from Eliezer's. My gloss of his point: The argument of the physical monist is that all substance is physical . Your mind is physical, so its thoughts (like math) are physical. All assertions about physical things are subject to empirical falsification, so math is falsifiable in principle, even thought it has never been actually falsified.

Personally, I think math (but definitely not physics) is objective, because there are important similarities between the statement of modus ponens and the statement that 2 + 2 = 4. Further, they are both different from the statement that the sky is blue.

If I understand the physical monist argument correctly, the response is that rocks don't do modus ponens, but we do, and that's just how it is.

[-]dlthomas14y00

Now that I believe I understand the point you were making, I think you are making an interesting distinction (or one whose non-existence is, itself, interesting). I think that labeling this "objective" vs. "subjective" is confusing. Generally, I think of "subjective" as "a function of the observer", and objective as "a function of the observed"; two different observers in the same universe should derive the same laws, right?

[-]TimS14y-20

I agree that A priori / a posteriori is not the same distinction as the objective / subjective distinction. But a priori truth is objective (i.e. universalizable). In ordinary circumstances, most empirically based statements are also objective. But I'm not sure that's true in very unusual circumstances. Maybe I'm excessively influenced by all the hard sci-fi that says physics inside a black hole does not correspond well to physics in "normal" conditions.

In my head, this is the alien problem. [Assuming aliens exist,] the different environment extraterrestrial intelligent aliens evolved in mean that there's no reason to think they experience the world anything like humans. No common moral precepts, and probably no communication possible at all. In short, I think it very plausible that aliens are so different that we can't even say, "Let's avoid each other." (p > .4)

If aliens are that different, I'm not sure what exactly it means to assert that we have the same physics as the aliens. But I still think it makes sense to say that we have the same math because mathematics statements are prior to experience.

[-]dlthomas14y00

Could your position on this alternately be phrased, "What we are building with physics is a map of (regions of) this territory; what we are building with math is a map of (regions of) any possible territory"? If not, where does it differ?

[-]TimS14y00

I don't understand what you mean by a "possible territory."

If you mean a Many-Worlds branch that isn't this one, then I'm not sure why I want to think anything about such a branch. There is not a good reason to expect useful correspondence between this branch and that branch that I'm aware of.

[-]dlthomas14y20

I had no precise definition in mind, but Many-Worlds branches in particular seem a poor fit. I was trying to express the notion that "it could not be the case that there is a reality and these things do not apply to it."

[-]TimS14y00

Ok. Do you think that your point differs from pragmatist's point about the difference between the distinction based on a priori / a posteriori and the distinction based on necessity / contingency?

Because I'm not trying to make any assertion about the necessity or contingency of the truth of math.

[-]dlthomas14y00

Because I'm not trying to make any assertion about the necessity or contingency of the truth of math.

Then I do not follow your original point.

[Math and physics] are both different from the statement that the sky is blue.

Presumably because there needs to be an observer to see the blue, and different people may draw different delineations between what is blue vs. purple vs. teal? If you describe it in wavelengths, is it the same as physics? If not, what is it that makes it not?

Personally, I think math (but definitely not physics) is objective, because there are important similarities between the statement of modus ponens and the statement that 2 + 2 = 4.

This seems to just be a fact about the territory. Presumably, there are similar similarities between a perfectly accurate and completely specified quantum theory and chemical reactions, they are just harder to work out.

[-]TimS14y00

[Math and physics] are both different from the statement that the sky is blue.

That is not a correct edit of what I said. At the level of generality I'm talking, "The sky is blue" is a physics statement. A better summary would be "[Math and logic] are both different from the statement that the sky is blue.

Personally, I think math (but definitely not physics) is objective, because there are important similarities between the statement of modus ponens and the statement that 2 + 2 = 4.

This seems to just be a fact about the territory. Presumably, there are similar similarities between a perfectly accurate and completely specified quantum theory and chemical reactions, they are just harder to work out.

Fair enough. But I assert that the particular similarity we are discussing does not exist between math and physics, no matter how hard we look.

[-]dlthomas14y00

Fair enough. But I assert that the particular similarity we are discussing does not exist between math and physics, no matter how hard we look.

Can you clarify the grounds for that assertion? It seems to me that in both cases the territory contains facts and rules, and combinations of these lead to other consequences. The big difference seems, to me, to be a historical question of where we started our mapping; with physics, we started looking at consequences very far removed from the facts and rules that are rigidly true, and so our map was by necessity fuzzier. This is a fact about the map, not the territory, though.

[-]TimS14y-20

I have heard a Strong Reductionist theory, which goes as follows: History is Psychology. Psychology is Biology. Biology is Chemistry. Chemistry is Physics. Physics is Math. In other words, you can (in principle) derive the higher order theory from the more fundamental theory.

If for no other reason, I reject that theory because Physics is not Math. Physics is inherently about making statements that have empirical content. Math is inherently about making statements that lack empirical content.

[-]dlthomas14y00

I have heard a Strong Reductionist theory, which goes as follows: History is Psychology. Psychology is Biology. Biology is Chemistry. Chemistry is Physics. Physics is Math. In other words, you can (in principle) derive the higher order theory from the more fundamental theory.

For any deterministic interpretation of quantum mechanics, it seems that this would necessarily have to hold (though for MWI, it would not tell you which universe you happen to be in).

If for no other reason, I reject that theory because Physics is not Math. Physics is inherently about making statements that have empirical content. Math is inherently about making statements that lack empirical content.

[-]TimS14y00

Would you say that you are expressing a difference in the territories covered by physics and math, in our existing maps of physics and math, in any potential map of physics and math, or in our methods of constructing the maps?

I think the answer to your question is "method of construction."

I'm almost tempted to say that for a priori truths, the map is the territory. I hesitate because I'm not confident I am using the metaphor correctly.

[-]dlthomas14y00

In principle, a Cartesian skeptic should be able generate the same map of "Math" that we use. In contrast, there is no reason that a Cartesian skeptic's map of Physics would have any resemblance to the territory at all. (I accept that it is hard to see what could motivate a Cartesian skeptic to generate Math).

I am not convinced this is the case. How do we pick which axioms to use, except by comparison to reality? Certainly, this is how it historically happened.

[-]TimS14y00

What can't the skeptic say "If you accept the Axiom of Choice, here's what follows. If you reject the Axiom of Choice, this follows instead."

And you are right that I misused the map/territory metaphor.

[-]dlthomas14y00

Why can't the skeptic similarly say, "If you accept that there is a particle at..., here is what follows; otherwise, this follows instead"?

[-]TimS14y00

After describing all possible physics models, the skeptic still has no idea which is right.

In contrast, all the math articulated is right. (There are probably some caveats I should make, like no inconsistent axioms, and some reference to Godel, but I suspect I don't know enough actual math to make all the necessary caveats).

[-]dlthomas14y00

I am not certain that the same objection cannot be made to math, but I at least follow what your objection is.

[-]dlthomas14y00

I'm almost tempted to say that for a priori truths, the map is the territory. I hesitate because I'm not confident I am using the metaphor correctly.

This definitely seems to be a slip up in application of the metaphor. The map is my beliefs, the territory is truth. I know from experience that I can believe something to be a mathematical truth, only to thereafter find a mistake in my proof - I don't expect "the statement was true for as long as your map represented it" is actually your position.

[-]dlthomas14y00

That is not a correct edit of what I said. At the level of generality I'm talking, "The sky is blue" is a physics statement. A better summary would be "[Math and logic] are both different from the statement that the sky is blue.

Ah, "they" was "modus ponens and 2 + 2 = 4"; completely missed that interpretation, sorry.

[-]pragmatist14y00

Perhaps I am misreading you, but I think your gloss is incorrect. Eliezer's point is about his map, not the territory. He is describing circumstances under which he would be convinced that 2 + 2 = 3, not circumstances under which 2 + 2 would actually be 3. I do not take him to be arguing (as you suggest) that math is physical, whatever that would mean. He is arguing that beliefs about math are physically instantiated, and subject to alteration by some possible physical process.

I'm afraid you lose me completely in the second part of your comment. Why is physics definitely not objective? And what does the similarity of math to modus ponens and its dissimilarity from empirical statements have to do with the subjective/objective distinction?

[-]TimS14y00

Perhaps I am misreading you, but I think your gloss is incorrect. Eliezer's point is about his map, not the territory. He is describing circumstances under which he would be convinced that 2 + 2 = 3, not circumstances under which 2 + 2 would actually be 3. I do not take him to be arguing (as you suggest) that math is physical, whatever that would mean. He is arguing that beliefs about math are physically instantiated, and subject to alteration by some possible physical process.

In brief, Eliezer rejects a priori truths, and I don't. An a priori truth is true without reference to empirical content, and believing that math has empirical content implies that other empirical evidence could appear that would falsify math. In short, Eliezer isn't describing how he could come to belief 2 + 2 = 3, but how new evidence might show 2 + 2 would truly equaled 3

I'm afraid you lose me completely in the second part of your comment. Why is physics definitely not objective? And what does the similarity of math to modus ponens and its dissimilarity from empirical statements have to do with the subjective/objective distinction?

I'm just saying that basic arithmetic and modus ponens are analytic truths, and physics is not. The truth of physics assertions depends on empirical content.

[-]lessdazed14y30

In brief, Eliezer rejects a priori truths, and I don't.

Have you always thought that? If not, what caused you to think that? When you were caused to think that, were you infinitely confident in what caused you to think that? If so, then how do you consider your failure to accept a priori truths while holding some? If no, then how do you justify believing several things likely and consequently believing something with infinite certainty, when each probable thing may be wrong?

[-]TimS14y20

I didn't always know that (1) mathematical statements did not have empirical content, but I also didn't always know (2) the pythagorean theory. I'm skeptical that those facts tell you anything about the truth of either assertion (1) or (2).

[-]lessdazed14y30

Not to commit the mind projection fallacy, but it does show that (3) is false, where (3) is "The pythagorean theory is so obviously true that all conscious minds must acknowledge it," (many religions have similar tenets to this).

So (2) is the sort of thing that one becomes convinced of by things not themselves believed infinitely likely to be true, or at some point down the line there was a root belief of that belief that was the first thing thought infinitely likely to be true.

It's this first thing infinitely likely to be true I am suspicious of.

What are the chances I have misread a random sentence? Higher than zero, in my experience. How then can I legitimately be infinitely convinced by sentences?

[-]TimS14y00

I think a better generalization is "Any intelligent being capable of recursive thought will accept the truth of a provable statement or be internally inconsistent." But that formulation does have a "sufficiently intelligent" problem.

Consider some intelligent but non-mathematical subsection of society (i.e. lawyers). There are mathematical statements that are provable that some lawyer has not been exposed to, and so doesn't think is true (or false). Further, there are likely to be provable statements that the lawyer has been exposed to that the lawyer lacks training (or intelligence?) to decide whether the statements are true.

I want to say that is a fact about the lawyer, or society, or bounded rationality. But it isn't a very good response.

What are the chances I have misread a random sentence?

Errors are errors. And we are fallible creatures. If you don't correct, then you are inconsistent without meaning to be so. If you do correct, then the fact of the error doesn't tell you about the statement under investigation. And if you'd like to estimate the proportion of the time you make errors, that's likely to be helpful in your decision-making, but it doesn't convert non-empirical statements into empirical statements.

And a priori doesn't mean true. There are lots of a priori false statements (e.g. 1=0 is not empirical, and also false).

[-]lessdazed14y20

There are mathematical statements that are provable that some lawyer has not been exposed to, and so doesn't think is true (or false).

Doesn't strongly believe are true, or false, or other. But the mind is not a void before the training, and after getting a degree in math still won't be a void, but neither will it be a computer immune to gamma rays and quantum effects, working in PA with a proof that PA is consistent that uses only PA. It will be a fallible thing with good reason to believe it has correctly read and parsed definitions, etc.

If you do correct

We're talking about errors I am committing without having detected. You discuss the case where I attempt to believe falsely, and accidentally believe something true? Or similar?

And if you'd like to estimate the proportion of the time you make errors, that's likely to be helpful in your decision-making, but it doesn't convert non-empirical statements into empirical statements.

Unfortunately, I have good reason to believe I imperfectly sort statements along the empirical/non-empirical divide.

[-]TimS14y00

Unfortunately, I have good reason to believe I imperfectly sort statements along the empirical/non-empirical divide.

"1 + 2 = 3" is a statement that lacks empirical content. "F = ma" is a statement that has empirical content and is falsifiable. "The way to maximize human flourishing is to build a friendly AI that implements CEV(everyone)" is a statement with empirical content that is not falsifiable.

Folk philosophers do a terrible job distinguishing between the categories "lacks empirical content" and "is not falsifiable." Does that prove the categories are identical?

We're talking about errors I am committing without having detected. You discuss the case where I attempt to believe falsely, and accidentally believe something true? Or similar?

I'm sorry, I don't understand the question.

neither will it be a computer immune to gamma rays and quantum effects

Yes, there are ways to become delusion [delusional - oops]. It is worthwhile to estimate the likelihood of this possibility, but that isn't what I'm trying to do here.

[-]lessdazed14y00

"1 + 2 = 3" is a statement that lacks empirical content. "F = ma" is a statement that has empirical content and is falsifiable. "The way to maximize human flourishing is to build a friendly AI that implements CEV(everyone)" is a statement with empirical content that is not falsifiable.

If you're trying to demonstrate perfect ability to sort all statements into three bins, you have a lot more typing to do. If not, I don't understand your point. Either you're perfect at sorting such statements, or not. If not, there is a limit to how sure you should be that you correctly sorted each.

If you do correct [errors that you made but have not identified - Ed.], then the fact of the error doesn't tell you about the statement under investigation.

I don't know what this means.

there are ways to become delusion

It is worthwhile to estimate the likelihood of this possibility, but that isn't what I'm trying to do here.

For each statement I believe true, I should estimate the chances of it being true < 1.

[-]TimS14y00

If you're trying to demonstrate perfect ability to sort all statements into three bins, you have a lot more typing to do. If not, I don't understand your point. Either you're perfect at sorting such statements, or not. If not, there is a limit to how sure you should be that you correctly sorted each.

It is interesting that the all statements that we would like to be able to assign truth value to can be sorted into one of these three bins. Additional bins are not necessary, and fewer bins would be insufficient.

[-]pragmatist14y10

In short, Eliezer isn't describing how he could come to belief 2 + 2 = 3, but how new evidence might show 2 + 2 would truly equaled 3.

From the beginning of his post:

I admit, I cannot conceive of a "situation" that would make 2 + 2 = 4 false. (There are redefinitions, but those are not "situations", and then you're no longer talking about 2, 4, =, or +.) But that doesn't make my belief unconditional. I find it quite easy to imagine a situation which would convince me that 2 + 2 = 3.

So on the point of interpretation, I'm pretty sure you are wrong.

On the substantive point, I think reliance on traditional philosophical distinctions (a priori/a posteriori, analytic/synthetic) is a recipe for confusion. In my opinion (and I am far from the first to point this out) these distinctions are poorly articulated, if not downright incoherent. If you are going to employ these concepts, however, an important thing to keep in mind is the hard-won philosophical realization, stemming from a tradition stretching from Kant to Kripke, that the a priori/a posteriori distinction is orthogonal to the necessary/contingent distinction. The former is an epistemological distinction (propositions are justifiable a priori or a posteriori), and the latter is a metaphysical distinction (propositions are true/false necessarily or contingently).

My position (and, I believe, Eliezer's) is that mathematical truths are necessarily true. A world in which 2 + 2 = 3 is impossible. This does not, however, entail that it is impossible to convince me that 2 + 2 = 3. Nor does it entail that empirical considerations are irrelevant to the justification of my belief that 2 + 2 = 4.

I am sure there is some proposition (perhaps some complicated mathematical truth) that you believe is necessarily true, but you are not certain that it is true. Maybe you are fairly confident but not entirely sure that you got the proof right. So even though you believe this proposition cannot possibly be false, you admit the possibility of evidence that would convince you it is false.

[-]TimS14y00

Thanks for a really interesting reply.

First, I do reject the analytic/synthetic distinction. It always seemed like Kant was trying to make something out of nothing there. But I do think that math lacks empirical content, which is why I label it a priori.

I am sure there is some proposition (perhaps some complicated mathematical truth) that you believe is necessarily true, but you are not certain that it is true. Maybe you are fairly confident but not entirely sure that you got the proof right. So even though you believe this proposition cannot possibly be false, you admit the possibility of evidence that would convince you it is false.

But if math is not empirical, then this way of talking about math makes it seem less certain than it really is. I may be fallible, and thus not know every mathematically or logically provable statement, but that doesn't show anything about the nature of provable statements. A proof of the Pythagorean Theorem is not (empirical) evidence that the theorem is true. The proof (metaphysically) is the truth of the theorem.

That said, I would certainly appreciate suggestions on a deeper overview of the necessary/contingent distinction.

[-]pragmatist14y20

A proof of the Pythagorean Theorem is not (empirical) evidence that the theorem is true. The proof (metaphysically) is the truth of the theorem.

Consider the four color theorem. We have a proof by computer of this theorem, but it is far too complex for any human to verify. Would you agree that the fact that a computer built and programmed in a certain way claims to have proven the theorem is empirical evidence for the truth of the theorem? If yes, then why treat a proof computed by a human brain differently?

[-]TimS14y-20

Consider the four color theorem. We have a proof by computer of this theorem, but it is far too complex for any human to verify. Would you agree that the fact that a computer built and programmed in a certain way claims to have proven the theorem is empirical evidence for the truth of the theorem?

No. The computer output is a strong justification for behaving as if all maps are four-colorable.

But if the "proof" cannot be understood, then the truth of the theorem is simply beyond human comprehension. We could petition the evolution fairy for a better brain. Then again, dogs don't seem to mind that they can't comprehend that the derivative of e^x is e^x.

[-]JoshuaZ14y20

No. The computer output is a strong justification for behaving as if all maps are four-colorable.

Would you feel differently if the proof were verified by a general AI? If not, how is this not just carbon chauvinism?

Also, if you want another example, consider the classification of finite simple groups. Here the combined proofs run into the 1000s of pages, and it is likely that no single human being has checked the entire thing. Is your analysis for that case different from that of the four color theorem?

[-]TimS14y00

Can the proof be understand by a motivated, human-intelligence Cartesian skeptic who is protected from errors of carelessness? Because a Cartesian skeptic will never derive true physics statements, no matter how much effort is applied, since the skeptic is cut off from empirical data by definition.

And I think that is an interesting distinction between math and physics.

I certainly admit that there are physical processes that could cause me to believe a false mathematical statement was true. But that is properly understood as a fact about me, and does not mean that math has any empirical content.

[-]JoshuaZ14y00

Can the proof be understand by a motivated, human-intelligence Cartesian skeptic who is protected from errors of carelessness?

To the same extent the proof of the four color theorem can be. It will just take orders of magnitude more time than any human has. So do you consider it to be proven in the same sense? Do you need to wait until such a person exists and does it? If so, why is that different?

[-]pragmatist14y10

Here's a quick overview of the necessity/contingency distinction in philosophy. For a deeper overview, try Kripke's Naming and Necessity.

[-]Hyena14y10

Subjective worlds must be causally closed; they cannot transmit information to other worlds since that would break the principle that each world is subjective. As such, there can be no subjective reality: if subjective reality were true, causal closure would demand that your observations about the world are semantically equivalent to a world in which you are alone as an observer.

For example, imagine that we lived in Minecraft, which has a procedurally generated world. We use a seed (say "404") to kick off the algorithm. But say instead that we use a seed and the username of the player. Is World 404 different for each user?

No; there is no "World 404", there is World 404-TheatreAddict and World 404-Hyena and so on. The reason is that the function we use to generate the world takes two variables, seed and username, to work. A world can only be defined by this pair and has no existence independent of it. Naturally, this world is causally closed; my playing does not effect yours, you will never see my buildings nor will you ever send me angry messages about burning down 16 chunks of forest.

While this world is trivially objective, all objections to a subjectivity thesis are trivial because it is trivially untrue or unprovable. Every attempt to prove it will require a condition, like causal closure, which collapses it to a special case of objective reality. The simplest of these is the resolution to the subjective proposition itself, independent of worlds: if everything is subjective, that principle itself is objective.

[-]lessdazed14y10

math is relative depending to where we are. In a black hole, math is different from on earth.

Federal income taxes in the US are relative depending on how much you make. If you make $5,000 a year, people who make $5,000 a year pay no income taxes. But if you make $500,000 a year, people who make $500,000 a year pay ~30% in income taxes.

So you see, the US tax code depends on how much you make.

Unless...unless it's also true that if you make $5,000 a year, people who make $500,000 a year pay ~30% in income taxes, and if you make $500,000 a year, people who make $5,000 a year pay no income taxes. In which case, the US tax code would not depend on how much you make, only how much you pay in taxes would depend on how much you make.

Hmm...

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