I What is the current status of Many Worlds?

[Demystifier]

Do you have a reference for this formulation?

See e.g.
https://plato.stanford.edu/entries/qm-bohm/#QuanPote
https://arxiv.org/abs/1704.08017 (especially Eq. (1) and Sec. 8)
https://www.mathematik.uni-muenchen.de/~duerr/Survey.pdf (especially Eqs. (2) and (3))

 

[PeterDonis]

See e.g.
https://plato.stanford.edu/entries/qm-bohm/#QuanPote
https://arxiv.org/abs/1704.08017 (especially Eq. (1) and Sec. 8)
https://www.mathematik.uni-muenchen.de/~duerr/Survey.pdf (especially Eqs. (2) and (3))

Thanks!

 

[bob012345]

I've already given you a couple of suggestions.

Fine. I'll figure it out elsewhere. Thanks.

 

[PeterDonis]

Fine. I'll figure it out elsewhere.

You mean, you've read all my posts and you don't see any suggestions? How about, for example, answering the question I posed in post #47?

 

[bob012345]

You mean, you've read all my posts and you don't see any suggestions? How about, for example, answering the question I posed in post #47?

What does standard QM say about the states of individual subsystems that are entangled? (The "subsystems" could just be two electrons, instead of an electron and a measuring device.)

That you don't know what state each system is in until you measure it? I'm not asking about standard QM. I'm asking if there is any reality to all this multiple worlds view or is it just math. Seems to me you are saying it is just math. If it is just math then why are physicists like DeWitt saying such misleading nonsense like every interaction branches the universe?

 

[PeterDonis]

That you don't know what state each system is in until you measure it?

No. That's not even true; if you prepare a system in a particular state, you know it's in that state.

What I had in mind was the fact that if two subsystems are entangled, then neither subsystem even has a well-defined state by itself. Only the whole entangled system does. See further comments below.

I'm not asking about standard QM.

If you don't understand what standard QM says about a particular scenario, you can't possibly expect to understand what any interpretation says about it. You have to understand the basics of standard QM--the math and the predictions--before you can understand any interpretation.

I'm asking if there is any reality to all this multiple worlds view or is it just math. Seems to me you are saying it is just math.

Not at all. The many worlds view says that the wave function is real. It does not say it is "just math".

So, if you have an electron and a measuring system entangled with two separate states as you showed in post #36, does MWI say there is some physical reality such as separate 'worlds' or is that merely a mathematical contrivance for computation purposes?

The MWI says that the wave function is real. That's all it says about what is "real". The "worlds" it talks about are all part of the wave function (as I've already described, they are the individual terms in an entangled state). Does that answer your question?

Instead of continuing to belabor the same question, let's go back to what I said above about entangled states. If we have an electron and a measuring device, and they are entangled, neither one has any well-defined state by itself. Only the total system of electron plus measuring device does.

However, according to the MWI, we can give a relative interpretation to the individual terms in the entangled state. For example, if we have measured an electron's spin, we can say that the electron has the state "spin up" relative to the state "measured spin up" of the measuring device, and vice versa; and we can say that the electron has the state "spin down" relative to the state "measured spin down" of the measuring device, and vice versa. In fact, the original name for what is now called the "many worlds" interpretation, in the paper and Ph.D. thesis by Hugh Everett that introduced it, was the "relative state" interpretation; the name "many worlds" was introduced and popularized later, mainly by DeWitt, whose claims about it were very different (and much more extreme) than Everett's original ones. It was DeWitt and others who shared his views who started using the term "worlds" to describe the individual terms in the entangled wave function after measurement.

 

[bob012345]

No. That's not even true; if you prepare a system in a particular state, you know it's in that state.

I was not speaking of prepared states.

What I had in mind was the fact that if two subsystems are entangled, then neither subsystem even has a well-defined state by itself. Only the whole entangled system does. See further comments below.

I am not a mindreader.

If you don't understand what standard QM says about a particular scenario, you can't possibly expect to understand what any interpretation says about it. You have to understand the basics of standard QM--the math and the predictions--before you can understand any interpretation.

I only said I wasn't asking about standard QM but the MWI version not that I had no standard QM background.

Not at all. The many worlds view says that the wave function is real. It does not say it is "just math".The MWI says that the wave function is real. That's all it says about what is "real". The "worlds" it talks about are all part of the wave function (as I've already described, they are the individual terms in an entangled state). Does that answer your question?

Yes. I have no more question beyond what then is such a wave function physically if it is real and what does it mean to be in an entangled state for a real macroscopic wave-function. Are there many me's after all if I am in an entangled state? I do not expect an answer.

Instead of continuing to belabor the same question, let's go back to what I said above about entangled states. If we have an electron and a measuring device, and they are entangled, neither one has any well-defined state by itself. Only the total system of electron plus measuring device does.

However, according to the MWI, we can give a relative interpretation to the individual terms in the entangled state. For example, if we have measured an electron's spin, we can say that the electron has the state "spin up" relative to the state "measured spin up" of the measuring device, and vice versa; and we can say that the electron has the state "spin down" relative to the state "measured spin down" of the measuring device, and vice versa. In fact, the original name for what is now called the "many worlds" interpretation, in the paper and Ph.D. thesis by Hugh Everett that introduced it, was the "relative state" interpretation; the name "many worlds" was introduced and popularized later, mainly by DeWitt, whose claims about it were very different (and much more extreme) than Everett's original ones. It was DeWitt and others who shared his views who started using the term "worlds" to describe the individual terms in the entangled wave function after measurement.

Ok. It's rather late and I'm tired so I'm signing off for tonight. Thanks for the discussion!

 

[PeterDonis]

Are there many me's after all if I am in an entangled state?

Suppose we have a two-electron system with electrons A and B in the singlet state:

$$
\frac{1}{\sqrt{2}} \left( \ket{A}_\text{up} \ket{B}_\text{down} - \ket{A}_\text{down} \ket{B}_\text{up} \right)
$$

Are there "many" electron A's and "many" electron B's in this state?

Whatever your answer is to this question, the answer will be the same to the question you asked that is quoted above.

 

[PeterDonis]

I am not a mindreader.

You shouldn't need to be to answer the question I asked about subsystems in entangled states. It's basic QM.

 

[Jarvis323]

My take is that there is what MWI says, and then there is what people claim that MWI implies.

I understand it could be a misconception, but I am trying to reason through it. Am I correct to say a real inaccessible world is identical mathematically and logically to an imaginary or hypothetical branch from the reference point of our branch?

If the wave function is real, with all of its terms, then the other worlds are real. If the wave function is not real, but just mathematics, then those other terms can still be in the wave function, yet only represent hypothetical imaginary worlds.

They may be mathematically equivalent within a limited view/context. Obviously they are logically distinguished, however, they are opposing statements of what is true. And thus, the structures of logic that follow these statements are not the same.

You may wonder whether it can ever be fruitful to try to work out logical deductions that depend on the truth values of these statements. Some people think that the ability to compare mathematics and logic with physical experiment hit a dead end here. In that case, perhaps the mathematics and logic that depend on these truth values aren't something physicists need to be concerned with. But a lot of mathematicians and philosophers could care less. And everyday people, as well as some physicists, don't mind pondering the logical implications of these kinds of statement either.

The motivation to do this, regardless of perceived experimental limitations, for QM specifically, is that the logic of QM is weird. Of course people want to try and wrap their minds around what kind of possibilities there might be for our reality given what we can learn from QM.

 

[lukephysics]

Schrodingers equation says there are many worlds, but can’t there be an equally explanatory equation that drops the many worlds since they seem unnecessary?

I guess none of this matters really anyway since schrodingers and qm works anyway.

 

[Jarvis323]

Suppose we have a two-electron system with electrons A and B in the singlet state:

$$
\frac{1}{\sqrt{2}} \left( \ket{A}_\text{up} \ket{B}_\text{down} - \ket{A}_\text{down} \ket{B}_\text{up} \right)
$$

Are there "many" electron A's and "many" electron B's in this state?

Whatever your answer is to this question, the answer will be the same to the question you asked that is quoted above.

If you want to ask this kind of question, why not go further and ask if there are any electrons in this state. All there are that I see are arrangements of black pixels. And if I could probe your mind, maybe I'd see some wrinkles where this state lives. If we say the wave function is real, it is already a statement about something that is a level of abstraction beyond (or below) just the mathematics. So isn't looking at the mathematics to understand what MWI means only half the picture.

 

[vanhees71]

In the financial case, only one of the possible outcomes in the PDF actually occurs. In many worlds, all of the possible outcomes occur.

Can you tell me, how to get into that very universe, where the content of my account is spontaneously doubled by some event on the stock market? SCNR.

 

[vanhees71]

What does standard QM say about the states of individual subsystems that are entangled? (The "subsystems" could just be two electrons, instead of an electron and a measuring device.)

If you have a quantum system that can be separated in two subsystems $A$ and $B$ the Hilbert space of the system is described as the product of the two Hilbert spaces of the subsystems $\mathcal{H}=\mathcal{H}_A \otimes \mathcal{H}_B$. Let $|u_j \rangle \in \mathcal{H}_A$ and $|v_k \rangle \in \mathcal{H}_B$ be complete orthonormal systems (CONSs) then $|w_{jk} \rangle=|u_j \rangle \otimes |v_k \rangle$ are a CONS in $\mathcal{H}$.

If the quantum system is prepared in some state $\hat{\rho}$ then the states of the subsystems are described by the reduced statistical operators $\hat{\rho}_A$ and $\hat{\rho}_B$, defined by taking the partial traces over the respective other subsystem:
$$\hat{\rho}_A = \sum_{j,k,l} |w_{kj} \rangle \langle w_{kj}|\hat{\rho}|w_{lj} \rangle |u_k \rangle \langle u_l |$$
and analogously for $\hat{\rho}_B$.
If you know the state of the complete system all subsystems take unique states defined by these "reduced statistical operators".

Take, as a simple example, the spin-singlet state of a system of two spins 1/2. Then
$$\hat{\rho}=|\Psi \rangle \langle \Psi|$$
with
$$|\Psi \rangle=\frac{1}{\sqrt{2}} (|1/2,-1/2 \rangle-|-1/2,1/2 \rangle).$$
It's a simple exercise to find that for this "Bell state" the subsystems are maximally indetermined, i.e., the corresponding particles are precisely unpolarized,
$$\hat{\rho}_A=\hat{\rho}_B=\frac{1}{2} \hat{1}.$$

That you don't know what state each system is in until you measure it? I'm not asking about standard QM. I'm asking if there is any reality to all this multiple worlds view or is it just math. Seems to me you are saying it is just math. If it is just math then why are physicists like DeWitt saying such misleading nonsense like every interaction branches the universe?

This is an enigma to me too, but usually when physicists enter the terrain of fuzzy philosophy, "misleading nonsense" is likely to occur (just an observation ;-)). For me the greatest progress of the thinking of mankind was the idea to strictly separate the "hard sciences" from the fuzzy "humanities" in the renaissance when modern natural sciences started to be developed.

 

[Jarvis323]

This is an enigma to me too, but usually when physicists enter the terrain of fuzzy philosophy, "misleading nonsense" is likely to occur (just an observation ;-)). For me the greatest progress of the thinking of mankind was the idea to strictly separate the "hard sciences" from the fuzzy "humanities" in the renaissance when modern natural sciences started to be developed.

For me, this line of thinking is highly confusing. The entire goal of philosophy is to make things not fuzzy. The thing that changed in the renaissance wasn't separating philosophy from science, it was to establish concrete philosophical foundations for science. This was also the time when we began to established concrete philosophical foundations for mathematics. The revolution in science was due to a breakthrough in philosophy, not an abandonment of it.

 

[WernerQH]

This is an enigma to me too, but usually when physicists enter the terrain of fuzzy philosophy, "misleading nonsense" is likely to occur (just an observation ;-)). For me the greatest progress of the thinking of mankind was the idea to strictly separate the "hard sciences" from the fuzzy "humanities" in the renaissance when modern natural sciences started to be developed.

It seems some people desperately try to make sense of MWI. Using stict logical deduction, it is of course possible to "derive" an infinity of absurd conclusions from just one nonsensical assumption.

 

[bob012345]

Suppose we have a two-electron system with electrons A and B in the singlet state:

$$
\frac{1}{\sqrt{2}} \left( \ket{A}_\text{up} \ket{B}_\text{down} - \ket{A}_\text{down} \ket{B}_\text{up} \right)
$$

Are there "many" electron A's and "many" electron B's in this state?

Whatever your answer is to this question, the answer will be the same to the question you asked that is quoted above.

My answer is no, of course not. I would not regard this wavefunction as involving two A electrons and two B electrons. The wavefunction is over states of the electrons. You seem to be saying to regard the MWI wavefunction in the same way. That makes sense to me. Going back and forth further about what MWI adherents really believe is counterproductive at this point. I found an essay by a Princeton physicist;

https://arxiv.org/pdf/1801.08587.pdf

Thanks for the discussion!

 

[PeterDonis]

If you want to ask this kind of question, why not go further and ask if there are any electrons in this state. All there are that I see are arrangements of black pixels.

"Electron" in this case is simply a name for the degrees of freedom referred to by the symbols $A$ and $B$. So of course there are electrons in this state. There are "electron A" degrees of freedom, and "electron B" degrees of freedom. They're right there in the wave function.

Of course when we write down a wave function like this, we are usually making some implicit assumption about how the degrees of freedom in the state correspond to measurements--for example, we might relate the "electron A" degrees of freedom to some measurement made by Alice, and the "electron B" degrees of freedom to some measurement made by Bob. That is not a matter of any particular QM interpretation; it's a matter of the basic math and how it relates to measurements. If you can't relate the math to measurements in some way, you can't test the theory's predictions.

isn't looking at the mathematics to understand what MWI means only half the picture.

For any interpretation, as I said, there has to be a grounding in the math. Otherwise it isn't an interpretation of QM to begin with.

For the MWI in particular, there is a sense in which "the math is all there is", because the central claim of this interpretation is that the wave function is real, and it's the only thing that's real. But I agree that advocates of the MWI have to do more than just point at the wave function to explain why they think the interpretation makes sense.

 

[PeterDonis]

My answer is no, of course not. I would not regard this wavefunction as involving two A electrons and two B electrons. The wavefunction is over states of the electrons.

That is my view as well.

You seem to be saying to regard the MWI wavefunction in the same way.

Yes. And then the challenge for MWI advocates is to explain how this can possibly be consistent with our experiences, since when we observe or measure something we experience a definite result having occurred. The MWI has to say that all of the possible results occurred, but it's not clear to start with what that means, since in an entangled state like the ones we have been looking at, it seems like nothing has "occurred"--neither subsystem is in a definite state at all.

The original "relative state" viewpoint explained this by saying that, for each subsystem, each of the possible results occurs relative to the corresponding result for the other subsystem. So it would say that in the singlet state, two results have occurred: "electron A up, electron B down" and "electron A down, electron B up". (Actually, since the development of decoherence theory, even a "relative state" interpretation would no longer say this, since no decoherence has occurred for two electrons in the singlet state. But it would still work for any case that does involve decoherence, which certainly includes any macroscopic measurement or any observation by a human.) This is still a change in the meaning of the term "occurs", since it no longer corresponds to a subsystem having a definite state period--now it only requires the subsystem to have a relative state with respect to another subsystem with which it is entangled.

The "many worlds" viewpoint, however, wants to make a stronger claim, one that seems to amount to there actually being multiple "copies" of each subsystem, one in each "world"--but, as we've seen, if we take such statements literally they are obviously false since that's not how entangled states in QM work. So the "many worlds" viewpoint still has to fall back on something like a "relative state" formulation when challenged, while trying to make the stronger-sounding "many worlds" claims whenever it can get away with it. As you can see from this description of mine, I am not a many worlds proponent myself (as I've already said).

 

[AndreiB]

Wave function is fundamental but not ontic, in the same sense in which Hamiltonian in classical mechanics is fundamental but not ontic.

Why is the Hamiltonian fundamental in classical mechanics? Newton was fine without it. Is Bohm's interpretation fine without the wave function?

 

[AndreiB]

Can you tell me, how to get into that very universe, where the content of my account is spontaneously doubled by some event on the stock market? SCNR.

You don't need to get there. There is a "you" there already. So, just be happy for him!

 

[AndreiB]

In this spirit of confusion I'd love to hear what the thoughts on Many Worlds are in 2021 by everyone here at PF.

As far as I know there is no way to derive Born's rule in MWI, so the theory cannot make any predictions. There is no way to ascribe any meaning for probabilities in MWI.

 

[Demystifier]

Why is the Hamiltonian fundamental in classical mechanics? Newton was fine without it. Is Bohm's interpretation fine without the wave function?

You can define classical mechanics without Hamiltonian $H(x,p)$, but then you need something equivalent, e.g. the force function $F(x)$. The wave function is something similar, the closest classical analogy of the wave function is in fact the Hamilton-Jacobi function $S(x,t)$.

 

[AndreiB]

You can define classical mechanics without Hamiltonian $H(x,p)$, but then you need something equivalent, e.g. the force function $F(x)$. The wave function is something similar, the closest classical analogy of the wave function is in fact the Hamilton-Jacobi function $S(x,t)$.

So you can replace the wave function with a force that acts instantaneously between particles?

 

[Demystifier]

So you can replace the wave function with a force that acts instantaneously between particles?

No, in Bohmian mechanics you can't really do that. Bohmian mechanics is a law for the velocity, not for the acceleration.

 

[AndreiB]

No, in Bohmian mechanics you can't really do that. Bohmian mechanics is a law for the velocity, not for the acceleration.

OK, so if you modify Newton's second law so that the "force" does not determine the acceleration, but the velocity of the particle can you replace the wave function?

 

[Demystifier]

OK, so if you modify Newton's second law so that the "force" does not determine the acceleration, but the velocity of the particle can you replace the wave function?

Replace with what? I think nobody found such a mathematical object yet.

 

[AndreiB]

Replace with what? I think nobody found such a mathematical object yet.

You claimed that the wave function is not ontic. That means that it should be possible to describe it in terms of something else which is ontic. Or maybe we have a different understanding of what ontic means. Would you consider the forces in Newtonian mechanics as ontic?

 

[PeroK]

For me, this line of thinking is highly confusing. The entire goal of philosophy is to make things not fuzzy. The thing that changed in the renaissance wasn't separating philosophy from science, it was to establish concrete philosophical foundations for science. This was also the time when we began to established concrete philosophical foundations for mathematics. The revolution in science was due to a breakthrough in philosophy, not an abandonment of it.

This is such a travesty that I couldn't let it go.

The philosopher Henri Bergson, who didn't understand and wouldn't accept relativity, blocked Einstein receiving a Nobel prize for the theory of relativity.

https://nautil.us/issue/35/boundaries/this-philosopher-helped-ensure-there-was-no-nobel-for-relativity

Bergson himself got the Nobel prize for Literature (!) in 1927 and - like other philosophers - battled against the progress of science and mathematics in the mistaken belief that their own supreme intellect and powers of pure thought outweighed that of mathematics and empirical science.

Ironically, of course, any decent undergraduate of physics or mathematics can understand the theory of SR in six weeks or so. That's what it took me.

The lesson is clear: if you want to make progress in science and mathematics, you have to ditch philosophy and the philosophers and their non-existent powers to know the world through pure thought alone.

 

[martinbn]

My view on the many worlds is that, when it talks about many worlds existing and many copies of everything, it is just a pile of words. On the other hand the idea of a relative state interpretation without the philosophical nonsense is very atractive.

 

[Demystifier]

You claimed that the wave function is not ontic. That means that it should be possible to describe it in terms of something else which is ontic. Or maybe we have a different understanding of what ontic means. Would you consider the forces in Newtonian mechanics as ontic?

I would not consider the forces in Newtonian mechanics as ontic. $F(x)$ is nomological, as is the wave function.

 

[Demystifier]

My view on the many worlds is that, when it talks about many worlds existing and many copies of everything, it is just a pile of words. On the other hand the idea of a relative state interpretation without the philosophical nonsense is very atractive.

What's the "relative state interpretation without the philosophical nonsense"? Do you have a reference?

 

[martinbn]

What's the "relative state interpretation without the philosophical nonsense"? Do you have a reference?

I didn't say the relative state interpretation. I said a relative state interpretation.

 

[Morbert]

I think MWI as a project was completed by Consistent histories.

MWI showed us how decoherence can let us assign probabilities to possible worlds/histories, and how QM treats these possibilities on equal footing apart from their probabilities.

But you need an exotic ontology underlying these probabilities. Consistent histories showed us i) how we can recover our intuitive understanding of these probabilities as likelihoods for mutually exclusive alternatives, as opposed to needing all alternatives to actually exist, and ii) How to more rigorously quantify the decoherence between worlds.

 

[vanhees71]

The paper defining the original relative-state interpretation by Everett or rather the version of Everett's view revised due to the advice of his thesis adviser J.A. Wheeler, who was a declared Bohr disciple, is

https://doi.org/10.1103/RevModPhys.29.454

 

[Demystifier]

I didn't say the relative state interpretation. I said a relative state interpretation.

What's a relative state interpretation without philosophical nonsense?

 

[PeterDonis]

Can you tell me, how to get into that very universe, where the content of my account is spontaneously doubled by some event on the stock market?

Sure, just invest in the right stock.

 

[*now*]

RQM involves relative states. This is an early paper, there could be further developments since,
https://link.springer.com/article/10.1007/BF02302261
Published: August 1996
Relational quantum mechanics
Carlo Rovelli
International Journal of Theoretical Physics volume 35, pages1637–1678 (1996)
Abstract
I suggest that the common unease with taking quantum mechanics as a fundamental description of nature (the “measurement problem”) could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer-independent time. I suggest that this incorrect notion that generates the unease with quantum mechanics is the notion of “observer-independent state” of a system, or “observer-independent values of physical quantities.” I reformulate the problem of the “interpretation of quantum mechanics” as the problem of deriving the formalism from a set of simple physical postulates. I consider a reformulation of quantum mechanics in terms of information theory. All systems are assumed to be equivalent, there is no observer-observed distinction, and the theory describes only the information that systems have about each other; nevertheless, the theory is complete.
https://arxiv.org/abs/quant-ph/9609002

 

[Jarvis323]

This is such a travesty that I couldn't let it go.

The philosopher Henri Bergson, who didn't understand and wouldn't accept relativity, blocked Einstein receiving a Nobel prize for the theory of relativity.

https://nautil.us/issue/35/boundaries/this-philosopher-helped-ensure-there-was-no-nobel-for-relativity

Bergson himself got the Nobel prize for Literature (!) in 1927 and - like other philosophers - battled against the progress of science and mathematics in the mistaken belief that their own supreme intellect and powers of pure thought outweighed that of mathematics and empirical science.

Ironically, of course, any decent undergraduate of physics or mathematics can understand the theory of SR in six weeks or so. That's what it took me.

The lesson is clear: if you want to make progress in science and mathematics, you have to ditch philosophy and the philosophers and their non-existent powers to know the world through pure thought alone.

You're talking about groups of arrogant Philosophers, not Philosophy.

There have also been arrogant groups of medical doctors that rejected the merits of hand washing with tragic consequences. The solution wasn't to abandon medicine.

Philosophy has given us the scientific method, formalization of computation, logic, and axiomatic systems in mathematics.

You really want scientists to ditch the scientific method, and you want mathematicians to ditch logic and axioms?

You can't expect to make progress by reason and intelect alone, but how much progress can you make without it at all?

 

[PeterDonis]

You're talking about groups of arrogant Philosophers, not Philosophy.

Even Philosophers should recognize this logical fallacy, namely No True Scotsman.

Philosophy has given us the scientific method, formalization of computation, logic, and axiomatic systems in mathematics.

Nope. None of those things were given to use by Philosophy. The scientific method, to the extent that term even has a definite meaning, was given to us by scientists. Formalization of computation, logic, and axiomatic systems was given to us by mathematicians. The fact that some of the people who contributed to those things also billed themselves as philosophers does not mean Philosophy gets to take credit for those things.

You really want scientists to ditch the scientific method, and you want mathematicians to ditch logic and axioms?

This is another logical fallacy that even Philosophers should recognize, namely the Straw Man.

 

[Jarvis323]

Even Philosophers should recognize this logical fallacy, namely No True Scotsman.

You've missed the mark on this one. I was pointing out the conflation between philosopher and philosophy. This is the mistake you're making now.

Nope. None of those things were given to use by Philosophy. The scientific method, to the extent that term even has a definite meaning, was given to us by scientists. Formalization of computation, logic, and axiomatic systems was given to us by mathematicians. The fact that some of the people who contributed to those things also billed themselves as philosophers does not mean Philosophy gets to take credit for those things.

It sounds like your concern is with which group of people get credit for something, and which identify they place on themselves.

 

[PeroK]

Philosophy has given us the scientific method, formalization of computation, logic, and axiomatic systems in mathematics.

There's no doubt that mathematics and the natural sciences began as part of philosophy - but, that was the problem. Real progress only began when science and mathematics were freed from religion and philosophy.

The great advances in mathematics in the 19th century are all mathematical. There's no great philosophy behind real and complex analysis, differential geometry and vector calculus, for example. It's just hard-nosed mathematics.

To take three concrete examples from the 20th Century: General Relativity, Goedel's Incompleteness Theorem and the Turing machine. Wittgenstein and Popper could not possibly have produced anything so definitive and concrete. Not by doing philosophy.

I know Wittgenstein wrote and thought about mathematics, but because (unlike Einstein, Goedel and Turing) he didn't actually do mathematics, there is nothing left to show for his efforts. He was never going to produce the theorems that settled the question of mathematical decidability, for example. Undecidability would have remained a point of philosophical debate, rather than an established theorem.

That's the difference. Philosophy can never really resolve anything - and, perhaps the endless shifting sands are what philosophers like about it. And, perhaps, that's what makes them generally poor scientists and mathematicians.

 

[Jarvis323]

There's no doubt that mathematics and the natural sciences began as part of philosophy - but, that was the problem. Real progress only began when science and mathematics were freed from religion and philosophy.

The great advances in mathematics in the 19th century are all mathematical. There's no great philosophy behind real and complex analysis, differential geometry and vector calculus, for example. It's just hard-nosed mathematics.

To take three concrete examples from the 20th Century: General Relativity, Goedel's Incompleteness Theorem and the Turing machine. Wittgenstein and Popper could not possibly have produced anything so definitive and concrete. Not by doing philosophy.

I know Wittgenstein wrote and thought about mathematics, but because (unlike Einstein, Goedel and Turing) he didn't actually do mathematics, there is nothing left to show for his efforts. He was never going to produce the theorems that settled the question of mathematical decidability, for example. Undecidability would have remained a point of philosophical debate, rather than an established theorem.

That's the difference. Philosophy can never really resolve anything - and, perhaps the endless shifting sands are what philosophers like about it. And, perhaps, that's what makes them generally poor scientists and mathematicians.

Maybe our disagreement is simply about what philosophy is and what it isn't. I think I may be thinking too literally.

To me, Goedel's Incompleteness Theorem is a work of philosophy. And the Church Turing thesis that underpins the Turing Machine is also in my opinion.

 

[PeterDonis]

I was pointing out the conflation between philosopher and philosophy.

If Philosophy does not mean what philosophers actually do, then it's a meaningless term. Anyone can make it mean whatever they want by just saying that the doings of any "philosopher" who doesn't do what they want Philosophy to mean don't count as Philosophy. That's what you were doing.

It sounds like your concern is with which group of people get credit for something, and which identify they place on themselves.

You're the one who said Philosophy gave us all these great things. That's a claim of credit. I was simply pointing out that it's not a justified claim of credit.

 

[Jarvis323]

If Philosophy does not mean what philosophers actually do, then it's a meaningless term.

This is a highly imprecise and logically problematic statement. But since we aren't philosophers I guess we don't use logic anyways?

That's what you were doing.

This isn't at all what I was doing.

 

[PeterDonis]

Maybe our disagreement is simply about what philosophy is and what it isn't.

Quite possibly, yes. See below.

To me, Goedel's Incompleteness Theorem is a work of philosophy. And the Church Turing thesis that underpins the Turing Machine is also in my opinion.

I have never seen anyone else take this position; everyone else that I'm aware of considers these to be works of mathematics, not philosophy. Of course you are free to adopt your own idiosyncratic definition of "philosophy" for your own use, but that doesn't mean you should expect everyone else to go along with it.

This is a highly imprecise and logically problematic statement. But since we aren't philosophers I guess we don't use logic anyways?

This isn't at all what I was doing.

Evidently we disagree, and it doesn't look like our disagreement will be resolved here. Which is fine, in this particular forum it is understood that many topics discussed will not be amenable to a definite resolution. But, once again, while you can adopt your own definitions of terms for your own use, that doesn't mean you should expect everyone else to use them.

 

[Jarvis323]

When an architect uses the pythagorean theorum, it seems not controversal that they are doing math.

I don't see why it should be different for philosophy. If a physicist uses logic or inductive reasoning, they are doing philosophy. Maybe it is more complicated, due to connotations about philosophy?

I sense that here people have certain branches of philosophy in mind, e.g. metaphysics.

 

[PeterDonis]

If a physicist uses logic or inductive reasoning, they are doing philosophy.

I think most people would consider logic and inductive reasoning to be general tools applicable to a variety of disciplines, not philosophy. If they are part of any particular discipline, I think most people would say that discipline is mathematics.

 

[PeterDonis]

When an architect uses the pythagorean theorum, it seems not controversal that they are doing math.

No, they are doing architecture, using math as a tool. One can similarly do philosophy using logic and inductive reasoning as a tool. That does not mean logic and inductive reasoning are philosophy, any more than math is architecture.

 

[Jarvis323]

I think most people would consider logic and inductive reasoning to be general tools applicable to a variety of disciplines, not philosophy. If they are part of any particular discipline, I think most people would say that discipline is mathematics.

I guess maybe you're right. I've been taking people's rejection of the use of philosophy in physics as a rejection of the tools of philosophy, or formal methods of reasoning in general, in physics.

It's still not clear to me where the line is between using/doing philisophy, and just using tools that were origionally developed as tools of philosophy. Philosophy is generally the study of discovering truth and knowledge, and its tools are methods of reasoning and analysis. I guess every discipline used to be a branch of philosophy.

I'm still not exactly sure what people are rejecting when they say they reject philosophy in physics. It would help to be more precise.