I What Is the Role of Ontology in the Interpretations of Quantum Mechanics?

[PeterDonis]

I believe the real question is whether statements like "There is an x such that for all y x is not the successor of y" mean something. If they do, then they must be either true or false.

No, such statements do not have a unique truth value, because you can get different truth values by picking different universal sets of which x and y are members. For example, if we say x and y are natural numbers, the statement is true; but if we say they are integers (i.e., they can be negative), the statement is false.

A better way of looking at statements like these is that they are assumptions that you can make in order to explore their implications. For example, we can assume that there is some set of objects for which your statement is true if x and y are members of that set; and we can then explore the properties of this set of objects. But that in no way means the statement is true for all sets of objects.

If we decide to call one of those collections "the Natural Numbers", then natural numbers exist in a very meaningful sense. (A sense in which unicorns don't exist.)

No, unicorns do exist in this sense, because I can define the concept of a unicorn as an object for which a certain set of statements is true, and by your definition, that is sufficient for such a concept to exist.

 

[vis_insita]

No, such statements do not have a unique truth value, because you can get different truth values by picking different universal sets of which x and y are members. For example, if we say x and y are natural numbers, the statement is true; but if we say they are integers (i.e., they can be negative), the statement is false.

It is irrelevant if the statement is false about some sets. All that matters is that it is true of some sets. At least one of the things of whatever is contained in any of the latter sets must exist, because that is what a true statement (by assumption) claims about it. And one of those sets contains all the natural numbers and nothing else.

As another example take the statement "There is an x, who wrote post #51 in this thread." It is also false about some sets of things. But the fact that it is true of, say, the set of all people living on planet Earth in 2020 is completely sufficient to establish the existence of PeterDonis, who is the unique individual who wrote that post in this thread.

A better way of looking at statements like these is that they are assumptions that you can make in order to explore their implications.

This is not a better way at all. It is, of course, completely legitimate to look at implications of statements, but it has nothing to do with what I am saying. Only the truth of certain statements (with regard to certain sets) is relevant for my point. And the truth of a statement has nothing to do with what statements it implies or by what statements it is implied, aside from the fact that true statements imply true statements.

For example, we can assume that there is some set of objects for which your statement is true if x and y are members of that set; and we can then explore the properties of this set of objects. But that in no way means the statement is true for all sets of objects.

Of course not. The only statements that are true for all sets of objects are tautologies. But I think that's besides the point.

No, unicorns do exist in this sense, because I can define the concept of a unicorn as an object for which a certain set of statements is true, and by your definition, that is sufficient for such a concept to exist.

No, it's not. My definition didn't allow you to arbitrarily define "unicorn". You are also not allowed to alter the definition of "first natural number" in any way that substantially differs from the one I gave. You have a point, though, that the term "unicorn" has some ambiguity. (So has the term "first natural number", but not in a way that affects its existence.) I was assuming that we would agree on a description of unicorns that implies that they would be some unusual assemblage of otherwise ordinary matter, or that they must have a position in space and time. Then they don't exist.

 

[Stephen Tashi]

and not "what" is actually there(ontology proper) as the ultimate ontology which we seek.

is foundation about ontology proper or not?

A mathematical approach would be to side-step all questions about the common language meaning of "exist" and "existence" and treat "things that exist" as an abstract set. Then we would state axioms that say if such-and-such is set of things that exist then so-and-so can be constructed from that set and also exists - or "exists" in some technically defined sense particular to the method of construction.

Expositions of physics don't obey this format!

The semi-philosophical issue of ontology might be clearer if we look at what "ontology" should mean in other branches of study - for example, economics and psychology. For example, most people agree that individual people exist. Does it follow that things like "love", "hate" and "paranonia" exist?

 

[PeterDonis]

@ftr Your argument amounts to choosing definitions of "exist" so that you are right and anyone who disagrees with you is wrong. Nothing you have said tells me why I should care about your definitions.

 

[ftr]

@ftr Your argument amounts to choosing definitions of "exist" so that you are right and anyone who disagrees with you is wrong. Nothing you have said tells me why I should care about your definitions.

Let me clarify. The argument for the nature of mathematics is usually put by philosophers/mathematicians/physicists as mathematics is either invented or discovered. Amounting to not exist, only because we humans have come up with it since it has no physical characteristics as we experience in reality, or it exist with the same status as physical reality since we can discover about its properties, although it is of different kind of existence.

So the question is well posed as far as many people who deal with the question. And both camps have their arguments and I am clearly in the later.

However, my original question

Suppose numbers did not exist, would reality exist? Could there be a reality that is not describable by quantities?

Was sort of proof by contradiction and to contemplate the question of a reality without any mathematical connection, it sounded like mind bending.

 

[ftr]

Expositions of physics don't obey this format!

Please see post #55 and the accompanying videos especially Penrose.

 

[PeterDonis]

So the question is well posed as far as many people who deal with the question. And both camps have their arguments and I am clearly in the later.

Then you should be able to show me a version of "numbers exist" that is well posed, as @A. Neumaier did. So far I haven't seen one from you.

 

[bhobba]

Let me clarify. The argument for the nature of mathematics is usually put by philosophers /mathematicians /physicists as mathematics is either invented or discovered.

Not quite - there are many views eg the view of Poincare and Wittgenstein that it is just a convention:
https://en.wikipedia.org/wiki/Philosophy_of_mathematics

Some may say that's invented, but that's the issue with philosophy - is following a convention inventing something? Its part of the reason we do not discuss philosophy here - but make a slight exception for some areas of quantum interpretations.

Thanks
Bill

 

[A. Neumaier]

I think it is hard to say what it means that numbers exist because they can not be observed.

Mathematicians have the notion of an existential quantifier to give a precise meaning to the notion of existence.

I believe the real question is whether statements like "There is an x such that for all y x is not the successor of y" mean something.

Mathematicians (who among all scientists have the most precise language) know how to give a precise meaning to all this. In the context of natural numbers, this uniquely specifies the smallest natural number (0 or 1, depending on whose conventions you follow).

Maybe in some language there's a different word 'exist' for something that exists physically and something that exists as a concept. But I think the existence of numbers is a bit more concrete than that of many other things people imagine.

Numbers are concepts like electrons, but the former's properties are much more familar to everyone than the latter's.

The pointer readings don't tell me how or where the electron was emitted, they tell me where the electron was detected. If I want to know where an electron was emitted, I design a source that tells me. If the source tells me an electron was emitted, yes, I will believe an electron was emitted even if I can't directly observe it--in short, I will believe that electrons exist.

We can decide to call certain things we observe "numbers", just as we can decide to call certain things we observe "electrons".

I can test an "electron source" to see if whatever thingies it emits act like electrons.

But this requires that you can measure something characteristic about electrons after they have been emitted. Which thingies do you call electrons?

[Numbers] 'exist' only within the framework of mathematics and have no separate, objective reality.

Electrons 'exist' only within the framework of physics and have no separate, objective reality.

 

[A. Neumaier]

One question I would have for physicists is whether the idea of space as a manifold is a modified idea of Absolute Space.

In classical relativity we have absolute space-time. In quantum gravity (for which we currently do not have a convincing theory) it is debatable whether or not spacetime is absolute; different approaches give different answers.

 

[PeterDonis]

Which thingies do you call electrons?

The thingies that have the properties of electrons.

 

[A. Neumaier]

The thingies that have the properties of electrons.

But which observable properties do they have, given that one can observe nothing but pointer readings?

 

[vis_insita]

Mathematicians have the notion of an existential quantifier to give a precise meaning to the notion of existence.

Mathematicians (who among all scientists have the most precise language) know how to give a precise meaning to all this. In the context of natural numbers, this uniquely specifies the smallest natural number (0 or 1, depending on whose conventions you follow).

I completely agree. The point I was trying to get at is this: Consistently applying the precise meaning that mathematicians give to the notion of existence, enables us to talk about "ontology" in a way that is completely free of vagueness. We just have to (in principle) state which existentially quantified statements we believe to be true. (Promising candidates I imagine to be statements taken from our best scientific theories and mathematics.) This makes it easy to have an ontology which contains numbers and electrons, but not unicorns. We just declare some appropriate set of arithmetical statements (like the Peano axioms) to be true and statements implying "There exists an x, such that x is a <precise description of unicorns>" to be false.

My question regarding the meaning of a particular arithmetical statement was directed generally at people who say that numbers don't exist. There are only three possibilities for any set of arithmetical statements

1) It is meaningless
2) it is false of everything (contradictory)
3) it is true of something.

The latter case 3) applied to, e.g the Peano axioms, I think, inevitably implies that numbers exist, because it implies "There exists an x, such that for all y x is no successor of y", which is true if and only if there exists something that is not the successor of any other thing. And one of those things for which this statement is true I can as well call "The smallest natural number." This is why I am interested to know whether people denying the existence of numbers believe all arithmetical statements to be meaningless. (I think they must.)

 

[PeterDonis]

which observable properties do they have, given that one can observe nothing but pointer readings?

The set of observable properties that we name "electron".

 

[A. Neumaier]

The set of observable properties that we name "electron".

''electron'' is not the name of a set of observable properties, but the name for a concept from theoretical physics (refining much older less precise concepts from experimental physics).

Observable are positions, currents, spectra, cross sections, decay rates, detector correlations - nothing that would characterize an electron.

 

[PeterDonis]

''electron'' is not the name of a set of observable properties, but the name for a concept from theoretical physics

And that concept from theoretical physics ultimately leads you back to observations: the particular observations that convinced theorists that "electron" was a concept that needed to be included in their theories, and the observations that continue to convince physicists to use those theories because they make accurate predictions.

Earlier you said that bytes stored in a computer's memory were "numbers"; that claim is open to all the same objections you are making against my statements about electrons. So now I'm confused about your position. I thought you were saying that "numbers exist" because we can observe them in the memories of computers, and similarly "electrons exist" because we can observe them in the measurements that confirm our theories. I have no objection whatever to that position. But now you seem to be arguing against it.

 

[lavinia]

And that concept from theoretical physics ultimately leads you back to observations: the particular observations that convinced theorists that "electron" was a concept that needed to be included in their theories, and the observations that continue to convince physicists to use those theories because they make accurate predictions.

So it seems that electrons exist as a concepts. But so do spheres and numbers.

There are concepts in Mathematics that lead back to further investigation and some concepts lead to new and unexpected insight. For instance, De Rham's theorem leads to the theory of differential extensions of cohomology theories.

 

[A. Neumaier]

And that concept from theoretical physics ultimately leads you back to observations: the particular observations that convinced theorists that "electron" was a concept that needed to be included in their theories, and the observations that continue to convince physicists to use those theories because they make accurate predictions.

Earlier you said that bytes stored in a computer's memory were "numbers"; that claim is open to all the same objections you are making against my statements about electrons. So now I'm confused about your position. I thought you were saying that "numbers exist" because we can observe them in the memories of computers, and similarly "electrons exist" because we can observe them in the measurements that confirm our theories. I have no objection whatever to that position. But now you seem to be arguing against it.

I don't see this analogy as that close. We never observe electrons but only their effects on detectors predicted by theory, while we explicitly manipulate numbers all the time. Thus numbers exist for much more elementary reasons than electrons. (The random number generator was not the answer to ''numbers exist'' but to your quest for a "number source" in post #30.)

How can I build a "number source" or "number detector" analogous to the electron source and electron detector above?

I was arguing against your comment in #30 to the last question in my statement

Though the term ''reality'' may have multiple meanings (and hence needs a philosophical analysis to disentangle their various uses), it is a term needed - even though people like @vanhees71 substitute it by phrasing things in terms of ''observational objective facts'' rather than ''reality''. But this compound term is not really less ambiguous. Are electrons factually emitted by a source though we only observe pointer readings?

My implied answer to this rhetorical question was: ''of course'', while you put it in doubt.

The ''observational objective facts'' imply the factual existence of electrons (as instances of the concept of excitations of the electromagnetic field), though they are not directly observable but only inferred through consistency of their manipulation in theory and experimental practice.

Similarly, numbers factually exist (as instances of the concept of a complex number or one of its special cases), because of the consistency of their manipulation in theory and computational practice.

This is the true analogy regarding existence of electrons and numbers.

 

[PeterDonis]

We never observe electrons but only their effects on detectors predicted by theory, while we explicitly manipulate numbers all the time.

Really? You explicitly manipulate the individual bytes in your computer's memory? You directly observe them?

Your evidence for the existence of "numbers" in the sense you defined them is just as indirect as my evidence for electrons.

 

[PeterDonis]

I was arguing against your comment in #30 to the last question in my statement

My implied answer to this rhetorical question was: ''of course'', while you put it in doubt.

Evidently I didn't make myself clear. In post #30 I wasn't questioning the existence of electrons, I was questioning the existence of numbers. Then you explained how to make a "number source"--just use your keyboard or mouse or a combination of them to cause your computer to store certain bytes in its memory, which you can then manipulate in ways that match the definition of numbers. I accept this as a "number source".

However, you then need to be consistent in your claims about numbers "existing". If there is no computer anywhere that stores bytes in its memory that can be manipulated in ways that match the definition of numbers, then numbers don't exist. Just as if there were no objects anywhere in the universe that could produce the observational objective facts that imply the factual existence of electrons, then electrons would not exist.

 

[A. Neumaier]

Then you explained how to make a "number source"--just use your keyboard or mouse or a combination of them to cause your computer to store certain bytes in its memory

Number generators are algorithms (the simplest of the form $x_{k+1}=ax_k+b\mod N$ for suitable $a,b,N$) that produce random numbers, not bytes. Bytes are not numbers but storage patterns.

Really? You explicitly manipulate the individual bytes in your computer's memory?

I didn't claim to explicitly manipulate bytes.

Like almost everyone, I explicitly manipulate the numbers I write on sheets of paper. In addition there are more indirect ways of manipulating them, such as with the help of a computer.

Your evidence for the existence of "numbers" in the sense you defined them is just as indirect as my evidence for electrons.

Yes, but not the way you claim. The evidence for their existence comes from the consistency of using them in calculations resp. experiments. We wouldn't have numbers if the Peano axioms (say) were not consistent with counting practice, as we wouldn't have electrons if QED (say) were not consistent with experimental practice.

you then need to be consistent in your claims about numbers "existing"

I don't see any inconsistency.

 

[hilbert2]

The same word can also describe a concept and a particular object, for instance "tomato" as in plant species, and "tomato" as one particular fruit produced by that plant. In the case of electrons, their indistinguishability is an additional complication.

One could probably start a pointless discussion about whether the "four" in "four apples" is the same entity as that in "four carrots", or whether "kilogram" is similar to "four" as an object (because they can be multiplied together to give 4 kg).

 

[PeterDonis]

Number generators are algorithms (the simplest of the form $x_{k+1}=ax_k+b\mod N$ for suitable $a,b,N$) that produce random numbers

Algorithms that are run on some kind of hardware. You mentioned two kinds of hardware: paper and computers.

I don't see any inconsistency.

As long as your claim that "numbers exist" is tied to hardware in the same way that the claim that "electrons exist" is tied to hardware (the "hardware" in the latter case being the experimental apparatus), there isn't. But I'm not entirely sure whether you intend your claim to be tied to hardware.

 

[A. Neumaier]

Algorithms that are run on some kind of hardware. You mentioned two kinds of hardware: paper and computers.

No, nothing is run. Algorithms that are carried out in someone's mind and whose input and output are represented on paper. A mind is not hardware; it is rather like software. Hardware only produces bytes, not numbers. Their interpretation as numbers is mindstuff.

As long as your claim that "numbers exist" is tied to hardware in the same way that the claim that "electrons exist" is tied to hardware (the "hardware" in the latter case being the experimental apparatus), there isn't. But I'm not entirely sure whether you intend your claim to be tied to hardware.

Unlike paper, hardware, is for most people an abstract concept vaguely related to silicon chips. Nothing like this figures in my claim. I tie my arguments to ordinary experience (''observational objective facts''), which is mindstuff, not hardware.

The existence of electrons is tied to mind in the same way as the existence of numbers.

 

[A. Neumaier]

The same word can also describe a concept and a particular object, for instance "tomato" as in plant species, and "tomato" as one particular fruit produced by that plant. In the case of electrons, their indistinguishability is an additional complication.

Indistinguishability means that nothing can be said about individual electrons beyond the properties (spin 1/2, charge -e, and mass) they share with all electrons. Only permutation invariant statements about the collection of all electrons (elementary excitations of the electromagnetic field) are well-defined.

 

[PeterDonis]

A mind is not hardware

A mind runs on hardware--a brain. To say a mind "exists" requires that it be running in a brain.

Unlike paper, hardware, is for most people an abstract concept vaguely related to silicon chips.

Feel free to suggest a better term if you think "hardware" is too specific to computers. I am using the term to include things like paper and brains.

The existence of electrons is tied to mind in the same way as the existence of numbers.

I have no problem with this as long as all of these existences, including the existence of minds, are tied to hardware (in the general sense I described above, where paper and brains count as hardware).

 

[PeterDonis]

Nothing like this figures in my claim. I tie my arguments to ordinary experience (''observational objective facts''), which is mindstuff, not hardware.

You can't have experiences without a brain, so "observational objective facts" are tied to hardware.

 

[A. Neumaier]

A mind runs on hardware--a brain. To say a mind "exists" requires that it be running in a brain.

Well, this is a matter not of physics but of metaphysics. Mine is obviously different from yours.

Without mind no perception and hence no criterion for deciding what exists. Physics is impossible without a mind that thinks about its perceptions. To understand language and hence notions of existence also requires a mind.

Feel free to suggest a better term if you think "hardware" is too specific to computers. I am using the term to include things like paper and brains.

Rather than call everything material hardware I prefer to attribute mind to software (i.e., executable algorithms - not their implementation) if it is sufficiently intelligent.

You can't have experiences without a brain

Who knows? But it is certain that you can't even talk about brains without having a mind.

Intellect: ''Ostensibly there is color, ostensibly sweetness, ostensibly bitterness, actually only atoms and the void.''
Senses: ''Poor intellect, do you hope to defeat us while from us you borrow your evidence? Your victory is your defeat.''

(quoted from https://www.mit.edu/~muno/quotes.html, with corrections of typos)

 

[PeterDonis]

Without mind no perception and hence no criterion for deciding what exists. Physics is impossible without a mind that thinks about its perceptions. To understand language and hence notions of existence also requires a mind.

I agree with all of these.

Rather than call everything material hardware I prefer to attribute mind to software (i.e., executable algorithms - not their implementation) if it is sufficiently intelligent.

I never said we should call everything material hardware. I didn't say the mind was material hardware. I said it runs on material hardware, just like any other software.

If the mind software is not running on any hardware, it won't perceive, experience, think, etc. It is true that the mind software has to be running in order to comprehend all of the things we are saying. That doesn't refute the statement that the mind has to be running on hardware in order to do anything.

 

[PeterDonis]

Mine is obviously different from yours.

Do you mean that your mind, as you compose and post here, is not running on a brain?

 

[A. Neumaier]

Do you mean that your mind, as you compose and post here, is not running on a brain?

Yes. Instead it runs the brain and what is controllable by it, including the keyboard used to create posts, and organizes their behavior.

 

[PeterDonis]

Yes. Instead it runs the brain

Does the software running on your computer run your computer?

 

[A. Neumaier]

Does the software running on your computer run your computer?

The minds using the computer run it, by controlling the inputs of the installed software. I run an algorithm by feeding a program implementing it with my input data.

Without a mind the activity of a computer is a meaningless mess of pulses in its hardware.

 

[Demystifier]

Mathematicians (who among all scientists have the most precise language) know how to give a precise meaning to all this. In the context of natural numbers, this uniquely specifies the smallest natural number (0 or 1, depending on whose conventions you follow).

It's not really the issue here, but it's interesting to note that Peano axioms in the first order logic do not really define natural numbers uniquely:
https://www.lesswrong.com/posts/i7oNcHR3ZSnEAM29X/standard-and-nonstandard-numbers

 

[A. Neumaier]

It's not really the issue here, but it's interesting to note that Peano axioms in the first order logic do not really define natural numbers uniquely:
https://www.lesswrong.com/posts/i7oNcHR3ZSnEAM29X/standard-and-nonstandard-numbers

Peano's axioms in their original, second order logic form do not have this defect.

 

[Demystifier]

Peano's axioms in their original, second order logic form do not have this defect.

True. But second order logic has its own unappealing properties due to which most logicians prefer first order logic. I'm just saying.

 

[vis_insita]

Earlier you said that bytes stored in a computer's memory were "numbers";

[...]

I thought you were saying that "numbers exist" because we can observe them in the memories of computers, and similarly "electrons exist" because we can observe them in the measurements that confirm our theories. I have no objection whatever to that position.

I thought we were talking about numbers as something constituting a particular model of arithmetics. Whatever we can observe in the memories of computers is no such model.

 

[A. Neumaier]

True. But second order logic has its own unappealing properties

Only that not every true statement is provable. But I regard this as a very natural property, as our knowledge is finite anyway, so that we cannot know all true statements.

 

[Demystifier]

Only that not every true statement is provable.

If you mean the Godel's incompleteness theorems, they are valid in the first order logic too. Godel proved also the completeness theorem for first order logic, but that's something else. The "incompleteness" in the Godel incompleteness theorems is not a negation of "completeness" in the Godel completeness theorem.

The lack of completeness theorem is indeed one of those unappealing properties of second order logic (in the standard semantics). The other is the compactness theorem, valid in first but not second order logic: https://en.wikipedia.org/wiki/Compactness_theorem

If you find it confusing, that's because it is.
https://www.lesswrong.com/posts/MLq...ss-incompleteness-and-what-it-all-means-first

 

[atyy]

Is there a fundamental difference between hardware and software?

 

[Demystifier]

Is there a fundamental difference between hardware and software?

No. Are you suggesting that physics is analogous to hardware and philosophy to software? If you do, it would help if you could better elaborate the analogy.

 

[EPR]

Is there a fundamental difference between hardware and software?

'Software' is the gates switching. Everything in a computer can be tracked down to hardware but i
software is a more sophisticated hardware. It's a constantly changing hardware configuration that is called software.

 

[atyy]

No. Are you suggesting that physics is analogous to hardware and philosophy to software? If you do, it would help if you could better elaborate the analogy.

Just commenting on @A. Neumaier's comment the the mind is more like software than hardware.

 

[A. Neumaier]

Is there a fundamental difference between hardware and software?

It depends on what you regard as fundamental.

Computer software, or simply software, is a collection of data or computer instructions that tell the computer how to work. This is in contrast to physical hardware, from which the system is built and actually performs the work.

(quoted from https://en.wikipedia.org/wiki/Software)

Thus the software is a kind of mind that can issue commands, the hardware a kind of brain that can execute them. I consider these to be fundamentally different.

 

[Lord Crc]

Is there a fundamental difference between hardware and software?

Yes, hardware can compute results without software. Hook gates together and you get a result, regardless if you want to or not. Software must be executed by hardware to compute results. That hardware might be gates, relays, or neurons (when I predict what my source code will do for example).

 

[EPR]

Computer software is quite unlike a mind.

 

[EPR]

Yes, hardware can compute results without software. Hook gates together and you get a result, regardless if you want to or not. Software must be executed by hardware to compute results. That hardware might be gates, relays, or neurons (when I predict what my source code will do for example).

Hardware like calculators that can compute have preinstalled 'software'(gates setup, invertors, counters, etc. setup in a specific and fixed way.).

 

[EPR]

Mind altering drugs can be thought of as 'software'

 

[Lord Crc]

Hardware like calculators that can compute have preinstalled 'software'(gates setup, invertors, counters, etc. setup in a specific and fixed way.).

Sure, you could have mask ROM or something containing software. That does not affect the distinction. Hook up gates at random you _will_ get a result. Software without hardware does nothing at all.

 

[A. Neumaier]

Computer software is quite unlike a mind.

The algorithmic part of the software is mindlike, its implementation in computer code or microchips not.

Hook up gates at random you _will_ get a result.

But software produces results with a purpose, not just random output (unless this is the purpose).