instead of imagining that particles miraculaously turn into waves, and then back again to form a dot on a detector, why not accept the simpler option of a hidden pool of stuff that is causing the wave which the particles ride? — Gary Enfield

Pilot wave theory does match that interpretation of the double-slit experiment and also manages to account for the mathematical parameters of nonlocal causation in general. How we can observe this hidden pool of stuff is the conundrum, and it is uncertain whether thus far undetectable waves even exist beyond the model.

It might be possible that pilot wave theory and my morphing wavicle/electric charge theory are two ways of describing the same phenomenon, not perhaps mutually exclusive merely as models. If we consider realism of the situation, the pilot wave could be a figurative representation of the way known substances and their effects such as electric charge manifest, or electric charge effects could be a fallacious hypothesis about what is actually caused by pilot waves.

I find an absolute wave/corpuscle duality problematic on philosophical grounds because it seems to me that reality must consist in different forms of a single substance. In essence, apparent dualism always resolves into a multifaceted monism within the most accurate explanations since initial conditions of all causal events are shared, even if this causality proves to arise from an eternal substrate. This doesn't necessarily preclude some realist model along these lines.

If electric charge effects can be ruled out as a factor, then alternate hidden variables such as pilot waves can be considered I suppose, but electric charge and like forces might be an essential mechanism of nonlocality, necessitating no dramatically different form of matter to explain what is going on. Considering how closely linked electromagnetic activity is to biology and consciousness as we presently comprehend them, the discovery that at least some important nonlocal effects are contributed to by known particles and their electromotive sorts of forces as per my account could be illuminating. If my lightning bolt model is accurate in some way, the double-slit experiment might support this.

Hi Enrique

it seems to me that reality must consist in different forms of a single substance. In essence, apparent dualism always resolves into a multifaceted monism within the most accurate explanations since initial conditions of all causal events are shared, even if this causality proves to arise from an eternal substrate. — Enrique

There is a difference between determinism and dualism.
In fact, a 2nd type of stuff underpinning reality is the prime way to preserve determinism (single cause & single effect), in the light of various unexplained experimental results.

I never liked the description of 'Pilot Wave' because is tends to ignore the other stuff that must be generating the wave. It places the emphasis on an effect - not the capabilities of this other stuff.

I don't see why the presence of 2 types of stuff underpinning reality is such a problem. Where is the conceptual difficulty in imagining two types of material underpinning the universe, and them interacting with each other? Why does that have to become two aspects of the same stuff?

Envisaging 2 types of stuff is also helpful to our analysis, because it can help to distinguish different effects and influences. In the same way that we can separate the Laws of Physics & Chemistry that apply to our level of existence, from the very different rules that seem to apply at the quantum level (within or smaller than atoms), there is a natural separation between these realms... which aids analysis.

There have been various concepts of 'other types of stuff', from matter vs antimatter through to the capabilities of an unspecified stuff that generates Thought - or which even constitutes an 'information layer' of existence'.

So conceptually, I don't have a problem with the concept of 2 types of stuff. The main problem has been in isolating, detecting, and analysing what it might be. Perhaps Matter/Energy isn't capable of detecting the other stuff and we can only observe subtle interactions between them?

I think we all realise that there is no direct evidence for this other stuff, but the Dual Slit experiment may be one of the best indirect pieces of evidence for it. As I said before, it is easy to imagine Dark Energy being another manifestation of this.... another factor, like gravity, that we can't detect directly. We only observe effects.

Imagining another type of stuff underpinning existence is the simplest way to explain the Dual Slit effect, while preserving all existing notions of how Matter/Energy operates - and avoiding the nonsence of 'wave-particle duality'. It is likely that such stuff would be everywhere around us too, so there are many other factors in existence that it might explain.

I don't see why the presence of 2 types of stuff underpinning reality is such a problem. Where is the conceptual difficulty in imagining two types of material underpinning the universe, and them interacting with each other? Why does that have to become two aspects of the same stuff? — Gary Enfield

Two types of stuff interacting in the Universe? Interacting in what? The fabric of the Universe. It is much more straight-forward to think of the fabric as a continuous wave form, similar to how one imagines a hologram. What is that waveform? My suggestion, it is the Mind (consciousness in its broadest definition, which includes
Unconsciousness). This would be similar to what Bohm proposed.

I don't see why the presence of 2 types of stuff underpinning reality is such a problem. Where is the conceptual difficulty in imagining two types of material underpinning the universe, and them interacting with each other? Why does that have to become two aspects of the same stuff? — Gary Enfield

Well the question then is how did these two types of stuff get differentiated if they interact? To explain that you have to presume the two types of stuff are different, divergent forms of the same stuff. Two fundamentally and eternally unfiliated stuffs that cocausate is preposterous.

Conversations between those having interests in physics but not deep knowledge go on and on, and can be entertaining. Even arguments between actual scientists on interpretations. But I wonder if Feynman wasn't onto something when he argued to do the calculating, focus on the math and stop speculating.

When he introduced his Integral of all Paths concept to a room full of professional physicists most were taken aback and some startled by his explanations and were prone to discard his discovery. But as time went on and experimental evidence mounted his approach was adopted to a large extent. Even today, as a mathematician, I'm not sure of the nature or underlying soul of the functional-type integral he described. And I use the word "soul" in a context that only mathematicians can understand. It means not only superficial comprehension but deeper context, what lies beneath even the proof of the theory, a feeling of the actual substance of the concept.

I would not be surprised if future development of quantum theory might arise from going to the soul of the math that seems to predict so well. If so, philosophers may be chipping away at pretty hard marble.

Don't ask me to describe "soul". After many years of thinking about a particular aspect of dynamical systems in the complex plane I can "see" processes as they act to some extent, and this enables a glimpse into the undiscovered.

Or, ignore my nonsense entirely! :cool:

I use the word "soul" in a context that only mathematicians can understand. It means not only superficial comprehension but deeper context, what lies beneath even the proof of the theory, a feeling of the actual substance of the concept. I would not be surprised if future development of quantum theory might arise from going to the soul of the math that seems to predict so well. If so, philosophers may be chipping away at pretty hard marble. — jgill

I incline to think you can only get so far with outlining real mechanisms by merely processing the math because the quantitative model in large measure subsumes only what it anticipates, and current quantum physics is quite limited. Its like a hotwheels corvette, you can do cool stuff with it like build lasers or superconductors as well as perform some relatively simple entanglement and retroactive causality experiments, but I want a blueprint for the equivalent of a real corvette that enables telepathically driven technology, teleportation, reverse engineered biochemical pathways and the like. That's going to require a fundamental reconceptualization of reality's structure, not merely calculation. Its similar to the soul idea you proposed, but directed primarily towards matter rather than math, though the math has an indispensable scaffolding function. I think my fine structure constant thread exemplifies this to a modest degree: Fine Structure Constant, The Sequel

But I wonder if Feynman wasn't onto something when he argued to do the calculating, focus on the math and stop speculating. — jgill

Hi jgill

The trouble with Feynman was that his deterministic approach, based on the traditional maths that underpins all of the scientific Laws of Physics and Chemistry, fails philosophically as soon as you introduce probabilities, which are an admission that there is no known cause in those circumstances.

Science deploys probabilities quite a lot. In some circumstances it is probably valid to presume that an outcome which cannot be specifically explained because we have failed to monitor precise circumstances, are still operating accorrding to the known laws.

But in many other circumstances where scientists do look carefully and find no other factor to generate an effect, such assumptions would not be valid. The double slit experiment is one such example.

Hi MondoR & Enrique

Well the question then is how did these two types of stuff get differentiated if they interact? To explain that you have to presume the two types of stuff are different, divergent forms of the same stuff. Two fundamentally and eternally unfiliated stuffs that cocausate is preposterous. — Enrique

We differentiate things because they display fundamentally different characteristics or effects. If Mater/Energy can't do something, then something else must, (if determinism is to be preserved as a concept). Alternatively, you have to accept the possibility of either spontaneity or randomness as the opposites to determinism.

Clearly, we have demonstrated that many physical aspects to our existence do conform to deterministic principles, but there are also many unexplained aspects of our existence which do not, from the double slit experiment to particle entanglement to the activities of motor proteins, consciousness etc

There is no conceptual logic that I can see which would prevent two types of stuff bouncing off each other for all eternity. Please explain it if one does exist.

It is much more straight-forward to think of the fabric as a continuous wave form, similar to how one imagines a hologram. — MondoR

Yes, it is more straightforward - but that doesn't make it true.
I'm not saying that the alternate is guaranteed to be true either, but it is a possibility driven by evidence.

There is no conceptual logic that I can see which would prevent two types of stuff bouncing off each other for all eternity. Please explain it if one does exist. — Gary Enfield

First, it is unlikely that there are exactly two types of stuff, particles and waves, absolutely differentiated. The reality must undoubtedly be so much more complex that duality ceases to have descriptive relevance. Second, all matter thus far experienced has evolved from common antecedents, so it is most likely that if particles ride a more foundational wave substance, the particles evolved out of it. Its not conceptually impossible for eternally distinct particle and "wave" substance to exist, nor is anything else, but the most probable explanation due to their pervasive interactiveness is that they have a common origin with impulsion towards combinatory states. As a fanciful example, if particles ride dark matter waves their behavior is probably mutualized enough with dark matter for whatever reason that this amounts to a synthetic substance in some degree.

I'm not aware of any evidence that a particle/fundamentally different stuff differentiation exists.

I don't know but you might like watching this video. :)

https://shrinke.me/Philosophy

Yes, it is more straightforward - but that doesn't make it true.
I'm not saying that the alternate is guaranteed to be true either, but it is a possibility driven by evidence. — Gary Enfield

It avoids the issues associated with dualism, i.e. how do they interact?

I'm not aware of any evidence that a particle/fundamentally different stuff
differentiation exists. — Enrique

The Double Slit experiment for one. Dark Energy and the accelerating expansion of the universe as another. What about particle entanglement? What about the loophole free Bell Tests?

if particles ride dark matter waves their behavior is probably mutualized enough with dark matter for whatever reason that this amounts to a synthetic substance in some degree. — Enrique

The word 'Probably' here is perhaps the giveaway. We can all set boundaries wherever we want, and if you are determined to only see things one way, that is indeed possible.

However I and others see merit in categorising things in different ways, which allows us to explore new potential answers in those areas where your approach cannot find them

First, it is unlikely that there are exactly two types of stuff, particles and waves, absolutely differentiated. The reality must undoubtedly be so much more complex that duality ceases to have descriptive relevance. Second, all matter thus far experienced has evolved from common antecedents, so it is most likely that if particles ride a more foundational wave substance, the particles evolved out of it. Its not conceptually impossible for eternally distinct particle and "wave" substance to exist, nor is anything else, but the most probable explanation due to their pervasive interactiveness is that they have a common origin with impulsion towards combinatory states. As a fanciful example, if particles ride dark matter waves their behavior is probably mutualized enough with dark matter for whatever reason that this amounts to a synthetic substance in some degree. — Enrique

The existence of waves necessitates the conclusion that there is a substance (commonly referred to as the ether) within which the waves are active. One might deny the reality of the ether, but this leaves the relationship between the waves and the particles as unintelligible. The Michelson-Morley experiments indicate that the ether is not a separate substance, i.e. it is not distinct from physical objects. This implies that particles must be conceived of as a feature of the wave substance (ether), not as something distinct from it, "riding" it.

The existence of waves necessitates the conclusion that there is a substance (commonly referred to as the ether) within which the waves are active. — Metaphysician Undercover

It doesn't have to be seen that way. I have only indirect voices of physicists about the nature of wave fields via the work of the German philosopher Gerold Prauss:

"[...] Physicists emphasize, that »constant passing and arising« of a force or energy in a wave field, as in electromagnetism, has to be considered as movement without any substrate, which is nevertheless from one side something caused and from the other side something causing." (my translation from Prauss' main work "Die Welt und Wir")

And:

"»The electromagnetic waves are not based on oscillations of any substance. They are spatio-temporal structures which do not need any material carrier«. It is rather about a »change of the field energy« which is to be understood as a »constant passing and arising« of it." (my translation from Prauss' main work "Die Welt und Wir")

Waves might be substrate-less. That is, they may not be like the waves in the water, which is the substrate for the waves. They are only waves.

In any case, this is controversial, as the discussion shows:

Johannes Röhl - Ontological categories for fields and waves
https://subs.emis.de/LNI/Proceedings/Proceedings220/1866.pdf

Classical Fields: Are They Real?
https://www.mathematik.uni-muenchen.de/~bohmmech/Teaching/ontologyofphysics1415/classical_fields.pdf

Waves and fields in bio-ontologies
http://ceur-ws.org/Vol-897/sessionJ-paper24.pdf

Against the field ontology of quantum mechanics
http://philsci-archive.pitt.edu/15476/1/wf-pw%20v99.pdf

Waves might be substrate-less. That is, they may not be like the waves in the water, which is the substrate for the waves. They are only waves. — spirit-salamander

When you start into basic physics in high school, they'll teach you about waves, and do demonstrations of waves in wave tanks, and you'll learn about sound waves and such. You learn the physical structure of waves. It is nonsense, completely illogical, and fundamentally contrary to good science, for anyone to say that "waves might be substrate-less", regardless of your appeal to authority.

It is nonsense, completely illogical, and fundamentally contrary to good science, for anyone to say that "waves might be substrate-less", regardless of your appeal to authority. — Metaphysician Undercover

That may be. But nevertheless there are physicists who think so. In any case, there is a controversial discussion about it:

From the above linked paper Waves and fields in bio-ontologies:

"While waves travelling in material media are perplexing, they are much more straightforward than electromagnetic waves such as light waves, where there does not appear to be any material medium involved. In these cases, we will argue that they are themselves material entities, which participate in their own wave processes"

From Classical Fields: Are They Real?

David Griffiths: "What exactly is an electric field? I have deliberately begun with what you might call the “minimal” interpretation of E, as an intermediate step in the calculation of electric forces. But I encourage you to think of the field as a “real” physical entity, filling the space around electric charges. Maxwell himself came to believe that electric and magnetic fields are stresses and strains in an invisible
primordial jellylike “ether”. Special relativity has forced us to abandon the notion of ether, and with it Maxwell’s mechanical interpretation of electromagnetic fields. (It is even possible, though cumbersome, to formulate classical electrodynamics as an “action-at-a-distance” theory, and dispense with the field concept altogether.) I can’t tell you, then, what a field is—only how to calculate it and what it can do for you once you’ve got it. [5, Sec. 2.1.3]"

"Against Fields
fields only introduced to account for the motion of particles.
fields not directly observable.
ontological status:
• stuff, substance?
• properties? of space-time points?
• new ontological category?
interpretation of the field as non-existent.
formulation of retarded distant action theory.
inconsistency: self-field"

From Johannes Röhl:

"I discuss two options for fields: fields as qualities of points or regions of space or spacetime and fields as substantial entities in their own right. Finally I get to waves as entities dependent on fields or spatiotemporal patterns of fields."

I find an absolute wave/corpuscle duality problematic on philosophical grounds because it seems to me that reality must consist in different forms of a single substance. — Enrique

This reminds me of the following passage:

"It's beginning to look as if everything is made of one substance-call it "quantumstuff"-which combines particle and wave at once in a peculiar quantum style all its own. By dissolving the matter/field distinction, quantum physicists realized a dream of the ancient Greeks who speculated that beneath its varied appearances the world was ultimately composed of a single substance. Some philosophers said it was All Fire; some All Water. We now believe the world to be All Quantumstuff. The world is one substance. As satisfying as this discovery may be to philosophers, it is profoundly distressing to physicists as long as they do not understand the nature of that substance. For if quantumstuff is all there is and you don't understand quantumstuff, your ignorance is complete." (Nick Herbert - Quantum Reality: BEYOND THE NEW PHYSICS)

"The world is one substance. As satisfying as this discovery may be to philosophers, it is profoundly distressing to physicists as long as they do not understand the nature of that substance. For if quantumstuff is all there is and you don't understand quantumstuff, your ignorance is complete." (Nick Herbert - Quantum Reality: BEYOND THE NEW PHYSICS) — spirit-salamander

My intuition is that quantum stuff consists of coherence between entangled waves and particles, in essence coherence fields with nonlocal properties. It is exciting that we might figure out what all this stuff actually is and utilize the knowledge to advance technological society in almost unimaginable ways.

Until you accept that there is a difference here, further discussion is pointless. — Metaphysician Undercover

[/quote]

I agree that the present phase of our ongoing convo has reached an impasse. I just wanted to close the loop on a couple of things you said.

Yes, "2+2=green" has meaning. But I would reject this statement as inconsistent with the principles that I already understand and accept. — Metaphysician Undercover

What does it mean?

I don't know, the answer to these questions. "Meaning" is not an easy topic. That's why there's so many philosophical debates about it. I really do not know what meaning is, or how I know that something has meaning. Those are questions yet to be answered. — Metaphysician Undercover

Ok. I find that an extremely fair minded statement. But I want to make a finer distinction.

When I say that 2 + 2 = 4 has meaning, it's because I have defined '2', '4', '=', and '+' according to the standard mathematical conventions, either within the Peano axioms or ZF set theory. In other words from my viewpoint 2 + 2 and 4 and '=' all refer to something. The somethings that they refer to are abstract mathematical objects. And I will stipulate that when you challenged me to define exactly what I mean by those, I was stuck. I admit that! But at least by saying what these expressions refer to (in my mathematical ontology), I can thereby assign meaning and value to them. The meaning and value of these expressions derive from the referents I have assigned to them.

But you say that 2 + 2 and 4 don't refer to anything. So it is now incumbent on you -- not just for me, but for working out your own thoughts for yourself -- to figure out how to define the meaning and value of syntax tokens that you claim don't refer to anything at all! Do you take my point here?

By asking this question you indicate that you paid not attention to my explanation of what "=" signifies, or means in common mathematical usage, and what "is the same as" signifies or means in the law of identity. Since you still cannot see the difference here, after I've explained it countless times to you, it seems pointless to explain it again. It's actually a very simple difference, and very easy to understand. — Metaphysician Undercover

There is nothing simple about your point of view. Nor have you explained "what '=' signifies" in the least. I haven't seen you do it.

We learn values in school. If you still haven't learned the value of 4 yet, you could talk to a primary school teacher, or look it up on the web. You'll find there's a lot of educational stuff like that if you google it . — Metaphysician Undercover

It's funny. You can't answer the question I put to you: If 2 + 2 has no referent, how does it obtain its meaning or value?

You can't answer that, so instead of challenging yourself to clarify your own ideas, you make a childish insult.

But I have a perfect understanding of what the meaning and value of 2 + 2 are. Not only at the grade school level, but at a sophisticated mathematical level. The meaning and value derive from the REFERENT of the symbolic expression. But in your case, you DENY there is a referent. So in your theory, from where come the meaning and value?

You are cornered on this point, and instead of tossing out silly insults, you should take the opportunity to challenge yourself to respond intelligently.

Yes, that's a very real problem. We often do not know whether a word signifies something with thinghood or not. That is the case with quantum physics and wave/particle duality. Physicists cannot determine the "thinghood" of the described phenomena. — Metaphysician Undercover

Ok. I appreciate your admitting when you are stuck on your own ideas. Better than childish insults to avoid answering sharp questions.

Since you seem to have no idea of what "value" means I suggest you do some research into this topic, and come back to me when you get above the primary school level. — Metaphysician Undercover

LOL. As Ronald Reagan said to Jimmy Carter, There you go again.

I DO have a crystal clear understanding of how the meaning and value of 2 + 2 derive from the mathematical REFERENT of the expression. Whereas you DENY there is a referent, so you are STUCK trying to figure out how to derive the expression's meaning and value. Why don't you work on this and let me know if you have any fresh ideas on the matter.

Obviously you never looked into this, and haven't looked beyond your own nose to see what others say about what "=" signifies. The following is the opening paragraph from the Wikipedia entry — Metaphysician Undercover

Wikipedia isn't too far beyond anyone's nose. That's all you got?

The equals sign (British English, Unicode Consortium[1]) or equal sign (American English), formerly known as the equality sign, is the mathematical symbol =, which is used to indicate equality in some well-defined sense.[2][3] In an equation, it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the same value.
— Wikipedia: equals sign[/url]

LOL. You're pasting that para to support some kind of argument? Your stuff is weak here. And you're agreeing with me. Because I can define the value of 2 + 2 very easily from first principles, based on the REFERENT that I assign to the expression. You on the other hand DENY there is any referent, so YOU are the one who can't figure out how to assign the expression a value.
— Metaphysician Undercover

Notice the mention of "the same value". — Metaphysician Undercover

Agreed on this point. But note that I can define what the value of 2 + 2 is, and you can't. Because you deny that 2 + 2 has any referent.

Do you accept that there is a difference between "is the same as" and "has the same value as"? — Metaphysician Undercover

I will stipulate that this is a tricky question. We agree that 2 + 2 and 4 have the same value (I think we agree on that). I claim that mathematically, they are literally the same thing. They have the same referent. They're two different symbol strings that point to the same mathematical object. And I'll stipulate that a long time ago you challenged me to tell you what a mathematical object is, and my response was not satisfactory even to me. So that's the point where I'm stuck.

But you deny the expressions have any referents at all, so I don't see how you're in a position to claim that they have the same value, or different values, or any values at all. How can we know their values if they have no referents? I, on the other hand, have a perfectly sensible way to define their values, based on the referents I have assigned them in PA or ZF. I can do this from first principles.

The former phrase is the phrase used by the law of identity. The latter phrase is what is signified by "=", as the Wikipedia entry indicates. — Metaphysician Undercover

I don't think the author of this particular Wiki pages had these distinctions in mind.

Until you accept that there is a difference here, further discussion is pointless. — Metaphysician Undercover

I do agree we're at an impasse for the moment. You claim that 2 + 2 has no referent. And you're stuck on your own theory here, because you can't tell me how to derive the meaning of a symbol string that has no referent. Can you see that this is problem for you? Why not think on it a bit. No hurry.

In fact I'll summarize as follows:

* You claim 2 + 2 has no referent, and since it has no referent, you can't tell me how to determine its value.

* I claim 2 + 2 has a referent, namely a particular mathematical object. But I can't tell you what a mathematical object is, other than "Whatever mathematicians think is a mathematical object," and I'll concede that this is not entirely satisfactory.

Would you call this a fair summary of the state of the discussion?

What does it mean? — fishfry

"2+2=green" means that whatever is represented by "2+2" is equal with whatever is represented by "green". Isn't that the way we use logic? We learn to apply the rules without regard for what the particular symbols represent.

When I say that 2 + 2 = 4 has meaning, it's because I have defined '2', '4', '=', and '+' according to the standard mathematical conventions, either within the Peano axioms or ZF set theory. In other words from my viewpoint 2 + 2 and 4 and '=' all refer to something. The somethings that they refer to are abstract mathematical objects. And I will stipulate that when you challenged me to define exactly what I mean by those, I was stuck. I admit that! But at least by saying what these expressions refer to (in my mathematical ontology), I can thereby assign meaning and value to them. The meaning and value of these expressions derive from the referents I have assigned to them. — fishfry

You are missing something in your interpretation of "2+2=4". The "+" signifies an operation, not an object. Do you understand that an operation, as an action, is something other than an object?

But you say that 2 + 2 and 4 don't refer to anything. So it is now incumbent on you -- not just for me, but for working out your own thoughts for yourself -- to figure out how to define the meaning and value of syntax tokens that you claim don't refer to anything at all! Do you take my point here? — fishfry

Sure, I see your point. It's not difficult, the task you ask of me; "2" signifies a quantity, "+" signifies an operation of addition, "=" signifies 'has the same quantitative value as', and "4" signifies a quantity. So, "2+2=4" signifies that a quantity of two, added to another quantity of two, through that operation of addition, has the same quantitative value as the quantity of four. See how easy it is? Grade school stuff.

There is nothing simple about your point of view. Nor have you explained "what '=' signifies" in the least. I haven't seen you do it. — fishfry

Come on fishfry I've said over and over again that "=" signifies having the same value. I even quoted Wikipedia in the last post:: "In an equation, it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the same value." Now don't come off saying that I haven't explained what "=" signifies. This is how I ended the last reply to you:

Do you accept that there is a difference between "is the same as" and "has the same value as"? The former phrase is the phrase used by the law of identity. The latter phrase is what is signified by "=", as the Wikipedia entry indicates. — Metaphysician Undercover

It's funny. You can't answer the question I put to you: If 2 + 2 has no referent, how does it obtain its meaning or value? — fishfry

That question is simple too. A word can derive its meaning through examples, like "green", without referring to any particular thing. It can derive meaning from a definition, like "square", and "circle" do, without referring to any particular thing. And there is a number of other ways, by which usage hands meaning to a word, which does not refer to any particular thing. In this case, we use "2" to signify a quantity, and "+" to refer to the operation of addition, and the symbols derive their meaning from that usage.

But I have a perfect understanding of what the meaning and value of 2 + 2 are. — fishfry

Clearly you do not have a "perfect understanding of the meaning of "2+2", because your interpretation does not include the operation of addition, which is signified by "+". You cannot simply leave out the meaning of some symbols in the phrase, then claim to have a perfect understanding of the phrase.

I DO have a crystal clear understanding of how the meaning and value of 2 + 2 derive from the mathematical REFERENT of the expression. Whereas you DENY there is a referent, so you are STUCK trying to figure out how to derive the expression's meaning and value. Why don't you work on this and let me know if you have any fresh ideas on the matter. — fishfry

OK, if you're so convince that you are correct in your crystal clear understanding, interpret the expression for me, "2+2", symbol by symbol, and show me how that expression signifies the object signified by "4".

Agreed on this point. But note that I can define what the value of 2 + 2 is, and you can't. Because you deny that 2 + 2 has any referent. — fishfry

Tell me please, in your mind, how is a value an object?

But you deny the expressions have any referents at all, so I don't see how you're in a position to claim that they have the same value, or different values, or any values at all. How can we know their values if they have no referents? — fishfry

A value is not a thing, or object, it is what a mind assigns to a thing, as a property, just like "big", "heavy", "green", etc. So a value is the product of a judgement. There is no referent because we assign the same property to multiple things, due to the abstract nature of properties. And, we assign the same value to multiple things, so there cannot be an object as a referent. "Green" doesn't refer to any particular thing, because many things are green, so there is no referent for "green". It is a judgement we make.

It is a similar situation with "2", we assign that value to many different situations, as the property of them, but it has no particular referent. We can start with, 'what a thing is worth' as a defining feature of "value", and see that a value exists in relation to a purpose. A thing is worth something only to the extent that it is desirable for some purpose, useful toward some goal or something like that. So we know the value of "2" by its usefulness. That is what the judgement is based in.

I, on the other hand, have a perfectly sensible way to define their values, based on the referents I have assigned them in PA or ZF. I can do this from first principles. — fishfry

One big problem here, your interpretation leaves out the operation signified by "+". And, it is by means of these various operations that the numerals obtain their signified values. They are useful for these operations. So your way, is really not at all sensible, because you completely neglect the operations by which the numerals get the values which are associated with them.

Not only that, but your way creates an unnecessary layer of separation between the numeral and the represented value, which is commonly called a number. This medium, or separation obscures the true meaning, and value represented by the numeral, making it much more difficult to understand the nature of quantities.

* You claim 2 + 2 has no referent, and since it has no referent, you can't tell me how to determine its value. — fishfry

You have obviously misunderstood. I have no problem telling you how we determine the value of "2+2". We simply look at how the symbols are used, just like when we determine the meaning of "green". That's why I said it's a matter for grade school, which you took as an insult. We see that in common use 2+2=4, so 2+2 clearly has the same value as 4, that's what the "=" tells us.

See how easy it is? Grade school stuff. — Metaphysician Undercover

You'd be the expert on that.

Participating at TPF has necessitated that I become an expert at grade school principles, because many people here do not seem to understand these very basic principles, like what "=" signifies. And so, I have to explain over and over again, the same principle, in as many different ways as possible, in an attempt to dispel the misunderstandings which these people hold. It seems to be much easier to teach young children these principles than it is to teach adults who have already developed bad habits of misunderstanding, by accepting contrary principles. So the teacher of adults, must become an expert, rather than just an average teacher, requiring not only to instill good habits of understanding, but first needing to dispel bad habits of misunderstanding.

Participating at TPF has necessitated that I become an expert at grade school principles, because many people here do not seem to understand these very basic principles, like what "=" signifies. And so, I have to explain over and over again, the same principle, in as many different ways as possible, in an attempt to dispel the misunderstandings which these people hold. It seems to be much easier to teach young children these principles than it is to teach adults who have already developed bad habits of misunderstanding, by accepting contrary principles. So the teacher of adults, must become an expert, rather than just an average teacher, requiring not only to instill good habits of understanding, but first needing to dispel bad habits of misunderstanding. — Metaphysician Undercover

LOL. Thanks for the chuckle.