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Double-slit Experiment, The Sequel

Enrique March 27, 2021 at 13:55 11350 views 83 comments
A brief essay I wrote that summarizes an interpretation of the double-slit experiment in quantum physics I've been ruminating on, along with its wider implications. I'm interested to get your opinions on the subject matter.


The Quantum Handshake: A Transactional Model for Results of the Double-slit Experiment Along with Wider Implications

Introduction: Basics of the Double-slit Experiment

The double-slit experiment ejects nanoscale particles from an emission device and towards a screen that records their final position as a florescent spot while it absorbs them. On the way, the particles pass through two slits. If the absorber screen is placed far enough behind the double slits, emission generates what seems to be an interference pattern, as if the particles are waves, but this effect only emerges from large quantities of particles, for each one contacts the screen at a specific point, as if not a wave. This interference pattern has shown up with photons, electrons, even molecules of as many as two thousand atoms. It works when streams of particles are emitted and also when one particle is emitted at a time, so scientists have postulated that matter involves an intrinsic wave/particle duality. All sorts of subatomic particles, atoms and molecules seem in actuality to be wave packets or “wavicles”. 

It is easy to imagine a stream of wavicles interfering as they diffract through the slits to produce an array of light and dark bands on the florescent screen corresponding to in phase and out of phase waves. This would resemble the classic experiment performed in the 19th century, where a beam of light was diffracted by a single aperture to then pass through double slits as a spreading field which apparently interfered with itself to similar result.  

Interference patterns from one at a time particle emission are a more difficult outcome to account for. The typical explanation is that the wavicle passes through both slits to interfere with itself, spreading out in the double-slit chamber and then spontaneously collapsing in some way upon contact with the absorber surface to give a particulate signature. This “wave function collapse” mechanism is quite the brain teaser: does the wavicle spread out invisibly in the chamber as it diffracts and then somewhat mystically end up at a very localized endpoint? Why would many localized endpoints with no likeness to waves at all look like in phase and out of phase waves as they accumulate on the absorber screen? What exactly is going on?          

This gets even trickier when a sensor is placed at one of the slits during the two slit experiment to detect the transmission of particles. Whether a photon, electron or larger molecule, the particle is detected 50% of the time, so there is an equal (and unpredictable) chance of it passing through either slit in any single trial. But when a sensor is present at one of the slits, this dissolves the interference pattern and the particles engender two narrow bands on the florescent screen, as if they were never a wave. This led researchers to propose a “decoherence” mechanism: diffuseness of the wavicle, according to this account, is easily disrupted by interaction with large collections of tightly knit atoms such as exist within the sensor or absorber screen. Particles supposedly assume a localized form that obeys principles of Newtonian mechanics as they jostle amongst themselves in vast quantities. Decoherence is attributed to sizable mass, and the double-slit experiment seems to set the size limit at an extremely microscopic level, around the scale of a couple thousand atoms. Anything bigger supposedly decoheres, failing to interfere with itself and bring forth the complementing interference pattern. But different experiments entangling trillions of atoms contradict this interpretation, where quantum coherence is unmistakably taking effect much more broadly. 

The plot thickens, for an absorber theory of particle interactions invented by Richard Feynman and John Wheeler was adapted by John Cramer into a transactional interpretation of the double-slit experiment. It asserts that certain solutions to the equations of wave dynamics which have traditionally been ignored because they necessitate much more rapid motion than the speed of light are as physically real and causal as those of the conventional wave itself, giving rise to a linear interference mechanism along the wavicle’s path that participates in steering it to the absorber. This extremely swift, “advanced” wave would travel fast enough to exact its causality as if flowing backwards through time relative to the so-called “retarded” wave, which it interferes with in cocausation. 

Actual experiments have not ironed out exactly what the real process consists in, but it seems suspect that a single particle interference at the slits brings about an interference pattern spanning the whole chamber, which only materializes from hundreds of trials that individually create point particle signatures. The verified fact that trillions of atoms can simultaneously engage in coherence also casts doubt, for wavicle entanglement clearly exceeds the mass constraints which seem to take effect in the double-slit experiment. And what precisely does interference between an advanced and retarded wave structurally entail? The relevant investigations remain to be carried out, but perhaps we can gain inspiration from the weather. By analogizing wavicle emission events to lightning bolts, which we solidly grasp from slow motion photography and video, can we describe the double-slit experiment? What role if any does electric charge play, and what can we infer if a lightning bolt mechanism proves to be the accurate explanation? 

A Lightning Bolt Model of the Double-slit Experiment

To start with, we can consider what a lightning bolt mechanism in the double-slit
chamber would look like. Almost immediately after the first retarded wave is formed by an emission event’s electric charge, comparable to the stepped leader produced by a thunder cloud, the complementary advanced wave arrives, then the two interfere to adjust the direction of this initial retarded wave while it travels towards the absorber, while the retarded wave in the backward direction (towards the emitter) cancels out the original retarded wave.

A further advanced wave instigated by this event dissipates into the emitter somehow and similarly interferes with a retarded wave eventually springing from the absorber, which resembles a return streamer, in a brief instant. The succession of retarded waves from emitter and absorber rapidly close the distance between them in a stairstepping sequence of zigzag motion caused by ricocheting interference with advanced waves, until contact is made and the quantum handshake occurs, a surge of charge briefly connecting the emitter and absorber directly, like a lightning bolt, in this case invisible.
Whether transmission of the particle itself flows in coordination with subsequent current of smoother, faster motion in likeness to a dart leader is uncertain, but this can perhaps be analyzed by experiment.

The double-slit instigates a symmetry in the chamber’s charge that makes the absorber’s charge-active sites comparably symmetrical, resulting in what looks like a precise interference pattern on the florescent screen despite the haphazard, seemingly randomized nature of each individual transmission “handshake” and its chance of passing through only one or more than one slit.

The key point is that individual electrons do not bring about the characteristic fringe on the screen primarily by a lateral interference. The electrons follow a relatively linear path parameterized by charge distribution. The spookiest aspect of this process is that wavicle emission events would be perturbing their medium of electrically charged volume at variable rates and energy levels simultaneously, resulting in cocausation backwards and forwards through what is typically interpreted as spacetime.

If this lightning bolt model is accurate, an inability to get the interference fringe from molecules larger than a couple thousand atoms does not imply an upper limit on capacity of the atoms composing molecules to be in a state of relatively macroscopic entanglement, as decoherence is not induced by architecture of the slits. Decoherence may occur minimally in this context, with the molecules squeezed or stretched in a longitudinal direction more than discomposed laterally.

The upper size limit to molecules when generating what might have erroneously been called an "interference pattern" would instead be a result of the strength of electric charge in the double-slit chamber being insufficient to influence the path of each molecule such that a wavelike statistical distribution materializes on the absorber screen.

The Significance if Electric Charge Effects Prove to Obtain

What are the implications if possible entanglement between molecules is not constrained as much by their size or an extremely unusual composition (the two thousand atom double-slit experiment used oligo-tetraphenylporphyrins enriched with fluoroalkylsulfanyl chains) as the charge distributions they subsist in?

With a large electric charge such as we find in the brain, a wide range of fairly massive molecules and molecular complexes might be able to entangle while avoiding decoherence. It may not only be possible to experimentally entangle trillions of separate atoms in a nonbiological context, but also for biochemical arrays of a million molecules of thousands of atoms each to entangle in a thousand different ways simultaneously given appropriately strong electrical charge conditions.

Trillions of entanglement systems within entanglement systems and their additiveness (similar to combinatorial properties of the visible light spectrum), integrated by an electrical field substrate, probably reaches enough complexity to constitute the substance of qualia and qualitative experience as it exists within the brain.

This charge distribution phenomenon can be likened to the thunderstorms during which clouds and the ground are positively charged with negatively charged atmosphere between them. Storms create charge peaks on numerous patches of ground that synchronize with electricity coming down from the sky, these prongs of current stairstepping towards each other until they connect and a surge of electricity is transmitted. All of this of course happens in a fraction of a second, undetectable to the naked eye.

The hypothesis is that the double-slit experiment is similar, during which an emission event and the absorbing material give rise to clouds of charge, presumably separated by a cloud of opposite charge induced between them. The apparent "interference pattern" would then not be due to interference at all, but rather consequent on patches of charge that form a symmetrical pattern along the absorber surface because of the symmetry of the experimental setup. As the emission event proceeds, absorber charges rise towards the emitter, setting the statistical distribution of particle transmission. Electric charges loosely parameterize the motion of a "chosen one" absorption event and the emission event as they approach each other in stairstep, zigzag fashion and link, with an individual particle stretched linearly as it travels through one or multiple slits, flowing within the path of what resembles a microscopic lightning bolt and making contact with the screen in a seemingly random manner, at a particular point.

In the brain, current flows through neurons as the relative positivity to negativity of charge alternates between internal and intermembrane space. This process is regulated by cyclical flow of ions into and out of the axon. Action potentials throughout the brain are happening trillions of times per second, so that the organ is like a highly organized electrical storm. These orderly periodicities of charge disequilibrium are presumably what generates brainwaves, and in line with the foregoing hypothesis would also provide the medium of nonlocality within which entanglement effects occur, similar to a thunderstorm and the double-slit experiment. This electrical charge nonlocality within the brain is strong and persistent enough that biomolecules within cells can entangle as described, far beyond the double-slit experiment's limits.

Nonlocality of an electrically charged field may establish entanglement relationships between particles in a way that is infused into the matter itself but also supervenient on local positions. This supervenient integration that is intrinsic to matter while it consists in electric charge might engender “qualia” as additive entanglement amongst particles, and with sufficient complexity in emergent organization would beget qualitative perception.

Essentially, charge distribution participates in piloting, synchronizing or blending particle interactions via entanglement within many circumstances, and this can show up in standard quantum mechanics as statistical probability.

In this account, the wavicle doesn't fill the double-slit chamber as if transmitted like aether and then engage in a radically disjuncted collapse mechanism, or else why would the phenomenon not be easily observed with particles under all naturally occurring conditions, a reality of total superposition? In this model, holism of charge distribution within matter is the entanglement mechanism instead of a phenomenon of particle position or state and the accompanying paradoxes of action at a distance.
Maybe compromise between the wave and particle models is possible that sustains realism in relation to the double-slit context, a wavicle which can stretch, elongate, flow in a particular direction with some likeness to a liquid or gas depending on globally active factors, in this case electric charge distribution.

A Tentative Hypothesis About the Nature of Wave/Particle Interactions

Then what is an advanced wave? Let’s start with the more intuitive facet of transmission, the retarded wave: it seems to be a flash of electrically charged current between the emitter and absorber that morphs the wavicle’s shape somehow via charge dynamics and within which the wavicle flows as a high energy cluster of matter, tightly knit enough to avoid being substantially absorbed by the environment as it travels to the florescent screen, and pliant enough to squeeze through the slit or slits.

If we were to launch a baseball at the screen by contrast, it would slow slightly due to macroatomic friction in the chamber and bounce off the slits rather than transmit through them because relatively massive size induces large enough decoherence effects and charge cancellation amongst its tangle of constituent particles that it cannot squeeze through nor respond to electromagnetic effects which pervade the subatomic scale, instead obeying classical laws of Newtonian motion.

Electromagnetic radiation near the visible portion of the spectrum is a sweet spot in relationship to Earthlike molecules, constantly being emitted at relatively high intensities that saturate the environment. However, it is absorbed in large amounts as well, which amongst the double-slit context and most Earthbound situations reduces average intensity over any given range of space such that negligible impact is had on outcomes. Moderately sized radio waves with their longer wavelengths could travel ever so slightly faster, but exist at such low intensities within the double-slit context that they are quickly absorbed by molecules and also have negligible effect.

Extremely long wavelengths may also be generated at very low intensities by the highly energetic emission/absorption event, but could move so rapidly that they skirt much interaction with molecules, reaching the opposite apparatus with their intensity almost undiminished. This might be enough to create advanced waves that ping pong between retarded waves and participate in steering their mostly linear motion.

The hypothesis is that the double-slit experiment involves something like two energy peaks, one at the low speed, high but relatively localized intensity, low absorption, particlelike portion of the spectrum, and one at the extremely high speed, very low intensity, extremely low absorption, long-range wave end of the spectrum, separated by a sizable gap of moderate speed, intensity and absorption that proves negligible. Earth’s molecular structure may cancel out everything but the very lowest and highest speeds in matter, so that far ends of the spectrum, particles and very long wavelengths, can interfere if conditions are conducive, and the highly sensitive double-slit experiment with its minuscule lightning bolt of current containing a tiny, relatively isolated wavicle might be such a context.

To conclude, electric charge properties within the double-slit chamber during the emission event have perhaps not been thoroughly examined, but if this factor does play a role in determining the behavior of particles involved, it could have significant ramifications for our comprehension of how naturally occurring phenomena such as brain function operate.


Do you find this framework for understanding quantum processes convincing?

Comments (83)

Gary Enfield March 28, 2021 at 16:44 #515869
In short - no I don't find it convincing. It may be that I missed some point in your very complex post, but the gist seems to again be playing to some of the standard misconceptions.

A lot of the ridiculous theorising (eg. wave - particle duality) is formulated to preserve certain principles over others, when there is no basis for choosing one over another. The whole principle of wave particle duality breaks every other thing that we know about matter/energy. So why are physicists so keen to embrace this nonsense?

To my mind it is there to simply preserve the philosophy that there is only one type of stuff that underpins existence, even when various experiments now show that this is ever-more unlikely.

Yes - it has been well known for some time that some of the permutations of the double slit experiment (eg. quantum eraser experiments), have led to bizarre findings - but they are only bizarre in the context of the assumptions that rule out other considerations.

Why do we have go into such bizarre territory as wave-particle duality when there is an obvious possibility that would explain everything we know in standard ways, instead of contradicting everything we know?

As Finipolscie said, all normal descriptions of 'a wave' occur when an object (eg particle) travels through a pool of other stuff.... like a train through air, or a ship through water. It is the air and the water which produced the wave... not the train or the boat, which never transform into a wave. Yet wave-particle duality is effectively saying that it is the train or boat which miraculously transforms into a wave and back again for no apparent reason - yet with perfect timing and co-ordination. It's nonsense.

But if you follow the logic of undisputed reality - if another hidden pool of stuff/energy is present, and a particle passing through this stuff creates & rides the waves in this hidden pool, then all results from all experiments are easily explained.

Yet scientists won't go there, because they are not prepared to accept the possibility of a 2nd type of stuff underpinning reality. They even prefer the absurdity of wave particle duality rather than admit that simple option!

By refusing to budge from established theory, scientists are falling into the same trap as as religious zealots - denying new evidence to preserve the false gods of the past while trying to smear and destroy those who dare to suggest anything else.

For this reason, it was refreshing to hear from CERN this week, that they may grudgingly have to admit that another previously unknown force may exist in nature. This may fit in with the long term concerns about our inability to detect something that should be everywhere - and in profusion - Dark Energy.

Perhaps now some basic common sense may re-assert itself and some of these observations may start pointing us towards a more simple and believable possibility. There are other basic factors underpinning existence than the official models currently acknowledge.
Metaphysician Undercover March 29, 2021 at 12:29 #516173
Quoting Gary Enfield
For this reason, it was refreshing to hear from CERN this week, that they may grudgingly have to admit that another previously unknown force may exist in nature. This may fit in with the long term concerns about our inability to detect something that should be everywhere - and in profusion - Dark Energy.


So, what's this new information?
Gary Enfield April 03, 2021 at 10:45 #518073
Reply to Metaphysician Undercover

As I said - CERN believes that it has uncovered proof of a new (5th ) force in nature.
I first heard about it on the BBC - but here's another article from a quick search of the web.

https://www.ctvnews.ca/sci-tech/evidence-emerges-of-brand-new-force-of-nature-at-cern-1.5360051

Many of the scientific results that appear to break known scientific principles could easily be explained by missing factors such as a different type of stuff that underpins existence and any associated force which it might exert. Here we have evidence for the existence of the force.
Enrique April 07, 2021 at 00:10 #519629
Quoting Gary Enfield
Here we have evidence for the existence of the force.


May the force be with you lol
Gary Enfield April 07, 2021 at 05:39 #519695
Reply to Enrique
Hi Enrique

May the force be with you too!

I have tried to re-read your initial post, and to some degree, I think you're suggesting that the electrical charge may indeed represent a different type of stuff that generates the interference - the sea or air in the examples I gave.

Am I right about what you're saying? I did find the post quite difficult to follow in terms of emphasis.

However, you have various things to explain. Why wouldn't this lightning mechanism produce the interference pattern when there is only one slit open. How do you get a build up of the interference patterns when single photons or electrons are fired? How would this work in the context of the Quantum Eraser experiments?

The big things that led me to agree with Finipolscie's logic are
1 - the width of the interference pattern - which goes well beyond the width of the two slits (when open).
2 - that wave particle duality requires the particle collapse to perfectly occur in one place, not many, to match the results of the single particle firings.
Enrique April 08, 2021 at 13:16 #520153
Reply to Gary Enfield

The idea is that electric charge permeates the entire double-slit chamber when all slits are open, but only for fractions of a second, due to activation of the emission apparatus. The shape of charge distribution depends on the position of the slits, which mediate the interaction between the like-charged emitter and absorber surface that have oppositely charged space between them.

The hypothesis is that if the slits are symmetrical, charge-activated absorber sites will be likewise symmetrical and establish a symmetrical statistical distribution looking as if it is an interference pattern, even though each individual emission event is somewhat haphazard, like a lightning bolt. So in the one at a time wavicle experiment, each individual trial seems random and particularized, but hundreds of trials produce an emergent pattern on the absorber screen from the slightly greater chance of a wavicle ending up within a certain range of locations as a result of electromagnetic attraction.

If one of the double slits is closed, the charge distribution and nature of the lightning bolt current must be drastically affected such that a florescent band appears behind the open slit rather than a partial interference fringe. Why exactly I'm not sure, but it could be investigated by experiment if my hypothesis of electric charge influence proves accurate.

The quantum eraser experiment seems to me an examination of measurement effects and proof of entanglement, but doesn't have significance for why the double-slit chamber produces what looks like an interference fringe in the first place, so doesn't apply to the problem we are discussing.

In this model, wave/particle duality is replaced by wavicle-charge-current interactiveness.
ernest meyer April 08, 2021 at 16:15 #520220
Reply to Enrique
Hi ) Physicists certainly enjoy trying to construct unified theories to explain observed phenomena, and there's nothing wrong with doing so in the philosophy of science. But from a metaphysical perspective there really is no requirement that reality should behave in a way that is rationally explicable by any single model, so being Popperian, to me it's quite reasonable to say light behaves like a particle in some cases and like a wave in others. That is to say, trying to construct a particle-theory explanation is unnecessary, and when the required theory reaches a certain level of complexity, counterproductive, but it' still great fun ) It should be mentioned though, the need to define models which for example 'explain light as a particle or a wave because it can't be both' has led to awfully misguided debates on some topics, as for example natural selection as a disproof of the necessity of a Creator. take care.
Enrique April 08, 2021 at 16:38 #520229
Quoting Gary Enfield
I did find the post quite difficult to follow in terms of emphasis.


A medley of multiple posts I had already made at this site, so not organized in a seamless linear argument, and much of the material is very spatial, requiring the reader to spend some effort envisioning the image I have in mind, so I'm not that surprised. To really get it I think the reader has to pause at points and give the thought experimentation some deep contemplating. I've also been known to make minor errors on occasion, hopefully that's not what threw you.
Enrique April 08, 2021 at 16:50 #520235
Quoting ernest meyer
It should be mentioned though, the need to define models which for example 'explain light as a particle or a wave because it can't be both' has led to awfully misguided debates


I would say that light isn't either a particle or a wave, but a wavicle which adopts the form of a true wave when traveling through many mediums and is more locally a tangle of distinct energy packets. So wave/particle duality depends on the context and is not the essence. But I think we can get close to the essence with theory in this case.
PoeticUniverse April 08, 2021 at 19:13 #520313
Quoting Enrique
I would say that light isn't either a particle or a wave


'Particles', as temporary excitations of the permanent underlying quantum fields, go through both slits because, well, as hinted, they are field quanta at heart.
fishfry April 08, 2021 at 19:22 #520316
Quoting Metaphysician Undercover
So, what's this new information?


2 + 2 = 4.

In other science news, the muons are misbehaving. It could be a very big deal, indicating a new force of nature. Additional confirmation is required.

https://www.nytimes.com/2021/04/07/science/particle-physics-muon-fermilab-brookhaven.html
Enrique April 08, 2021 at 20:47 #520346
Quoting PoeticUniverse
'Particles', as temporary excitations of the permanent underlying quantum fields, go through both slits because, well, as hinted, they are field quanta at heart.


Your mission if you choose to accept it: explain skipping a stone to me as temporary excitations of the permanent underlying quantum fields.
James Riley April 08, 2021 at 20:57 #520352
Quoting Enrique
A medley of multiple posts I had already made at this site, so not organized in a seamless linear argument, and much of the material is very spatial, requiring the reader to spend some effort envisioning the image I have in mind, so I'm not that surprised. To really get it I think the reader has to pause at points and give the thought experimentation some deep contemplating.


I've been following this thread, but I confess I do appreciate the dumbing-down and the visuals associated with what one wag on this forum called "pop physics." I assume he was referring to "Science" or "Nature" or Neil, or Carl, or Steven, et al. But I do appreciate the challenge of trying to figure our what you are saying based solely on the King's English. Carry on.
PoeticUniverse April 09, 2021 at 00:43 #520447
Quoting Enrique
Your mission if you choose to accept it: explain skipping a stone to me as temporary excitations of the permanent underlying quantum fields.


Particles can be long-lasting as excitations due to their unit strength/charge as energy quanta…and from there we know the rest of the story.
Enrique April 09, 2021 at 01:44 #520463
Quoting PoeticUniverse
Particles can be long-lasting as excitations due to their unit strength/charge as energy quanta…and from there we know the rest of the story.


Big crunch or big freeze...oh well, it was a world while it lasted.
Metaphysician Undercover April 09, 2021 at 01:56 #520469
Reply to fishfry
Oh no! The muon is a fiction and now the whole Standard Model is fucked. Oh well, I'm sure the physicists can apply the appropriate mathematical smoke and mirrors to make it all work out just fine.
PoeticUniverse April 09, 2021 at 02:03 #520471
Quoting Enrique
oh well, it was a world while it lasted.


When You and I behind the cloak are past
But the long while the next universe shall last,
Which of one’s approach and departure it grasps
As might the sea’s self heed a pebble cast.

Or a stone skipped across a pond…
fishfry April 09, 2021 at 02:07 #520472
Quoting Metaphysician Undercover
Oh no! The muon is a fiction and now the whole Standard Model is fucked. Oh well, I'm sure the physicists can apply the appropriate mathematical smoke and mirrors to make it all work out just fine.


I understand this remark even less than I do your claim that 2 + 2 and 4 don't represent the same mathematical object. Do you object to the entire process of science? Would you put the earth at the center of the universe in denial of subsequent discoveries? Congratulations, you've outdone yourself.
Metaphysician Undercover April 09, 2021 at 02:35 #520489
Reply to fishfry
Doesn't the evidence of the cosmological background radiation put the earth at the center of the universe?
Gary Enfield April 09, 2021 at 15:25 #520690
Reply to Enrique

Hi Enrique

I think a basic problem with your idea is that the first experiments were conducted with light, and therefore an electric field wouldn't apply. I can't help believing that whatever mechanism applies - it would apply to both mediums equally.

I'm not sure what sort of field 'light beams/photons' could generate, but the idea that I ran with (above) - poached from Finiposcie, was of a wave being generated in a hidden pool of other stuff. The photon or electron particles would therefore ride the troughs of the wave without having to change from particle to wave themselves (which seems a nonsense to me anyway).

If you substitute waves in a field, for waves in a pool of 'other stuff' - there may be some merit in it.

The Quantum Eraser Experiments weren't just about entanglement, although they used paired particles.
They were trying to demonstrate whether the same split particle of light would produce different effects under similar conditions. The patterns achieved were significant in ruling out certain possible explanations.
Enrique April 09, 2021 at 17:38 #520743
Quoting Gary Enfield
I think a basic problem with your idea is that the first experiments were conducted with light, and therefore an electric field wouldn't apply. I can't help believing that whatever mechanism applies - it would apply to both mediums equally.


How are you so sure that an electromagnetic field generated in the double-slit chamber by the electronic emission device wouldn't affect electromagnetic radiation in addition to particles with their electric charges?
fishfry April 09, 2021 at 22:23 #520825
Quoting Metaphysician Undercover
Doesn't the evidence of the cosmological background radiation put the earth at the center of the universe?


You're off on some strange tangent. Someone alluded to a recent discovery in physics. You asked what it was. I gave you a link to a New York Times article on the subject. Your next post was bizarre and off the wall. I know you think you're making a point, but you're not.

However you did ask a very good technical question, namely whether the CMB is a preferred frame of reference, contradicting special relativity. I googled around and found this interesting page. I'm not a physics expert so I can't really comment, but you'll find some good pointers and clues here.

https://physics.stackexchange.com/questions/25928/is-the-cmb-rest-frame-special-where-does-it-come-from

Here is the relevant passage from https://www.astro.ubc.ca/people/scott/faq_basic.html


How come we can tell what motion we have with respect to the CMB?

Doesn't this mean there's an absolute frame of reference?

The theory of special relativity is based on the principle that there are no preferred reference frames. In other words, the whole of Einstein's theory rests on the assumption that physics works the same irrespective of what speed and direction you have. So the fact that there is a frame of reference in which there is no motion through the CMB would appear to violate special relativity!

However, the crucial assumption of Einstein's theory is not that there are no special frames, but that there are no special frames where the laws of physics are different. There clearly is a frame where the CMB is at rest, and so this is, in some sense, the rest frame of the Universe. But for doing any physics experiment, any other frame is as good as this one. So the only difference is that in the CMB rest frame you measure no velocity with respect to the CMB photons, but that does not imply any fundamental difference in the laws of physics.


I am not personally sure of why we appear to be at the center of it, or if an observer in a distant galaxy would also see themselves at the center.
Metaphysician Undercover April 10, 2021 at 11:54 #520984
Quoting fishfry
You're off on some strange tangent. Someone alluded to a recent discovery in physics. You asked what it was. I gave you a link to a New York Times article on the subject. Your next post was bizarre and off the wall. I know you think you're making a point, but you're not.


You asked me "Would you put the earth at the center of the universe in denial of subsequent discoveries?". I only wanted to show you that, "subsequent discoveries" indicate that the evidence points toward the earth being at the center of the universe. So as much as you are having difficulty understanding what I am saying, this is due to the confused nature of your questioning.

We can go back to what I said before that if you want. You referred me to an article which said that the muon doesn't behave as it is supposed to, and this calls into question the validity of the Standard Model. I said, this is no problem because they'll just dream up some mathematical principles to account for these exceptions. That's what they do, it's evident with dark energy, dark matter, etc.. When anomalies appear, instead of questioning the underlying theories which produce the anomalies in application, they dream up some principles which account for them.

Quoting fishfry
I am not personally sure of why we appear to be at the center of it, or if an observer in a distant galaxy would also see themselves at the center.


We appear to be at the center, because this is a map of the expanding universe. If the substratum of the universe, space-time itself, is expanding, then it must expand from every point. The result is that any point becomes the center point, when mapped in this way.

The overall point of my somewhat random replies, is that until we get an understanding of what spatial expansion actually is, there's no point to thinking that any of the models which physicists or cosmologists come up with are correct models.
James Riley April 10, 2021 at 14:46 #521025
Quoting Metaphysician Undercover
We appear to be at the center, because this is a map of the expanding universe. If the substratum of the universe, space-time itself, is expanding, then it must expand from every point. The result is that any point becomes the center point, when mapped in this way.


I alluded to that at some point on this forum. I tried to account for the possibility that I am at the center of this expanding universe while it is itself expanding away from fewer than infinite others, which would then allow for me to not be at the center. I also tried to account for the possibility that I'm not at the center of this expanding universe because different parts are expanding at different rates. That would allow me to not be at the center of this one. But I don't recall anyone schooling me on that. It seems to be the most probable, but then there would have to be a forward and a backward if the different rates had anything to do with deceleration. If some other force is at play to cause the different rates, then I guess I might not be at the center so long as there was an equally spaced, equal number of parts speeding away at their various rates. But it does seem that whenever something doesn't fall in line with the way someone says it should, they just pull something out of their ass to explain it, without proving what that thing is. So, when some troglodyte like me wanders by and says "Hey, maybe dark matter is the past, or dark energy is the future, and time, like energy and matter, can convert too" then has slapped on the back of the head, ignored or laughed at. The wizards like to use numbers and symbols (other than the alphabet put together in words and sentences that dummies like me can read) like a clique to keep others out. I too understand the need for shorthand, and a desire to work on the problem instead of explaining it to the masses, but I also stay in my lab and talk to my peers when I do so, and don't venture into the public, spreading my shit without expecting some questions.
Metaphysician Undercover April 11, 2021 at 02:13 #521264
Quoting James Riley
If some other force is at play to cause the different rates, then I guess I might not be at the center so long as there was an equally spaced, equal number of parts speeding away at their various rates.


I would say the evidence suggests that gravity is the other force which is at play here, causing different rates of expansion. But gravity and expansion might actually just be two aspects of, or two ways that we approach, the very same thing.
James Riley April 11, 2021 at 02:28 #521270
Quoting Metaphysician Undercover
I would say the evidence suggests that gravity is the other force which is at play here, causing different rates of expansion. But gravity and expansion might actually just be two aspects of, or two ways that we approach, the very same thing.


That makes sense to me. It was my understanding though, that space only grow between those aspects of non-space that are so far apart that gravity no longer influences them? I don't know if that is a cluster, or super cluster or what, but space is not increasing the distance between us and the earth, earth from sun, sun from galaxy etc.
fishfry April 11, 2021 at 03:46 #521297
Quoting Metaphysician Undercover
there's no point to thinking that any of the models which physicists or cosmologists come up with are correct models.


Are you under the impression that this is a unique or deep insight? That's the sense I get. That you think everyone else doesn't already know this. Your sneering response to the possible discovery of a new force of nature struck me as childish. Especially in response to my simply giving you an NYT link that answered the question you asked.
Metaphysician Undercover April 11, 2021 at 10:56 #521404
Quoting James Riley
That makes sense to me. It was my understanding though, that space only grow between those aspects of non-space that are so far apart that gravity no longer influences them? I don't know if that is a cluster, or super cluster or what, but space is not increasing the distance between us and the earth, earth from sun, sun from galaxy etc.


Imagine that wherever there are massive objects, spatial expansion is slowed, and the result is what we observe as gravity.

Reply to fishfry
Thanks for the link fishfry, I do appreciate it. If I had a bad attitude at the time, it was probably because you started the post with "2+2=4".
fishfry April 11, 2021 at 19:18 #521558
Quoting Metaphysician Undercover
Thanks for the link fishfry, I do appreciate it. If I had a bad attitude at the time, it was probably because you started the post with "2+2=4".


I confess you're absolutely right. That was a bit of cheap bait.
James Riley April 11, 2021 at 19:54 #521570
Quoting fishfry
That was a bit of cheap bait.


Indeed, but it calls to mind a digression:

The first time I argued with a philosophy professor some 40 years ago, after he taught us to trace all premises back to a point of agreement before moving forward, he posited that very equation of 2+2=4. I asked "Two what plus two what; and what do you mean by 'plus' and what do you mean by 'equal.' After all, two people plus two people could equal five people if one couple had a single child. Likewise two drops of water plus two drops of water could equal one drop of water." He agreed and took a step back to set definitions. That was my first exposure to the "gentlemen's agreement" which subsequently fell apart on the burden of proof. LOL! We had fun but I think there was another kid in the room, looking for a grade, who hated digressions. Carry on.
fishfry April 11, 2021 at 20:35 #521578
Quoting James Riley
The first time I argued with a philosophy professor some 40 years ago, after he taught us to trace all premises back to a point of agreement before moving forward, he posited that very equation of 2+2=4. I asked "Two what plus two what; and what do you mean by 'plus' and what do you mean by 'equal.' After all, two people plus two people could equal five people if one couple had a single child. Likewise two drops of water plus two drops of water could equal one drop of water." He agreed and took a step back to set definitions. That was my first exposure to the "gentlemen's agreement" which subsequently fell apart on the burden of proof. LOL! We had fun but I think there was another kid in the room, looking for a grade, who hated digressions. Carry on.


@Metaphysician Undercover is on record stating that he does not believe that 2 + 2 and 4 denote the same mathematical object. He's wrong but confirmed in his belief. I did at one point present to him a clean proof from the Peano axioms in which I defined "2", "4", "+", and "=", and proved that 2 + 2 = 4. Of course the truth of any symbolic expression depends on the interpretation given to the symbols; but it is NOT in dispute that 2 + 2 and 4, with their standard interpretations, denote the same mathematical object.

It was wrong of me to bait @Meta when he asked a simple factual question regarding this recent possible discovery in physics. But if baiting @Meta is wrong, I don't wanna be right.
James Riley April 11, 2021 at 20:44 #521582
Quoting fishfry
Of course the truth of any symbolic expression depends on the interpretation given to the symbols;


And hence the gentlemen's agreement.

I'm over my head here but some wag once said, if you are the smartest person in the room, find another room. So I left a political conservative echo chamber and came to tread water in yuse guys, including @Meta and you and everyone else. I'll watch you bait, and learn.
Metaphysician Undercover April 12, 2021 at 01:21 #521710
Quoting fishfry
I did at one point present to him a clean proof from the Peano axioms in which I defined "2", "4", "+", and "=", and proved that 2 + 2 = 4.


I never denied that 2+2=4. That would be stupid. What I deny is that "=" indicates is the same as. I think that to believe such a thing would be stupid as well. So your proof that 2+2=4 really does nothing for your claim that "2+2" denotes the same object as "4".
fishfry April 12, 2021 at 04:35 #521738
Quoting Metaphysician Undercover
I never denied that 2+2=4. That would be stupid. What I deny is that "=" indicates is the same as. I think that to believe such a thing would be stupid as well. So your proof that 2+2=4 really does nothing for your claim that "2+2" denotes the same object as "4"


I don't believe I have ever said that you deny 2 + 2 = 4. I am always careful to note that you deny that 2 + 2 and 4 denote the same mathematical object. Can you please point me to an instance where I failed to make that distinction?

Quoting fishfry
Metaphysician Undercover is on record stating that he does not believe that 2 + 2 and 4 denote the same mathematical object.


This is what I said and this is what I always say. Will you agree that I characterized your position fairly and that I did NOT say what you claim I said?
Metaphysician Undercover April 12, 2021 at 11:19 #521829
Quoting fishfry
I don't believe I have ever said that you deny 2 + 2 = 4. I am always careful to note that you deny that 2 + 2 and 4 denote the same mathematical object. Can you please point me to an instance where I failed to make that distinction?


You just said:
"I did at one point present to him a clean proof from the Peano axioms in which I defined "2", "4", "+", and "=", and proved that 2 + 2 = 4."
If you knew that I didn't dispute 2+2=4, then your so-called proof is an intentional strawman.

If your definition of "=" is "denotes the same object as", then you're begging the question with a false premise.
fishfry April 12, 2021 at 20:04 #521989
Quoting Metaphysician Undercover
"I did at one point present to him a clean proof from the Peano axioms in which I defined "2", "4", "+", and "=", and proved that 2 + 2 = 4."
If you knew that I didn't dispute 2+2=4, then your so-called proof is an intentional strawman.


The proof shows that the two expressions denote the same mathematical object. But we're making progress. For three years (has it been that long?) you totally ignored the proof. Now at least you're acknowledging it.
Metaphysician Undercover April 13, 2021 at 02:04 #522101
Quoting fishfry
The proof shows that the two expressions denote the same mathematical object. But we're making progress. For three years (has it been that long?) you totally ignored the proof. Now at least you're acknowledging it.


I didn't ignore the proof, I showed you how it was not a proof of what you claimed it was. But we could go through it again if you want.
fishfry April 13, 2021 at 02:13 #522106
Quoting Metaphysician Undercover
I didn't ignore the proof, I showed you how it was not a proof of what you claimed it was. But we could go through it again if you want.


It took you three years to even acknowledge its existence. I don't wish to go through it again.
Metaphysician Undercover April 13, 2021 at 10:46 #522293
Reply to fishfry
I've just been ignoring those claims because you ignored my reply to your proof.. And you continue to ignore this. If I remember correctly, your proposed proof violated the law of identity, and you refused to acknowledge this. And that violation of the law of identity was what I was already discussing in the first place, so your proposed proof was completely irrelevant because it did nothing to mitigate this violation..
fishfry April 13, 2021 at 18:17 #522428
Quoting Metaphysician Undercover
I've just been ignoring those claims because you ignored my reply to your proof.. And you continue to ignore this. If I remember correctly, your proposed proof violated the law of identity, and you refused to acknowledge this. And that violation of the law of identity was what I was already discussing in the first place, so your proposed proof was completely irrelevant because it did nothing to mitigate this violation..


You never even bothered to acknowledge my proof. I asked you repeatedly to criticize it or disagree with it and you just ignored those posts too. And now you're making claims contrary to facts. Your recent objections to the proof are three years after the fact. This is a silly conversation. I'm not playing anymore.
Metaphysician Undercover April 14, 2021 at 01:17 #522593
Quoting fishfry
You never even bothered to acknowledge my proof. I asked you repeatedly to criticize it or disagree with it and you just ignored those posts too. And now you're making claims contrary to facts. Your recent objections to the proof are three years after the fact. This is a silly conversation. I'm not playing anymore.


I really don't remember the specifics of your so-called proof. I remember that you produced something you called a proof, and it was very easy for me to show that it did not prove what you intended it to prove, through reference to the law of identity. So I demonstrated this and moved along. You did not seem to have a firm grasp of the law of identity at the time, so you did not seem to understand how your supposed proof failed. Then you kept referring back to this supposed "proof", as if it really proved what it didn't.

If you really think that you have a proof that "2+2" denotes the same mathematical object as "4", when "same" is held to the rigorous definition of the law of identity, then produce it again, and I'll show you how it fails, again. Maybe this time you'll pay respect to the law of identity.
fishfry April 14, 2021 at 02:57 #522617
Quoting Metaphysician Undercover
I really don't remember the specifics of your so-called proof. I remember that you produced something you called a proof, and it was very easy for me to show that it did not prove what you intended it to prove, through reference to the law of identity. So I demonstrated this and moved along. You did not seem to have a firm grasp of the law of identity at the time, so you did not seem to understand how your supposed proof failed. Then you kept referring back to this supposed "proof", as if it really proved what it didn't.


You pointedly ignored it for three years. It's a basic proof that 2 + 2 = 4 from the Peano axioms. I had a perfectly good grasp of the law of identity at the time and still do. You didn't move along. You kept engaging with my posts but refused to acknowledge the proof I showed you.

Quoting Metaphysician Undercover

If you really think that you have a proof that "2+2" denotes the same mathematical object as "4", when "same" is held to the rigorous definition of the law of identity, then produce it again,


It would be pointless. It's a basic proof from PA that 2 + 2 = 4. At the time you indicated a terror of symbolic reasoning. Perhaps you've gotten over it.

Quoting Metaphysician Undercover

and I'll show you how it fails, again. Maybe this time you'll pay respect to the law of identity.


Our previous conversation is still up. If you cared, you could go back and check it out. And if you did, and you happened to find a post of yours that directly addressed the proof I gave, I would apologize for falsely claiming you didn't. That should be sufficient motivation. I see no need to type it in again. You are on record that 2 + 2 and 4 do not represent the same mathematical object. You are absolutely wrong about that. There's no need to rehash the conversation and no inclination on my part to do so.
jgill April 14, 2021 at 03:28 #522622
Bill Clinton clarified the Law of Identity in his unique way: "It depends on what the meaning of the word ‘is’ is. If the—if he—if ‘is’ means is and never has been, that is not—that is one thing. If it means there is none, that was a completely true statement. … Now, if someone had asked me on that day, are you having any kind of sexual relations with Ms. Lewinsky, that is, asked me a question in the present tense, I would have said no. And it would have been completely true."

That should put an end to the discussion.
Metaphysician Undercover April 14, 2021 at 10:41 #522728
Quoting fishfry
It's a basic proof that 2 + 2 = 4 from the Peano axioms.


You know I do not dispute the fact that 2+2=4. That's why I'm fulling justified in ignoring your strawman proof.

fishfry April 14, 2021 at 17:39 #522817
Quoting Metaphysician Undercover
You know I do not dispute the fact that 2+2=4. That's why I'm fulling justified in ignoring your strawman proof.


For the record: You do deny that 2 + 2 and 4 represent the same mathematical object. Is that correct?

Why are you going on about this? We've had this pointless conversation, it was over long ago. After I gave up talking to you about it, many others have taken their shot and given up. For whatever reason, my recent offhand 2 + 2 = 4 remark seems to have triggered you. I don't know why. Do you?
Metaphysician Undercover April 14, 2021 at 22:50 #522961
Quoting fishfry
Why are you going on about this?


Me? I was happy to participate in this thread, and proceed in many other discussions with you, without ever mentioning this small disagreement we have. We probably agree on many other things. But it seems you have some need to keep bringing it up.

Quoting fishfry
Metaphysician Undercover is on record stating that he does not believe that 2 + 2 and 4 denote the same mathematical object. He's wrong but confirmed in his belief. I did at one point present to him a clean proof from the Peano axioms in which I defined "2", "4", "+", and "=", and proved that 2 + 2 = 4. Of course the truth of any symbolic expression depends on the interpretation given to the symbols; but it is NOT in dispute that 2 + 2 and 4, with their standard interpretations, denote the same mathematical object.


See, it's you who brought up the past. Obviously, for you it's not yet over. But that doesn't surprise me.
fishfry April 14, 2021 at 23:17 #522975
Quoting Metaphysician Undercover
See, it's you who brought up the past. Obviously, for you it's not yet over. But that doesn't surprise me.


You made a claim that you did acknowledge my proof three years ago. If that were true you could produce your post doing so. But you can't because you didn't.

I agree it was a cheap shot to bait you with 2 + 2 = 4. I'd say it was beneath me but of course it's not :-) I was surprised at your reaction since we already know where we both stand on the matter. It was not intended to provoke such a strong reaction and if I'd known it would I'd have skipped it.
Metaphysician Undercover April 15, 2021 at 02:07 #523032
Reply to fishfry
As you yourself have repeatedly stated, in this thread, your proof is that 2+2=4. And, you've also stated that you recognize that I do not dispute the fact that 2+2=4.

So, I am acknowledging that your proof is irrelevant, as I've done before.

Why do you keep bringing up, and referring to, an irrelevant proof, as if it is something which is relevant to our disagreement?
fishfry April 15, 2021 at 02:08 #523033
Quoting Metaphysician Undercover
Why do you keep bringing up, and referring to, an irrelevant proof, as if it is something which is relevant to our disagreement?


Enough.
j0e April 15, 2021 at 07:25 #523085
Quoting James Riley
I'm over my head here but some wag once said, if you are the smartest person in the room, find another room.


:point: :up: :clap:
fishfry April 18, 2021 at 12:37 #524324
Quoting Metaphysician Undercover
As you yourself have repeatedly stated, in this thread, your proof is that 2+2=4. And, you've also stated that you recognize that I do not dispute the fact that 2+2=4.


I was listening to a podcast on Frege, and the speaker mentioned his insight into sense and reference.

She (Patricia Blanchette) said that Frege noted that 2 + 2 and 4 refer to the same thing; but they have a different sense. 2 + 2 = 4 tells us something about 4 that merely saying 4 = 4 does not.

I believe this is the point you have been making, and in fact I might almost agree with you about this

However as I understand it, you are on record as saying that 2 +2 and 4 do not REFER to the same thing. And in this, you are wrong. You're wrong mathematically, and you're wrong according to Frege.

Is it possible for you to clarify your thinking here? Are you saying that 2 + 2 and 4 don't refer to the same thing, in which case you're wrong; or rather that 2 + 2 and 4 tell you different things about 4, in which case Frege would say you're right, and I myself am still on the fence.

Frege published this work in 1882 and Peano's axioms date from 1889. In terms of Peano arithmetic, 4 is just another name for 2 + 2 once we break everything down to the successor function. Which is why I don't even think they have a different sense. But if we drop the Peano formalism, I can indeed see that 2 + 2 = 4 gives more information about 4 than 4 = 4 does. So I can go both ways on this.

But regardless, 2 + 2 and 4 do REFER to the same object, namely the number that we call 4. So if you are saying they refer differently, you're wrong about that. Can you please clarify your intent?
Metaphysician Undercover April 18, 2021 at 19:56 #524421
Quoting fishfry
However as I understand it, you are on record as saying that 2 +2 and 4 do not REFER to the same thing. And in this, you are wrong. You're wrong mathematically, and you're wrong according to Frege.


Look at what you say above, "2+2" says something about 4. What is 4? It is a quantity, or a value, it is not a thing. Remember, my argument is only applied to a strict definition of "thing", in which a thing has an identity according to the law of identity.

If for example, you assume that green is a thing, you might say yellow and blue make green, so that you might argue that "yellow and blue" refer to the same thing as "green". But this is what I deny. "Yellow and blue", might as you say above, say something about green, but neither "yellow and blue" nor "green" refer to a thing. Green is a property, something we attribute to a thing. Likewise 4 is a property, something we attribute to a group of things.

The intent of the law of identity is to distinguish true things, which have a real identity, from concepts, platonic ideas, which have no true identity and are therefore not things. So it makes no sense to say that "4" refers to a thing, or "an object" in any sense, as 4 has no true identity. It has an infinite number of representations, 2+2, 3+1, etc., and none can be said to be the true representation. If we affirm that 4 is the true representation, then the others must refer to other true objects, represented by 1 and by 2 and by 3.

Quoting fishfry
Is it possible for you to clarify your thinking here? Are you saying that 2 + 2 and 4 don't refer to the same thing, in which case you're wrong; or rather that 2 + 2 and 4 tell you different things about 4, in which case Frege would say you're right, and I myself am still on the fence.


Yes, this is exactly what I am saying, 2+2 does not refer to the same thing as 4 because neither refers to a thing. They refer to properties, which are not things, by the law of identity. So, take my example, "blue and yellow" does not refer to the same thing as "green", because neither refers to a thing. Notice that there can be many green things in the world, just like there are many groups of 4. But through the application of the law of identity we see that "green" itself does not refer to a thing, otherwise all the distinct instances of green would be the very same thing in violation of that law. Likewise "4" does not refer to a thing.

Quoting fishfry
But regardless, 2 + 2 and 4 do REFER to the same object, namely the number that we call 4. So if you are saying they refer differently, you're wrong about that. Can you please clarify your intent?


To make up an imaginary object, a platonic idea, called a number, and say that this is the object referred to by "4" does not resolve the problem, as I've explained to you already. Then, "2" must also refer to such an imagunary object. So, when you write "2+2", you denote the object, the number two twice. By what principle do you say that this object, the number two, when denoted twice actually refers to the number four? That's completely nonsensical, to say that two instances of occurrence of this object which we call the number two, magically becomes the object called the number four. You must respect the object actually referred to by "2", just like if you say that the colours are this type of platonic object you must respect the colours actually referred to by "blue" and "yellow", and not falsely conclude that "green" is being referred to when someone says "blue and yellow".
fishfry April 18, 2021 at 22:09 #524472
Quoting Metaphysician Undercover
Look at what you say above, "2+2" says something about 4. What is 4? It is a quantity, or a value, it is not a thing. Remember, my argument is only applied to a strict definition of "thing", in which a thing has an identity according to the law of identity.


For the first time I understand what you're saying. If you've been explaining this all along and I didn't understand, that's on me. But you haven't been explaining your position this clearly, well now you have. What you say is interesting. Still extremely wrong IMO but at least you have staked out a position that is coherent, and I would say very interesting.

Let me say this back to you. In the past I thought you were saying that 2 + 2 and 4 refer to different things. But what you are saying in fact is that 2 + 2 and 4 don't refer to anything at all. Because they are properties, or attributes. 4 is a property of a string quartet, for example. There is no number 4 by itself as an object. So it's wrong to say that 4 refers to anything at all.

Do I have that right? I disagree but I will put that aside so we can catch up to each other.

Your position: 4 and 2 + 2 are qualities or attributes or properties of things; but they do not refer to a specific thing. 4 is a property of a string quartet. But 4 by itself is a "potential property," if I may call it that, but it's not any particular thing and it does not refer to any particular thing except something that enjoys thinghood, like a string quartet. Have I got this about right?

As I say I will defer my objections to the end and for now content myself with merely understanding you after all this time.

Quoting Metaphysician Undercover

If for example, you assume that green is a thing, you might say yellow and blue make green, so that you might argue that "yellow and blue" refer to the same thing as "green". But this is what I deny. "Yellow and blue", might as you say above, say something about green, but neither "yellow and blue" nor "green" refer to a thing. Green is a property, something we attribute to a thing. Likewise 4 is a property, something we attribute to a group of things.


I don't like the color mixing example because color theory, additive and subtractive, is relevant to painters and physicists but not to philosophers or mathematicians. But I will take your point that green does not refer to anything except the "things" it does refer to, like houses and traffic lights. But there is no color green. There are green houses and green traffic lights but no green by itself. Forget the color mixing, that's not a good analogy IMO.

Quoting Metaphysician Undercover

The intent of the law of identity is to distinguish true things, which have a real identity, from concepts, platonic ideas, which have no true identity and are therefore not things.


Ok! I understand you. The law of identity x = x only applies to "true things," things that are deserving of thinghood; and not properties, which can apply to things, but are not themselves things. A green house is green, but green by itself is not a thing. Therefore green = green is meaningless. Is that your point? I wish you had said this earlier, and I suppose you'll say you did. But I understand you now. Green is not a thing and 4 is not a thing. 4 does not refer to anything at all. It's a property. 4 = 4 is therefore meaningless.

Do you assert that 4 = 4 is meaningless? Can you please explicitly confirm this and don't skip over it?

You assert that 4 = 4 is meaningless because 4 does not refer to a "true thing."

May I ask, who decides what is a true thing. But nevermind, I said I'd defer my objections to later.


Quoting Metaphysician Undercover

So it makes no sense to say that "4" refers to a thing, or "an object" in any sense, as 4 has no true identity. It has an infinite number of representations, 2+2, 3+1, etc., and none can be said to be the true representation. If we affirm that 4 is the true representation, then the others must refer to other true objects, represented by 1 and by 2 and by 3.


I would never say that 4 is the "true representation." All representations are equally NOT the thing they represent. 4, 2 + 2, 3 + 1, 3.999..., and 47 - 43 are all representations of the number (represented by) 4. I'm sorry I can't actually name the thing itself! Tricky, that. But YOU say that none of those representations represent ANYTHING. I bizarre belief but like I say, I'm happy I finally understand what your belief is.

Quoting Metaphysician Undercover

Yes, this is exactly what I am saying, 2+2 does not refer to the same thing as 4 because neither refers to a thing.


I really don't think you've ever been as explicit. I understand your point of view perfectly. 2 + 2 and 4 are properties that can apply to string quartets and, um, gallons of milk that contain 4 quarts of milk. But by themselves, they don't refer to anything ... and that therefor you claim that:

2 + 2 = 4 is MEANINGLESS.

Is that what you say? Please give me a clear yes or no on this. You assert that 2 + 2 = 4 is meaningless because neither expression refers to anything.

Are you SURE this is a position you want to defend?


Quoting Metaphysician Undercover

They refer to properties, which are not things, by the law of identity.


Can you point me to a discussion of the law of identity that explicitly confers thinghood on some symbols and not others? Do you call them symbols? There are "true things" and "false things," by what word do you call things in general? Entities perhaps? An entity can be a true thing or a property? What is your terminology?

Quoting Metaphysician Undercover

So, take my example, "blue and yellow" does not refer to the same thing as "green", because neither refers to a thing.


Color theory isn't a good example but I don't know, maybe it is. It's not resonating with me so I'm skipping over it.

Quoting Metaphysician Undercover

Notice that there can be many green things in the world, just like there are many groups of 4. But through the application of the law of identity we see that "green" itself does not refer to a thing, otherwise all the distinct instances of green would be the very same thing in violation of that law. Likewise "4" does not refer to a thing.


Yes I get that. So green = green is meaningless; and 4 = 4 is meaningless; and 2 + 2 = 4 is meaningless. Is this the proposition you're prepared to go forward defending?

Quoting Metaphysician Undercover

To make up an imaginary object, a platonic idea, called a number, and say that this is the object referred to by "4" does not resolve the problem, as I've explained to you already.


Let's not argue about whether you've explained it before. Let's just say I understand your point. When mathematicians say that 4 and 2 + 2 refer to the abstract thing called the number (that we call) 4, you are disagreeing. You say there IS NO number 4. That the symbol '4' does not refer to anything.

You do know you're kind of out of step with pretty much everyone, right? Not that this is an argument against your idea. You could be right and everyone else wrong. But you do agree that virtually all philosophers and mathematicians believe in abstract numbers as "true things."

Tell me, do you believe that "4 is an even number," or "4 represents an even number," have truth values? If so, what would you say the truth values are?


Quoting Metaphysician Undercover

Then, "2" must also refer to such an imagunary object. So, when you write "2+2", you denote the object, the number two twice. By what principle do you say that this object, the number two, when denoted twice actually refers to the number four?


I could go nominalist and invoke the Peano axioms, or empiricist and note that 2 pebbles and 2 more pebbles is 4 pebbles. But why bother, i'm sure you've thought of this. For now I will defer direct argument with your ideas. I just want to confirm I've got your ideas right.


Quoting Metaphysician Undercover

That's completely nonsensical, to say that two instances of occurrence of this object which we call the number two, magically becomes the object called the number four.


I must say it seems rather commonplace to me. But let's defer that for the moment.

Quoting Metaphysician Undercover

You must respect the object actually referred to by "2", just like if you say that the colours are this type of platonic object you must respect the colours actually referred to by "blue" and "yellow", and not falsely conclude that "green" is being referred to when someone says "blue and yellow".


Ok. I am not going to write anymore in this post. I just want to make sure that I understand your position.

* 2 + 2 = 4 is meaningless because neither 2 + 2 nor 4 refers to anything. You would agree that 2 fish plus 2 fish is 4 fish, but you would NOT go so far as to agree that 2 + 2 = 4.

* 4 = 4 is meaningless because the law of identity only applies to "true things" and not to properties, and 4 is a property and not a "true thing."

* You would NOT agree that 4 represents an even number, because you don't think 4 represents anything at all.

* You do understand that you haven't got much if any agreement in the math or philosophy communities, yes?

* Who is the arbiter of "true thingness?"

Ok very interesting. I eagerly await your comments.

Can you tell me (I've asked this before) where you came up with these ideas? Are they written down somewhere? I've never heard it said that abstract numbers are not "true things" deserving of being equal to themselves. The Wiki page on the law of identity does not mention any distinction between "true things" and properties.
Metaphysician Undercover April 19, 2021 at 02:32 #524522
Quoting fishfry
Let me say this back to you. In the past I thought you were saying that 2 + 2 and 4 refer to different things. But what you are saying in fact is that 2 + 2 and 4 don't refer to anything at all. Because they are properties, or attributes. 4 is a property of a string quartet, for example. There is no number 4 by itself as an object. So it's wrong to say that 4 refers to anything at all.


Right, "2+2=4" has meaning without referring to anything, just like "green is a colour", and "the acceleration of gravity is 9.8 metres per second per second" have meaning without referring to anything. These are generalizations, abstract rules or laws, which have a broad application without referring to any particular thing. But even though they don't refer to any particular thing, they still have meaning.

Quoting fishfry
Ok! I understand you. The law of identity x = x only applies to "true things," things that are deserving of thinghood; and not properties, which can apply to things, but are not themselves things. A green house is green, but green by itself is not a thing. Therefore green = green is meaningless. Is that your point? I wish you had said this earlier, and I suppose you'll say you did. But I understand you now. Green is not a thing and 4 is not a thing. 4 does not refer to anything at all. It's a property. 4 = 4 is therefore meaningless.

Do you assert that 4 = 4 is meaningless? Can you please explicitly confirm this and don't skip over it?

You assert that 4 = 4 is meaningless because 4 does not refer to a "true thing."

May I ask, who decides what is a true thing. But nevermind, I said I'd defer my objections to later.


The law of identity states that a thing is the same as itself. So when it is expressed using = then "=" signifies is the same as. So if the law of identity is expressed as "A=A", then A=A is supposed to signify that an object is the same as itself. I wouldn't say "4=4" is necessarily meaningless though, because "=" in mathematics signifies "has equal value to". Do you recognize the difference between "the same as" and "equivalent to"?

As for your question of who decides what a true thing is, that's what the law of identity is the criteria for. If it has its own identity as unique particular, it is a thing. Of course you do not have to agree with the law of identity, many philosophers have argued against it.

Quoting fishfry
Can you point me to a discussion of the law of identity that explicitly confers thinghood on some symbols and not others? Do you call them symbols? There are "true things" and "false things," by what word do you call things in general? Entities perhaps? An entity can be a true thing or a property? What is your terminology?


The law of identity is not about symbols, it is about things. That's why it is quite difficult to grasp, and also why many argue against it. The intuitive response to "identity" is to think of the name of the thing as the thing's identity. But this is not what the law says, it says that the identity of the thing is the thing itself. This creates a separation between the identity which we assign to the thing, (it's name, description, or whatever we say about it to identify it), and its true identity, which is itself.

You might say then, that to have "thinghood", is to have independent existence, separate from whatever we might say about the thing. This is to have an identity, to be something.

Quoting fishfry
Yes I get that. So green = green is meaningless; and 4 = 4 is meaningless; and 2 + 2 = 4 is meaningless. Is this the proposition you're prepared to go forward defending?


No, this is not what I am saying at all. What I say, is that "=", when used in mathematics, does not mean "the same as", as dictated by the law of identity. So these uses of "=" have meaning, but the meaning is not "the same as", as dictated by the law of identity.

Quoting fishfry
You do know you're kind of out of step with pretty much everyone, right? Not that this is an argument against your idea. You could be right and everyone else wrong. But you do agree that virtually all philosophers and mathematicians believe in abstract numbers as "true things."


I don't agree with this. Many philosophers argue against platonic realism. Saying that "4" refers to an object which is a number is nothing other than platonic realism.

Quoting fishfry
Tell me, do you believe that "4 is an even number," or "4 represents an even number," have truth values? If so, what would you say the truth values are?


No, philosophically I believe in a correspondence type of truth, so strictly speaking these statements are valid within a logical system, but it doesn't make sense to talk about truth here. I might in common speaking, say that such things are true, but I would be using "true" in a less rigorous way.

Quoting fishfry
* 2 + 2 = 4 is meaningless because neither 2 + 2 nor 4 refers to anything.


No, "=" as it is used in mathematics means to have the same value. It does not mean "the same as" as dictated by the law of identity. This has always been the heart of our disagreement. So "2+2=4" has meaning, it just does not mean that "2+2" refers to the same thing as "4", it means that they have equal value.

Quoting fishfry
* 4 = 4 is meaningless because the law of identity only applies to "true things" and not to properties, and 4 is a property and not a "true thing."

* You would NOT agree that 4 represents an even number, because you don't think 4 represents anything at all.

* You do understand that you haven't got much if any agreement in the math or philosophy communities, yes?

* Who is the arbiter of "true thingness?"

Ok very interesting. I eagerly await your comments.


These I think I've already addressed.

Quoting fishfry
Can you tell me (I've asked this before) where you came up with these ideas? Are they written down somewhere? I've never heard it said that abstract numbers are not "true things" deserving of being equal to themselves. The Wiki page on the law of identity does not mention any distinction between "true things" and properties.


I've studied philosophy for many years. Have you not heard of platonic realism, and that some philosophers are opposed to it?
fishfry April 21, 2021 at 07:36 #525278
Quoting Metaphysician Undercover
Right, "2+2=4" has meaning without referring to anything, just like "green is a colour", and "the acceleration of gravity is 9.8 metres per second per second" have meaning without referring to anything.


I have a quibble about that. You say 2 + 2 = 4 has meaning even though you assert that neither 2 + 2 nor 4 refer to anything. And you've said that green doesn't refer to anything. Questions so that I can better understand:

* Does 2 + 2 = green have meaning? If no, then why does 2 + 2 = 4 have meaning? None of 2 + 2, 4, and green refer to anything by themselves. So why can we combine 2 + 2 and 4 on either side of an equal sign, but not 2 +2 and green?

* Does 2 + 2 = 5 have meaning? What does it mean? If none of 2 + 2, 4, or 5 have meaning; then how can you distinguish 2 + 2 = 4 from 2 + 2 = 5?

Quoting Metaphysician Undercover

These are generalizations, abstract rules or laws, which have a broad application without referring to any particular thing. But even though they don't refer to any particular thing, they still have meaning.


If they don't refer to anything, how do you know they have meaning and what that meaning is? Does dfslkjf have meaning? Does it refer to anything? What gives 2 + 2 meaning; and what exactly does it mean, if it doesn't refer to anything?


Quoting Metaphysician Undercover

The law of identity states that a thing is the same as itself.


Yes. And you assert that it only applies to "things." So that Joe Biden = Joe Biden is an instance of the law of identity; but 4 = 4 is not.

And I asked you, how do we determine thinghood?


Quoting Metaphysician Undercover

So when it is expressed using = then "=" signifies is the same as. So if the law of identity is expressed as "A=A", then A=A is supposed to signify that an object is the same as itself. I wouldn't say "4=4" is necessarily meaningless though, because "=" in mathematics signifies "has equal value to".


Well now you have introduced a brand new term, "value." What does it mean? If 4 does not refer to anything, how do I know what it's value is? If fglfdkjgldj does not refer to anything, how can I determine what its value is?

Quoting Metaphysician Undercover
Do you recognize the difference between "the same as" and "equivalent to"?


Of course. I wonder if you do. Equality is a special case of equivalence. But there are equivalences that aren't equalities. For example 4 = 4 is an equality. [math]4 \equiv 6 \pmod 2[/math] is an equivalence that is not an equality. Is that what you mean? That's the mathematical sense of the word but perhaps you have something else in mind.

In general, two things are equivalent when they live in the same equivalence class of some equivalence relation. For example if we say two people are equivalent if they live in the same state, then the equivalence classes are the states, and I am equivalent to Gavin Newsom. That's equivalence.

Equality is a special case of equivalence in which each equivalence class contains exactly one element.

I fail to see how equivalence has anything to do with what we're talking about, though.



Quoting Metaphysician Undercover

As for your question of who decides what a true thing is, that's what the law of identity is the criteria for. If it has its own identity as unique particular, it is a thing.


Isn't that circular? The law of identity only applies to things. And how do we know if an entity (if I may use that word to mean something that might or might not have thinghood) has thinghood? It does if the law of identity applies to it. That's circular!

Given an entity, like Joe Biden or 4, how do I know that the former has thinghood, so that Joe Biden = Joe Biden is an instance of the law of identity; and 4 DOESN'T have thinghood, and 4 = 4 is NOT an instance of the law of identity?

Yet in the latter case you assert that although 4 = 4 is not an instance of the law of identity, it does nevertheless have meaning. And what is its meaning, exactly? Does 4 = 5 have meaning? If so, what is its meaning?

@Meta you are tying yourself into knots trying to make sense of your claim that 4 does not refer to anything.


Quoting Metaphysician Undercover

Of course you do not have to agree with the law of identity, many philosophers have argued against it.


I'm not disagreeing with the law of identity, you are. You claim that 4 = 4 is not an instance of the law of identity. That is a radical claim that requires much more evidentiary support than you've so far provided.

And you THEN claim that even though 4 = 4 is not an instance of the law of identity, it nevertheless has "meaning," by virtue of the "value" of 4. But you haven't defined these terms and clearly seem to be using them in a nonstandard way. If 4 has a value but doesn't refer to anything, you have some 'splainin' to do.

Quoting Metaphysician Undercover

The law of identity is not about symbols, it is about things. That's why it is quite difficult to grasp, and also why many argue against it.


But I'm not arguing against it. I'm asking you to give me a coherent account of your idea that 4 = 4 is not an instance of the law of identity, yet 4 = 4 has "meaning" by virtue of the "value" of 4. If 4 doesn't refer to anything, how can it have a value?

By the way philosophers of mathematics have long settled on perfectly sensible answers to this question. We can define 4 as the class of all sets of cardinality 4 (which was the original definition, but suffers from the drawback that this class is not a set); or we can use the modern definition, which isthat we choose a canonical representative of 4-ness, namely 4 = {0, 1, 2, 3}. This was von Neumann's clever idea..

Quoting Metaphysician Undercover

The intuitive response to "identity" is to think of the name of the thing as the thing's identity.


I am not making that error, this is a strawman argument.

Quoting Metaphysician Undercover

But this is not what the law says, it says that the identity of the thing is the thing itself. This creates a separation between the identity which we assign to the thing, (it's name, description, or whatever we say about it to identify it), and its true identity, which is itself.


More strawmen. You claim that 4 = 4 is not an instance of the law of identity; yet it has "meaning" by virtue of the "value" of 4. I am asking for a coherent account of that claim.

Quoting Metaphysician Undercover

You might say then, that to have "thinghood", is to have independent existence, separate from whatever we might say about the thing. This is to have an identity, to be something.


How do I know that Joe Biden has thinghood and that 4, 2 + 2, and green, don't?

And if 4, 2 + 2, and green don't have thinghood, how can you claim that 2 + 2 = 4 has "meaning," but 2 + 2 = green doesn't?

Quoting Metaphysician Undercover

No, this is not what I am saying at all. What I say, is that "=", when used in mathematics, does not mean "the same as", as dictated by the law of identity.


You're just flat out wrong about that. In math, = means "the same as" as dictated by the law of identity. As I've been telling you for three years.

But the problem is that having denied that, you can't give a coherent account of "meaning" and "value" by which 2+ 2 = 4 has meaning and 2 + 2 = green doesn't.

So it's not that you're not allowed the opposite opinion. It's that your account of the opposite opinion is not coherent. I'm not just disagreeing with your position. I'm asking you to make sense of it.

Quoting Metaphysician Undercover

So these uses of "=" have meaning, but the meaning is not "the same as", as dictated by the law of identity.


As I say. Give me an account of your idea so that I too may see why 2 + 2 = 4 has meaning but 2 + 2= green does not, even though none of the terms have thinghood and neither equality (according to you) is an instance of the law of identity.


Quoting Metaphysician Undercover

I don't agree with this. Many philosophers argue against platonic realism. Saying that "4" refers to an object which is a number is nothing other than platonic realism.


I'd be willing to accept that 4 doesn't refer to anything, since my claim is that it refers to the "abstract number 4" which has much less claim on thinghood than a rock or Joe Biden. Mathematicians get around that problem either by defining 4 to be the proper class of all sets of cardinality 4; or else they choose a canonical representative of that class, {0, 1, 2, 3}, to stand in for the number 4. Although as Benacerraf points out, 4 "can not possibly be" {0,1,2,3} and of course he is right about that.

So I'm willing, for sake of discussion, to grant you that 4 has a rather tenuous grasp on thinghood.

But then 4 = 4 is not an instance of the law of identity, yet you say it has MEANING by virtue of the VALUE of 4. That's where your thesis is in need of support.

It's easier to just take 4 as {0,1,2,3} so that we can have a sensible theory by which 4 = 4 IS an instance of the law of identity. That's what I do and that's what most philosophers of math do.

What you have done is propose an alternative but you are stuck on "value" and "meaning." If you can explain these, please do.




No, philosophically I believe in a correspondence type of truth, so strictly speaking these statements are valid within a logical system, but it doesn't make sense to talk about truth here. [/quote]

This was in response to my question of whether you think "4 is an even number" is true. I agree that if one is a strict formalist then it's not a true fact about the world. But that's an argument against strict formalism, and not an actual stance one should take if one wishes to be sensible.

Quoting Metaphysician Undercover

I might in common speaking, say that such things are true, but I would be using "true" in a less rigorous way.


As I say, I take this as an argument against formalism, and not as a sensible position to take. Even on my formalist days I am stuck on "5 is prime." That seems to be a true fact of the world no matter how we fight against Platonism.

Quoting Metaphysician Undercover

No, "=" as it is used in mathematics means to have the same value. It does not mean "the same as" as dictated by the law of identity.


As I've noted, you're wrong about that. But if you're not, then you need to give a coherent account of "meaning" and "value."


Quoting Metaphysician Undercover

This has always been the heart of our disagreement. So "2+2=4" has meaning, it just does not mean that "2+2" refers to the same thing as "4", it means that they have equal value.


Once you explain to me what meaning and value are, I'll be in better position to understand your viewpoint. If 4 and 2 + 2 don't refer to anything, how can they have meaning or value? And how can I know that 4 has meaning and value but dflsklsjlslds doesn't?

Quoting Metaphysician Undercover

* 4 = 4 is meaningless because the law of identity only applies to "true things" and not to properties, and 4 is a property and not a "true thing."


You've been saying it has meaning, even though it's not an instance of the law of identity because 4 lacks thinghood. Now you say 4 = 4 is meaningless.

In fact in your very first sentence of the post I'm replying to you said: "Right, "2+2=4" has meaning without referring to anything, ..."

And now yuou say 4 = 4 is MEANINGLESS. Can you see that you contradicted your own position? And how could you not? You are claiming that 4 doesn't refer to anything, and that 4 = 4 is therefore not an instance of the law of identity, and now you are hard pressed to give an account of 4 = 4. You say it has meaning and then you say it's meaningless. And then you wave your hands and say that I don't understand the law of identity, as if that would make your position coherent.

Quoting Metaphysician Undercover

These I think I've already addressed.


Not to my satisfaction. But I'll settle for a coherent account of 4 = 4. Does it have meaning? Does 4 have value? Does kfkdfjkdjdkd have meaning or value?

Quoting Metaphysician Undercover

I've studied philosophy for many years. Have you not heard of platonic realism, and that some philosophers are opposed to it?


I take your point, but even a Platonist has to come to terms with the truth of "5 is prime" and "4 is even." And "4 = 4".

Gary Enfield April 21, 2021 at 09:23 #525293
Reply to Enrique

Hi Enrique

Sorry - I missed your post on 9th April, due to all the other comments.

The reason why I don't think that an electromagnetic field generated by the equipment would explain the effect is because the original experiment conducted by Thomas Young in the early 1800s used candles, not lasers.
Metaphysician Undercover April 21, 2021 at 12:03 #525321
Quoting fishfry
Does 2 + 2 = green have meaning?


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

Quoting fishfry
If they don't refer to anything, how do you know they have meaning and what that meaning is?


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.

Quoting fishfry
Yes. And you assert that it only applies to "things." So that Joe Biden = Joe Biden is an instance of the law of identity; but 4 = 4 is not.


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.

Quoting fishfry
Well now you have introduced a brand new term, "value." What does it mean? If 4 does not refer to anything, how do I know what it's value is? If fglfdkjgldj does not refer to anything, how can I determine what its value is?


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 .

Quoting fishfry
Isn't that circular? The law of identity only applies to things. And how do we know if an entity (if I may use that word to mean something that might or might not have thinghood) has thinghood? It does if the law of identity applies to it. That's circular!


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.

Quoting fishfry
But I'm not arguing against it. I'm asking you to give me a coherent account of your idea that 4 = 4 is not an instance of the law of identity, yet 4 = 4 has "meaning" by virtue of the "value" of 4. If 4 doesn't refer to anything, how can it have a value?


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.

Quoting fishfry
You're just flat out wrong about that. In math, = means "the same as" as dictated by the law of identity. As I've been telling you for three years.


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

[quote=Wikipedia: equals sign]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.[/quote]

Notice the mention of "the same value".

Quoting fishfry
But then 4 = 4 is not an instance of the law of identity, yet you say it has MEANING by virtue of the VALUE of 4. That's where your thesis is in need of support.


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.

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

Enrique April 21, 2021 at 18:23 #525402
Quoting Gary Enfield
The reason why I don't think that an electromagnetic field generated by the equipment would explain the effect is because the original experiment conducted by Thomas Young in the early 1800s used candles, not lasers.


I address this in the OP, might as well quote it for clarification purposes.

Quoting Enrique
It is easy to imagine a stream of wavicles interfering as they diffract through the slits to produce an array of light and dark bands on the florescent screen corresponding to in phase and out of phase waves. This would resemble the classic experiment performed in the 19th century (nonelectronic context), where a beam of light was diffracted by a single aperture to then pass through double slits as a spreading field which apparently interfered with itself and produced a similar result.

Interference patterns from one at a time particle emission (the modern electronic emitter context) are a thornier outcome to account for. The typical explanation is that the wavicle passes through both slits to interfere with itself, spreading out in the double-slit chamber and then spontaneously collapsing in some way upon contact with the absorber surface to give a particulate signature. This “wave function collapse” mechanism is quite the brain teaser: does the wavicle spread out invisibly in the chamber as it diffracts and then somewhat mystically end up at a very localized endpoint? Why would many localized end points with no likeness to waves at all look like in phase and out of phase waves as they accumulate on the absorber screen? What exactly is going on?


A single wavicle experiment has never been performed nonelectronically.
Razorback kitten April 21, 2021 at 20:27 #525428
I believe the wave spreads out and where it converges and crosses the sensor, a single atom is excited, the wave carries on but some energy has exchanged. Wave with no collapse. Its just my idea, probably wrong but solves the riddle. If you can believe a wave of light can lose some part of its energy but carry on anyway.
Gary Enfield April 22, 2021 at 00:20 #525505
Reply to Enrique
Hi Enrique

True - single particle experiments can only be done with modern equipment, but I don't see why there is a need to imagine a different mechanism at work. All we are trying to do is find out about the original effect and why it is occurring. Unless you can show a reason why a different mechanism might be kicking-in, there is no reason to suppose that it's a different factor.

There may be different factors in some of the strange effects recorded in certain experiments - eg. the disappearance of the interference pattern when monitoring equipment was put near the slots, but that is not what you seemed to be discussing here.

Again - 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?
Enrique April 22, 2021 at 01:24 #525535
Quoting Gary Enfield
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?


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.
Gary Enfield April 22, 2021 at 13:19 #525674
Reply to Enrique

Hi Enrique

Quoting 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.


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.

MondoR April 22, 2021 at 13:49 #525681
Quoting Gary Enfield
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?


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.
Enrique April 22, 2021 at 14:56 #525692
Quoting Gary Enfield
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?


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.
jgill April 22, 2021 at 23:41 #525922
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:
Enrique April 23, 2021 at 05:36 #526031
Quoting jgill
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.


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
Gary Enfield April 27, 2021 at 08:42 #528199
Reply to jgill

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


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.
Gary Enfield April 27, 2021 at 08:56 #528208
Reply to MondoR Reply to Enrique

Hi MondoR & Enrique

Quoting 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.


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.

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


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.
Enrique April 27, 2021 at 11:06 #528237
Quoting Gary Enfield
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.


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.
Adolf Festejo April 27, 2021 at 11:33 #528248
I don't know but you might like watching this video. :)

https://shrinke.me/Philosophy
MondoR April 27, 2021 at 12:54 #528278
Quoting Gary Enfield
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.


It avoids the issues associated with dualism, i.e. how do they interact?
Gary Enfield April 29, 2021 at 05:04 #529071
Reply to Enrique

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


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?

Quoting Enrique
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.


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

Metaphysician Undercover April 29, 2021 at 10:42 #529152
Quoting Enrique
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.


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.
spirit-salamander April 29, 2021 at 12:09 #529171
Quoting Metaphysician Undercover
The existence of waves necessitates the conclusion that there is a substance (commonly referred to as the ether) within which the waves are active.


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
Metaphysician Undercover April 29, 2021 at 12:23 #529179
Quoting spirit-salamander
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.


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.
spirit-salamander April 29, 2021 at 12:44 #529187
Quoting Metaphysician Undercover
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.


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."

spirit-salamander April 29, 2021 at 13:06 #529195
Quoting Enrique
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.


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)
Enrique April 30, 2021 at 19:48 #529699
Quoting spirit-salamander
"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)


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.
fishfry May 01, 2021 at 01:32 #529862
Quoting Metaphysician Undercover

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

[/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.


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


What does it mean?

Quoting Metaphysician Undercover

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.


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?

Quoting Metaphysician Undercover

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.


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.

Quoting Metaphysician Undercover

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 .


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.

Quoting Metaphysician Undercover

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.


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

Quoting Metaphysician Undercover

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.


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.


Quoting Metaphysician Undercover

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


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

Quoting Metaphysician Undercover

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.

[quote="Metaphysician Undercover;525321"]
Notice the mention of "the same value".


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.

Quoting Metaphysician Undercover

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


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.

Quoting Metaphysician Undercover

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.


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

Quoting Metaphysician Undercover

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


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?


Metaphysician Undercover May 02, 2021 at 03:10 #530332
Quoting fishfry
What does it mean?


"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.

Quoting fishfry
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.


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?

Quoting fishfry
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?


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.

Quoting fishfry
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.


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:

Quoting Metaphysician Undercover
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.


Quoting fishfry
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?


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.

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


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.

Quoting fishfry
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.


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".

Quoting fishfry
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.


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

Quoting fishfry
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?


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.

Quoting fishfry
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.


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.

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


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.



fishfry May 02, 2021 at 04:02 #530345
Quoting Metaphysician Undercover

See how easy it is? Grade school stuff.


You'd be the expert on that.
Metaphysician Undercover May 02, 2021 at 11:51 #530429
Reply to fishfry
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.
fishfry May 02, 2021 at 20:04 #530637
Quoting Metaphysician Undercover
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.


LOL. Thanks for the chuckle.