Ladyman and Ross: Every Individual Must Go? (5)

[This piece is an account of parts of James Ladyman and Don Ross's book, Every Thing Must Go: Metaphysics Naturalized.]

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Two simple things pose a problem for anyone wanting to embrace ontic structural realism: 1) The various two-slit experiments. 2) Problems with terminology.

Firstly, let's discuss the well-known two-slit experiments.

1

The Firing of Single Particles

How can we acknowledge the two-slit experiments without also acknowledging the nature and existence of single particles – or single things?

A photon (for example) is a single quantum of light. In fact it's referred to as a "light quantum" or as a “light particle”. It's also the case that single particles have been fired (in double-slit experiments) at relatively long intervals between each firing!

In terms of detail, let's forget here when particles-in-the-plural have been fired (e.g., by J.J. Thomson, Ernest Rutherford, Ernest Walton, etc.) and concentrate on the firing of single particles.

Take Pier Giorgio Merli, Giulio Pozzi and Gianfranco Missiroli who did so in the 1970s in order to demonstrate what's called “interference”. And, in 1989, Akira Tonomura and his colleagues also fired electrons one at a time at the Hitachi research laboratories. Then Herman Batelaan and his team did the same thing and the results were published in 2013.

(Alain Aspect's well-known experiment is actually said to have used many pairs of photons to demonstrate “spooky action at a distance” or “entanglement”.)

However, were single particles really fired in these experiments?

It's worth noting here that even atoms don't have rigid boundaries (or really any boundaries at all ). This is even more the case with particles. Thus these facts must surely raise particular questions as to how single particles can be fired in experiments. Having said that, this may well only be a technical (rather than scientific or philosophical) question.

Of course something must be fired.

Though is it the case that some individual thing is fired each time? Perhaps, instead, only spatiotemporal chunks (or spatiotemporal slices) of fields are fired. What can't be fired, however, are what philosophers call “individuals”, as we shall now see.

Terminology

All the above is partly a terminological issue.

Take the notions of a thing, an individual and a particle again.

The word “thing” is an everyday word. It can applied to anything (or to any thing). The word “individual” (as used by James Ladyman and other philosophers) is a philosophical technical term. And, finally, the word “particle” is mainly used within a scientific context. (It's true that Isaac Newton's use of of the word “particle” is at odds with many 20th-century uses; though all such uses are still fundamentally scientific.)

Particles (such as electrons) can't be individuals (as most philosophers see individuals) simply because all the particles of a specific kind share all their properties (i.e., spin, mass, charge, etc.). So, semantically, these properties can't be seen as intrinsic or essential because particles don't actually have contingent properties. However, that's unless we bring in the relations which particles have with other things/particles or with fields! And this is where ontic structural realism comes in.

Thus, on a philosophical reading, particles - by definition - can't be individuals. Every particle of a given kind has the same properties – that's if, again, we rule out relational or spatial properties. A single particle, then, isn't like a single human person, who can easily be distinguished from other human persons. Indeed a single human person may well have both essential and contingent properties. (That will depend on one's metaphysical position.)

In addition, what Ladyman, Ross and other philosophers call “identity dependence” and “existence dependence” doesn't seem to automatically rule out an entity being an individual. Or, if it does, we'd still need to know why that's the case. And then there's the added problem of using a philosophical technical term (i.e., “individual”) and then foisting it into discussions of the particles of physics.

This also applies to Ladyman and Ross's term “self-subsistent”. If that term is taken literally, then has any entity in the entire history of the universe ever been self-subsistent? Of course all that will depend on what each philosopher who uses that term actually takes it to mean.

So if a particle can't be an individual, can't it still be a thing?

Finally, the words “particle” and “electron” are scientific terms. That must surely mean that if physicists say that “electrons are particles”, then electrons are particles. Full stop. Thus since the word “particle” is seen by both laypersons and scientists as a technical scientific term, then naturalist philosophers shouldn't encroach on the territory of physicists by questioning their usage.

2

Individuals and Modern Logic

Ladyman and Ross stress the fact that modern logic (from Leibniz onward) has been fixated on “individual objects”. However, it may turn out that it's Ladyman and Ross who're fixated on individual objects.

In modern logic (at its most basic) we have individual objects which are symbolised by variables (such as x and y). Those variables (of objects or things) are the subjects of predication (or seen to be members of sets).

Ladyman and Ross, on the other hand, see “logical constants and variables as being mere placeholders” which are used for practical purposes. In other words, there are no “ontological commitments” to the things/objects the variables symbolise. Instead, the variables and constants are placeholders which plot relations and structures.

So it's fairly clear that quantum mechanics is on the minds of Ladyman and Ross when they cite the limitations of modern logic. However, modern logic wasn't designed to discuss quantum mechanics. Of course it can now be said that (in theory) modern logic must also be applicable to... well, everything. Therefore it must also be applicable to the phenomena of quantum mechanics.

Mathematical Structures and the Physical

What is fundamental?

That's a classic question of western metaphysics and it's been asked for over two thousand years. In both quantum mechanics and ontic structural realism, we're told that fields are fundamental, not particles. More precisely, particles in Quantum Field Theory (QFT) are seen as “excitations” of fields. Thus, to state the obvious, it's particles which are the excitations of fields, not fields which are the excitations of particles.

This makes fields fundamental. Or does it? Perhaps it's a difference which doesn't really make a difference – at least it doesn't to most hands-on physicists. (As the physicist John Polkinghorne once put it: “The average quantum mechanic is no more philosophical than the average motor mechanic.”)

Here again we can question this fixation on what is and what isn't fundamental. In certain respects, physics itself shows us that particles/things aren't fundamental, despite the long history of attempts to find the fundamental entities of the world.

So let's be specific about this. When Ladyman and Ross claim that physics shows us that physical objects aren't spatially located, aren't they only referring to particles? The same is the case when they say that things aren't “self-subsistent” (yet surely macro-objects aren't self-subsistent either); they lack “primitive indentity”; and that they aren't “ontologically fundamental”.

It's troublesome to say that things aren't “self-subsistent”. It's perhaps even more troublesome to claim that relational structures are “ontologically subsistent” and that relations are “primary to things”. At a prima face level, this appears to be a Platonic position not on numbers or mathematics, but on structures and relations. This isn't a surprise if the structures and relations in physics are themselves mathematical.

In addition, Ladyman and Ross say that “things are nonexistent” or that “things are dependent on relational properties for their existence”. Thus can we also argue that structure/relations are nonexistent or that structure/relations are dependent on things for their existence? In concrete terms, a pragmatist or instrumentalist may say that whether or not one stresses fields or particles depends on one's explanatory or experimental purposes.

So not only can we ask Ladyman and Ross how abstract mathematical structures relate to things/objects: we can also ask how they relate to anything physical (or concrete). However, Ladyman and Ross appear to reject these questions outright when they write:

“The ‘world-structure’ just is and exists independently of us and we represent it mathematico-physically via our theories.... the fact that we only know the entities of physics in mathematical terms need not mean that they are actually mathematical entities.”

Here we need to know what's meant (philosophically meant) by the word “represent”. That is, what is the ontological (i.e., not representational) relation between structures and the “entities of physics”?

So it's helpful (if only in a limited sense) that Ladyman and Ross explicitly state that they aren't eliminativists about physical entities when they say that

“the fact that we only know the entities of physics in mathematical terms need not mean that they are actually mathematical entities”.

So how does that admission (if it is an admission) help us? Nothing is said about physical entities. Indeed Ladyman and Ross more or less say (in a Kantian manner) that nothing can be said about physical entities (i.e., other than what's said via the medium of mathematical structures). Perhaps, then, we should bite the bullet and accept this limitation if there's no way around it.

Yet Ladyman and Ross are explicit about their Platonism (or Pythagoreanism). Or, at the very least, their position is Platonic/Pythagorean by default. They write:

“What makes the structure physical and not mathematical? That is a question that we refuse to answer. In our view, there is nothing more to be said about this that doesn't amount to empty words and venture beyond what the PNC allows. The 'world-structure' just is and exists independently of us and we represent it mathematico-physically via our theories.”

So whereas Platonists would be explicit and say it's all mathematics, Ladyman and Ross say that questions about their mathematical structuralism are “question[s] [they] refuse to answer”. Indeed they don't want to indulge in “empty words” in doing so. Ladyman and Ross are quite happy to express their Platonic and (structural) realist position by saying that the

“'world-structure' just is and [it] exists independently of us and we represent it mathematico-physically via our theories”.

Despite all that, the abstract and mathematical scheme of Ladyman and Ross does eventually give way to the physical (on concrete) when they say that the mathematical structures they endorse are “physically realized” and that the predicates they use are (as it were) attached to entities.

Thus this raises the question as to whether or not Ladyman and Ross are only realists about mathematical structures; or whether they're also realists about things - if via the route of mathematical structures. After all,

i) If Ladyman and Ross say that mathematical structures represent “real patterns”,
ii) then surely they can't also be saying saying that mathematical structures represent mathematical structures.

What's more:

i) If mathematical structure x represents a real pattern y,

ii) and this real pattern y represents a physical (or concrete) z,
iii) then mathematical structure x must also represent a physical (or concrete) z.

Structures: Syntax and Semantics

It's of course structures which are meant to save the day when it comes to both scientific realism and the well-known pessimistic meta-induction. That is, structures are real and they're passed on from (some) old scientific theories to (some) new scientific theories. But here too there's a problem.

We can say that it's the mathematical syntax of scientific theories which is passed on - not their semantics. That is, we have a possible (or actual) structural continuity; though that only takes the form of mathematical equations.

However, doesn't syntax (at least in this case) require a semantics? In other words, what is the subject matter of the syntax/mathematical equations? If the subject matter is a Lockean “something-I-know-not-what”, then how can things we can't know be the subject matter of equations (or of anything else for that matter)?

What's more, in physics the same equations can be mapped onto (or they can model) what are taken to be different physical phenomena. This is the inverse of the “underdetermination of theory by evidence”; in which the same evidence/observations (or the same physical phenomena) can give rise to different theories.

So this shows us some disjunctions between abstract mathematical structures and concrete physical phenomena. That is, the same physical phenomenon can be mapped by different mathematical structures; and the same mathematical structure can map different physical phenomena. Perhaps this must mean that there's always a remainder when it comes to any mapping of the concrete/physical by abstract mathematical structures.

In more relevant terms, in Quantum Field Theory, different structures are used to map the same spatiotemporal section of the physical world. Now it can also be added that different structures must surely have different ontologies. However, in practical term or in terms of prediction, it can be said that any different ontologies of a spatiotemporal x are differences which don't really make a difference.

(For those who buy string theory, we have the examples of different theories (such as type 1 and heterotic SO(₃₂)) which are mathematically equivalent. And even in the case of Maxwell's equations for electricity and magnetism, if one interchanges the electric fields for the magnetic fields and vice versa, then the resulting equations are almost identical.)

Conclusion

It would help if Ladyman and Ross explicitly stated that when they talk of “things”, “objects” and “individuals”, what they have in mind are the things, objects and individuals which exist within the domain of quantum mechanics. Indeed once that's acknowledged, the ontic structural realism of Ladyman and Ross is far less radical than it appears at first sight. Having said that, it's also true that Ladyman and Ross do sometimes talk about things, objects and individuals at the “classical” or macro-scale; though they do so far less often. Not only that: what they do say about the “classical world” will require supplementary arguments and data to that which is used to justify their philosophical positions on things, objects and individuals at the quantum-mechanical level.

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Ladyman and Ross on Quantum-Mechanical Particles: Things, Structure and Relations (4)

Things and Structures

The most important aspect of ontic structural realist position can be expressed in the following way:

Relata (i.e., things/objects/particles/etc.) can be eliminated. Then all we will have left is relations.

James Ladyman and Don Ross ground their own philosophy by expressing Bertrand Russell's position in the following manner:

“... many philosophers have followed Russell in arguing that it is incoherent to suppose there could be individuals which don’t possess any intrinsic properties, but whose individuality is conferred by their relations to other individuals.”

Indeed that passage can be rewritten to make it more germane to Ladyman and Ross's own ontic structural realism. Thus:

It is incoherent to suppose there could be individuals (e.g., particles, etc.) which don’t possess any intrinsic properties, but whose individuality is conferred by their relations to other individuals, structures, fields, states, etc.

Thus we can ask the following question:

Does a thing/object gain its identity from its place in a structure or does it have its place in a structure because of its (prior) identity?

Indeed Ladyman and Ross state that Paul Benacerraf believed that

“an object with only a structural character could be identified with any object in the appropriate place in any exemplary structure and could not therefore be an individual”.

In other words, Benacerraf seems to have taken the position cited earlier. Namely, an object/individual has its place in a structure because of its (prior) identity. That is, an object/individual doesn't gain its (entire) identity from its place in a structure.

To elaborate on Benacerraf's position. It can be said that if structure is everything (or, at the least, if an thing/object gains its identity from its place in a structure), then any thing/object can take a place in that structure. Indeed any thing/object can take specific place x in a given structure if the individuality or identity of an object is passed onto it (as it were) by the structure it is a part of.

The problem with this (or perhaps any) form of structuralism, however, is summed up by Ladyman and Ross who state that “individuals are nothing over and above the nexus of relations in which they stand”. However, they do preface that by saying that this position – only? - applies to “individuals in the context of quantum mechanics”.

Ladyman and Ross continue by saying that “the identity or difference of places in a structure is not to be accounted for by anything other than the structure itself”. Not only that: the mathematical structuralism just discussed “provides evidence for this view”.

Despite all that, Ladyman and Ross often state that they don't actually deny the existence of entities or individuals per se. Yet it's hard to make sense of their claim that “there are objects in our metaphysics” and then go on to state that

“but they have been purged of their intrinsic natures, identity, and individuality, and they are not metaphysically fundamental”.

In other words, if you take away “intrinsic natures, identity, and individuality”, then what's left of things/objects after all that has been taken away? Only structure and/or relations? But what does that mean?

In any case, Ladyman and Ross see individuals as “abstractions from modal structure”. By “modal structure” they mean

“the relationships among phenomena events, and processes) that pertain to necessity, possibility, potentiality, and probability”.

It can easily be said that structures involve individuals and relations involve relata. At a prima facie level we can also ask:

In what way do “abstractions” involve themselves in modal realities?

Well, mathematics itself involves necessity, possibility and probability. And if structures are inherently mathematical, then structures have modal properties. All that may be true. Though what about modality as applied to the concrete world of objects, events, conditions, states, etc? What about metaphysical modality as understood by philosophers like Saul Kripke, David Lewis, D.M. Armstrong and so on?

Ladyman and Ross also quote the American philosopher of science John Stachel when he says that entities “'inherit [individuality] from the structure of relations in which they are enmeshed'”. However, saying that is a long way from saying that individuals don't exist. Even the very use of the word “inherit” surely means that it must be things which are doing the inheriting.

Now is it that Ladyman and Ross reject this position and simply deny ontological status to things/objects - full stop? Or is their position that entities inherit their individuality from the “structure of relations in which they are enmeshed” as far as they need to go? Thus it's not that Ladyman and Ross are eliminitivists about things/objects. It's simply that they have a radical philosophical take on things/objects. A take which claims that entities gain their individuality from structure. That is, before things/objects are “enmeshed” in structures, they have no intrinsic natures.

Can we go so far as to say that before things/objects are enmeshed in structures, they don't exist? Thus it's not just the nature of entities we're talking about: it's also their existence. Do entities spring into being only when they're enmeshed in structures?

This position would go against the claim (for example, of David Lewis) that objects have intrinsic natures regardless of the rest of the world.

So now we still have the following positions:

i) Things gain their natures from the structures they belong to.

ii) Things come into existence in structures.

How is i) different from saying that entities are structures? In other words, the temporal and grammatical construction of i) may seem to imply that we have an entity at time t¹ - and at t² it gains its nature from the structure it's embedded in. However, if ii) is correct, than that entity comes into existence in the structure. It doesn't only gain its nature from a structure – it comes into existence in the structure in which it's embedded.

Such abstract metaphysics is made concrete when Ladyman and Ross take the example of fermions. They cite the position that

“that fermions are not self-subsistent because they are the individuals that they are only given the relations that obtain among them”.

What's more, “[t]here is nothing to ground their individuality other than the relations into which they enter”. And, according to Ladyman and Ross, even Albert Einstein once claimed that particles don't have their own “being thus”.

Substantivalism

As just hinted at, one problem which can be raised about things/objects (as well as about Ladyman and Ross's position) can be expressed by stating two positions:

i) Things/objects have their intrinsic natures independently of the rest of the world.

ii) Things/objects can exist independently of the rest of the world.

This problem specifically arises in the context of “points of spacetime” rather than objects. (Although it may be said that they amount to the same thing.) In this case, Ladyman and Ross use the word “exist” (as in ii) above). This is also a product of two different positions: substantivalism and relationalism. Thus:

i) According to substantivalism, the “points of the spacetime manifold exist independently of the material contents of the universe”.

ii) According to relationalism, “spatio-temporal facts are about the relations between various elements of the material contents of spacetime”.

The idea that “points of the spacetime manifold exist independently of the material contents of the universe” is similar to David Lewis's take (1982) on the intrinsic properties of things. Lewis wrote:

“A thing has its intrinsic properties in virtue of the way that thing itself, and nothing else, is.”

Lewis's position (if not the substantivalist position) can be taken to its most extreme in the following statement:

Object a would still have intrinsic property P if, after the world around it disappeared, a would still have P.

In Ladyman and Ross's rendition of substantivalism, it's said that an object or point in spacetime could “exist” regardless of everything else. Could there ever be “the way that a thing itself is” regardless of everything else? That is, can object x be the way that it is regardless of its relations to other properties/objects/events/states/etc. and its place in spacetime?

Things and Relations

Ladyman and Ross provide a useful set of four positions which focus on the nature of relations and things. Thus:

i) There are only relations and no relata.

ii) There are relations in which things are primary, and their relations are secondary.

iii) There are relations in which relations are primary, while things are secondary.

iv) There are things such that any relation between them is only apparent.

At first glance one would take ontic structural realism to endorse (i) or (iii). However, if things are themselves structures (according to Ladyman and Ross), then we must settle for (i) above: “There are only relations and no relata.”

Looking at (i) to (iv) again, couldn't it be said that (ii) and (iii) amount to the same thing? In other words, how can we distinguish

(ii) There are relations in which the things are primary, and their relations are secondary.

from

(iii) There are relations in which relations are primary, while things are secondary.

Isn't this a difference which doesn't make a difference? One can still ask - in the metaphysical pictures of (ii) and (iii) - the following question:

Can things exist without relations and can relations exist without things?

That's a question of existence. Now what about natures?

One can now ask:

Can things have their natures without relations and can relations have their natures without things?

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To follow: 'On Quantum-Mechanical Particles: Conclusions (5)'

Ladyman and Ross on Quantum-Mechanical Particles (3)

In Every Thing Must Go: Metaphysics Naturalized, the philosophers James Ladyman and Don Ross give a clear account of the physics which underlies the problematic nature of seeing elementary particles as single things or objects. (Everything Must Go is a controversial and fairly well-known book — at least in philosophy.)

Firstly, Ladyman and Ross put the position of classical physics:

“[C]lassical physics assumed a principle of impenetrability, according to which no two particles could occupy the same spatio-temporal location. Hence, classical particles were thought to be distinguishable in virtue of each one having a trajectory in spacetime distinct from every other one.”

Clearly, in quantum mechanics (QM), many — or all — the assumptions in the classical picture are rejected. (Or, at the least, on many interpretations of QM all these assumptions are rejected.)

Take the notion of impenetrability.

Impenetrability

The “principle of impenetrability” is rejected by Ladyman and Ross.

On the classical picture, if particles are impenetrable, then that must mean that “no two particles could occupy the same spatio-temporal location”. However, if they are penetrable (or if the notion of impenetrability doesn’t make sense), then one can conclude that two particles “could occupy the same spatio-temporal location”.

Now one can immediately ask the following question:

If two particles can (or do) occupy the same spatiotemporal location, then is it correct to talk about two particles in the first place?

As a consequence of that question, the second part of the classical picture is rejected too. That second part (which follows from the first) is that

“classical particles were thought to be distinguishable in virtue of each one having a trajectory in spacetime distinct from every other one”.

Clearly, if the penetrability argument is true (i.e., two particles may occupy the same location), then each particle can’t be seen to have its own trajectory in spacetime. In other words, it will — or may — share its trajectory with another particle.

All this has the result (at least according to Ladyman and Ross) that the Leibnizian picture breaks down in the case of quantum-mechanical particles. On the other hand and according to Ladyman and Ross:

“Thus for everyday objects and for classical particles, the principle of the Identity of Indiscernibles is true [].”

So what about the notion of individuals?

Individuals

Ladyman and Ross then offer us two statements which they believe summarize the position of “standard metaphysics” on, if not particles, then on what they call “individuals”.

Take (i).

“There are individuals in spacetime whose existence is independent of each other. Facts about the identity and diversity of these individuals are determined independently of their relations to each other.”

The problem is how to take the word “independent” in the passage above.

One can accept the reality (or existence) of individuals yet also believe they that they aren’t (entirely) independent of other individuals. That is, the reality (or existence) of individuated objects and their lack of independence aren’t mutually exclusive. What’s more, one can accept the “identity and diversity of these individuals” yet also deny that such “individuals are determined independently of their relations to each other”. In other words, why does a commitment to individuals necessarily mean that one must also accept their complete independence from all other individuals (or from other events, processes, conditions, states, fields, systems, structures, etc.)?

In addition, it’s simply false that metaphysicians have accepted all that’s claimed in (i) above. Randomly, take the various monists and holists in the history of philosophy; as well as philosophers like F.H. Bradley and A.N. Whitehead. Such philosophers certainly didn’t believe that individuals are “independent of each other”.

What about Ladyman and Ross’s second statement?

They say that “standard metaphysicians assume” the following about individuals or particles:

“Each has some properties that are intrinsic to it.”

Here again what was said about claim (i) partly goes for claim (ii) as well.

Throughout the history of Western metaphysics there have been metaphysicians who’d now be classed as “anti-essentialists”. Indeed we could go back to Heraclitus (c. 535 — c. 475 BC) to find anti-essentialists (or at least to find proto anti-essentialists). In addition, we had the medieval nominalists. Come the 20th century, there’ve been many anti-essentialist metaphysicians and philosophers.

So what, in very basic terms, do essentialists (see essentialism) believe?

They believe that an individual “has some properties that are intrinsic to it”. However, here again it can be said that some/most of the ontologists who’ve (broadly speaking) accepted the bundle theory of individuals could also be classed as anti-essentialists in that they’d have denied the statement that each individual must have at least some intrinsic properties.

Discernibility and Individuality

One method for distinguishing two individuals (or two objects/particles) is basically W.V.O Quine’s reworking of Leibniz.

Quine called it “absolute discernibility”. Ladyman and Ross express his position this way:

“Quine called two objects [] absolutely discernible if there exists a formula in one variable which is true of one object and not the other.”

This is a reworking of Leibniz’s logical position (with the addition of references to “formulas”). Thus:

(x) (y) (F) (x = y ⊃. F (x) ≡ F (y).)

One obvious way in which a and b can be deemed to be “absolutely discernible” is if they “occupy different positions in space and time”.

Now for “relatively discernible” objects.

According to Ladyman and Ross,

“[m]oments in time are relatively discernible since any two always satisfy the ‘earlier than’ relation in one order only”.

This clearly makes a moment in time relational in nature (see relational theory). Or at least its relatively discernible nature is accounted for by its relational nature (i.e., “earlier than” and “later than”).

What’s just been said about time is similar to what can also be said about space (as well as about the “mathematical objects” which measure it). Ladyman and Ross write:

“An example of mathematical objects which are not absolutely discernible but are relatively discernible include the points of a one-dimensional space with an ordering relation…”

More precisely:

“[F]or any such pair of points x and y, if they are not the same point then either x > y or x < y but not both.”

In the above there’s a fusion of points in space with moments in time. Thus x and y are absolutely discernible because x is before (or “earlier than”) y or x is after (or “later than”) than y. In other words, x can’t be both earlier than and later than y (as well as vice versa) at one and the same time.

Now let’s take Ladyman and Ross’s definitions of discernibility and individuality. They write:

“The former epistemic notion concerns what enables us to tell that one thing is different from another. The latter metaphysical notion concerns whatever it is in virtue of that two things are different from one another, adding the restriction that one thing is identical with itself and not with anything else.”

At first glance, these characterisations come across as two different ways of saying the same thing. Clearly the second characterisation (“whatever it is in virtue of that two things are different from one another”) is ontological in character. The former (“what enables us to tell that one thing is different from another”) is, as Ladyman and Ross say, epistemic in character. However, don’t these two characterisations fuse? That is, in order to know “whatever it is in virtue of that two things are different from one another” one would need to employ the epistemic tools which “enable us to tell that one thing is different from another”. Thus the ontological question merges with the epistemological question (or vice versa).

We can also say that because of the spatial differences between Max Black’s two (identical) spheres (in his well-known thought experiment), sphere a and sphere b can only be classed as “weakly discernible” on Ladyman and Ross’s picture.

Ladyman and Ross make Max Black’s example more concrete (as well as scientific) by talking about two fermions (which are a mile apart) instead of spheres. According to Ladyman and Ross:

“Clearly, fermions in entangled states like the singlet state violate both absolute and relative discernibility…”

Fermions “in entangled states like the singlet state” (see singlet state) aren’t absolutely discernible because there are neither spatial nor temporal means to disentangle each fermion from other fermions. (Hence the technical term entanglement.) However, Max Black’s two spheres are also spatially indiscernible in that they’re in constant movement around a figure of eight. Thus sphere a would be continuously occupying a spatial point which had only just been occupied by sphere b — as well as vice versa. (The only way out of this would be to either literally or imaginatively freeze the movements of both spheres — though that would be unacceptable because it defeats the object of the thought-experiment.)

Fields and States

It can be seen that the notion of a field plays an important part in Ladyman and Ross’s philosophy.

The central argument is that fields and particles are intimately connected. Indeed they’re so strongly connected that a distinction between the two hardly seems warranted.

Ladyman and Ross’s position on the fields of physics can be traced back to — among others — Ernst Cassirer. (Cassirer died in 1945.) Indeed Ladyman and Ross have much to say about Cassirer. For example, they wrote the following:

“OSR [ontic structural realism] agrees with Cassirer that the field is nothing but structure. We can’t describe its nature without recourse to the mathematical structure of field theory.”

What Ladyman and Ross say about Ernst Cassirer’s position on objects is almost exactly the same as their own. Indeed it was also quantum mechanics which provided Cassirer with the motivation to reject “individual objects”. Ladyman and Ross write:

“Ernst Cassirer rejected the Aristotelian idea of individual substances on the basis of physics, and argued that the metaphysical view of the ‘material point’ as an individual object cannot be sustained in the context of field theory. He offers a structuralist conception of the field.”

One can firstly ask whether or not a commitment to the existence of objects is also automatically a commitment to “individual substances”; as well as to intrinsic (or essential) properties. (As stated earlier on in this essay.)

We can also ask whether or not these positions are equally applicable to objects in the “classical” (or macro) world.

Let’s put it this way.

Ernest Cassirer’s and Ladyman’s positions are far more acceptable when applied the the quantum world than when applied to the classical world (or to the world of experience). More precisely, all this is far easier to swallow in the “context of field theory” than it is in relation to, say, human beings (or persons), trees or cups.

There’s also the problem of distinguishing particles from the states or fields they “belong” to. Thus, in an example given by Ladyman and Ross, we can interpret a given field/particle situation in two ways:

i) A two-particle state.

ii) A single state in which two “two particles [are] interchanged”.

Since it’s difficult to decipher whether it’s a two-particle state or a single state in which two particles are interchanged, Ladyman and Ross adopt the “alternative metaphysical picture” which “abandons the idea that quantum particles are individuals”. Thus all we have are states. That means that the “positing [of] individuals plus states that are forever inaccessible to them” is deemed to be (by Ladyman and Ross) “ontologically profligate”.

Ladyman and Ross back up the idea that states are more important than individuals (or, what’s more, that there are no individuals) by referring to David Bohm’s theory. In that theory we have the following:

“The dynamics of the theory are such that the properties, like mass, charge, and so on, normally associated with particles are in fact inherent in the quantum field and not in the particles.”

In other words, mass, charge, etc. are properties of states or fields, not of individual particles. However, doesn’t this position (or reality) have the consequence that a field takes over the role of an individual (or of a collection of individuals) in any metaphysics of the quantum world? Thus does that also mean that everything that’s said about particles can now also be said about fields?

Particle Trajectories

On Bohm’s picture ( if not on Ladyman and Ross’s), “[i]t seems that the particles only have position”. Yes; surely it must be a particle (not a field) which has a position. Indeed particles also have trajectories (if probabilistically accounted for) which account for their different positions.

To Bohm (at least according to Ladyman and Ross), “trajectories are enough to individuate particles”.

It’s prima facie strange how trajectories can individuate.

Unless that means that each type of particle has a specific type of trajectory. In that case, the type trajectory tells you the type of particle involved in that trajectory.

Ladyman and Ross spot what they take to be a problem with Bohm’s position. That problem is summed up in this way:

If all we have is trajectories (as with structures), then why not dispense with particles (as individuals at least) altogether?

This is how Ladyman and Ross themselves explain their stance on Bohm’s theory:

“We may be happy that trajectories are enough to individuate particles in Bohm theory, but what will distinguish an ‘empty’ trajectory from an ‘occupied’ one?”

Here again Ladyman and Ross are basically saying that if all we’ve got are trajectories (which are part of the “structure”), then let’s stick with them and eliminate particles (as individuals) altogether.

Ladyman and Ross go into more detail on this by saying that

“[s]ince none of the physical properties ascribed to the particle will actually inhere in points of the trajectory, giving content to the claim that there is actually a ‘particle’ there would seem to require some notion of the raw stuff of the particle; in other words haecceities seem to be needed for the individuality of particles of Bohm theory too”.

If the physics of Ladyman and Ross is correct, then what they say makes sense. Positing particles seems to run free of Occam’s razor. That is, Bohm was filling the universe’s already-existing “ontological slums” with yet more superfluous entities.

One way of interpreting this is by citing two different positions. Thus:

1) The positing of particles as individuals which exist in and of themselves.

2) The positing of particles as part of package-deals which include fields, states, trajectories, structures, etc.

Then there’s Ladyman and Ross’s position.

3) If there are never particles in splendid isolation (apart from fields, states, etc.), then why see particles as individuals in the first place?

Ladyman and Ross are a little more precise as to why they endorse 3) above.

They make the metaphysical point that “haecceities seem to be needed for the individuality of particles of Bohm’s theory too” (see haecceity) . In other words, in order for particles to exist as individuals (as well as to be taken as existing as individuals), they’ll require “individual essences” (see individual essence) in order to be individuated. However, if the nature of a particle necessarily involves fields, states, other particles, trajectories, structures, etc., then it’s very hard (or impossible) to make sense of the idea that it could have an individual (or indeed any) essence.

(Can’t all this also be said about objects in the large-scale world too — that is, about human beings, tables, chairs and so on?)

In basic terms, then, all particles are parts of various package-deals. Particles simply can’t be individuated without reference to what’s called extrinsic or relational factors.

To Ladyman and Ross, this means that particles simply aren’t individuals at all.

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