These pieces are primarily commentaries on the 'Ontic Structural Realism and the Philosophy of Physics' chapter of James Ladyman and Don Ross's book Every Thing Must Go. There are also a handful of references to – and quotes from – other parts of that book.
Ladyman and Ross (L & R) offer a list of four statements which they believe summarise the position of “standard metaphysics”.
(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 above. One can accept individuals and also believe they that they aren't independent of other individuals. That is, the 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” and also deny that such “individuals are determined independently of their relations to each other”. In other words, I don't see why a commitment to individuals necessarily means that one also accepts their complete independence from all other individuals (or from events, processes, conditions, states, etc.).
In addition, it's simply false that metaphysicians have accepted all that's claimed in (i). Randomly, take the various monists in history and philosophers like Bradley and A.N. Whitehead. They certainly didn't believe that individuals are “independent of each other”.
What about L & R's second statement? They say that “standard metaphysicians assume” the following:
(ii) “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 would now be classed as anti-essentialists. Indeed we could go back to Heraclitus to find anti-essentialists (or at least to find proto anti-essentialists).In addition, we had the medieval nominalists. Come the 20th century, there have been many anti-essentialist metaphysicians and philosophers.
What do essentialists believe? That an individual “has some properties that are intrinsic to it”. In addition, some of the ontologists who've (broadly speaking) accepted the bundle theory of individuals could also be classed as anti-essentialists. (In that they would have denied the statement that each individual must have at least some intrinsic properties.)
Discernibility and Individuality
One method for distinguishing two objects is basically Quine's reworking of Leibniz. Quine called it “absolute discernibility”. L & R 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 (with the addition of references to “formulas”) thus:
(x) (y) (F) (x = y ⊃. F (x) ≡ F (y).)
One way a and b can be deemed to be “absolutely discernible” is if they “occupy different positions in space and time”.
Now for “relatively discernible”.
According to L & R,
“[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. Or at least its relatively discernible nature is accounted for by its relational nature (i.e., ‘earlier than’, 'later than', etc.).
What's just been said about time is similar to what's also said about space (as well as the “mathematical objects” which measure it). L & R 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...”
“... for 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.”
Here 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 L & R'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 definitions come across as two different ways of saying the same thing. Clearly the second definition (“whatever it is in virtue of that two things are different from one another”) is ontological in character and the former (“what enables us to tell that one thing is different from another”) is, as L & R say, epistemic. However, don't the two definitions fuse? That is, in order to know “whatever it is in virtue of that two things are different from one another” (an ontological fact) 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).
Black's Spheres, Substantivalism & Relationalism
We can say that because of the spatial differences between Max Black's two spheres (in his well-known thought experiment), sphere a and sphere b would only be classed as “weakly discernible” on L & R's picture.
L & R make Max Black's example more concrete (as well as scientific) by talking about fermions instead of spheres (which are a mile apart). According to L & R:
“Clearly, fermions in entangled states like the singlet state violate both absolute and relative discernibility...”
Fermions “in entangled states like the 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 spacial 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 surely that's unacceptable.)
One problem which can be raised about objects (as well as about L & R's position on objects) can be expressed by stating two positions:
i) Objects have their intrinsic natures independently of the rest of the world.
ii) 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, L & R 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” sounds a little like David Lewis's take (1982) on intrinsic properties. 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 L & R'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 a be the way that it is regardless of its relations to other properties/objects/events, its place in time and space and so on?
Black, Max. (1952) 'The Identity of Indiscernibles'.Ladyman, James, Ross, Don. (2007) Every Thing Must Go: Metaphysics Naturalised.
Lewis, David. (1982) 'Extrinsic Properties'.
Quine, W. V. O. (1976) 'Grades of Discriminability'.