Priest (2.4) One, ‘Identity and Gluons,’ summary

 

by Corry Shores

 

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[The following is summary. You will find typos and other distracting mistakes, because I have not finished proofreading. Bracketed commentary is my own. Please consult the original text, as my summaries could be wrong.]

 

 

 

 

Summary of

 

Graham Priest

 

One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness

 

Part 1:

Unity

 

Ch.2

Identity and Gluons

 

2.4

Identity and Gluons

 

 

 

 

Brief summary:

(2.4.1) We define the identity statement in the following way:

a = b iff X(Xa ≡ Xb)

(2.4.2) A gluon is defined in the following way, keeping in mind that in our paraconsistent logic, identity is non-transitive: “Given a partite object, x, a gluon for x is an object which is identical to all and only the parts of x. By being identical to each of the parts and to only those, it unifies them into one whole” (20). Thus what we might call the “intimacy” of the paraconsistent identity binds the parts to the gluon and thereby together into one object, but the non-transitivity of the paraconsistent identity keeps the non-gluon parts distinct (being non-identical to one another). (2.4.3) Priest then illustrates with an example gluonic structure to show how a gluon may both have and not have a property if one part of the whole has it and another part does not have it.

 

 

 

 

 

 

Contents

 

2.4.1

[The Paraconsistent, Leibnizian Definition of Identity]

 

2.4.2

[Gluonic Unity Defined, with the Heterogeneity of the Parts Ensured]

 

2.4.3

[An Example Gluonic Structure]

 

 

 

 

 

 

Summary

 

2.4.1

[The Paraconsistent, Leibnizian Definition of Identity]

 

[We define the identity statement in the following way: a = b iff X(Xa ≡ Xb).]

 

[In the previous section 2.3, we discussed the material conditional in paraconsistent logic. We thought of truth-evaluation in terms of formulas being in either the true zone, the false zone, or in an overlap of both zones. A formula in the overlap is both true and false. If two formulas are in the same zone, then their material conditional is in the true zone. If they are in opposite zones, then their material conditional is in the false zone. But if one formula is in the overlap zone, and another is exclusively in the true or the false zone, then their material conditional will also be in overlap zone (see section 2.3.3). We learned also in section 2.3.4 that material equivalence in paraconsistent logic is reflexive and symmetric, but not transitive. Priest will now use the material conditional to define identity. He will use a second-order predicate logic. Recall some ideas from section 14.1 of Nolt’s Logics. (The following is taken from our brief summary).

In first-order logic, we can have quantifiers that quantify over variables that stand for individuals. In second-order logic, we can have quantifiers that quantify over predicates. In this way, we can express the following inference, for example: “Al is a frog. Beth is a frog. Therefore, Al and Beth have something in common.” We can write it as: ‘Fa, Fb ⊢ ∃X(Xa & Xb)’. Here we have the predicate variable ‘X’, which allows us to refer to some unspecified predicate as a variable.

[...]

We can use second-order logic to express a number of important logical ideas. One of them is identity. Leibniz’s law says that objects are identical if and only if they share exactly the same properties. It is written:

Leibniz’s Law

a = b ↔ ∀X(Xa ↔ Xb)

It is analyzable into two subsidiary principles.

The Identity of Indiscernibles

∀X(Xa ↔ Xb) → a = b

This says that if two things are indiscernible, as they share exactly the same properties, then they are identical. The other is

The Indiscernibility of Identicals

a = b → ∀X(Xa ↔ Xb)

This says that if two things are identical, then they share exactly the same properties. [...]

(From the brief summary to Nolt’s Logics section 14.1)

Also recall some notation from section P7. is the universal quantifier, normally written ∀. And is the particular quantifier, normally written ∃. Priest will now define the identity statement in the following way:

a = b iff X(Xa ≡ Xb)

The X here is a variable for predicates. Normally in a classical logic, this is saying that a = b whenever a has exactly the same predicates as b has. (But things are more complicated, as we will see, now that we are using a paraconsistent logic. It will be possible for something to both have and not have some predicate. We return to this in a second.) Since we are using the material conditional here and using it to define =, that means = will also be reflexive, symmetric, but not transitive. Priest then shows this non-transitivity. We suppose that we have only one predicate, and object a has it, object b both has it and does not have it, and object c simply does not have it. Now, since a has it and b at least has it, then Pa ≡ Pb. And since c does not have it and b at least does not have it, then Pb ≡ Pc. But that does not mean that Pa ≡ Pc. (For, it is just true that a has it and just false that c has it.) With that being the case, we can see how this applies to the identity relations between a, b, and c: “Since P is the only property at issue, we have a = b and b = c, but not a = c.” (So as we mentioned above, matters are more complicated with a paraconsistent logic. We have some object b that both has and does not have property P. And we are assuming this is the only property, and a just has it and c just does not have it. So in a classical logic, we would say that b = c if b and c have exactly the same properties. But here, b has property P and c does not, yet b = c (this is because b also does not have property P. But it is odd, because we can no longer say that two things are identical if they have exactly the same properties). Perhaps we need to say now that they have “at least” the same properties, meaning that a first object that has a certain property can be identical to another object that lacks this same property, so long as the first one also at least lacks that property too. But I am not sure yet how to grasp this perfectly. But while all this is odd, we should keep in mind that the inconsistent objects here are the gluons, which are odd things already.)]

So much for the background. Against this, we can define identity. The definition is the standard Leibnizian one. Two objects are the same if one object has a property just if the other does. In the language of second-order logic, a = b iff:

• X(Xa ≡ Xb)

The second-order quantifiers here are to be taken as ranging over all properties. Whatever these are exactly (and we will come back to the matter later) | the behaviour of identity is going to be inherited from the behaviour of ≡.⁴ In particular, it is going to be reflexive and symmetric, but, crucially, not transitive. Suppose, for the sake of illustration, that there is only one property in question, P, and that Pa, Pb and ¬Pb, and ¬Pc.⁵ Then Pa ≡ Pb, Pb ≡ Pc, but not Pa ≡ Pc. Since P is the only property at issue, we have a = b and b = c, but not a = c.⁶

(20)

4. I note that the property of being identical with something is normally ruled out in a Leibnizian definition of identity on pain of triviality. For given that X(Xa ≡ Xb), it would then follow that a = b ≡ b = b, and so a = b. This is not the case in the present context, due to the non-detachability of ≡.

5. For ease of the informal exposition, I collapse the notational distinction between properties and predicates in a harmless fashion.

6. A consequence of this definition is that any object with contradictory properties is not self-identical. This consequence can be avoided by taking X(Xa ≡ Xb) to give the truth conditions for an identity statement, but giving different falsity conditions. One simple way to do this is to define a = b as: ⟨a, b⟩ satisfies ‘X(Xx ≡ Xy)’. Given the naive satisfaction scheme, this gives the appropriate truth conditions. But, arguably, negation does not commute with truth: T⟨¬A⟩ does not entail ¬T⟨A⟩. (See Priest (1987), 4.9.) Similarly, it does not commute with satisfaction. So the fact that ⟨a, b⟩ satisfies ‘¬X(Xx ≡ Xy)’ does not entail that ⟨a, b⟩ does not satisfy ‘X(Xx ≡ Xy)’; that is that ¬a = b.

(20)

[contents]

 

 

 

 

 

 

2.4.2

[Gluonic Unity Defined, with the Heterogeneity of the Parts Ensured]

 

[A gluon is defined in the following way, keeping in mind that in our paraconsistent logic, identity is non-transitive: “Given a partite object, x, a gluon for x is an object which is identical to all and only the parts of x. By being identical to each of the parts and to only those, it unifies them into one whole” (20). Thus what we might call the “intimacy” of the paraconsistent identity binds the parts to the gluon and thereby together into one object, but the non-transitivity of the paraconsistent identity keeps the non-gluon parts distinct (being non-identical to one another).]

 

[Priest next notes that when the middle, bridging object is consistent (not having contradictory properties), then identity can be transitive (see details in the quote below). Then Priest gives a more formal definition for a gluon. (Recall from section 2.1.1 that a gluon is the factor that binds parts into a unity, and it has the contradictory properties of both being and not being an object.) Here is the definition of a gluon now:

Given a partite object, x, a gluon for x is an object which is identical to all and only the parts of x.

(20).

So recall the diagram of a gluonic structure from section 2.2.3

x

xxxxb

xxxx||

ax=x中x=xc

xxxx||

xxxxd

xxxx

We have the parts a, b, c, and d. And the gluon 中 is identical to all the parts. But on account of the non-transitivity of identity, that does not make the parts be identical with one another. The next line is important but tricky.

By being identical to each of the parts and to only those, it unifies them into one whole.

(20)

Here, being identical is like a logical property of the factor that binds parts into whole. Being-identical is something like a full intimacy. But as a paraconsistent identity, it is not an exclusive, full intimacy. The gluon is identical to part a, but it is no less identical to part b, even though a is not identical to b. So in that sense of its identificatory immediacy, it binds a and b into one unity, but it does not by that intimate binding thereby reduce the distinctness of a or of b. In Dupréel’s La consistance et la probabilité constructive, section 1.4, he discusses something similar. He notes how things whose parts bind more strongly and strongly, thereby constituting a unified object whose wholeness and integrity likewise grows stronger, can take two paths of development. Either its parts fuse and homogenize, subtracting from their individuality as the whole increases its unity. Or instead, as in life forms, the parts continue to bond together and into a strengthening whole all while maintaining and increasing their individual diversity. In other words, what Dupréel calls consistance seems to share this paraconsistent logical property of Priestian gluonics, namely, a binding of the parts that constitutes a whole all without equalizing or homogenizing those parts. (And by extension, this would apply to Deleuze’s and Deleuze & Guattari’s similar theories of composition). Priest’s next observation is:

Note that a gluon is identical to itself; it follows that it is a part of x.

(20)

I think the idea might be the following here. Being a part of x means being paraconsistently identical to x’s gluon. Since the gluon of x is identical to x’s gluon (which is itself), then the gluon of x is also a part of x. Priest’s final point in this paragraph is:

Note also that the gluon of an object is unique. For suppose that g and g′ are gluons of an object, x, then, since g and g′ are parts of x, g = g′ (and g′ = g).

(20)

(I think I do not follow this well, but maybe it is the following. We will conclude that the gluon of an object is unique, which I assume means there is only the one defining gluon. We show this by first proposing that there be two gluons for an object x, namely, g and g′. Next we recall that gluons are parts of their object. Every part of the object is identical to the object’s gluon. So g = g′, because gluon g as a part is identical with gluon g′, taken to be the binding factor; and g′ = g, because  g′ as a part is identical to g, taken to be the binding factor. But that then means that g = g′, and thus the distinction between them was superfluous, and rather there is just one unique gluon. I may have that wrong, so please check it yourself.)]

It should be noted that though we do not have transitivity of identity in general, we do have it when the “middle” object is consistent, that is, has no contradictory properties. For suppose that a = b = c, and that b is consistent. Consider any property, P. Then Pa ≡ Pb and Pb ≡ Pc. Hence, (Pa ≡ Pc) ∨ (Pb ∧ ¬Pb). Given that the second disjunct can be ruled out, we have Pa ≡ Pc. So a = c. There is much more to be said about identity, but we may leave the matter for the moment. Given this understanding of identity, we may now define formally what a gluon is. Given a partite object, x, a gluon for x is an object which is identical to all and only the parts of x.⁷ By being identical to each of the parts and to only those, it unifies them into one whole. Note that a gluon is identical to itself; it follows that it is a part of x. Note also that the gluon of an object is unique. For suppose that g and g′ are gluons of an object, x, then, since g and g′ are parts of x, g = g′ (and g′ = g).

(20)

7. To keep the account as general as possible, I leave it open here whether ‘part’ includes the improper part which is the whole.

(20)

[contents]

 

 

 

 

 

 

2.4.3

[An Example Gluonic Structure]

 

[Priest then illustrates with an example gluonic structure to show how a gluon may both have and not have a property if one part of the whole has it and another part does not have it.]

 

[Priest will now show how this works with an example gluonic structure. We have four objects, g, i, j, and k. We put aside k for the moment, because it is like a distinct entity, but g, i, and j are parts of one entity x, with the g as its gluon. (Now, as the gluon, that means it has the paraconsistent material conditional relation with each of the parts, meaning that if it is true one of the parts has some property, then the gluon has that property too, and if it if false that the other part has that property, then it is false that the gluon has it. But under our paraconsistent logic, gluon g can both have a property (if one other part has it) and not have that property (if yet another part does not have it.) So look at the distribution of property possessions for the various parts of x, including the gluon g (and forget k for the moment. Just look at the first three, i, g, and j).

 

	P1	P2	P3
i	+	−	+
g	±	±	+
j	−	+	+
k	+	+	−

 

As we can see, since i has the first property but j does not, then gluon g both has and does not have that property (since it is identical to both), and since both i and j simply just have the third property, that means gluon g just simply has that property too. So given the sharings and lackings of properties, we have: i = g (because i has the first and third properties, but lacks the second; and g at least does too), g = g (of course), and g = j (because j lacks the first property but has the second and third; and g at least does too). Priest next looks at object k. Look at the third property for all of the parts. We see that all parts of object x have property 3, but k does not. That means no part of x is identical to k. Priest’s final point seems to be the following. We will conclude that g ≠ g. (We see that g is ± for the first property. That means P₁g is at least false and P₁g is at least true, meaning that P₁g ≡ P₁g is at least false (it is also true) and thus that ¬(P₁g ≡ P₁g) is then at least true (it is also false). Now, since the first property both holds and does not hold for g, that means there is a property for which it both holds of g and does not, or: X(Xg ∧ ¬Xg), which furthermore means that it is not the case that for all properties that if they hold for g then then it cannot be that they do not also hold for g, or: ¬X(Xg ≡ Xg). Now, since a = b iff X(Xa ≡ Xb), and since ¬X(Xg ≡ Xg), that means g ≠ g. Please see the quotation to be sure.)]

Let me illustrate a gluon structure with a simple example. Suppose that we have four objects, g, i, j, and k. g, i, and j are the parts of some object, x, and g is its gluon. Suppose that there are just three properties, P₁, P₂, and P₃, possessed as follows. ‘+’ indicates that the object is in (just) the extension; ‘−’ indicates that it is in (just) the anti-extension; and ‘±’ indicates both.⁸ |

 

	P1	P2	P3
i	+	−	+
g	±	±	+
j	−	+	+
k	+	+	−

 

It is easy to check that for each of the three properties, P, we have Pi ≡ Pg , and so X(Xi ≡ Xg), and similarly for g and j (and of course for g and g). Hence i = g, g = g, and g = j. However, we have none of the following: P₃i ≡ P₃k, P₃g ≡ P3k, P₃j ≡ P₃k. Hence, none of i = k, g = k, and j = k holds. g is identical to all and only the parts of x.⁹ Note that ¬(P₁g ≡ P₁g), so X(Xg ∧ ¬Xg), that is ¬X(Xg ≡ Xg); that is, g ≠ g.¹⁰

(20-21)

8. Recall, from Section P.5, that we need to specify both the places where P holds—the extension of P—and the places where ¬P holds—the anti-extension of P—since, unlike the classical case, neither determines the other. (20)

9. Suppose that the object of our diagram had another part, l, which was in the anti-extension of P1, P2, and P3. Then g would be in the anti-extension of P3 too. Hence, k would be part of the object as well. This bespeaks a certain failure of atomism, but hardly a surprising one. If you build a room between a house and an out-house, and join them internally, the out-house becomes part of the house.

10. [Not included in this quotation. See p.21.]

(21)

[contents]

 

 

 

 

 

 

 

 

From:

 

Priest, Graham. 2014. One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford: Oxford University.

 

 

 

 

Priest (2.2) One, “Breaking the Regress”, summary

 

by Corry Shores

 

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[Central Entry Directory]

[Logic and Semantics, entry directory]

[Graham Priest, entry directory]

[Priest, One, entry directory]

 

[The following is summary. You will find typos and other distracting mistakes, because I have not finished proofreading. Bracketed commentary is my own. Please consult the original text, as my summaries could be wrong.]

 

 

 

Summary of

 

Graham Priest

 

One:

Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness

 

Ch.2

Identity and Gluons

 

2.2

Breaking the Regress

 

 

 

Brief summary:

(2.2.1) To explain how gluons bind parts into a unified whole, we need to break the Bradley regress, which prevents gluons from simply being object-parts. (2.2.2) We might name the parts of a unified object with letters, as for example, a, b, c, and d. The gluon, symbolized 中, is what binds all the other parts into the unified whole. If the gluon were distinct from the other parts (in the sense of not being identical to them), there would always be room for another gluon to intervene between the first gluon and the given parts, which leads to the Bradley regress. To avoid it, we say that the gluon is identical to each of the parts, thereby closing those “gaps”. (2.2.3) The gluon is non-transitively identical with each and every part. That means that although each part is identical to the gluon, they are not thereby identical to one another. And, parts can themselves be composed of parts by means of another internal gluon.

x

xxxxb

xxxx||

ax=x中x=xc

xxxx||

xxxxd

x

(2.2.4) Gluonic unity involves non-transitive identity, meaning that a = 中 and 中 = c, but not thereby a = c.

 

 

 

Contents:

 

2.2.1

[Gluons as Needing to Break the Bradley Regress]

 

2.2.2

[The Gluon as Identical to the Parts]

 

2.2.3

[The Non-Transitive Identity of Parts to the Gluon, Part 1]

 

2.2.4

[The Non-Transitive Identity of Parts to the Gluon, Part 2]

 

Bibliography

 

 

 

 

 

Summary

 

2.2.1

[Gluons as Needing to Break the Bradley Regress]

 

[To explain how gluons bind parts into a unified whole, we need to break the Bradley regress, which prevents gluons from simply being object-parts.]

 

[Recall from section 1.4.2 that we cannot think of the gluon as an object-part, because as such, it would require yet another gluon to explain its binding among the parts it binds, and that newer gluon will need its own to bind it into the unity, and there can be no end to this regress. Priest reminds us that to explain how gluons bind parts into the unity, we need to break this regress.]

The problem of unity is to explain how it is that gluons glue. What stands in the way of an explanation is the Bradley regress. As we saw in Section 1.4, this is vicious, and so it must be broken. But how?

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[contents]

 

 

 

 

2.2.2

[The Gluon as Identical to the Parts]

 

[We might name the parts of a unified object with letters, as for example, a, b, c, and d. The gluon, symbolized 中, is what binds all the other parts into the unified whole. If the gluon were distinct from the other parts (in the sense of not being identical to them), there would always be room for another gluon to intervene between the first gluon and the given parts, which leads to the Bradley regress. To avoid it, we say that the gluon is identical to each of the parts, thereby closing those “gaps”.]

 

[Priest will symbolize the gluon with the Chinese (and maybe also Japanese) character 中. We think of a thing having a number of parts, which we can give letter names to, like a, b, c, and d. The gluon 中, then, is what binds these parts into the whole. Now, the gluon cannot simply be another part, for then it will cause our account to fall victim to the Bradley regress. Priest notes that the regress happens when we come to think of the gluon as being another object for which yet another gluon could intervene between the first and the other parts. Priest then says that if we make the gluon identical to the parts, that closes the metaphysical “gap” that otherwise would stand between the gluon and the parts. So we will need to make the gluon identical to the parts to avoid the Bradley regress.]

Suppose that an object has parts a, b, c, and d, and that these are held together by a gluon 中.¹ The Bradley regress is generated by the thought that 中 is distinct | from each of the other parts. If this is the case, then there is room, as it were, for something to be inserted between 中 and a, and so on. Or to use another metaphor, there is a metaphysical space between 中 and a, and one requires something in the space to make the join. Thus, the regress will be broken if 中 is identical to a. There will then be no space, or need, for anything to be inserted.

(16-17, boldface mine)

1. The character 中 (Chinese: zhong; Japanese: chu) means centre, which seems like a pretty good symbol for a gluon. (By coincidence, it is also sometimes used as part of one of the Chinese names for Madhyamaka Buddhism: zhong dao zong.) As the amount of logic increases, it also seems a good time for Western logicians to move to some less familiar languages in search of symbols. Unfortunately, | I will use the character in this section only, due to the current difficulty of typesetting Chinese characters in heavily symbolic contexts.

(16-17)

[contents]

 

 

 

 

2.2.3

[The Non-Transitive Identity of Parts to the Gluon, Part 1]

 

[The gluon is non-transitively identical with each and every part. That means that although each part is identical to the gluon, they are not thereby identical to one another. And, parts can themselves be composed of parts by means of another internal gluon.]

 

[The gluon is non-transitively identical with all of the parts, including itself. We can depict it by having all of the parts equal the gluon, but none of the parts equaling one another.

x

xxxxb

xxxx||

ax=x中x=xc

xxxx||

xxxxd

x

Priest then gives an analogy to explain why the identity here is not transitive. We think of how the mortar between bricks binds the bricks without making them one solid brick. Likewise, the gluon binds the parts by being identical to them, without making those parts be identical with each other. The footnote here is important, but I did not quite grasp it all. The basic idea seems to be that each part can be consider as being made of parts, bound with their own subgluon of sorts (not his term). These subparts still form parts of the whole, but how all this works I did not quite follow. Let me just go slowly through that footnote, line by line:

Of course, the parts of an object can themselves have parts.

This we noted.

Thus, it could be the case that, for example, c has parts m and n.

That simply sets up a naming convention.

These will be joined by a gluon, 中′.

That would seem to be what I called the subgluon, namely, the gluon that unifies the subpartitions of a thing’s main parts.

So we will have m = 中′ = n.

This simply says that the subgluon bears the same non-transitive identity relation with respect to the subpartitions it unifies.

If one takes the parthood relation to be transitive, m, 中′, and n, are also parts of the original object. So we will have 中 = m, 中 = 中′, and so on.

Here is where I get lost. As far as I can tell, such main parts as a, b, c, d, 中 are bound by non-transitive identity. And I would assume also that for m and n we would also not want them to be identical. So when Priest says, “If one takes the parthood relation to be transitive,” I am guessing by “parthood relation” he refers to the subpartition’s relation to the main part. But how does that work? Let us try to make a figure for it:

x

xxxxb

xxxx||

ax=x中x=xc {m = 中′ = n}

xxxx||

xxxxd

xSomething we have not established here, which would show the

In order to get enough levels of parthood for a transitive relation, let us call the whole object Ω:

x

Ω {xxxxb

xxxxxx||

xxax=x中x=xc {{m = 中′ = n}}

xxxxxx||

xxxxxxdxx}

x

My best guess at the moment is that when Priest says, “If one takes the parthood relation to be transitive” he does not mean that the parthood relation is one of identity. I am guessing he simply means that if m is a part of c, and if c is a part of Ω, then m is a part of Ω. But then, I do not understand the line using equations: “So we will have 中 = m, 中 = 中′, and so on.” Because if 中 = m and 中 = n, and this is a transitive identity relation, then we have n = m. In the two given formulas, 中 = m, 中 = 中′, there is in both cases an equation of a higher scale part with a lower scale part. So the only way I can think of this all working is if we think instead of the parthood relation as a non-transitive identity relation. And maybe specifically it is the non-transitive identity relation between the subpartitions specifically with the main gluon. This would bind each subpartition into the whole without equating them. I apologize; please read the text below to see what is really meant here.]

Of course, 中 must be identical with b, c, d, for exactly the same reason. Thus, 中 is able to combine the parts into a unity by being identical with each one (including itself). The situation may be depicted thus:

x

xxxxb

xxxx||

ax=x中x=xc

xxxx||

xxxxd

x

The explanation of how it is that the gluon manages to unite the disparate bunch is, then, that it is identical with each of them.² Consider, if it helps, an analogy. Suppose that one wants to join two physical bricks together with physical glue. The glue is inserted between the bricks. It bonds to each one, and so joins them. It does not make the two bricks one, but the molecules of the glue and each brick become physically indissoluble. In the metaphysical case, the parts of an object do not become identical either, but the gluon bonds with each part in the most intimate way, by being identical with it.

(17)

2. Of course, the parts of an object can themselves have parts. Thus, it could be the case that, for example, c has parts m and n. These will be joined by a gluon, 中′. So we will have m = 中′ = n. If one takes the parthood relation to be transitive, m, 中′, and n, are also parts of the original object. So we will have 中 = m, 中 = 中′, and so on.

(17)

[contents]

 

 

 

 

2.2.4

[The Non-Transitive Identity of Parts to the Gluon, Part 2]

 

[Gluonic unity involves non-transitive identity, meaning that a = 中 and 中 = c, but not thereby a = c.]

 

[Priest now explains how the transitivity of identity fails under this conception of gluonic unity. For, “We have a = 中 and 中 = c, but we will not have a = c.” Priest will now provide a more precise theory of non-transitive identity to show how it is a coherent notion.]

It should be immediately obvious that the relation of identity invoked here will not behave in the way that identity is often supposed to behave. In particular, the transitivity of identity will fail. We have a = 中 and 中 = c, but we will not have a = c. Two bricks of a house are not identical. It might be doubted that there is any such coherent notion, or that, if there is, it is really one of identity. These concerns cannot be set aside lightly, and the only way to assuage them is to provide a precise theory of identity which delivers what is required. Let us turn to this.

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[contents]

 

 

 

 

 

Bibliography:

 

Priest, Graham. 2014. One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford: Oxford University.

 

 

 

.

Priest (2.1) One, “How Gluons Glue”, summary

 

by Corry Shores

 

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[The following is summary. You will find typos and other distracting mistakes, because I have not finished proofreading. Bracketed commentary is my own. Please consult the original text, as my summaries could be wrong.]

 

 

 

Summary of

 

Graham Priest

 

One:

Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness

 

Ch.2

Identity and Gluons

 

2.1

How Gluons Glue

 

 

 

Brief summary:

(2.1.1) The gluon is the factor that binds parts into a unity. It has the contradictory properties of both being and not being an object. We now will see how gluons bind parts into unities, which involves breaking the Bradley regress. (2.1.2) The binding action of gluons involves non-transitive identity.

 

 

 

 

Contents:

 

2.1.1

[How Gluons Will Glue]

 

2.1.2

[Gluons’ Non-Transitive Identity]

 

Bibliography

 

 

 

 

 

Summary

 

2.1.1

[How Gluons Will Glue]

 

[The gluon is the factor that binds parts into a unity. It has the contradictory properties of both being and not being an object. We now will see how gluons bind parts into unities, which involves breaking the Bradley regress.]

 

[In section 1.3.1 we noted how things have parts that together compose the unity they belong to by means of a factor that binds the parts together in a unifying way. This unificatory binding factor is called the gluon. We discussed the problems with seeing it just as an object-part and with seeing it just as not being an object-part (as for example being instead a relation) (see section 1.4, section 1.5, and section 1.6). As a result, in section 1.6.6, Priest proposed that it is best to hold the dialetheic position that gluons both are and are not objects. In sections 1.3.4 and 1.6.6, Priest noted that the gluon is a contradictory entity, having the contradictory properties both of being an object and of not being an object (and see section 1.3.5). But we still need to explain how the gluon binds the parts into a unity. (On this importance of the how question when accounting for something philosophically, see section 1.5.5.) This is what we now endeavor, which involves us seeing how we will break the Bradley regress (see section 1.4 especially).]

In the previous chapter we saw that there must be something which accounts for a unity composed of parts where one exists – a gluon; and we saw that a gluon may be expected to have contradictory properties. But we have not yet faced the question of how the gluon does its job: how does it bind the parts (including itself) into a whole? Its having contradictory properties does not immediately address this question (though, one might suspect, it is going to play an important role). In this chapter, we look at the answer. The key is breaking the Bradley regress. We will start by seeing how.

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[contents]

 

 

 

 

2.1.2

[Gluons’ Non-Transitive Identity]

 

[The binding action of gluons involves non-transitive identity.]

 

[In order to explain how gluons glue, we will also need to change the logical properties that we normally ascribe to identity, namely, we need to conceive it as being non-transitive. First Priest will give an informal account of gluonic non-transitive identity, and at the end, he provides a more technical account.]

This will immediately launch us into a discussion of identity. Identity cannot work in the way that orthodoxy takes it to if gluons are to do their job. In particular, it must be non-transitive. How so? The rest of the chapter explains, and articulates the nature of gluons more precisely in this theoretical context. The ideas are spelled out informally. Full technical details can be found in the technical appendix to the chapter, Section 2.10, which can be skipped without loss of continuity by those with no taste for such things.

(16)

[contents]

 

 

 

 

 

Bibliography:

 

Priest, Graham. 2014. One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford: Oxford University.

 

 

 

.

Priest (1.6) One, “The Aporia”, summary

 

by Corry Shores

 

[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

[Central Entry Directory]

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[The following is summary. You will find typos and other distracting mistakes, because I have not finished proofreading. Bracketed commentary is my own. Please consult the original text, as my summaries could be wrong.]

 

 

 

Summary of

 

Graham Priest

 

One:

Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness

 

Ch.1

Gluons and Their Wicked Ways

 

1.6

The Aporia

 

 

 

Brief summary:

(1.6.1) None of our available options of explaining unity in terms of the factor that binds parts together into the whole (which is called the “gluon”) are viable. (1.6.2) We might say there are no gluons, thereby claiming that there are parts in the world but no wholes. This cannot be so, because in thought there are unified mental entities. (1.6.3) We also cannot argue that there are no gluons on account of the world being one whole without containing any parts. For, even in this case we do in practical life think of wholes with parts, meaning that the mental entities involved in those conceptions are wholes with parts and thus have gluons. (1.6.4) Gluons can be referred to, so we cannot claim they are not objects. (1.6.5) We cannot say that the gluon is an object, because that takes unity for granted rather than explain it. (1.6.6) Our best option for understanding gluons is with the dialetheic claim that they both are and are not objects.

 

 

 

 

 

 

Contents:

 

1.6.1

[The Lack of Available, Viable Options to Explain Gluonic Unification]

 

1.6.2

[The Inadequacy of Rejecting the Existence of Gluons and Positing a Wholeless World]

 

1.6.3

[The Inadequacy of Rejecting the Existence of Gluons and Positing a Partless World]

 

1.6.4

[Gluons as Necessarily Objects on Account of Being Referable]

 

1.6.5

[Gluon as not Being an Object]

 

1.6.6

[Gluons as Dialetheias]

 

Bibliography

 

 

 

 

 

Summary

 

1.6.1

[The Lack of Available, Viable Options to Explain Gluonic Unification]

 

[None of our available options of explaining unity in terms of the factor that binds parts together into the whole (which is called the “gluon”) are viable.]

 

[In section 1.5, we discussed the problem of explaining unity. We noted all of our available options, and we saw how none are satisfactory. The unifying factor we want to give an account of is called the gluon (see section 1.3.4). Priest then notes a point he makes in section 1.3.4 and section 1.3.5, namely, that gluons are contradictory objects, because in order to be what they are, they must both be entities while also not being entities. They are entities in that we are talking about them (and anything you can talk about is an entity, for what else would it be?), and yet they are not entities on account of the Bradly regress (see section 1.4, especially 1.4.2), and so by thinking of a gluon simply as an entity makes it a part of the problem of explaining unity rather than a part of the solution. We are thus at an impasse or aporia. Priest says we have three options:

{1} We can say that there are no gluons.

(I suppose for this option, we are claiming that there is no binding, unifying factor in things. But then we are giving up the question altogether it seems. And that is not what we want, because the question is of great philosophical importance.)

{2} We can reject the claim that a gluon is an object.

(Here we would solve the problem of the Bradley Regress, but then we would seem to be unable to talk about it, which is very unhelpful for trying to account for it.)

{3} We can reject the claim that it is not an object.

(This will allow us to talk about it, but then we encounter the Bradley Regress, which prevents us from accounting for unity or the gluon.) (Note, Priest gives his own reasoning in the following sections.) Given that all these options are highly problematic, we seem not to have any good way to proceed.]

We have, then, an aporia.Whatever it is that constitutes the unity of an entity must itself both be and not be an entity. It is an entity since we are talking about it; it is not an entity since it is then part of the problem of a unity, not its solution. ‘Aporia’ is often glossed as ‘puzzle’ or ‘uncertainly’, but it literally means something like ‘impasse’. An aporia is a source of puzzlement and uncertainty precisely because it seems to leave no way to go forward. In the present case, if we wish to go back, there are only three options:

1. We can say that there are no gluons.

2. We can reject the claim that a gluon is an object.

3. We can reject the claim that it is not an object.

Prospects look bleak.

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[contents]

 

 

 

1.6.2

[The Inadequacy of Rejecting the Existence of Gluons and Positing a Wholeless World]

 

[We might say there are no gluons, thereby claiming that there are parts in the world but no wholes. This cannot be so, because in thought there are unified mental entities.]

 

[Recall the first option from section 1.6.1 above.

{1} We can say that there are no gluons.

Because gluons are the binding factor that unifies parts into wholes, if we deny they exist, we also deny that there can be a difference between a unity that has parts and a simple plurality of those parts. (For, without this factor, there would be nothing to make a plurality of parts unified into a whole, and thus it would be no different from an unified plurality of parts.) One way to work around this could be to say that there are just parts but no wholes, and thus “the world is just a congeries of congeries” (14). But this cannot be so. For, we have unities in thought, which although being mental entities, still qualify as unities and thus their gluonic unification still needs to be accounted for.]

Consider the first case. If there are no gluons, then we are bereft of an explanation as to the difference between a unity with parts and the plurality of the parts, which there certainly is. We could avoid this by supposing that there are no unities: the world is just a congeries of congeries. All parts, no unities. But this does not seem to help either. If there are no unities, there certainly appear to be; that is, there are unities in thought. This means that the mind constitutes unities— as, perhaps, for Kant. But in this case, there are gluons.These are mental entities, but they fall foul of the aporia in the usual way.²²

(14)

22. The view that there are no material wholes, only simples, is defended in Unger (1979). There are no tables: only atoms ‘arranged table-wise’ (as van Inwagen puts it (1990), p. 72ff). Sider (1993) points out that this commits the view to the (counterintuitive) necessity of the existence of physical simples (partless wholes). (Gluon theory is not so committed.) And Uzquiano (2004) argues that | attempts to paraphrase away talk of unities in the way suggested is problematic. In any case, the view hardly seems credible for abstract objects. A proposition is a single thing: one can believe it, express it. You can not do this to a plurality of meanings arranged proposition-wise, whatever that might be supposed to mean. (14-15)

[contents]

 

 

 

1.6.3

[The Inadequacy of Rejecting the Existence of Gluons and Positing a Partless World]

 

[We also cannot argue that there are no gluons on account of the world being one whole without containing any parts. For, even in this case we do in practical life think of wholes with parts, meaning that the mental entities involved in those conceptions are wholes with parts and thus have gluons.]

 

[Recall yet again the first option from section 1.6.1 above.

{1} We can say that there are no gluons.

Priest now notes another way this could be so. Suppose the world is one whole unity without any parts. It in this sense would also not have any gluons; for there would be no parts to be bound together into wholes. But this goes against common sense and practical life, where for example our car certainly has parts that would render the car inoperable if they were missing. But someone might say that the car is not really such a unity of parts (I am not sure what else it would be, I suppose we only have the one world, and the car is not some unity within it, but I am not sure), and we only mistakenly think that the car is a whole. But even in that case, we are admitting that we conceive of it as a whole containing parts, which means the mental entity of that conception would still involve gluons.]

At the other extreme, one might suppose that there are unities, but that they have no parts, and hence that there are no gluons. All unities, no parts. A very extreme form of this position is to the effect, not only that there are only unities, but there is only one of them. All else is appearance. The view is to be found in Parmenides and Bradley. Supposing that there are only unities with no parts is a desperate move. It flies in the face of common sense: if someone steals a wheel of my car then it is missing an essential part. And before one says that the car is not really a whole, but we only think of it in that way, recall that this means that there is a unity in intention, and we are back with intentional gluons.

(15)

[contents]

 

 

 

 

1.6.4

[Gluons as Necessarily Objects on Account of Being Referable]

 

[Gluons can be referred to, so we cannot claim they are not objects.]

 

[Now recall the second option from section 1.6.1 above.

{2} We can reject the claim that a gluon is an object.

But “we can refer to it, quantify over it, talk about it.” Priest says that there is little other sense to what would qualify something as being an object.]

In the second case, we must insist that the gluon is simply not an object. But this seems even more desperate: we can refer to it, quantify over it, talk about it. If this does not make something an object, I am at a loss to know what could. Anything we can think about is an object, a unity, a single thing (whether or not it exists). There seems little scope here.

(15)

[contents]

 

 

 

1.6.5

[Gluon as not Being an Object]

 

[We cannot say that the gluon is an object, because that takes unity for granted rather than explain it.]

 

[Now finally recall the third option from section 1.6.1 above.

{3} We can reject the claim that it is not an object.

We have seen from section 1.4 (see especially 1.4.2) that this leads to the Bradley Regress. (But Priest’s point this time seems different. I do not quite grasp it, so consult the quotation below. He seems to be saying the following. Let us suppose the gluon is an object. But what we are trying to explain are unified objects. He next says that the only way an object can constitute the unity of another object is by taking unity for granted. That is the part I do not follow so well. Are we talking about taking the unity of the gluon for granted, so that it does not lead to a regress? Or are we taking the whole thing’s unity for granted? At any rate, this somehow involves simply thinking that the unity of things are obvious or unquestionable. But examples of unities very often involve combinations of parts, and we do not explain their compositional bonding by claiming that gluons are objects ((or by otherwise taking unity for granted)). But I am guessing here.]

Finally, in the third case, we may suppose that the gluon is simply an object. But we have seen that this just leaves us bereft of an explanation of the unity of an entity. How could we even have had the impression that any object could constitute the unity of another bunch of objects? Only because of taking the unity for granted. Thus, we write ‘Socrates is a person’ and the rest is obvious. But putting ‘Socrates’ and ‘is a person’ next to each other does not do the job; it just produces a plurality of two things. When we think of the two as cooperating, the magic has already occurred.

(15)

[contents]

 

 

 

1.6.6

[Gluons as Dialetheias]

 

[Our best option for understanding gluons is with the dialetheic claim that they both are and are not objects.]

 

So we cannot use any of the available options, and we should instead say that gluons both are and are not objects. What prevents us is the Principle of Non-Contradiction. But since it is not a well-founded logical principle and since also it is best not obeyed in all cases, we will take the dialetheic position that Gluons have contradictory properties (again, they both are and are not objects.)

If we cannot go back, then we must go forward. What stands in the way? Evidently, the Principle of Non-Contradiction. If we accept that gluons both are and are not objects, then some contradictions are true. Whilst it must be agreed that horror contradictionis is orthodox in Western philosophy, at least since Aristotle’s canonical –but fundamentally flawed – defence, the friends of consistency have done little as yet to establish that there is anything rational in this.²³ So let us go forward. Gluons are dialetheic: they have contradictory properties. Of course, if this were all there were to matters, the situation would not be particularly interesting. Going on means crossing the bridge of inconsistency;²⁴ and what is important is what lies on the other side.

(15)

23. See Priest (2006).

24. Not that there are no other good reasons to do so. See Priest (1987) and (1995a).

[contents]

 

 

 

 

 

 

 

Bibliography:

 

Priest, Graham. 2014. One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford: Oxford University.

 

 

Or if otherwise cited:

 

Priest, G. (1987), In Contradiction, Dordrecht: Martinus Nijhoff; second (extended) edn., Oxford: Oxford University Press, 2006.

 

Priest, G. (1995a), Beyond the Limits of Thought, Cambridge: Cambridge University Press; second (extended) edn., Oxford: Oxford University Press, 2002.

 

Priest, G. (2006), Doubt Truth to be a Liar, Oxford: Oxford University Press.

 

Sider, T. (1993a), ‘Parthood’, Philosophical Review 116: 51–91.

 

Sider, T. (1993b), ‘Van Inwagen and the Possibility of Gunk’, Analysis 53: 285–9.

 

Unger, P. (1979), ‘There are no Ordinary Things’, Synthese 41: 117--54.

 

Uzquiano, G. (2004), ‘Plurals and Simples’, Monist 87: 429–51.

 

 

 

 

.

Priest (1.5) One. ‘Explaining Unity,’ summary

 

by Corry Shores

 

[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

[Central Entry Directory]

[Logic and Semantics, entry directory]

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[The following is summary. You will find typos and other distracting mistakes, because I have not finished proofreading. Bracketed commentary is my own. Please consult the original text, as my summaries could be wrong.]

 

 

 

Summary of

 

Graham Priest

 

One:

Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness

 

Ch.1

Gluons and Their Wicked Ways

 

1.5

Explaining Unity

 

 

 

Brief summary:

(1.5.1) One possible explanation for what a gluon (the unifying factor in something’s composition)  is, is that it is the binding relationality of the thing’s internal arrangement or structure. (1.5.2) But not all relations are compositional, as for example the relation of child to a mother. (1.5.3) The relational interpretation of the gluon only makes matters worse, because it then presents a difficult metaphysical problem of explaining how something non-physical can bind physical things. (1.5.4) (The relational interpretation of the gluon also fails because the thing’s relationality only presents itself as another entity needing yet another to explain its integration in the whole, and that new binding entity would need yet another, and so on. (1.5.5) Another possible sort of account for unity is ontological dependence. One might claim that whenever the identity of the parts depends on the identity of the whole, that this very dependence itself is what accounts for the thing’s unity. But this fails as an account, because it does not yet explain how the parts cooperate to form a unity. (1.5.6) There are a lack of conventional accounts of unity. Priest will propose a new one, which will involve modifications in our notion of identity. (1.5.7) Accounts of unity that merely describe the causal processes that go into something’s generation or production, like a carpenter’s explanation of how to construct a table, satisfy to some extent the how curiosity we have for an account of unity. But they fall short for a number of reasons. {1} They do not explain the unity brought about but only the processes bringing it about. {2} They lack an explanation for what makes unifying causal processes different from non-unifying ones. And {3} they cannot explain the unity of abstract objects. (1.5.8) Thus, we do not have any easy ways to account for unity.

 

 

 

 

 

Contents:

 

1.5.1

[The Gluon as a Relation That Binds]

 

1.5.2

[Relations as Not Necessarily Compositional]

 

1.5.3

[The Failure of the Relational Interpretation of the Gluon on Account of Metaphysical Incompatibility]

 

1.5.4

[The Failure of the Relational Interpretation of the Gluon on Account of the Bradley Regress]

 

1.5.5

[The Ontological Dependence Account of Unity and Its Failure]

 

1.5.6

[Priest’s Offer]

 

1.5.7

[The Causal Process Account of Unity and Its Failure]

 

1.5.8

[The Lack of Convenient Accounts of Unity]

 

Bibliography

 

 

 

 

Summary

 

1.5.1

[The Gluon as a Relation That Binds]

 

[One possible explanation for what a gluon (the unifying factor in something’s composition)  is, is that it is the binding relationality of the thing’s internal arrangement or structure.]

 

[Previously in section 1.3.4 we discussed the notion of the gluon, which is the unifying factor in the composition of something. Priest now addresses a possible notion of how to explain the gluon. Some might say that what accounts for the unity is the “configuration, arrangement, structure” or the like of the parts. As such, this would be saying that the gluon is a relationship between the parts, and it would cast this relationship as having binding properties.]

A common thought at this point is that what accounts for the unity of the parts of an object, its gluon, is their configuration, arrangement, structure, or some such. Whatever you call it, it is a relationship between the parts, and relationships relate, | by definition. Call relationships objects if you wish; but they are a special kind of object; and they bind together the parts by their very nature.¹⁹

(11-12)

19. We are not a million miles away here from Aristotle’s proposed solution to the problem.We will look at the details of his account in Chapter 3.

(12)

[contents]

 

 

 

1.5.2

[Relations as Not Necessarily Compositional]

 

[But not all relations are compositional, as for example the relation of child to a mother.]

 

Priest notes that this conception of the gluon (see section 1.5.1 above) confuses two ideas, namely, between relating and unifying. A relation by its own is not normally something that compositionally unifies what it relates. To illustrate, Priest has us consider for example the relationship of oneself being a child to one’s mother. Here the relationship does not unify the two people. [I would have expected another sort of example, given the biological and psychological bond that such a relation is thought to have. Perhaps the idea is that simply by being a mother’s child is not sufficient a bond to compose a unity of the two into one object. Deleuze when discussing Spinozistic composition gives the example of a married couple composing one composite thing. I would think that a mother-child relation would not be too far off from such a structure, but I am not sure.]

There is already a confusion at the heart of this thought –and not an uncommon one. The confusion is between relating and unifying. Relations do not, in general, unify. I am related to my mother by bearing the relationship of child to her. This may even be an internal relation (whatever, exactly, that means) – at least as far as I am concerned: I could not have been me had I not had that relation. But obviously the relation does not serve to render my mother and myself a unity in the appropriate sense.

(12)

[contents]

 

 

 

1.5.3

[The Failure of the Relational Interpretation of the Gluon on Account of Metaphysical Incompatibility]

 

[The relational interpretation of the gluon only makes matters worse, because it then presents a difficult metaphysical problem of explaining how something non-physical can bind physical things.]

 

[Priest’s next point seems to be the following. The notion of the gluon as a composition-forming relation that we noted above in section 1.5.2 still construes it as an entity. As we noted, it is a different kind of entity than the thing’s parts, namely, it is a relation, and what it relates are “things” more straightforwardly understood. In our example of the house, the bricks are the things, and the gluon under this relational interpretation would be the particular relational organization of the parts on account of which the parts compose a whole house rather than a mere collection of independent bricks. Priest now says that this does not help, and his reasoning seems to be the following. The main problem lies in the fact that not only is a relation a different kind of thing than its parts, it is of such a kind that we now have yet a greater problem of understanding how it can be said to combine with those parts. His raises the mind-body problem, which stems largely from the mind being of such a different kind of thing as the body that it is very difficult to both maintain their conventional distinction while also understanding how they have the intimate relation we think them to have. So suppose we take this relational interpretation of the gluon. We now have the even greater challenge of explaining how a relation, being so very different than a part, especially a physical part, “latches-on” so to speak to the parts and binds them in their physical unity but in a way that is different from the normal physical properties and interactions we assign to the objects. To venture to put it another way, the gluon that organizes the house under this relational interpretation would need to have some sort of “sense” to it, like the houseness or house-form expressed by the bricks in their entire inter-relationality. But this sense cannot be something that is in itself physical. The mortar binding the bricks is physical, but the mortar can bind them haphazardly or under a different sense, like “wall”. The gluon however is not something physical like the mortar is. But as such, how does something not physical bind together physical things? (So as we see, our account of unity must include a notion of a binding factor, hence the gluonics. But that “binding” we seek to explain is not a physical thing but rather a principle to understand how it is that things by being so bound constitute a unity, I think. To venture a rewording, what we seek is a notion of compositional binding that accounts for unity. For, the main aspect of unity to be explained is not the oneness as much as the factor that brings the multiple parts together into a oneness.)]

Even setting aside the confusion, though, the thought still does not work. The fact that a gluon is a different kind of object does not solve the problem of unity. If anything, it simply makes it worse. Thus, what it is that joins the mind and body into a unity is a traditional and vexed problem in dualistic theories of mind. It is the very fact that they are different kinds of thing that seems to make the problem so intractable. In a similar way, suppose that it is the configuration of the bricks that binds them together to form a house. The bricks are physical objects; the configuration is, presumably, an abstract object. (Different sets of bricks can have the same configuration.) Any interaction between the bricks and the configuration would therefore seem just as problematic, perhaps even more so, as that in the mind/body case.

(12)

[contents]

 

 

 

 

1.5.4

[The Failure of the Relational Interpretation of the Gluon on Account of the Bradley Regress]

 

[The relational interpretation of the gluon also fails because the thing’s relationality only presents itself as another entity needing yet another to explain its integration in the whole, and that new binding entity would need yet another, and so on.]

 

[Priest’s next point seems to be the following. We said in section 1.5.3 above that one problem with the relational interpretation of the gluon is that it posits an entity whose metaphysical compatibility with its parts is not easy to account for. Now we return to the Bradley regress. By positing the relationality as the binding, organizing element, we have only created another entity which calls for yet another binding entity to explain how it binds with the parts, and that new entity will need yet another, and so on. Priest may be saying something else or more, so let me quote:]

So it has to be the particular nature of the special object that is supposed to solve the problem. But how does it do so? To say that it just does do this – by its nature – is not to solve the problem; it is simply to name it. As Bradley puts it (speaking of the mind, but with considerations that apply quite generally):²⁰

When we ask ‘What is the composition of [an object]’, we break up [that object], which comes to us as a whole, into units ... But since it is clear that these units by themselves are not all the ‘composition’, we are forced to recognize the existence of relations. But this does not stagger us. We push on with the conceptions we have brought to the work, and which of course can not be false, and we say, Oh yes, we have there more units, naturally not quite the same as the others, and – voilà tout. But when a sceptical reader, whose mind has not been warped by a different education, attempts to form an idea of what is meant, he is somewhat at a loss.

For when one invokes the object in question, one simply adds an extra element to the melange. If one is puzzled by the unity in the first case, one should be equally puzzled by the supposed unity in the second. Thus, for example, instead | of a plurality of physical parts of an object, we now have a plurality of [parts plus configuration]. Or more generally, we have the parts plus the relationship between them (or the action of the relation, or the fact that they are so related). How is this any better? This is exactly what the Bradley regress highlights.

(12-13)

20.

Bradley (1922), sect. 65. Here and throughout the book, all italics in quotations are original unless otherwise specified.

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[contents]

 

 

 

 

1.5.5

[The Ontological Dependence Account of Unity and Its Failure]

 

[Another possible sort of account for unity is ontological dependence. One might claim that whenever the identity of the parts depends on the identity of the whole, that this very dependence itself is what accounts for the thing’s unity. But this fails as an account, because it does not yet explain how the parts cooperate to form a unity.]

 

[Priest now notes another way to account for the unity of an object. I may not summarize this properly, so it is best to skip to the quotation below. But let us follow the reasoning first. We first consider a pile of stones. Now, what gives the pile of stones its identity? To be a pile of stones means first that it is a pile, and thus a pile of things, and secondly it means that what it is a pile of are stones. In other words, the identity of a pile of stones depends entirely in the identity of its parts. But what about the identity of the stones, the parts of the pile? They would have the same identity as being whatever stone they are, independently of the pile they happen to be in. Were they in another pile or lying outside a pile, they would have the same identity. Next consider some person’s body. Each body part, like a hand, has (it seems from the text) an identity related to the owner. Priest writes: “We would not have that hand unless it were part of that body.” This means that the identity of the body part (being, it seems, individualized and identifiable by means of the body it belongs to) depends on the identity of the body it is a part of. (I am not sure if the body’s identity also depends on the parts’ identities or not.) Some use this notion to explain unity. They say that this dependence of the parts’ identities on the whole’s identity is what explains the unity of the thing. (Perhaps the insight here is the following, but this is a spontaneous guess, sorry. The parts have identities. That is something fundamental to them, maybe even what is most fundamental to them. Now, what is most fundamental to the parts is not something lying within them but rather is something lying in their belonging-together to the whole. The parts as such would not even exist were they not part of that whole (or at least they would be different things altogether). So we might think then of this dependence of the parts on the whole as being a fundamental “bond” they hold with each other; for without this bond, they would not be what they are. This “bond” would seem to be some fact of their “being” or some such metaphysical concept. To put it another way, we have established that the parts’ being, identity, existence, etc. stems from their being in the particular whole they are in. But that being in some particular whole is a matter of their particular relational combination with the other parts. Thus this very dependence on the whole for identity is at the same time the inter-relative bonding dependence of the parts. I am reaching.) Priest next explains why this notion of ontological dependence does not still account for unity. He says that this account only provides a description of some feature of unified things. What it cannot do, but needs to for such an account, is to explain how the parts interrelate so to compose a unified thing. (Philosophically speaking, I find this claim striking, but perhaps it is obvious. In philosophy, when we want to give an account of something, the question we ask is how. For example, to give an account of unity, we ask, how do the parts form the whole. What sort of an answer would satisfy such how questions? In the case of unity, we will find out as we go. But I suspect that it could involve identifying structural elements and describing both the structural features they have which play a role in forming the unity and also their manner of interaction or interrelation in that formation. In other words, we might need something more of a mechanical explanation, or an account or story that tells us, how it all works.)

A quite different possibility for explaining the unity of an object is one which appeals to the notion of (ontological) dependence. Consider a pile of stones and a person’s body. The former, it might be suggested, is not a true unity; the latter is. And what makes the difference is that the identity of the pile depends on the identity of its parts, the stones; whereas in the case of the body, it is the other way around: the identity of the parts depends on the identity of the whole. (We would not have that hand unless it were part of that body.) Thus, the thought continues, what explains the oneness of a partite genuine unity is the dependence of its parts on the whole. There will be much to be said about dependence in Part III of the book. For the moment, let us grant the claims about what depends on what. Even given these, the suggestion will not work. The fact that in a unity the natures of the parts depend on the nature of the whole in no way explains how they cooperate to form a unity. For all their dependence, the parts are still parts; and facts about identity do not bear on cooperation. Granted, the parts would not be the parts they are unless they were parts of the whole. But that hardly explains how it is that the various parts do what they do to create the whole. We know, by their nature, that they are parts of that whole; but how is it that they have this nature?

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21. This possibility was suggested to me by Jonathan Schaffer. It is hinted at in his (2010b).

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[contents]

 

 

 

1.5.6

[Priest’s Offer]

 

[There are a lack of conventional accounts of unity. Priest will propose a new one, which will involve modifications in our notion of identity.]

 

Priest now notes that unity could be one of those things that are impossible to explain and that thus we must just accept without further investigation. Priest says that we should not quit so fast, because if we are willing to modify certain concepts like identity, we can arrive upon a satisfactory account, which is what Priest will be doing.

One could, I suppose, be a quietist about the whole matter: one might just accept that one cannot provide an explanation. All one can say about the phenomenon is to aver, every time one walks past a united object, ‘there it goes again’. Perhaps one has to be a philosophical quietist about some things. But giving up without a fight is an untoward defeatism. And if a perfectly good explanation can be found, as I shall argue that it can, unwarranted. Of course, explanations always come at a cost—some kind of commitment; and the explanation I shall offer is no exception. The cost in this case is revising how it is we currently think that certain things, and especially identity, work. But such is to be expected in any conceptual advance.Thus, for several hundred years scientists had no account of how gravitational effects are transmitted. Everything has an instantaneous effect on everything else, and that is that. No explanation. Since Einstein, we now have an explanation; but the explanation has caused major revisions in our conceptions of space, time, matter. The cost of a revision may be entirely warranted.

(13)

[contents]

 

 

 

 

1.5.7

[The Causal Process Account of Unity and Its Failure]

 

[Accounts of unity that merely describe the causal processes that go into something’s generation or production, like a carpenter’s explanation of how to construct a table, satisfy to some extent the how curiosity we have for an account of unity. But they fall short for a number of reasons. {1} They do not explain the unity brought about but only the processes bringing it about. {2} They lack an explanation for what makes unifying causal processes different from non-unifying ones. And {3} they cannot explain the unity of abstract objects.]

 

Priest next discusses explanations of unity that are simply accounts of the causal processes that are needed for the unity to come about. He says that such explanation are not satisfactory. For, such explanations do not tell us about what the thing actually is as the unity that it is. It simply tells us how that unity comes into being. He gives the example of marriage. To explain how to get married tells us nothing about what marriage is. Also, not all causal processes produce unities [so to use causal processes as the basis of the account still requires an explanation of what makes these unifying causal processes different from those that do not produce unities.] And lastly, even if we were satisfied with such causal accounts, they would only work for explaining the unities of physical things and not of “abstract objects, such as propositions, pieces of music (types, not tokens), sets” (14).

Alternatively, one might suggest that no explanation in the pertinent sense is called for. What constitutes the unity of a table? Simply that I take a piece of wood and nail four legs to it in appropriate places. There is nothing more to be | said. This will not do, however. What we are being offered here is an explanation of how the unity came into being – the causal processes that brought it about. Now, explaining how something is brought about is not explaining what it is that has been brought about. To explain how to get married is not to explain what a marriage is. One who nails the legs to a table top in the appropriate way has indeed brought the table into existence by certain causal processes. But causal processes are going on all around us, and only some of them bring objects into existence. So what is it that one which does so, actually does? In any case, the suggestion, appealing as it does to causal processes, can account at best for the unity of things subject to such processes. It cannot account for the unity of abstract objects, such as propositions, pieces of music (types, not tokens), sets.

(13-14)

[contents]

 

 

 

 

1.5.8

[The Lack of Convenient Accounts of Unity]

 

[Thus, we do not have any easy ways to account for unity.]

 

Priest ends by saying, “There are no easy roads here” [for, we have seen all of our viable options, and none works well enough. Priest’s own suggestion is probably not an “easy” road either, as it will involve tweaking some fundamental concepts. But although it is not easy, at least it will work, unlike with our other options.] (14)

[contents]

 

 

 

 

 

Bibliography:

 

Priest, Graham. 2014. One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford: Oxford University.

 

 

Or if otherwise cited:

 

Bradley, F. H. (1922), The Principles of Logic, Oxford: Oxford University Press.

 

Schaffer, J. (2010b), ‘The Internal Relatedness of All Things’, Mind 119: 341–75.

 

 

 

 

 

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