Dupréel (1.6) La consistance et la probabilité constructive, sect 1.6, ‘Hiérarchie des êtres spatio-temporels’, summary

 

by Corry Shores

 

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[The following is summary and not translation. Bracketed commentary is my own, as is any boldface. Proofreading is incomplete, so typos are present, including in the quotations. Please consult the original text to be sure about the contents. Also, I welcome corrections to my interpretations, because I am not especially good with French.]

 

 

 

Summary of

 

Eugène Dupréel

 

La consistance et la probabilité constructive

 

Part 1

“La consistance”

 

1.6

Hiérarchie des êtres spatio-temporels

 

 

 

Brief summary:

(1.6.1) At the middle stage of consistency of spatio-temporal objects is the solid stage. Solids are things that are directly perceivable and that are capable of enduring for some time all while undergoing slow degradations, for example: stones, tools, jewels, and even whole planets. (1.6.2) At the lower stage of consistency of spatio-temporal beings are inconsistent objects. They are inconsistent in that they lack consistency in Dupréel’s sense of being self-holding and independent (and not in the sense of having contradictory properties). Inconsistent objects have properties that vary in relation to the consistencies of other objects they relate to physically. For example, the shape that liquids and gasses take on is determined by the shapes of the more solid objects that contain them. (1.6.3) The highest beings are those that not only can resist and endure detrimental external influences but as well are able to repair themselves after undergoing such alterations, with the outcome of that self-repair often increasing their consistency to a higher degree than before the attack. Examples of the highest kind of beings (those with the greatest consistency) are living beings, with thinking beings as the highest among them. (1.6.4) While this consistency-building repair process may happen for simple solids, it would not be something we could easily observe; however, it is very easy for us to see it in humans and non-human animals. (1.6.5) When we examine and discuss the degrees of consistency of beings, we must give special attention to collective beings in general, which include assemblages of differents and also mixtures of similars and differents. Too often such collective beings or groups – especially with regard to how they can be distinguished from the mere sums of their parts – are ignored and neglected.

 

 

 

 

 

 

 

 

Contents

 

1.6.1

[Solids]

 

1.6.2

[Inconsistent (Not Very Self-Holding) Spatio-Temporal Beings]

 

1.6.3

[Living Beings at the Highest Level of Consistency]

 

1.6.4

[Humans and Non-Human Animals as Obvious Cases for Consistency-Building Self-Repair]

 

1.6.5

[The Importance of Consistent,  Heterogeneous Groupings]

 

 

 

 

 

 

 

 

 

Summary

 

 

1.6.1

[Solids]

 

(p.13: “Sujet immense qui demanderait la compétence du savant ...”)

 

[At the middle stage of consistency of spatio-temporal objects is the solid stage. Solids are things that are directly perceivable and that are capable of enduring for some time all while undergoing slow degradations, for example: stones, tools, jewels, and even whole planets.]

 

[Recall from section 1.2.2 that the consistency of a being is its capacity to endure throughout a series of its vicissitudes. In section 1.3, we saw that sets of things often undergo a filtering process on the basis of shared powers of affection. We had for example the set of things first found together: sand, gravel, and large stones. They were all placed under the influence of wind. Each of these three things shares powers of affectivity, so the stones were largely unmoved and stayed in place, the gravel was pushed off a little bit away from the stones, and the sand was blown far away but deposited in the same depression in the ground some ways off. In section 1.4, we saw how such filtered groupings, under continued shared influences and vicissitudes, came to become more and more accommodated to one another. This causes the whole grouping they form to gain consistency all while its parts gain consistency too. However, there comes a point where there are two possible ways this group consistency-building can go. One way is toward solidification. Here the parts start to lose individuality and thus consistency as they fuse and homogenize all while the whole they form continues to gain consistency on account of that solidification of its parts. The other direction is toward increased consistency of both the parts and the whole. We see this in life-forms, for example, where the parts continue to diversify and maintain heterogeneity and relative individual independence  all while the whole living being they form also gains consistency on account of its internal heterogeneity that enables it to survive more vicissitudes and variational affections. In our current section, we will now discuss spatio-temporal beings, evaluated on a scale of more or less consistency. As we saw in section 1.4.2, many of the spatio-temporal beings around us tend toward the solidification process. There are three stages here, the middle one being that of the solid, where things are compact and inert. Examples of spatio-temporal things at this stage are stones, tools, jewels, and even a whole planet. They are any thing which is directly perceptible and capable of enduring for some time while also undergoing slow degradation.]

Sujet immense qui demanderait la compétence du savant jointe à l’expérience de l’homme d’action. Pour en marquer seulement la mise en place nous y relèverons trois étages. L’étage du milieu est celui du solide, compact et inerte ; tels sont une pierre, un outil, un bijou, même une planète!, toutes choses directement perceptibles, capables d’une longue durée tout en subissant une lente dégradation.

(13)

[contents]

 

 

 

 

 

 

1.6.2

[Inconsistent (Not Very Self-Holding) Spatio-Temporal Beings]

 

(p.13: “Au dessous de cet étage moyen on rangera tous les êtres ...”)

 

[At the lower stage of consistency of spatio-temporal beings are inconsistent objects. They are inconsistent in that they lack consistency in Dupréel’s sense of being self-holding and independent (and not in the sense of having contradictory properties). Inconsistent objects have properties that vary in relation to the consistencies of other objects they relate to physically. For example, the shape that liquids and gasses take on is determined by the shapes of the more solid objects that contain them.]

 

[Below this middle stage of solids are all the beings that we might call inconsistent beings. But here we should be careful it seems. We do not seem to mean inconsistent as lending to contradictions or heterogeneities. It seems rather to mean not consistent in Dupréel’s sense of “consistency”. So such inconsistent beings are ones that lack their own consistency, meaning that they do not hold well together on their own. Rather, they depend on beings at a higher level of consistency. I do not quite grasp the next point, but I will guess until we get to an example, which is much clearer. So such bodies with a low degree of self-consistency (meaning that they vary in accordance to variations with respect to the higher being they depend upon) will have certain qualities or properties that will undergo those variations, even though the whole body itself will maintain. Fox example, a liquid or a gas has among its properties its physical form in the sense of the shape it finds itself having at some moment. That shape will often depend on the shape of the container that is holding it. So its consistency is not null, because it remains as the liquid or gas that it happens to be, but its consistency is subject to the consistency of an external consistency of another object with its own greater consistency.]

Au dessous de cet étage moyen on rangera tous les êtres que l’on peut appeler les inconsistants en voulant marquer par là leur dépendance de quelque être du niveau supérieur, ainsi les qualités ou attributs des solides, comme la couleur ou une partie d’un corps, varieront comme variera le corps dont elles sont un complément ; un liquide, un gaz, incapables de se soutenir sont soumis au récipient qui les porte ou les retient et dont ils partageront plus ou moins la plupart des variations. Leur consistance n’est jamais nulle, mais toujours soumise à une consistance étrangère.

(13)

[contents]

 

 

 

 

 

 

1.6.3

[Living Beings at the Highest Level of Consistency]

 

(p.13-14: “Les Êtres supérieurs. – Il y a enfin au dessus ...”)

 

[The highest beings are those that not only can resist and endure detrimental external influences but as well are able to repair themselves after undergoing such alterations, with the outcome of that self-repair often increasing their consistency to a higher degree than before the attack. Examples of the highest kind of beings (those with the greatest consistency) are living beings, with thinking beings as the highest among them.]

 

[Beings at the highest level of consistency obtain their consistency on the basis of their own means of action. Such beings cannot only avoid or endure detrimental external influences that cause alterations to them, they can also repair themselves after having been detrimentally altered, sometimes even being stronger than before. (Perhaps we might here think about building immunities to pathogens or repairing damaged muscle material, which builds those muscles stronger.) Beings of this highest level of consistency are living beings, and highest among them are thinking beings. (I am guessing the next point is: So as we can see, we can order beings on the basis of consistency in this way where the higher ones are those that are most resistant to external attacks and that even increase in consistency as a result of them.)]

Les Êtres supérieurs. – Il y a enfin au dessus des solides et des inconsistants les êtres dont la consistance particulière repose sur des moyens d’action desquels ils sont intérieurement pourvus. Ceux-là ne sont pas seulement capables d’atténuer les altérations subies, ou d’éviter certains d’entre elles, mais il leur arrive même de restaurer les dégradations subies par le fait de l’extérieur, au point de se retrouver dans le même état qu’avant le détriment, voire dans un état plus avantageux. Ce troisième étage est celui des êtres vivants ; à leur sommet sont les êtres pensants. Notre analyse de la consistance en général nous permet d’y joindre les | êtres collectifs en voie de progression et qui doivent à la similitude de leurs éléments de riposter aux attaques du dehors par un progrès relatif de leur consistance.

(13-14)

[contents]

 

 

 

 

 

 

1.6.4

[Humans and Non-Human Animals as Obvious Cases for Consistency-Building Self-Repair]

 

(p.14: “Lorsqu’il s’agit de collections de solides simples, ...”)

 

[While this consistency-building repair process may happen for simple solids, it would not be something we could easily observe; however, it is very easy for us to see it in humans and non-human animals.]

 

[(I do not grasp the next idea. I am for now guessing it is the following. In section 1.6.3 above we saw that beings of the highest level of consistency can self-repair after detrimental external influences and even thereby attain yet a greater consistency as a result (perhaps like muscle-building or immunity-building). Maybe now Dupréel is saying that such processes could be found among simple solids, only these processes are too hard to detect by means of normal human observation; however, this process we very easily can observe among non-human animals and humans. See the quotation below.)]

Lorsqu’il s’agit de collections de solides simples, ce processus est toujours trop rare, ou plutôt trop peu accusé, trop partiel, interrompu ou trop lent pour tomber directement sous notre observation, mais il se confirme entièrement quand la collection est celle d’éléments déjà pourvus du plus haut degré de consistance, tels que les animaux et les hommes.

[contents]

 

 

 

 

 

 

1.6.5

[The Importance of Consistent,  Heterogeneous Groupings]

 

(p.14: “Dans l’enquête sur le degré de consistance des êtres ...”)

 

[When we examine and discuss the degrees of consistency of beings, we must give special attention to collective beings in general, which include assemblages of differents and also mixtures of similars and differents. Too often such collective beings or groups – especially with regard to how they can be distinguished from the mere sums of their parts – are ignored and neglected.]

 

[(ditto)]

Dans l’enquête sur le degré de consistance des êtres une place importante est à réserver aux êtres collectifs en général (y compris les rassemblements de différents, et les mélanges de semblables et de différents). L’importance des être collectifs, des groupes en tant que tels, à distinguer de la simple somme de leurs éléments, a toujours été méconnue et négligée.

[contents]

 

 

 

 

 

 

 

 

Dupréel, Eugène. (1961). La consistance et la probabilité constructive. (Classe des lettres et des sciences morales et politiques 55, no.2). Brussels: Académie Royale de Belgique.

PDF at:

http://www.academieroyale.be/fr/les-publications-memoires-detail/oeuvres-2/la-consistance-et-la-probabilite-constructive/.\

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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.

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[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.

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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.

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[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.

 

 

 

 

Dupréel (1.4) La consistance et la probabilité constructive, sect 1.4, ‘L’amalgamation’, summary

 

by Corry Shores

 

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[The following is summary and not translation. Bracketed commentary is my own, as is any boldface. Proofreading is incomplete, so typos are present, including in the quotations. Please consult the original text to be sure about the contents. Also, I welcome corrections to my interpretations, because I am not especially good with French.]

 

 

 

Summary of

 

Eugène Dupréel

 

La consistance et la probabilité constructive

 

Part 1

“La consistance”

 

1.4

L’amalgamation

 

 

 

Brief summary:

(1.4.1) As similars come more to group and mutually accommodate to one another, they may advance to becoming a single “solid” where the consistency of the parts gives way to the consistency of the whole agglomerated unit. (1.4.2) Many groupings continue this process toward solidification where the parts fuse and thereby lose their individuality and thus their consistency all while the whole they form, which is solidifying, increases its consistency. But while many of the things around us follow this path of development, there are other things which follow a different developmental trajectory. In their case, the whole they form increases in consistency as the parts mutually affect one another, but the parts in that process likewise increase in consistency, as they increase their individuality and ability to maintain their identity. But even though there is an increase of consistency both on the level of the whole and on the level of the parts, the process of consistency-increase itself may not be a concordant one (as the parts are still further individualizing even as the whole they form increases its consistency.) (1.4.3) Living creatures like plants and animals are the sorts of beings whose parts may increase in heterogeneity and individuality, and thus in their own consistency, all while the whole benefits from this and increases in its consistency too. It is also possible in such advanced beings that the parts will resist the whole’s totalizing tendencies, which can place restrictions on the liberties and consistencies of the parts; these acts of resistance thereby place caps on the grouping’s ability to increase the consistency of the whole.

 

 

 

 

 

 

 

 

Contents

 

1.4.1

[The Amalgamation of Agglomerations of Similars]

 

1.4.2

[Beings Whose Whole Increases in Consistency While the Parts Do Too, Despite Increasing Heterogeneity]

 

1.4.3

[Living Beings as Heterogeneously Consistent Wholes]

 

 

 

 

 

 

 

Summary

 

 

1.4.1

[The Amalgamation of Agglomerations of Similars]

 

(p.11: “Comme on vient de le voir les semblables ”)

 

[As similars come more to group and mutually accommodate to one another, they may advance to becoming a single “solid” where the consistency of the parts gives way to the consistency of the whole agglomerated unit.]

 

[Recall first from section 1.2.2 that we defined the consistency of a being as its capacity to maintain its identity throughout the variations or “vicissitudes” it undergoes as a result of its interactions and relations with other beings (p.7, section 1.2.2). And next recall some other important notions from the prior section 1.3. The following comes from our brief summary.

(1.3.1) Beings’ vicissitudes can be analogously affected by shared influences, like wind blowing all the different things on a plain. We notice here that beings with analogous vicissitudes have features in common but also distinct ones too. We wonder, do differences in their fates result from differences in their features? To perform our analysis on this matter, we will begin with beings that share more common traits than differences, and we call such beings: similars. (1.3.2) When a variety of things are haphazardly mixed together, that mass can be easily disassembled by one common influence, like wind blowing on a mass of sand, gravel, and large stones. The sand will blow far away but in the same direction and probably all deposit in the same place, while the gravel will move only slightly and the large stones not at all. There groupings were sorted on account of shared powers of affection (of affecting and being affected), and elements with different powers were filtered out from one another. So while they were still their haphazard mixture (sand-gravel-stones), they had little consistency, because their various powers of affection made it such that the identity of the mass was easily disrupted. But after that sorting influence, the parts held together more readily, because they were not contaminated by other elements that would split-off from the group and thereby break the collection apart when a common influence affects the whole conglomerate. (1.3.3) We can thus observe the following. Outside influences affecting a plurality of similars probably result in {1} the similarity of the similars maintaining throughout the affective influences, and {2} the elements coming closer together on account of the separation of the different things and the increase of the consistency of the collective being that constitutes their whole, or otherwise to give rise to this collective being on account of their increased capacity to conserve under the altering factors.

(from the brief summary to section 1.3)

Dupréel reminds us now of similars under the prolonged effect of shared vicissitudes (like the wind blowing the sand out from the sand-gravel-stone mixture) come to form a more homogeneous body where the sand grains are now more intimately in contact. Dupréel now says that all the members of such filtered groupings may come to be so agglomerated to one another that they are transformed into a single solid where the consistency of the members gives way to a more fundamental consistency of their compact gathering. (I am not entirely sure that I follow. Let us keep with our example. We have sand grains as members of the sifted sand body. Each grain apparently has consistency. But that seems odd, because I thought we were taking each grain as elemental and thus its consistency was guaranteed. So perhaps we might think of a sand-gravel mixture, and we think of them tumbling around somehow in an open tumbler such that the gravel grinds the sand grains so much they become tiny air-born particles that sort of “evaporate” away so to speak. Thus under the vicissitudes of the tumbling gravel interaction, each sand grain has lowered consistency. But under the vicissitudes of wind interaction, the sand grains instead flee off to a dune where they reside together. Given how this process has made it such that all the members of the sand, namely, each of the grains, has become very well accommodated to each other, that means they often live, die, move, and modify by the same influences. That got them in the dune to begin with. And suppose further that a particularly well purified part of that sand body is appreciated for the physical properties of its high degree of mutual affective accommodation among the parts that it is placed into an hour-glass. Here the regularity of the physical features and dynamics of the sand grains make it form one agglomerated substance. Even when split between the bulbs, that is normally because it was flipped and the particles in each bulb are connected by a fluid stream of sand from one end to the other. We can thus see an hour’s worth of sand as being like one “solid” body rather than a group of grains that can go off their own ways. And in this state, their mutual accommodation will not strongly destroy one another like the gravel and sand tumbling mixture would. So the consistency of each grain in the hour glass gives way to the consistency of the whole hour’s worth of sand in the glass, now forming one “solid” unit rather than a set of dispersible or mutually destructible individuals/similars.]

Comme on vient de le voir les semblables sous l’effet prolongé de leurs vicissitudes, ont chances de se trouver enfin rapprochés les uns des autres et, par l’éviction corrélative des corps différents d’abord intercalés, ils en viendront à se toucher d’un manière continue. Un pas de plus dans la même évolution pourra les conduire à s’agglomérer les uns aux autres, de telle sorte que la collection des éléments se transforme en un solide unique, et que la consistance de chacun aura disparu au profit de la consistance de leur rassemblement compact.

(11)

[contents]

 

 

 

 

 

 

1.4.2

[Beings Whose Whole Increases in Consistency While the Parts Do Too, Despite Increasing Heterogeneity]

 

(p.11-12: “Au fait, tout ce qui nous entoure n’est-il pas composé ...”)

 

[Many groupings continue this process toward solidification where the parts fuse and thereby lose their individuality and thus their consistency all while the whole they form, which is solidifying, increases its consistency. But while many of the things around us follow this path of development, there are other things which follow a different developmental trajectory. In their case, the whole they form increases in consistency as the parts mutually affect one another, but the parts in that process likewise increase in consistency, as they increase their individuality and ability to maintain their identity. But even though there is an increase of consistency both on the level of the whole and on the level of the parts, the process of consistency-increase itself may not be a concordant one (as the parts are still further individualizing even as the whole they form increases its consistency.)]

 

[In fact, much of the solids around us are composed more or less of these agglomerates that over time have grouped in accordance to their similarities. Now, drawing again from section 1.4.1 above, we have the following idea. The sifting of dissimilar parts and the mutually accommadatory modifications of the similar parts allows the parts themselves each to maintain greater consistency, as they are able to maintain their individual identities better with destructive influences being eliminated, all while the group they form develops a consistency, as the parts are better able to hold together. The idea Dupréel now seems to be saying is that there is like a threshold in this process when the parts start to lose consistency while the whole continues to gain more of it, and that is when, I am guessing, the parts fuse to create a solid, meaning that they lose their identities all while the whole gains a stronger one of its own. Let us consider for example sand that has become sandstone. The grains have fused so much that we would not look at it as a shaped block of sand, like we might find in a sand-castle, but rather something with an altogether different identity that is not “bunch of sand” but is rather, a rock. So we must distinguish these two parallel developments of consistency, that of the group, like the pile of sand, the packed block of sand in the sand castle, or the sand particles fused firmly and ultra compactly in the sandstone block, and alternatively, the consistency of the parts, namely, that of each of the grains individually. So as a group becomes a solid, the grouping gains consistency while the parts lose it, as they shed their individuality. But, Dupréel explains, this sort of homogenizing, unifying, and fusing consolidation that forms solids (where the parts lose their individuality) should not be our concern here. Rather, we should focus instead on those cases where the group’s consistency increases without the parts fusing and thereby losing their own individuality and consistency. The sorts of beings we have in mind have parts that are so sufficiently consistent in themselves that they resist the loss of consistency that would come from their mutual adhesion. In these cases, the increase in the consistency of the group will correlate with an increase in the consistency of the individual parts, even though the process itself may not be a concordant one even while the consistencies of the whole and of the parts may increase. (This last point is still vague for me, but consider a rock and roll band that is starting out with people who are also beginners in music. As they each develop their styles while jamming with each other, they increase their own individual consistency, as their identities as musicians strengthens, and likewise the band as a whole develops an identity that strengthens simultaneously. However, note two things. The players do not develop one same musical “voice,” but rather each is a different voice in a shared musical “dialog.” In other words, the parts maintain their individuality even though the identity of the group strengthens. Also, the process of this development may have been a rocky one, in the sense that their egos may have often come up against each other discordantly. It is not that they must each sacrifice individuality in order to be one band, but rather, through their conflicts and tensions, each must individualize in a way that maximizes heterogeneity while keeping the group and the music together in a consolidated whole.)]

Au fait, tout ce qui nous entoure n’est-il pas composé plus ou moins directement, moyennant force opérations intermédiaires, d’agglomérés de ce genre ? Dès lors, l’évolution d’une collection de semblables que nous avons décrite, avec le double progrès en consistance serait, dans un grand nombre de cas un simple état préparatoire au passage à l’unité d’un solide dont la consistance serait un produit des consistances des éléments et de celle, toute provisoire, du groupe qu’ils ont formé, préalablement à l’agglomération. Des deux progrès en consistance celui du groupe et celui des éléments, seul le premier irait à grandir par l’abolition | de celle des éléments. Mais ce n’est pas ce phénomène très général, dont l’examen et les variétés relèvent directement de la science, qui doit retenir notre attention. C’est au contraire le cas où le processus se poursuit sans que les éléments fusionnent. Il suffit pour cela que l’on se trouve devant une espèce d’êtres semblables assez consistants déjà pour se refuser à cette perte de consistance que serait l’adhérence de l’un avec un autre ou avec plusieurs. Dans ce cas l’évolution probable du groupe comportera un progrès parallèle de la consistance du tout et de celle des individus sans que ce progrès soit assuré d’être toujours exactement concordant.

(11-12)

[contents]

 

 

 

 

 

 

1.4.3

[Living Beings as Heterogeneously Consistent Wholes]

 

(p.12: “Ce cas existe et il est d’importance, ”)

 

[Living creatures like plants and animals are the sorts of beings whose parts may increase in heterogeneity and individuality, and thus in their own consistency, all while the whole benefits from this and increases in its consistency too. It is also possible in such advanced beings that the parts will resist the whole’s totalizing tendencies, which can place restrictions on the liberties and consistencies of the parts; these acts of resistance thereby place caps on the grouping’s ability to increase the consistency of the whole.]

 

[In section 1.4.2 above, we discussed a sort of being whose whole’s consistency increases even while the parts’ consistency (and thus the internal heterogeneity) increases as well. Dupréel says now that an instance of such beings are living creatures. Plants and animals consist of individuals that, throughout their interrelations, are able to resist {1} fusion with one another or getting absorbed one into the other, {2} loss of their individuality, or {3} their mutual destruction until only one is left; and all the while the whole group’s consistency increases. Furthermore, in some of the most developed beings, individual parts might act to resist the tendency of the group to place constraints on the parts’ initiatives and individual consistencies, which can thereby place limits upon the group’s capacity to increase its consistency as a whole.]

 

Ce cas existe et il est d’importance, c’est celui des êtres vivants. Plantes et animaux comportent des individus capables dans leurs rapports communs de résister à des adhérences ou à des absorptions, qui les aboliraient comme individus, ou n’en laisseraient qu’un seul, et cette résistance profite à la consistance du groupe qu’ils forment en commun. Au reste, chez les êtres les plus développés, une autre résistance peut se produire, par laquelle l’individu s’efforce d’opposer un frein à l’emprise du groupe, qui menace, sous couleur d’organisation, de restreindre les initiatives et par suite la consistance propre des particuliers. On trouve ainsi dans le progrès même des êtres, des limites éventuelles au progrès de leur consistance.

[contents]

 

 

 

 

 

 

 

 

 

Dupréel, Eugène. (1961). La consistance et la probabilité constructive. (Classe des lettres et des sciences morales et politiques 55, no.2). Brussels: Académie Royale de Belgique.

PDF at:

http://www.academieroyale.be/fr/les-publications-memoires-detail/oeuvres-2/la-consistance-et-la-probabilite-constructive/.\

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