Luhtala (5.5.4.3) On the Origin of Syntactical Description in Stoic Logic, “Stoic Predicate Types”, summary

 

by Corry Shores

 

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[The following is summary. All boldface and bracketed commentary are my own. Paragraph enumerations are also my own, but they follow the paragraph breaks in the text. Please forgive my distracting typos, as proofreading is incomplete.]

 

 

 

Summary of

 

Anneli Luhtala

 

On the Origin of Syntactical Description in Stoic Logic

 

Ch.5 The Stoics

 

5.5 Stoic Logic

 

5.5.4

The Component of Meaning (Σημαινόμενα)

 

5.5.4.3

Stoic Predicate Types

 

 

 

 

Brief summary:

The Stoics recognized a variety of predicate types, including {1} congruities and {2} direct, {3} reversed, {4} neuter, and {5} reflexive clauses. The Stoics may not have had a fully unified way to categorize predicates, as they took various overlapping views: {a} on congruity and incongruity, {b} on activity and passivity, and {c} on completeness and incompleteness. Of the commentators on the Stoic theory of predicates, Apollonius Dyscolus gives the most authentic account, while Porphyry, Priscian, and other commentators on Aristotle’s Peri hermeneias commit errors in their interpretations.

 

 

 

 

 

Summary

 

5.5.4.3.1

[The Stoic recognized propositional clause structures of the following types: transitive, intransitive, and two sorts with impersonal verbs.]

 

The classic example for Stoic propositions is ‘Dion walks’ (Δίων περιπατεῖ). This is an intransitive clause. But Luhtala argues that transitive sorts of clauses, as for example ‘Plato loves Dion’ (Πλάτων φιλεῖ Δίωνα) are equally important in Stoic logic (94). However, Stoic propositional analysis goes beyond these two sorts of clause structures. Note that the Stoics did not discuss propositions with copula (94). The other two types of propositions the Stoics studied were ones with “impersonal verbs” (94).

 

 

5.5.4.3.2

[The Stoics recognized a variety of predicate types, including congruities, direct, reversed, neuter, and reflexive.]

 

While “Diogenes Laertius’ account of the Stoic predicate types is unfortunately damaged,” we can still see that these types “form a unity” (94). Here are the classifications for the predicates: {1} congruities (συμβάματα), “after which there is a lacuna”; {2} direct (ὀρθά), {3} reversed (ὕπτια) and {4} neuter (οὐδέτερα). Luhtala then explains that direct predicates have an oblique case [that is, one that allows for a patient to the action to be designated, as by direct object for example, and that is transitive], such as ones with the Greek words for ‘hears’, ‘sees’, and ‘converses’. Reversed predicates take a passive formation, as in the Greek formulations meaning ‘I am being heard’, ‘I am being seen’. Neuter predicates have neither the features of directness [they are active] nor of reversal [they are not passive], as for example the Greek words for ‘to think’ and ‘to walk’. She also says there are {5} reflexive predicates that are passives and that “resemble actions” as for example the Greek formulation meaning ‘he shaves’ (94-95. See these pages for details, as I did not comprehend and present it very well.)

 

 

5.5.4.3.3

[The Stoics did not categorize all the predicates in a unified way. Rather, they had two distinct classifications, base on {1} congruity and incongruity or {2} activity and passivity. ]

 

The Stoics had two distinct ways to classify predicates: on the basis of {1} congruity and incongruity, and on the basis of {2} activity and passivity. The texts describing congruity are corrupt. [The idea seems to be that there is congruity established somehow by conjoining a nominative case with a simple predicate as in ‘I walk’. See p.95, because there is more to it, but I did not follow.] In the second classification, which is about activity and passivity, the transitive formation is considered the prototype, while the intransitive structure is considered ‘neuter’ (95).

 

 

5.5.4.3.4

[The Stoics disunified classification stems from the different viewpoints they took on predicates.]

 

Rather than having a “unified set of predicate types”, “the Stoics discussed predicates from different points of view” (95). Luhtala then mentions the different ways predicates were understood. One point of view has to do with congruity, and another with activity and passivity (95). Another view was concerned with “completeness of thought, which gave rise to yet another classification, that into complete and deficient predicates (κατηγόρηματα αὐτοτελές versus ἐλλιπές)” (95). One same predicate can be found in various different categories, “a fact which vividly suggests that one uniform classification was not at issue | here” (96). [See 96a for examples.]

 

 

5.5.4.3.5

[One context that Apollonius Dyscolus discusses Stoic predicate types is with regard to cases with transitive verbs.]

 

Luhtala will now examine the textual evidence of grammarians on the topic of Stoic predicate types. Apollonius Dyscolus discusses the types in two contexts. One context is about oblique cases with transitive verbs. [These matters involve grammatical technicalities. For details, see p.96.]

 

 

5.5.4.3.6

[In another context, Apollonius Dyscolus notes that transitive verbs without an oblique case (to indicate the patient of the action) make incomplete predicates and express incomplete thoughts.]

 

[The other context seems to regard incomplete predicates that happen when transitive verbs lack oblique cases. So to say “Tryphon harms” is an incomplete predicate, because it needs a noun with an oblique case to indicate who is receiving the harm. Intransitive verbs when simply joined to a nominative are already complete predicates.] “It is the incompleteness of thought expressed by a transitive verb without the oblique case that has, according to Apollonius, given rise to the term ‘less than a predicate’” (96).

 

 

5.5.4.3.7

[While Apollonius’ accounts of Stoic predicate types is not as full as those given by Priscian and the commentators of the Peri hermeneias, it nonetheless is more authentic.]

 

Apollonius’ discussion of Stoic predicate types is not as full as accounts given by Priscian and the commentators of the Peri hermeneias, but Apollonius’ is more authentic to the Stoic’s system. Luhtala will now examine Priscian’s account, “which is fuller but clearly distorted” (93).

 

 

5.5.4.3.8

[Priscian’s account of Stoic predicate types makes a number of mistakes and misattributions of concepts to the Stoics.]

 

Priscian’s account of Stoic predicate types probably depends “on a later synthesis made of the Stoic predicate types, probably by Porphyry” (97). Luhtala then shows certain mistakes and misattributions Priscian makes in his accounts [see 97-98 for details.]

 

 

5.5.4.3.9

[We see a corruption of the Stoic predicate types in elaborations of Porphyry’s commentaries on the Aristotle’s Peri hermeneias]

 

Porphyry’s commentaries on the Aristotle’s Peri hermeneias have been lost. But others have elaborated on Porphyry’s commentary, and here we also see a corruption of the Stoic predicate types. [For details see p.98-99.]

 

 

5.5.4.3.10

[Porphyry confused certain aspects of the Stoic theory of predicates and neglected others.]

 

Porphyry combined two distinct aspects of the Stoic theory of predicates, namely, congruity and completeness (or deficiency) of predicates (99). Porphyry also neglected the central aspect of activity. Priscian “is likely to depend on a tradition which ultimately goes back to Porphyry” (99).

 

 

5.5.4.3.11

[Porphyry’s discussion of congruity is the only philosophical source that relates congruity to the grammatical notion of congruence.]

 

Incongruity in a predicate means that there is a lack of congruence [or “agreement”, as it might also be called] of person and number [perhaps between the verb and nominative, but I am not sure.] Porphyry’s discussion of this is the only philosophical source that relates congruity to the grammatical notion of congruence [but I am not sure what the difference is between congruity and congruence. I would guess that congruity could be a logical notion regarding the fittingness of the predicate with its subject while congruence is the grammatical agreement in person and number, but I am not at all sure.] Later grammarians gave the name ‘accidents’ for the “grammatical features that congruence is based on”, but many scholars were puzzled as to why this term was used (100).

 

 

5.5.4.3.12

[Congruity in predicates was understood as ‘accidents’ by philosophical commentators.]

 

[A substance has its accidents. The accidents could perhaps be understood as properties or other determinations of the substance. We might also think of the substance-accident metaphysical structure grammatically as the nominative-predicate syntactical structure. In this case, accidents would be the predication.] “Other philosophical commentators associate ‘congruity’ (σύμβάμα) with ‘accidents’ (συμβεβηκότα) in a purely philosophical sense, in terms of the predicate belonging to the subject. [See p.100 for textual examples.]

 

 

5.5.4.3.13

[While the Stoics, as far as we know, did not conceive of congruity in terms of grammatical congruence, were they to have done so, it would have been natural for them to employ the notion of accidents (συμβεβηκότα).]

 

We do not have any textual evidence to support the claim “that the Stoics should have distinguished between σύμβάμα (‘congruity’) and παρσύμβαμα (‘incongruity’) in terms of grammatical congruence” (100). Yet, were they to have done so, “it would have been quite natural for them to apply the philosophical notion of συμβεβηκότα (‘accidents’) to the grammatical accidents on which such congruence is based” (100).

 

 

 

 

From:

Luhtala, Anneli. 2000. On the Origin of Syntactical Description in Stoic Logic. Münster: Nodus.

 

 

 

 

 

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Somers-Hall, (3.2), Deleuze’s Difference and Repetition, ‘3.2 Feuerbach and the Postulate of the Principle (129–33/164–8)’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

 

Chapter 3. The Image of Thought

3.2 Feuerbach and the Postulate of the Principle (129–33/164–8)

 

 

Brief summary:
The “dogmatic image of thought” is the problematic way that philosophy understands philosophical thinking. Deleuze discusses eight “postulates” of it. The first is the belief that rational thought itself is good-willed and trustable for the task of arriving at truth, since it supposedly can be utilized without any other presuppositions that might contaminate the inquiry. Thus Descartes thinks that the method of doubt can lead all people to rational thinking itself, on the basis of which we may safely and fruitfully conduct our philosophical inquiries. Hegel as well begins with thought itself. Feuerbach criticizes this notion, since it forgets that such methodologies assume many things, like the philosopher is speaking the truth, as this is required to understand what she is saying in the first place. Instead, Feuerbach argues, philosophical thinking must go outside reason to encounter pure sensuous intuition. Deleuze agrees that philosophical thinking must encounter something outside reason, but it would not be sensuous intuition. Rather, it would be the transcendental ground for the passive synthesis of sensuous intuition, which is not a transcendental active ego like in Kant.

 

 

 

Summary

Recall how in Chapter 1, Deleuze criticizes Aristotle’s “representational” philosophy. Now Deleuze turns to Descartes, who was also critical of Aristotle (97d), referring specifically to Descartes unfinished dialogue The Search for Truth by means of the Natural Light (98a). This dialogue has three main characters. Eudoxus represents Descartes. He has a modern intellect, and his judgments are uncorrupted by false beliefs. He is debating with two other characters on how to properly conduct philosophy. Epistemon (Knowledgeable) “represents the Aristotelian Scholastic tradition,” and Polyander (Everyman) “is ignorant of philosophy” (98). “Descartes’ aim in the dialogue is to show the insufficiency of the Aristotelian method of definition, and to replace it with a method that relies on reason alone” (98). Descartes will accomplish this by showing that Aristotle’s method of definition by genus and specious does not work on the most indubitable thing, namely, one’s own existence as a doubting thing. As we saw with Aristotle’s interpreter Porphyry, were we to give a definition for man, we could say that man is a rational animal. But this is using concepts not available to pure reason alone. Were we instead to doubt everything, we would not have at our disposal such concepts that define animal and rational. So following Aristotle’s method, we might define animal as an animate body, and a body as a corporeal substance. But “A term such as ‘corporeal substance’ does not tell us anything more about the world than a term such as ‘body’, because if we cannot conceive of the terms corporeal and substance clearly, then conjoining them will not help us to conceive of the term ‘body’” (98). Thus without additional concepts, how could we determine “the meaning of the ‘I’ of the cogito?” (98). Now, in the method of doubt, we still having thinking itself available to us. This, Polyander concludes, is the best resource we would have for defining the doubting self.

Once Polyander has concluded his exercise in Cartesian doubt, guided by Eudoxus, he realises that ‘of all the attributes I once claimed as my own there is only one left worth examining, and that is thought’ (Descartes 1984b: 415). That is, the I is determined according to an attribute that is clearly conceived by reason itself.
(98)

So the Aristotelian scholastic approach is inadequate for Descartes, since it relies on determinations from the senses [which are doubtable] and it requires an endless chain of terms to define other terms (98-99). SH then notes key claims Descartes is here making regarding the true method of philosophy. 1) It grants reason the privileged status of being able to decide truth from falsity [thereby saying reason has a ‘natural light’]. 2) Because reason has this truth-determining power, philosophy’s method operates within reason and should not be contaminated by the other faculties which might mislead our reasoning. 3) This method would not presuppose anything except reason itself. Deleuze also notes how it is Polyander, the “Everyman”, who conducts the method of doubt. This suggests that for Descartes, good sense is equally distributed among all people and also that all people’s reason has a pure nature that can be trusted in its investigation into truth. Thus there is a “good will on the part of the thinker” and an “upright nature on the part of thought” (DR 131/166), and this is Deleuze’s first “postulate of the image of thought” (SH 99). But it assumes that there is a way, namely by light of reason, that all people can begin inquiries into truth without any presuppositions (99-100).

However, Deleuze thinks that this method still is hindered by certain subjective presuppositions (100).

Deleuze turns to Feuerbach’s Towards a Critique of Hegelian Philosophy to elaborate on these presuppositions. In this text, Feuerbach criticizes both Hegel and philosophy in general (100). It will take a few steps to follow through the ideas here. We first note that thinking is an activity, since “a philosophical argument is not of value in itself, but only in so far as it is taken up by the understanding of the person to whom it is addressed” (SH 100). Thus in Descartes’ dialogue, Eudoxus does not just state his argument but rather walks Polyander through a series of cognitive actions to arrive upon his basic point. “[P]hilosophical texts do not impart information, but simply act as a trigger for the reader’s own reason to determine truths for itself” (100). But this means that philosophical texts are primarily means of communication rather than being themselves demonstrations. If so, then “under what conditions is thought able to be communicated?” (101).

In order for another person to understand our own thought, we need to make it less particular to ourselves. We must strip it of its “mine-ness,” which is what we do when we express that thought in language (SH 101, citing Feuerbach 1997: 104). Thus, “philosophical thought abstracts from the particularity of my thinking, and operates by presupposing that which is universal to all thinkers. As Deleuze puts it, ‘Everybody knows, no one can deny, is the form of representation and the discourse of the representative’ (DR 130/165)” (SH 101). And so, for Feuerbach, “there is a fundamental distinction between thinking and the presentation of thought” (SH 101). [Feuerbach also seems to assume that thinking is not something temporal, since the parts of that thinking are somehow simultaneous, but presenting thinking in language places one’s thoughts into a temporal sequence. I do not understand how thinking is not something temporal, since it is an activity. Here is the Feuerbach quotation:]

And yet, systematic thought is by no means the same as thought as such, or essential thought; it is only self-presenting thought. To the extent that I present my thoughts, I place them in time; an insight that contains all its successive elements within a simultaneity within my mind now becomes a sequence. (Feuerbach 1997: 101)
(SH 101)

The problem comes when philosophers “mistake the successive, abstract representation of thinking for thinking itself” (101). One reason we may make this mistake is that our conventions for presenting philosophical ideas have been systematized in a rational way and thus the very presentation of the ideas itself can have the appearance of being philosophical thought (101). “We therefore mistake the abstract, communicable element of thought for thinking itself” (101). Deleuze also notes the moral assumption in this view, since “to trust in the structure of thinking as communicative implies a fundamental accord between man and the world, and presupposes the belief that ‘thought has a good nature and the thinker a good will’ (DR 132/167)” (SH 101d).

SH says that

Feuerbach’s claim that ‘every system is only an expression or image of | reason’ (Feuerbach 1997: 106) can be seen as a forerunner of Deleuze’s own claim that representational thinking rests on an ‘image of thought’, and the aim of Chapter 3 of Difference and Repetition is to explore in more detail what this image consists in, and how it is possible to think outside of it. This error of mistaking the image of thought for thinking itself has a number of implications for Feuerbach which are directly relevant for Deleuze’s account. 
(101-102)

SH then addresses those implications. The first is that “even projects such as those of Descartes and Hegel that attempt to remove all objective presuppositions still make a number of presuppositions in order to operate” (SH 102). For example, Hegel wants abstraction to stand at the beginning, when in fact it is sensible, concrete, empirical being which is only secondarily stripped of its mine-ness to become abstract and communicable (102). This also presupposes a form of the representation of thinking that is sharable with all people. Feuerbach says for example that before we can understand a philosopher’s thoughts, we need to assume that they are true (SH 102, citing Feuerbach 103). Thus, “The history of philosophy can from this perspective be seen, not as a progressive extension of our knowledge of the world, but rather as a series of more and more accurate ways of providing a systematic image of the presentation of reason” (102).

[So the first implication is that in fact systems that try to remove all presuppositions still will bear them.] “The second implication is that if philosophy simply maps out the | image of thought in systematic terms, then it will be incapable of novelty” (102-103). This is because by working according to some such method, we are only reworking and developing thinking that is already given within us rather than creating new thinking (103).

“The third implication is that philosophy must begin with something that is outside of thought” (102). Descartes and Hegel both begin with thought itself and arrive at philosophy. This only works because they assume the good nature of thought [that is, that it has the tendency and ability to arrive at truth, and this possibility is available to anyone who employs rational thinking]. [The next idea seems to be that those who take this image of thought believe that first there is thinking, then on its basis, we can arrive at philosophical thought. However, Deleuze’s and Feuerbach’s point seems to be that since philosophy is not inherent to reason, philosophy must encounter something radically outside reason in order to operate. Let me quote, as I might have gotten this point wrong:]

if systematic philosophy is simply an expression of pre-philosophical reason, Deleuze argues that philosophy must ‘find its difference or its true beginning, not in an agreement with a pre- philosophical Image but in a rigorous struggle against this Image, which it would denounce as non-philosophical’ (DR 132/167). That is, if it is not simply to draw out what is contained in our (rational) commonsense prejudices, it must not begin with reason as we discover it either in its naive or systematic forms. Here, Deleuze is referring directly to Feuerbach’s rejection of reason as a foundation for philosophy. In contrast to the Cartesian account, philosophy must begin with a radical encounter with something outside of it [the following up to citation is Feuerbach quotation]:

Demonstrating would be senseless if it were not also communicating. However, communication of thoughts is not material or real communication. For example, a push, a sound that shocks my ears, or light is real communication. I am only passively receptive to that which is material; but I become aware of that which is mental only through myself, only through self-activity. (Feuerbach 1997: 105)

We will see that Deleuze presents a similar need for an encounter.
(SH 103)

SH ends this section by explaining the difference between Deleuze’s and Feuerbach’s positions. They do not agree on what it is that philosophy is supposed to encounter (103d). “For | Feuerbach, true thinking begins through an encounter with sensuous intuition, which is prior to the abstractions that generate the ‘mediating activity of thought for others’ (Feuerbach 1997: 102)” (SH 103-104). Recall something similar in Kant’s active and passive syntheses: “the understanding was responsible for active synthesis, and therefore organised the world according to its own categories. The active, synthetic nature of the understanding meant that it rediscovered on an empirical level what it had previously put into the world on a transcendental level” (SH 104). So for Kant, as perhaps also for Hegel and Descartes, “the understanding is incapable of discovering genuine novelty, since sensibility merely provides the material that is organised by the understanding” (SH 104). Feuerbach rejects the active synthesis as the source of philosophy, and so he turns to the passive synthesis of sensibility. But, we can still inquire into the transcendental grounds that possibilize the passive synthesis of the sensible, which is what Deleuze thinks needs to be encountered.

Once we have recognised the possibility of a passive synthesis, however, we open the possibility that what is given in sensibility is not the sensible itself, but that which gives rise to the sensible. It is this transcendental which is prior to the sensible that will be the site of an encounter for Deleuze. In order to explore how thought is able to operate outside of the image of thought provided by representation, Deleuze proposes to analyse in more detail how the image of thought operates, developing in parallel an alternative account of thought that takes account of its non-representational origins.
(104)

 

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

DR:
Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

Feuerbach, Ludwig (1997), ‘Towards a Critique of Hegelian Philosophy’, in Lawrence S. Stepelevich (ed.), The Young Hegelians: An Anthology, Amherst, NY: Humanities Press, 95–128.

 

 

 

 

Somers-Hall, (1.4), Deleuze’s Difference and Repetition, ‘1.4 Duns Scotus (35–6/44–5, 39–40/48–9)’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH, and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

 

Chapter 1. Difference in Itself

1.4 Duns Scotus (35–6/44–5, 39–40/48–9)

Very brief summary:

The Aristotelian concept of classification and definition places being higher than God. The medieval theological tradition that builds from Aristotle’s system treats God’s being as different in kind from humanity’s being, which poses other theological problems. Duns Scotus solves all these problems by making being be a degree of perfection that modifies other things. God has an infinite degree of perfection and humans have a finite degree. Thus unlike in the Aristotelian system, being is understood univocally in both cases, as it is the same being in each case. Yet Scotus ultimately compromises this univocity by making the theological claim that the infinite difference in degree between God and humanity is enough to be a difference in kind. Deleuze, however, prefers a more univocal sense of intensive variation.

Brief summary:

The Aristotelian system of genus-species categorization and definition places ‘being’ as the highest category (or highest categories of senses of being). This presents a problem for medieval theologians who want God as the highest category. We note first that the Aristotelian / Aquinian solution is to say that ‘being’ is understood equivocally, in that there is the finite being of our world and the infinite being of God. But being applies to both, since they are analogical (as they have the same cause, God). Duns Scotus objects that we cannot know they are analogical unless we already knew of God’s perfection. Thus our own finite perfection cannot be the basis for us knowing of God’s perfection. Scotus identifies the problem as resulting from making finite and infinite be different in kind rather than different in degree. The infinite being / infinite perfection of God is just a much higher degree of being / perfection than our own. Thus when God’s infinite being is understood intensively, we understand being univocally. It also means that being is not a higher genus than God, since degrees of being / perfection are modes and not properties (and thus not predicates and thus not higher genera) of substances. However, Scotus’ theological position is that, nonetheless, the infinite difference in degree is a difference in kind between God and humanity, which compromises the univocity of his concept of being.

Summary

[We saw previously that Aristotle’s system of classification and definition, which is based on the genus-species distinction, runs into a problem at the highest level of the most general genus, ‘being’. As the most general, all things whatsoever have it has a predicate, since all other things fall under this most general category. However, we cannot define it, since doing so requires a higher genus and other species to distinguish it from. Aristotle offers a solution that compromises the consistency of his system. But perhaps the desire for univocity in a metaphysical system is what is important here. For,] Deleuze then claims that “‘there has only ever been one ontological proposition: Being is univocal’ (DR 35/44)” (SH 30). SH will examine Deleuze’s point of view by tracing his tradition of influence from Duns Scotus through Spinoza to Nietzsche. This will all us to better understand the univocal conception of being. (SH 30d)

We begin with the theological context of Scotus. Medieval theologians thought that God was infinite and as well there are other finite things that are fundamentally different from God. God’s nature is simple, meaning that it is not composed of parts, and God possesses every perfection, for example, God is infinitely good, infinitely wise, and so on (SH 31a). But when we look at objects that we have access to, objects in the finite world, we see that an object having several properties is a complex object” (SH 31) [unlike God, who has several properties but is a simple thing]. [SH then makes a point about equivocation. It seems the reasoning is this. God is of a fundamentally different nature than finite things. But we use the term ‘good’ for God and for finite things. This one term really refers to two concepts, the good of God and the Good of finite things. Since it is the same term in both cases, we are equivocating. By recognizing it as equivocation, we acknowledge that God is transcendent to our world.]

Now the very fact that a term like ‘good’ operates in these different ways when we use it to describe an object or person in the world or to describe God implies that when we use this term, we are equivocating. That is, that the same term names two different concepts, good-for-God, and good-in-the-finite-world. Such a position has certain advantages – in that it makes clear that God is a transcendent entity that cannot be adequately understood according to our categories of thought – but is ultimately untenable as it renders any relation to or understanding of God impossible.
(31)

[Recall that paronymous meanings refer to a focal meaning. SH refers again to this notion of focal meaning, but now in the context of analogy. (It is not clear to me if paronymous meanings are analogous.) Analogy here is matter of likeness. For Aquinas, if one cause causes two equivocal things, then they are analogous. Thus on the basis of finite good, we can understand by analogy God’s goodness, since God caused both.]

It is here that Aquinas brings in the notion of analogy. As we saw with Aristotle, analogy allows us to relate terms that have something in common (a focal meaning), but yet differ. Aquinas’ use of analogy relies on the likeness of cause and effect (our goodness is caused by God, so there must be some analogy between infinite and finite goodness, since effects resemble their causes). In this instance, therefore, God’s goodness is the focal meaning by which finite goodness gets its own meaning.
(31)

[We now get Scotus’ definition of univocity. But we do not get an example but rather only a counter example, so it as of now a little unclear to me. The counter example is health. It is not univocal. For, since it has a different sense in different applications, any some of those senses can be used in a particular case and others not. Nutrition is a cause of health, but it may not be a sign of health, as perhaps people who are otherwise unhealthy for other reasons can still eat nutritionally.]

It is against this view that Scotus develops his own position: a univocal theory of religious language. He defines univocity as follows: ‘I designate that concept univocal which possesses sufficient unity in itself, so that to affirm or deny it of one and the same thing would be a contradiction’ (Duns Scotus 1978b: 20). Effectively, univocity therefore means that a word is used in the same sense in all contexts, unlike ‘health’, for instance, whose meaning changes depending on what we are relating it to.
(SH 31)

[The implication here seems to be that, contra Aristotle, ‘being’ is univocal in this more absolute sense and not in Aristotle’s analogical sense.] There are two basic reasons Scotus thinks that ‘being’ has this sort of univocity. 1) [In the analogical account of knowledge of God, it might be implied that in order to know that God exists, we might need to see some kind of causal proof of his existence in the world. However,] “we can believe that God exists without knowing anything further about him, even whether he is finite or infinite” (31). And 2) [This one is built on a premise that I cannot explain. For some reason, in order to make the analogy that for example finite goodness is like infinite goodness, we need to have some knowledge of the relationship between God’s nature and his attributes. Perhaps the idea here is that we might see goodness in the finite world, but so long as we do not already have knowledge that God has goodness, we would never make the analogical association between finite and his infinite goodness. I will quote for your interpretation:] “Second, the alternative theory of analogy suffers from a key problem: in order for the analogy to work, we seem to require some knowledge of the relationship between God’s nature and his attributes. Such an analogical argument presupposes some form of understanding of God’s nature” (31d). [The reasoning in the following step is also unclear to me. It seems the thinking is this. To understand God in the Aristotelian / scholastic approach, we need to already know God is infinite and we finite. For otherwise, perhaps, there is no basis to say one is fundamentally different from the other and nonetheless analogical. I am not sure, but perhaps we also here must equate God with being. But if we take God/being to be univocal, we are not concerned with infinite and finite, since God/being is univocal only if it has the same sense in all its applications. I again quote for your interpretation:] “Scotus instead takes being to be univocal and ‘indifferen[t] to what is infinite and finite’ (Duns Scotus 1987a: 2)” (SH 32d). [Perhaps we are also assuming here that both the infinite of God and the finite of our world both have being. This also means that on the basis of the concept of being alone, we cannot differentiate God’s being from our own.] “Now | this raises a problem, since we want to see God as separate from man” (SH 31-32). [But by making the meaning of being dependent on whether or not it is finite or infinite, we seem to be placing it as a higher genus. Thereby, we make it higher in the hierarchy than God. Moreover, now that God is lower than being, we would say that ‘being’ is a predicate to God, in the sense of the sentence: God is a being / God has being / God is. So being is one of God’s attributes. Also, as we noted, God is not finite, so he also has infinitude as one of his attributes (but it is not clear to me if ‘infinite’ is a higher genus).]

This view is clearly heretical, since it appears to be the case that as being is somehow prior to finite and infinite beings, being appears to operate as a genus, with finite and infinite beings as its species. Thus being would seem to occupy a place higher in the Porphyrian hierarchy than God. We might also want to ask how Scotus is able to explain the simplicity of the nature of God, given that God’s nature seems to now be a compound of two different attributes: being and infinitude.
(SH 32)

Scotus has a solution for this problem of possible heresy. To understand it, we need first to return to Aquinas in his Summa Theologica. Here we get a definition of infinite as non limited. The passage adds the complicating issues of form and matter. Both in themselves are infinite, but in their union they limit one another. A form can take any instantiation, but as soon as it is, it is limited to being that particular determination. Matter can take any form, but as soon as it takes one, it is limited to that formation (SH 32c). [The reasoning in the next part is not entirely clear to me. It seems that because infinite and finite are relational concepts, with each co-defining the other, and because they are opposed, then the being must be the highest genus. Perhaps this is because neither one can be said to be higher than the other, but both can be said to have being.]

The concepts of finite and infinite are here relational concepts. The infinite is defined by not being limited, whereas the finite is defined through limitation (by matter). If the finite and infinite are understood in these terms, it is clear that we are going to end up with being as the highest genus, or at best an analogical conception of being, as these two terms are opposed to one another. Rather than finitude being defined by relation to a limit, Scotus instead therefore introduces the notion of an ‘intrinsic degree’ of being.
(32cd)

[Since Scotus does not want to place being above God, he also does not want to co-define infinite and finite. As we saw, this co-definition was based on finite being understood as having a limit and infinite as not having a limit. Thus] Scotus will not define finitude in relation to a limit. We will see how he instead uses the notion of ‘intrinsic degrees’ of being.

SH follows Richard Crosses’ (1999, p.40) account of Scotus’ ‘intrinsic degrees’ of being. [The following is complicated. We first must recognize that the for some reason, infinity for Aquinas is understood as extensive and divisible. This somehow applies also to God’s infinitude and his infinite perfection. But it is not clear to me how Aquinas thinks that God’s perfection is extensive and divisible. Perhaps by saying that the infinite is unlimited and the finite limited, we are saying that the infinite is an indefinite amount of finites, or in other words, that there is no limit to how many finites make it up. But again, how does this apply in the case of perfection? At any rate, we take it for granted that the Aquinas understanding of God’s infinite perfection is extensive and divisible, and we conceive instead that there are different degrees of perfection, none of which are divisible into constituent quantitative parts. They only admit of more-or-less, but not of divisible composition. Thus infinite perfection, and also all finite degrees of perfection, are intensive and indivisible magnitudes.]

Scotus firsts asks us to imagine an infinitely large magnitude. He then asks us to apply this model of extensive infinity to a qualitative perfection, such as goodness. The central claim is that much as we can determine spatial | magnitudes, we are also capable of ranking perfections in such a way that we can conceive of an infinite perfection. In the case of a perfection, however, it cannot be constituted of parts in the way that the extensive magnitude is. An infinite extensive magnitude is constituted from an infinite number of finite extensive parts, but a perfection would not be infinitely perfect if it were composed of finite (and hence imperfect) qualities. The notion of infinity that Scotus is developing is therefore of an intensive, indivisible form of infinity, rather than the extensive, divisible form that Aquinas favours.
(32-33)

[What seems to be important here is the notion that now infinity is no longer a genus, that is something substantial, but rather it is a modality / modification of some substance. Perhaps we might have some reason to say that a human has more perfection than a rock, but infinitely less perfection than God. Perhaps also built into this thinking is that levels of perfection are amounts of being. This way, an infinite amount of being is not higher to God but is equated with God. There is also a somewhat confusing quote of Scotus about degrees of whiteness. We can have different degrees of intensity of white. The quoted material does not mention infinite whiteness. But SH says that infinite being is like infinite whiteness in this example. It is not entirely clear to me what that would be in this example. If we have different degrees of whiteness, then the higher degree, the closer we are to the infinite and also the closer to the absolute. Perhaps we are to think of it like this. Between Black (no degree of whiteness) and White (infinite degree of whiteness) we have an infinity of variations of white. So in order to go from black to white, we need to proceed through an infinity of variations, meaning that the highest one would itself be an infinite variation. But still the situation is not entirely clear to me. Say for example we look just at some middle section of grey variations between black and white. If we can keep finding smaller and smaller variations, would there not be an infinite number of variations within any one limited part or swath of the continuum? So even before arriving at pure white, we would still need to proceed through an infinity of variations of white, thus making the variation just prior to pure white still infinite, in the sense we began with. It must be infinite in some other sense. I can only also think that pure white is an infinite degree of white because there is no limit to how white it is. However, we already ruled out understanding infinity by means of the concept of limit. So one of SH’s points is that in this example, infinite whiteness is not defined by a lack of limitation. Yet I do not know how to conceive of why it is infinite. His second point is that we are not using some external concept to understand whiteness. Likewise for being, it would seem, perfect being, infinite being, and God, which may all be synonymous, do not require another concept for their perfection to be understood. This makes sense, but we might wonder if the infinite degrees of whiteness can be understood without reference to its lowest degree, which is either black or the first variation between black and white. And pure black is different in kind and not degree from pure white, I would think. The main idea we get from this is that finitude and infinity in this understanding are not properties of being, it seems because they are not predicated of being but are rather degrees of being. They thus instead are modes or modulations or modifications of being.]

God is not, therefore, superior to man in the quantitative extension of his being, but rather in the qualitative nature of his being’s intensity. This ultimately allows Scotus to solve the two difficulties of the highest genus and the simplicity of God. Instead of understanding infinity and finitude as species of being, they are rather modes or ways in which being subsists. Scotus gives the following example in terms of colour [the following up to citation is block quotation of Scotus]:

When some reality is understood along with its intrinsic mode, that concept is not so absolutely simple that it is impossible that this reality be conceived apart from this mode, although it is then an imperfect concept of a thing. For example, if there were whiteness in the tenth degree of intensity, however simple it may be in reality, it is nonetheless possible that it be conceived under the concept of so much whiteness, and then it would be conceived perfectly by means of a concept adequate to the thing itself. Or, it is able to be conceived precisely under the concept of whiteness, and then it is conceived according to a concept that is imperfect and lacking in perfection in the thing. But the imperfect concept is common to this and that white, and the perfect concept is more proper. (Scotus, Ord. I, d. 8, pars 1, q. 3 n. 138–9, taken from Hall 2007: 107)

Infinite being is like infinite whiteness in this example. Finite being in turn is like a finite degree of whiteness. In neither case are the notions relational. Infinite whiteness is not defined by a lack of limitation, but positively, in terms of its own intensity. Likewise, a finite degree of whiteness is not defined in relation to some other quality, but is intrinsic to the colour itself. Finitude and infinity are therefore modes, rather than properties of being.
(SH 33)

We recall Porphyry’s Aristotelian system of species and genera. Being would be the highest category. It is higher than humans, since humans exist, and it is also higher than God, since we can as well make the predication “God has being”. This is a problem of course for the medieval theologians, and Scotus has solved the problem. [We can have God as being different from other beings, as an infinite degree of being.] “Scotus’ notion of the distinction allows us to avoid this difficulty. Clearly there is a difference between whitenesses of different degrees of intensity” (34).

[It seems in the following paragraph that we return to the idea of perfection in the previous blocked Scotus quote. Here a concept is imperfect if it does not adequately correspond to what it is a concept of. In our experience, we only see different degrees of whiteness, whether that be finite or infinite. We never see whiteness without it taking on some degree of whiteness. The same it seems goes for being. We see only degrees of being (I am not sure how specifically. What existing things in our world of experience have less being than others?) Therefore, if we formulate a concept of being without involving the notion of its intensity, it is merely a formal conception.]

When we look at the concept of the intensity itself, however, it should be apparent that this notion of intensity cannot be grasped as really distinct from the whiteness itself. If we take away the concept of whiteness, we simply have the concept of ‘degree’, which is meaningless on its own – ‘degree of what?’ Nevertheless, the degree clearly does distinguish different ‘whitenesses’. We can note however, that it is possible to formulate a concept of whiteness that does not make reference to its degree of intensity. Such a concept would, however, be ‘an imperfect concept of a thing’ as whiteness always shows itself with a given intensity. It should be clear that we can apply this conception to the notion of being. Scotus’ claim would then be that being always presents itself with a given degree of intensity which is inseparable from it. While we can therefore formulate a concept of being without reference to its intensity, such a conception is only formal, as actual being is always finite or infinite.
(34)

[We might think of water heated or cooled to different degrees. There is only relative quantitative difference between each degree. But there is a difference in kind if we look at the states of matter the water changes through while its temperature varies. But the intensities themselves do not admit of such categories of difference in kind. So we would think that God and man stand at different degrees of intensity of being, and as such, are not yet understood as being different in kind. It is this understanding of intensity that Deleuze seems to be after. However, Scotus still maintains the theological position that God is fundamentally different than man, and this would be because the infinite perfection is so much greater than our own degree of perfection that an absolute gap divides us. As a result, his understanding of univocity is compromised, since God’s being in the end is a different kind of being than our own, and not just another degree of the same being.]

Intensity as it stands is purely a difference in the degree of something’s being, and is also pre-categorial. As such, it does not constitute the kind of distinction that would allow a proper separation between God and man. Such a position in fact is the one that Deleuze wants to develop in his own philosophy. For Scotus on the contrary, the difference in degree between God and his creation becomes a difference in kind once we recognise that infinite intensity is simply incommensurate with any form of finite intensity. The gap between finite and infinite is therefore still a chasm which allows the separation of God and his creation to be maintained. While being can conceptually be said univocally, in practice, we always encounter being with a given intensity, and so in reality being is always encountered in different forms [the following up to citation quotes Scotus]:

As said of the ten categories, neither metaphysically nor naturally does the term ‘being’ signify one concept; and being is not a genus of these, neither naturally nor metaphysically. However, logically speaking, being is univocal. (Duns Scotus, In De an., q. 22, n. 33 taken from Hall 2007: 20) |

By making this difference a difference in kind, Scotus separates man from God, but at the cost of making the thesis of univocity a purely formal thesis. This is why Deleuze claims that Scotus ‘only thought univocal being’ (DR 39/49).
(SH 34-35)

 

 

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

Cross, Richard (1999), Duns Scotus, Oxford: Oxford University Press.

Duns Scotus, John (1978a), ‘Concerning Metaphysics’, in Allan Wolter (trans. and ed.), Philosophical Writings, Cambridge: Hackett Publishing, 1–12.

Duns Scotus, John (1978b), ‘Man’s Natural Knowledge of God’, in Allan Wolter (trans. and ed.), Philosophical Writings, Cambridge: Hackett Publishing, 13–33.

Hall, Alex (2007), Thomas Aquinas and John Duns Scotus: Natural Theology in the High Middle Ages, London: Continuum.

Somers-Hall, (1.3), Deleuze’s Difference and Repetition, ‘1.3 Aristotle’s Conception of Being (32–5/41–4)’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH, and Difference and Repetition as DR.]

[UPDATE: My lack of knowledge, cleverness, and time prevent me in some cases from being able to re-explain in my own way some ideas in Somers-Hall's text. We are fortunate that the author has taken the time to remedy these gaps in my summary. Please see his clarifications in the comments section.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

 

Chapter 1. Difference in Itself

1.3 Aristotle’s Conception of Being (32–5/41–4)

Very brief summary:

Aristotle’s system of genus-species classification and definition runs into a problem when we reach the highest category, being or unity. Normally, each genus is understood  as serving as a species to a higher genus. But ‘being’ or ‘unity’ can have no higher genus. Aristotle’s solution is to say that rather than having a higher genus, there is a focal concept to which the genera refer; and to still have difference so to make being conceptualizable in a determinate and specifiable way, he says that there are multiple senses of being which refer to this focal concept. This compromises the coherence of his system, since the genus-species structure does not operate consistently throughout, despite the structure holding throughout. At the highest level, equivocity in the senses of being is required to terminate the ascension of levels in a way that makes ‘being’ sensible, while all the species, many of which also serve as genera, require univocity in order for their meanings to be specific and defining.

Brief summary:

Aristotle’s system of categorization and definition involves designating the essential differences between species within a genus. Thus we might have these definitions and classifications: ‘man (species) is an animal (genus) that reasons (species difference),’ while ‘fish (species) is an animal (genus)  that lives under water (species difference)’. A grave problem this presents to the system is that it undermines its own foundations. All the elements that are classified in the system presuppose a concept of unity or being. As well, the notion of difference which is required to distinguish the parts is also something that has being, and thus it too requires a concept of being for it to be a sensible part of the system. However, being cannot be given a clear conceptualization, since there is no higher genus under which it can be distinguished from other species of its general type. Aristotle’s solution is that there is no one highest genus but rather there are many senses of being that all refer to the same focal concept of being, which is not to be understood as a higher genus. It is like paronymous  meanings, that is, meanings which are related by morphology, like grammarian and grammar. Nonetheless, this solution compromises the coherence of the system, since genus, especially the highest one that encompasses all others, functions by means of a different rule than the species do. Species require univocity in order to be specific and determinate. But genera require equivocity in order to be multiple yet ultimately terminal.

Summary

[We saw previously that for Aristotle, there are three basic elements in classification. We need first to recognize that something is distinguished from something else on the basis of its classification. To define something, and thereby establish what makes it different from something else, we first designate its higher grouping, the genus, and then what makes it specifically different from other members of that group. Here we are dealing just with species and genus. So {species} man is {genus} an animal {specifying difference} that reasons, unlike other species of animals, which do not reason. The lowest division would be the individuals, each of which differ from one another by means of accidental features. However, groups of individuals may share the same essence, and as a group would form the species for a genus.] Now SH will look at some problems with Aristotle’s (and his commentator Porphyry’s) system. Deleuze thinks that there are two main classes of problems with this model, the problems of the Large and the problems of the Small. The Large problems concern difficulties with conceptualizing the highest genus, and the Small problems “relate to the unity of empirical objects” (26). According to Deleuze, Aristotle’s model falls short when it needs to deal with these extreme ends of the hierarchy. [I am not sure how the next sentence follows from the prior. It seems that the structure of a generic layer encompassing from above specific items is imposed in our experience, if we assume that we experience directly an undifferentiated flux of sense data that is processed according to conceptual unities.]

Thus, Aristotle’s model relies on the ‘extraction or cutting out of generic identities from the flux of a continuous perceptible series’ (DR 34/43). This involves a problematic notion of resemblance between changing perceptions and an unchanging essence.
(SH 26)

[Recall the discussion previously about the undifferentiated. We said that: Deleuze gives two examples of indifference: 1) The undifferentiated abyss into which everything dissolves, and 2) The white nothingness on which are scattered unconnected determinations (SH 21-22). In the first case, a lack of difference makes everything seem indistinguishable and seemingly be identical. In the second case, the lack of difference prevents things from forming determinate relations with one another.] SH now recalls the previously discussed distinction between the dark abyss of indifference (where things are too murky for anything to be differentiated) and the white surface (where nothing can enter into relation with anything else [but I am not sure why. Keeping with the metaphor, perhaps we are blinded by the light. But what that metaphor refers to is not evident to me.]) SH claims that this polarity is like the two kinds of problems in Aristotle’s system of classification.

We can relate these difficulties to the two forms of indifference which are to be avoided. As we have seen, these are ‘the black nothingness, | the indeterminate animal in which everything is dissolved – but also the white nothingness, the once more calm surface upon which float unconnected determinations like scattered members’ (DR 28/36). While Deleuze’s characterisation of these problems may seem obscure, they relate to two key issues with Aristotle’s theory. First, how do we determine the nature of the highest genus in the Aristotelian hierarchy (black nothingness), and second, how do we explain the constitution as well as the determination of the subject (the problem of white nothingness)?
(26-27)

Aristotle himself was aware of the problem of the highest genus. [SH then quotes Aristotle, but its meaning is not immediately clear to me. One reason is that it introduces a concept we have not dealt with yet at least under this name: differentiae. Let us for the moment guess that a differentia is a species difference. Still, interpreting this passage is difficult. We said before that predicated of seems to mean “is a predicate to”. Aristotle will write: “it is not possible for the genus to be predicated of the differentiae taken apart from its species”. We think of the highest genus, ‘being’ or ‘unity’. It would help to know what comes next. Let us guess that the two most basic kinds of things are real (physical) things and unreal (abstract) things. Let us also guess that the differentiae are ‘real vs unreal’. Were that to be so, we could make the following substitutions into the definition: “it is not possible for the genus ‘being’ to be the predicate for the differentiae ‘real & unreal’ were these differentiae taken apart from the genus being’s species, ‘real things’ and ‘unreal things’. It is still not clear how a difference can itself be predicated, so let us assume that we are speaking of predication to the different species. Still I cannot grasp the meaning. Aristotle’s conclusion will be that were unity or being the genus (thus the highest genus), then no differentiae will be unified or have being. I wonder if this is because were unity or being the highest genus, then we cannot formulate a concept for unity or being. This is because, in order to define it, we need to differentiate it from some other species belonging to a common genus, which in this case does not exist, as none are higher. Then maybe the reasoning continues like this. Since we cannot define unity, that means we have no basis to say that the differentiated species groupings have unity either. Please read the Aristotle quotation for your own interpretation.]

It is not possible that either unity or being should be a genus of things; for the differentiae of any genus must each of them both have being and be one, but it is not possible for the genus to be predicated of the differentiae taken apart from its species (any more than for the species of the genus to be predicated of the proper differentiae of the genus); so that if either unity or being is a genus, no differentiae will either be one or have being. (Aristotle 1984b: 998b)
(SH 27)

We return now to the idea that a genus is what is the predicate to the shared essence of things (species) that otherwise differ in kind, such that for the genus animal, we might predicate it to such various species in this manner: ‘man is an animal’, ‘dog is an animal’, ‘elephant is an animal’ and so on. [Or as Aristotle puts it, perhaps meaning something slightly different: “a genus is ‘what is predicated in the category of essence of a number of things exhibiting differences in kind’ (Aristotle 1984d: 102a)” (SH).] We thus can define what it means to be an X by designating its genus and what differentiates it (its differentiae) from all other species in that genus. [The next part is a little confusing for me. The conclusion will be that a difference cannot be of the same type of that which it differentiates, with the problem of infinite regress being the reason why. To illustrate, SH has us consider the example of living bodies. We are to first consider the possibility that “the difference between living bodies was itself a living body”. It is not clear to me yet how to conceptualize or imagine this possibility. If a difference is understood as a sort of relation, how would it be understood as well as a living body? Also, the conclusion is hard for me to arrive at. In the prior section we distinguished types of differences, namely, common difference and proper difference. Is not the difference between them a difference itself? And thus, is not the difference of the same kind as that which it differentiates? Perhaps the issue is that it is neither a common nor a proper difference. But recall that a common difference is accidental but proper differences are essential. Would not the difference between common difference and proper difference itself be a proper difference, if indeed they are two species of difference? If we were defining our terms, perhaps there would be a problem here. What is an essential difference? It is what makes a difference not accidental. What makes a difference not accidental? It is not accidental if it belongs to a category, namely ‘essential difference’, which itself is defined in terms of its essential difference to accidental difference. Please read the following to find a better interpretation.]

a genus, along with the differentiae, determines what it is to be an X. It should be clear that a difference cannot be the same type of thing as that which it differentiates. We can show this by taking as an example the case of living bodies. If the difference between living bodies was itself a living body, then we would be caught in an infinite regress, as in order for this living body to function as a difference, we would need to differentiate it from other living bodies. Thus, we would require a further difference, which would in turn need to be differentiated and so on to infinity. What thus differentiates living bodies, the difference sensible/non-sensible, must itself not be a living body.
(SH 27)

[If we take this point that a difference cannot be of the same type of that which it differentiates, we will conclude that] “what differentiates beings into different species cannot itself be a type of being. Therefore, if being is a genus, then difference itself cannot be a being” (SH). [However, since we know that differences do have being, that means being cannot itself be a genus.] “As Deleuze puts it, ‘Being itself is not a genus . . . because differences are’ (DR 32/41)” (SH 27). [The next point seems to be that there can be no highest genus if there be any differentiation in the system. It seems that instead somehow there are multiple highest genera, since no higher one can be conceived.]

It is not simply the difference in being that would lack being, but as differences are inherited (man is a rational animal, but also a material substance), all differences would lack being. For this reason, the ultimate categories through which being is understood must be multiple, as they themselves are species in relation to the undefined genus.
(SH 27)

If there are multiple highest genera, this is a problem for Aristotle, who wanted a coherent metaphysical system, which, in order to be scientific, would need  unity at its basis [a science needs to be defined in terms of the objects it studies, but if they cannot be univocally determined, the science would perhaps be unable to designate its own objects of study. In this case, metaphysics as the study of beings would be unable to designate what beings are in the first place and thus be unable to properly begin its studies of them.] So we have different senses of being [different highest genera each for being but also each somehow different, in a way not yet specified]. Their senses cannot be identical [as then we would really just have one genus]. As we will see, it will be by using a grammatical metaphor, namely, the concept of paronymy, that we will understand how the senses differ while also are senses of the same thing.

If there was no governing principle to how the things in our world are grouped, then we would not be able to speak sensibly about them [since what we are talking about are not coherent concepts or coherent groups of things]. This is Aristotle’s motivation for differentiating the groupings in terms of what is essentially common to them. [Somehow on account of this], Aristotle begins his Categories with the following three terms: homonymy, synonymy and paronymy. If things are homonymous, then they share the same name but really they are different. For example, if we show a picture of an ox and we also show a live man himself, we would in both cases say, ‘this is an animal’ and ‘that is an animal’ even though what defines each is very different [one is a piece of paper while the other is a living, breathing creature]. [Now consider if we have a man and a real ox before us, and we say, “this is an animal” and “that is an animal”, both cases of ‘animal’ are synonymous, since the definition for ‘animal’ is the same in both cases and as well the names are the same.] “When things have a name in common and the definition of being which corresponds to the name is called the same, they are called synonymous. Thus, for example, both a man and an ox are animals” (Aristotle 1984a: 1a), (SH 28). [How the third case of paronymy fits into these distinctions is not so clear, but it would seem important given the role this concept plays in helping us understand how we can have multiple categories for being. We take the example of a grammarian getting his name from grammar. When words get their name from other words, they are paronymous. It is not stated this way, but to fit this concept in with the other definitions, it would seem that two things are paronymous if their definitions are not identical but their names are morphologically derivative. But this does not help me understand how the highest genera of being are paronymous. It would be nice if these different senses were each stated, described, and named.] “When things get their name from something, with a difference in ending, they are called paronymous. Thus, for example, the grammarian gets his name from grammar, the brave get theirs from bravery. (Aristotle 1984a: 1a)” (SH 28). SH says that what we gain from this is that “some attempts to define species may not capture what is essential to the species itself” (SH 28). In the case of the picture of an animal, we use the same name, which might lead us to believe they are of the same species, when in fact they are not. We need instead to look beyond the names and seek instances of synonymity. Now, the genera with the name ‘being’ cannot be synonymous, since then they would be identical. They also cannot be homonymous, since then they are really different and have no good reason for all being called being. So instead, for Aristotle being is a paronymous concept. [Explaining this will involve an analogy, so we begin first with a different concept, health. We think of all things that are healthy. Let us guess that we have nutrition, Olympian athletes, positive emotions, smooth clear skin, and such things. They do not all fall into the same categories. However, they all refer to health in one manner or another. Perhaps they produce health (nutrition, positive emotions) or perhaps they are signs of health (smooth clear skin, positive emotions), or perhaps they can receive health (Olympian athletes perhaps). We also will need to think of being this way too. Aristotle will refer specifically to being’s representation as the copula ‘is’. We use ‘is’ in several ways, so perhaps these are the different senses of being. I can think of ‘is’ used as an equating function, as in “that person is Roger”, or as a predicating, “that person is angry”. I am not sure what else. Also, I am not sure how these can be senses of being understood in terms of unity or as the highest category.]

Aristotle proposes that we consider being to be a paronymous concept. What would such a concept look like? Aristotle gives the following example [the following is quotation of Aristotle]:

Just as that which is healthy all has reference to health – either because it preserves health, or because it produces it, or because it is a sign of health, or because it is capable of receiving health – . . ., so too that which is is said in several ways, but all with reference to a single principle. (Aristotle 1984b: 1003a)
(SH 29)

Before moving back to the notion of being, we begin first with the idea that health is paronymous, and SH draws the following consequences from this.

1) Different things can be healthy. 2) In each case, we apply the definition for health in a different way. 3) All of these meanings of health, although different, refer to a focal meaning.

SH writes, “It is quite straightforward to relate this idea of paronymy to the concept of being” (29). Thus as noted in point 3 above, all the senses of being refer to the focal concept of being. SH then lists some concepts. [It would seem that these would each be different senses of being, and perhaps thus also each a different highest genus. But I am not sure.]

Rather than simply being a heap, the different categories of being are all related to a single concept. Things can therefore be said to be. For instance, properties, substance and differentia can all be said to exist, despite being different from one another.
(SH 29)

SH’s next point is that although the senses are different, they relate to one another [and not just independently to one focal meaning]. His third point is that all these notions refer to the central concept being [this is like his first point. The difference here seems to be that now he specifies that concept as ‘being’.] [The explanation that follows is not clear to me. It exemplifies how all the senses of being refer to the central concept of being. The example is that properties must be properties of some substance, thus the notion of property is secondary to a focal concept of substance. However, I am not sure if this is just an example unrelated to the focal concept of being or if ‘substance’ is to be understood as one of the senses of being.]

Third, these different notions of being will all relate to a central concept of being. If we look at the notions of substance and properties, for instance, it is clear that a property can only exist as a property of something. Therefore it is going to be logically secondary to a focal meaning, in this case the notion of substance to which properties are attributed.
(29)

SH notes that paronymy is a concept that will return in our discussion of the Scholastic tradition. For now, however, we return to the original idea that the problem of the Large is also to be understood in terms of the black abyss of the undifferentiated. [The point here seems to be that we really seem not to have a way to differentiate things in Aristotle’s system, since the basic notion underlying all others, the notion of being, cannot itself be explicated. This means that even difference cannot be understood in this system. Thus furthermore nothing can be understood as different from anything else, at least not in any clear determinate way. In the quote SH uses, Deleuze uses a term that we have not yet discussed, so it might be a bit confusing. He uses here the term Logos. Perhaps we mean by this just ‘rational basis’. We then distinguish the logos of species and the logos of genera. As we noted, genera do not operate according to univocity, but rather in accordance with the equivocity of paronymous senses. Species, however, need to be clearer and more coherent, since they definitively divide the genera, and thus the logos of species is one of identity and the univocity of the genera that they divide. In other words, in this one system seemingly based merely on the logos of class inclusion, we really need two different and perhaps incompatible laws of operation, which compromises its coherence.]

To deal first with the question of black nothingness, we can see that even if we can now solve the logical problem of how the terms at the top of the hierarchy are related, we are still left with a question as to how we are able to define the concept of being. Being still cannot be defined without presupposing a yet higher concept. Being is therefore put outside of the world of species and genera. As Deleuze writes, ‘it is as though there were two “Logoi”, differing in nature, but intermingled with one another: the logos of species . . . which rests upon the condition of the identity or univocity of concepts in general taken as genera; and the logos of Genera . . . which is free of that condition and operates both in the equivocity of Being and in the diversity of the most general concepts’ (DR 32–3/41).
(SH 30a)

[The final point that SH makes seems to be a preparation for a later elaboration, and so here we may be unable to present it clearly. His point seems to be that Aristotle’s system is lacking in another way. It tells us what determines something as being what it is. But it does not tell us how that thing could have come about. We always ask in his system, what is it? (What genus belongs to its species’ essence?) For this, we presuppose the existence of the thing, and thus we do not probe into its genesis. This is somehow related to the undifferentiated white nothingness, but I am not sure how. Perhaps it will be explained later. It may have something to do with the fact that the genetic relations between things is not evident, like how the relations between things in the white nothingness are not given. But I do not understand how at the moment.]

Second, Deleuze argues that while Aristotle provides an account of the determination of objects, he cannot provide an account of the constitution of objects. As we saw, properties are understood as properties of something, and the same could be said of differences. When we ask the question, ‘what is it?’, we have already presupposed the existence of a logical subject to which predicates will be attributed by means of an answer. This rules out in advance any possible account of the genesis of the subject. It is for this reason that Deleuze introduces the indifference of white nothingness. He is going to argue that we need to think the faintly paradoxical notion ‘unconnected determinations’ if we are to think of the emergence of the subject itself.
(SH 30)

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

Aristotle (1984a), ‘Categories’, trans. J. L. Ackrill, in Jonathan Barnes (ed.), The Complete Works of Aristotle, Princeton: Princeton University Press, 3–24.

Aristotle (1984b), ‘Metaphysics’, trans. W. D. Ross, in Jonathan Barnes (ed.), The Complete Works of Aristotle, Princeton: Princeton University Press, 1552–1728.

Aristotle (1984d), ‘Topics’, trans. W. A. Pickard-Cambridge, in Jonathan Barnes (ed.), The Complete Works of Aristotle, Princeton: Princeton University Press, 167–277.

 

Somers-Hall, (1.2), Deleuze’s Difference and Repetition, ‘1.2 Aristotle’s Conception of Difference (30–3/38–42)’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH, and Difference and Repetition as DR.]

[UPDATE: My lack of knowledge, cleverness, and time prevent me in some cases from being able to re-explain in my own way some ideas in Somers-Hall's text. We are fortunate that the author has taken the time to remedy these gaps in my summary. Please see his clarifications in the comments section.]

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

 

Chapter 1. Difference in Itself

1.2 Aristotle’s Conception of Difference (30–3/38–42)

Summary

Brief summary:

Aristotle’s conception of difference is bound up with his theory of classification. A genus is divided into species, which differ in kind. The division terminates in the individuals, which differ in number and only accidentally [rather than essentially like species do]. The genus-species distinction is relative, such that any genus can be a species to a higher genus, just as any species can be a genus to a lower species. The one exception is the species-individual relation, in which the species cannot again serve as genus, given that there are no species below it; instead there are only individuals. Difference in its truest sense is the difference in kind which distinguishes one species from another.

Summary

Deleuze’s critique of representation begins with Aristotle, whose philosophy in this account is thought to have presented “the first formulation of representation” (23). Aristotle conceived of difference in terms of opposition: “x differs from y if x is not y”. Deleuze says that this implies a certain concept of being.  Deleuze will instead formulate a univocal conception of being in terms of intensive difference. Later Deleuze will discuss two ways of understanding difference, either spatially or as intensity. If spatially, then being is understood as fragment. If intensively, then being is understood univocally. In the following, SH will go over Aristotle’s basic ontological concepts of genus, species, difference, and accident, drawing primarily from his commentator Porphyry. Afterward we will see why Aristotle’s thinking leads him to certain problems. (24)

[The following can be confusing for a number of reasons. For example, there is terminology used in a way that is unfamiliar to me, and also the terminology is slightly inconsistent, namely in the cases of the phrases: predicated in and predicated of. Perhaps their meanings are identical, but even if so, I am not exactly sure I know how to define them. Also, there are two definitions given for genus, but in subtle ways they do not seem to line up, since the second one adds concepts not found in the first one. Another problem is that we might be familiar with this pairing: subject – predicate. And we might also be familiar with this pairing: genus – species. But somehow we need to combine them such that a genus, species, or individual can be predicated of or in something else. How to clearly conceptualize this is not apparent to me yet. The conclusion we will arrive at is that we need a species in between genus and individual. Yet, the exact reasoning for this is also unclear to me. The basic reason seems to be that the definition necessitates it. However I am not sure why the definition is formulated exactly in this way and not in some other manner. So according to the definition, the genus is made of different things that differ in kind. Working just with this definition, perhaps the reasoning is like this. We think of a set of individuals. If they are included in the genus, then so far we only know what generically is common to all of them (what is essential to them all) but their distinctions are not thereby designated. So it is as if they are all the same. In order for there to be a real diversity such that there are numerous members for the group, the individuals need to have differences in kind, which would be like subgroupings, and thus be species intermediateing between genus and individual. What is not clear to me is why genus is defined in this way and rather not just defined as a group of members. Perhaps the idea is that in order for it to be a group, it needs different things and not just one thing. And in order to have different things, they cannot be many instances of the same thing (or different quantitative variations of the same thing), since these could collapse again into one thing (or into one thing having different degrees of itself). They need to be different in kind in order to be a real multiplicity, and thus perhaps there needs to be species groupings among the members. Please read and discern the correct meaning of this paragraph for yourself.]

Porphyry defines the genus as ‘what is predicated in answer to “What is it?”, of several items which differ in species, for example, animal’ (Porphyry 2003: 4). This follows from Aristotle’s own definition: ‘what is predicated in the category of essence of a number of things exhibiting differences in kind’ (Aristotle 1984d: 102a). What does it mean to be predicated of items that differ in kind? If we take the case of Socrates, it should be clear that ‘animal’ can be predicated of him, to the extent that Socrates is a man (a rational animal). For Porphyry and Aristotle, however, there is no difference in kind between different men, but rather a difference in number. While it is the case that a given genus, such as animal, is predicated of an individual, such as Socrates, the genus cannot simply be directly used to define the individual. If it were used in this way, the genus would be the only function which was essential to each individual. This would mean that in essence each individual would be different only in number, whereas the definition of genus requires that it is predicated of what also differs in kind. We therefore need the intermediary category, which Aristotle and Porphyry call the species.
(24)

[The terms predicated of and predicated to would seem to mean: “is a predicate to”. So for example, animal can be predicated of Socrates, since it is a predicate to Socrates as in the formulation: Socrates is an animal. Now we move to the definition of species. The genus, we saw above, is what can be the predicate to a species, which would be groups of individuals that differ in kind to other species. So the genus animal can be predicated to various species, such that, ‘man is an animal’, ‘dog is an animal’, and so on.] Species we now see are what are predicated to things which differ in number. [So perhaps there is no difference in kind between Socrates and Plato. They is just difference in number. They are different instances of the same species man. So, “Socrates is a man” and “Plato is a man”.] Thus the individual can be predicated of both its genus and its species. [But we ask now, how would we define the grouping above “animal”? Perhaps it might be, “living creature”, including also plants and whatever else. It would seem that ‘genus’ and ‘species’ are relative terms, such that a genus can serve as a higher genus’ species.]

Porphyry writes that ‘the intermediate | items will be species of the items before them and genera of the items after them. Hence these stand in two relations, one to the items before them (in virtue of which they are said to be their species), and one to the items after them (in virtue of which they are said to be their genera)’ (Porphyry 2003: 6).
(SH 24-25)

[This also means that only the lowest species has individuals as its more basic members. We need to define species now in terms of its genus, and not just in terms of having members differing in kind, like we saw above. I am not exactly sure how this is done. Perhaps the new definition of species would be: ‘a species is the subgrouping of the genus, and this grouping is based on differences in kind.” But that does not add anything to the definition of genus, so I am not sure.]

A consequence of this is that we now need to define the species in terms of something other than the individual, since only the lowest species relates directly to things which differ only in number. Instead, we now define the species in terms of its genus. Thus we have a hierarchy, reaching from the highest genera to the individual, through which the individual is specified by a process of division from the genus through the various species, gaining determinations as it goes, since each genus will determine the essence of that below it.
(25)

[Next we look at ‘accidents’. SH says they do not define species, so it is not clear yet why we need to mention them. Perhaps they are what distinguish individuals, which differ in number, but not in essence. There are separable and inseparable accidents. This distinction is not very clear to me. Separable accidents are not defined, but they are exemplified, for example, Socrates can be sitting or not sitting. It is clear why this is accidental, since it is arbitrary and does not change Socrates himself. Inseparable ones are explained as being accidental traits that were they removed from the individual, that individual could still keeps his essence. The counter example is a trait that were it removed, the individual does lose its essence. All this is clear, except it is not clear why the second kind of accidents are called inseparable, since they can be separated without changing the individuals essence. Perhaps they are inseparable in the sense that they are inherent to the individual and physically inseparable, even though they are non-essential.]

The last category we need to consider are accidents, which do not define a species. These can either be separable (as in the case of Socrates, who can be sitting or not sitting), or not separable (for instance, ‘being black is an inseparable accident for ravens and Ethiopians’ [Porphyry 2003: 12]), in that an Ethiopian could lose his skin colour without ceasing to be an Ethiopian, whereas a man without reason (at least potentially) is no longer a man.
(25)

SH now asks what the role of difference is in this hierarchical schema. For Aristotle, only things sharing something in common can also differ, for otherwise the difference would be so great as to disallow any basis for them to stand in relation to one another. [The commonality seems to be a shared genus at some higher level]. SH then asks “If differences between things of different genera are too broad, how can we formulate a narrower conception of difference?” [But it is not yet clear to me yet how some genera are similar enough to have an evident difference and others do not, and I also do not understand what is meant by a narrower conception of difference and how it would solve this problem.] SH explains that [in the face of this problem] there are three forms of difference, namely, common difference, proper difference, and the most proper difference. Yet Porphyry only considers the most proper difference to be real difference. Common difference is not real difference, because it is the difference between accidents, meaning that that the difference is between “non-essential predicates, and is not effective in determining a real difference between entities” (SH 25). Proper differences are in fact real differences because they are inseparable properties of things [above we looked at inseparable accidents, like the black of the Ethiopian. It is not clear how that notion fits here into proper differences. Perhaps they are the same, and here proper differences distinguish individuals but perhaps like inseparable accidents they do not distinguish species.] (25) Then we have the most proper difference, which is specific difference. It “is what allows species to be defined in Porphyry’s tree by dividing the genus” (25d). [It is not clear to me what the ‘proper’ means here and why more proper brings the difference to the difference between species. Accidental traits it seems distinguish individuals. Proper differences do too. And somehow, the more proper, the less distinguishing of individuals and the more of species.] [So now we are somehow no longer thinking of proper difference as distinguishing individuals but instead as dividing genera into species. Recall also that difference between genera can be so great such that the genera are too other to one another that they cannot be properly distinguished. (There was no example for this, so it is difficult to conceptualize. Perhaps this would happen if the genera are at least two steps removed. So consider these two classifications: 1) Socrates – Man – Animal – Living Thing. 2) The largest cut diamond – Gem – Stone – Non-Living Thing. Perhaps Gem and Man are too other, since we cannot say, Both Man and Gem are X, except Man is has these distinguishing traits and Gems have these other distinguishing traits. For, the next most common genus is ‘thing’, but to make the comparison, we would say, a man is a thing, that is also a living thing, that is also an animal, while a Gem is a thing, which is also, … etc. So specific difference, which would also for some reason be equated with conceptually significant difference, is in between the otherness of genetic difference and the ultimate specificity of individual difference. Perhaps also to see just individual difference is to be aware of metamorphoses, on account of very specific changes which cannot be reduced to a single common thing happening over those changes. I am not sure, so please judge for yourself the meaning of these sentences.]

The most proper difference, however, is specific difference. Specific difference is what allows species to be defined in Porphyry’s tree by dividing the genus. So, if we take the genus, animal, we are able to determine the species, man, by dividing animals into two kinds: rational and non-rational animals. Difference is the criterion by which | we divide the genus into two species. Conceptually significant difference therefore occupies a middle point between the extremes of otherness and accidental difference: ‘Specific difference refers only to an entirely relative maximum, a point of accommodation for the Greek eye – in particular for the Greek eye which sees the mean, and has lost the sense of Dionysian transports and metamorphoses’ (DR 32/40).
(25-26)

Porphyry then, by means of these divisions based on essential differences, “provides an account of the determination of objects that allows us to characterise all of their essential determinations through a process of division. We begin with a property which belongs to everything, for instance, substance, and by a repeated process of division of things into contrary classes, we eventually arrive at a complete determination of the subject” (SH 26). [SH then quotes Porphyry who speaks of the form-matter distinction in this context. It seems to add concepts that we will not need later, so I will just replicate the text without commenting on it.]

He puts this point as follows [quoting Porphyry up to the citation]:

For in the case of objects which are constituted of matter and form or which have a constitution at least analogous to matter and form, just as a statue is constituted of bronze as matter and figure as form, so too the common and special man is constituted of the genus analogously to matter and of the difference as shape, and these – rational mortal animal – taken as a whole are the man, just as they are the statue. (Porphyry 2003: 11)

Of course, Porphyry is not implying that what we have here is a temporal constitution (we don’t find in the world beings that are only determined as animals, for instance). Rather, his point is that the series of genera and species provide an account of the logical order of determinations of a particular object.
(SH 26)

 

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

Aristotle (1984d), ‘Topics’, trans. W. A. Pickard-Cambridge, in Jonathan Barnes (ed.), The Complete Works of Aristotle, Princeton: Princeton University Press, 167–277.

Porphyry (2003), Introduction, trans. Jonathan Barnes, Oxford: Clarendon Press.