What does Parmenides mean by thinking and being are the same? How does Plato read Parmenides and why does Aristotle’s interpretation of Parmenides and Plato matter? Such questions hinge on how many meanings do the Greek words identity and relation signify? Three paradigms emerge from these readings: Parmenides proposes a numerical identity and a se relation of thinking and being; Plato maps a qualitative identity and per se relation of thinking and being; and Aristotle offers a pros hen numerical identity and a se relation of thinking and being.
Que veut dire Parménide quand il affirme que penser et être sont identiques ? Comment Platon lit-il Parménide et pourquoi l’interprétation aristotélicienne de Parménide et de Platon est-elle importante ? Ces questions dépendent du nombre de significations que présentent les mots grecs « identité » et « relation ». Trois conceptions émergent de ces lectures : Parménide propose une identité numérique et une relation a se entre pensée et être ; Platon établit une identité qualitative et une relation per se entre pensée et être ; Aristote suggère une identité focale numérique et une relation a se entre pensée et être.
This enquiry is parsed from two similes from the Theaetetus. Three metaphors are transposed from these similes: Hunting stands for thinking, ringdoves for being, and pigeons for identity. In hunting some one kind of knowledge – as the various kinds fly about – a ringdove and a pigeon are caught. Is it possible to clarify what exactly Parmenides means by thinking and being are the same? How does Plato read Parmenides and why does Aristotle’s critique of Plato’s Eleatic reflections matter? Parsing such questions ultimately hinge on how many meanings do the Greek words identity and relation signify. Why does Parmenides propose a numerical or qualitative identity of thinking and being; Plato a qualitative identity and per se relation of thinking and being; and Aristotle a numerical identity and a se relation of thinking and being?
The problem of hunting [of thinking] doves [being] and pigeons [identity] commences with the question – if knowledge is found only in the unity of the knower and the known in intellect – does not the concept of self-knowledge necessarily include a distinction between knower and the known? And moreover, does such a distinction explain why for Platonists the soul must ascend and for Aristotelians there is no need for soul’s ascent at all? It is a commonplace that Plato and Aristotle part ways on both counts – but why? In attempts to clarify these differences we are reminded that in any philosophical enquiry there is not only the immediate problem being investigated but others as well – such as the problem of self-knowledge which leads back to the Platonic thesis of the unity of intellect with its object the Forms; and a Peripatetic Nous who is self-knowledge thinking itself in an absolute activity of form – but with no need of Forms at all.
1. Eleatic Horizons
We begin by observing an enigmatic fragment where a Goddess hints of an ontological identity and relation between thinking and being reducible to an ineluctable law of being.
Come now and I will tell you the roads alone for seeking [that] be for thinking for you could not know non-being [for it cannot be accomplished] nor could you declare it, for the same is thinking as well as being [for it is the same to think and to be].
Parmenides poses the question of the identity of thinking and being in four possible ways: 1] thinking as a problem in philosophy of mind; 2] identity as a surd addressed in philosophy of language; 3] being as a question of physicalism; and 4] identity of thinking and being associated with ontological monism. It is the last of these options that guides enquiry. Although the shape of what-is is not divided, there are three claimants to the share of being: 1] thought; 2] time; and 3] the plurality of ordinary empirical objects. The first option – thought as claimant to a share of being – is our focus. Parmenides notes: “…thought is identical to its own object, what-is… …you will not find thinking separate from being [34-36].” He proceeds by applying the law of the excluded middle to prove that the identity of “what is” precludes the possibility of any characteristic save just being. To think of anything is to think of it as being and the nature of being is that a thing is [numerically] identical with itself which allows it neither to come to be nor to pass away as established by the logical consequences of identity. Since nothing but being can be, Being is all that is, in an increate, imperishable, immobile, indivisible, homogeneous and continuous unit that neither was nor will be but simple is.
Parmenides does not deny that thinking happens, but since being is all there is, thinking is inseparable from being. Since that which thinks is, and that what is thinks, the numerical identity of thinking and being and the relation of thinking and being is a se. As for all false notions of a world of difference and change, the Goddess claims the error that underlies them is derivable from the error of positing two things that need not be identified – that to be and not to be are the same thing and not the same. Hence the possibility of motion and multiplicity; of a physical world at all was impugned and its advocates forced to face the logical, epistemological and metaphysical problems of identity and difference, of appearance and reality, of truth and error.
2. Unity and Plurality
We can make several observations as we move from Parmenides to Plato. A reading of the first hypothesis of the Parmenides is pivotal. The view of more recent scholarship is that Plato’s theory of Forms is what is subject to criticism in hypothesis I of the Parmenides. If so, a critique of Parmenides’ doctrine of the unity one being or the identity of thinking and being from the precipice of the theory of Forms resonates.
Plato begins by assessing what unity means in the first hypothesis. He begins by enumerating a list of the parts or attributes of being proposed by Parmenides. These include circularity, perfection, sameness, limit and being. Plato notes that an attempt at a unity of thinking and being in line with such attributes fails. In the wake of this critique Parmenides is forced to admit that parts cannot be reconciled with a partless being which encompasses the identity of thinking and being:
Well then, said Parmenides, if there is a one, of course the one will not be many. Consequently, it cannot have any parts or be a whole. For part is part of a whole, and a whole that from which no part is missing; so whether you speak of it as a ‘whole’ or as ‘having parts’ in either case the one would be many and not-one; but it is to be one and not many. Therefore, if the one is to be, it will not be a whole or having parts.
Plato’s argument is straight-forward. If being is to be accorded some dignity among real things, it will have to be as a distinct nature for unity does not indicate being, and being does not indicate unity. Such a move occurs in the second hypothesis of the Parmenides where unity is conceded as the qualification for any object that can be referenced or talked about.
When you use any word, you use it to stand for something. You can use it once or many times but in either case you are speaking of the thing whose name it is. However many times you utter the word, you must always mean the same thing. Now, different is a word that stands for something; so when you say it, whether once or many times, you are using it to stand for, or naming that thing whose name it is. Hence when we say the others are different from the one, and the one is different from others, we use the word different twice, but nevertheless we use it always to refer to just that character whose name it is.
As soon as this is asserted, Parmenides’ thesis is fated for oblivion.
Unity does not admit plurality. Here Parmenides is lead to various incompatible conclusions that prove useful for Plato. Although Parmenides offers a list of attributes for unity including circularity, perfection, sameness with itself, limit and being, it immediately becomes clear that unity cannot lay claim to any of these attributes. Unity would have to be a “many” to accommodate his definition. Here Plato’s ups the ante claiming: 1] unity can have no cause other than the nature of unity itself; and 2] nor can it one other property into itself since that would cause it to be other than itself, or many [137cd].
Plato focuses his attack next by examining Parmenides’ claim that the one has the properties of limit, rest, shape, no parts, sameness, equality, place and timelessness. Here Parmenides is forced to admit that the “one has neither beginning nor end and is without limits.” He also admits that “if the one had either a straight or a round shape, it would have parts and so be many and since it has no parts, it is neither straight nor round.” [138a]. He eventually concedes the one cannot be either [a] in another, or [b] in itself [138a]. “It could not be anywhere in anything” [138d] and what is never in the same place or condition is not at rest or stationary [139a]. Finally, when forced to address sameness, equality and timelessness, he concludes: 1] the character of unity is one thing, sameness another [139c]; 2] the nature of the one is not equal to anything neither to another or itself results in the one being either [a] equal or [b] unequal either to itself or to another [140b]; and 3] the one cannot have any relation to time at all, not even to the present [141de].
Plato offers two arguments which transform Parmenides’ simple a se: to einai into a complex per se: ta onta or ousiai. His proposal is that unity, which encompasses “all things,” is really a “many.” This claim is based on the argument: since unity can have no cause other than the nature of unity, and since the nature of unity cannot admit one other thing into itself, for that would cause it to be other than itself or many all things must be “many not one.” The inference Parmenides is forced to draw is that his alleged “seamless one” is “many.” Indeed, “it cannot even be one for then it would be a thing that is and has being” [142a]. In the end, the first hypothesis is a false phantom and claims to the numerical identity and an a se relation of thinking and being involves contradiction and thus is false.
3. Unity, Plurality and the Forms
Plato’s next move is to reformulate Parmenides’ claim that “thinking and being are the same” in the context of his theory of Forms. He begins by claiming “Being” is not an object. Rather it is part of any object that is real, has existence and where one name corresponds to one property alone. A problem immediately surfaces. In the first hypothesis of the second part of the Parmenides [142a], and in the Sophist [243b-245e] Plato claims Parmenides’ unity cannot encompass “being” for to on/ousia is complex. Moreover, whatever exists is distinct from the existence it has. This applies not only to that which exists in the world of genesis but also to the distinction between an archè of ousia and complex ousia itself. If ousia is complex, it cannot be the source of being for all things. Complexity presupposes simplicity which is why the archè of all must be beyond ousia. Plato also argues that the arche of ousia is the archè of knowability [to gignoskesthai] itself in two tropes. Firstly, all that is knowable, even ousia itself and the Ideai require a simple archè beyond each which is the idea tou agathou, the Form of the Good. Secondly, since an archè of ousia beyond ousia exists, identified with the idea tou agathou and the anypothetos archè of Republic 509ab, all things again must be “many not one.”
Finally, in Theaetetus [188d-189b] Plato suggests that Parmenides’ claim that “thinking and being are the same” ultimately rests on a per se analogy, not an a se identity, between believing, seeing, and touching. Just as touching what is not is touching anything, which is not touching at all, so false belief [believing what is not] does believe nothing, which does not believe at all. In the Sophist [236d-237e] he claims that speaking may be understood in the same way – as per se contact with an object. We give a name to something by pointing to it and uttering the name. If we point at nothing, we are naming nothing, and just utter empty noise. Hence, speaking of what is not is not really speaking of any-thing at all.
4. Degrees of Identity and Relation
Plato, a water-diviner pointing out the metaphysical traps of his predecessors, raises two final objections that undercut Parmenides’ version of the claim that thinking and being are the same. Firstly, he asks, is the identity of thinking and being numerical or qualitative?; and secondly, is the relation of thinking to being of a se or per se? Behind such questions lies an attempt to construct a chain of qualitative/per se identity arguments grounded in his theory of Forms.
Plato proposes his qualitative/per se option on five grounds. First in the Parmenides [183e-184a] he challenges Parmenides’ notion of a divisionless unity. In its place he proposes an argument from a variety of distinct natures which reconciles the divisionless and partlessness of being. Secondly, he combines the knowledge argument from the Phaedo [79a6-7] and the meaning argument from the Sophist [248a6-7] to underscore that all thinking is necessarily a duality of thinking and of object of thought. Since all thought including self-thought is constituted through a duality of act and of the object of thinking, and the object as constitutive of thought, exists prior to thought as well as in thought, thinking implies plurality not unity. Thirdly, he proposes another way in which thinking shows itself to be composite is in the multiplicity that characterizes any object of thought. Using the example of the demiurgic intellect at Timaeus [30d1-2; 37a1-2] he shows that it thinks manifold Forms. Fourthly, he notes that all thinking implies deficiency. Since it reaches toward its objects, again being cannot be absolutely simple, ultimate and unitary as Parmenides proposes.
Plato has undermined Parmenides’ assertion of a numerical unity of thinking and being and thus the possibility of an Eleatic a se monism. The identity of thinking and being is qualitative and the relation of thinking to being is per se. It is here that a bridge to Aristotle’s critique of Plato’s reading of Parmenides emerges.
5. Peripatetic Pathways
At the beginning of Metaphysics Γ Aristotle claims that there is a science [epistèmè] which is concerned with being qua being.
There is knowledge [epistèmè] that contemplates [theôrei] being as being [on hè on] and that which belongs to it per se [kath’ auto].
Being is constituted within epistèmè, in accordance with the logic proper to being. G.E.L Owen translates this pros hen formula as “focal meaning,” and in his paraphrase, it means that all the “senses [of “being”] have one focus, one common element,” or “a central sense,” so that “all its senses can be explained in terms of substance and of the sense of “being” that is appropriate to substance.” According to Owen, “focal meaning” is new and revolutionary in Metaphysics Gamma, and introduces a “new treatment of to on and other cognate expressions” expressed in the following two theses:
(1) “Focal meaning” contradicts and replaces Aristotle’s earlier view in the Organon, EE and others that beings differ in different categories, and “being” has various distinct senses.
(2) “Focal meaning” makes it possible for Aristotle to establish a universal science of being qua being in Meta. Γ which contradicts and replaces his earlier view that because beings differ, a universal science of being is impossible.
(3) “Focal meaning” makes it possible to propose two pros hen notions of identity and relation: per se [qualitative] and a se [numerical].
Two theses concerning identity and relation follow:
(4) While Plato proposes a qualitative identity of thinking and being and a per se relation of thought thinking being and the Forms.
(5) Aristotle offers a numerical identity of thinking and being and an a se relation of thought thinking itself [noèseôs noèsis].
6. Being, Language and Categories
Aristotle frequently says that “being” is pollachôs; that “being” is said in many senses and different beings are not said to be purely homonymous, but rather to be “related to one thing (pros hen)”(Meta Γ 1003a33-34). The pros hen formula is as follows: Some things are said to be because they are substances, others because they are affections of substance, others because they are a process towards substance, or destruction or privations or qualities of substance, or productive or generative of substance, or of things which are relative to substance (Meta Γ 1003b6-10). In Γ2 when all other things are pros hen, to substance, substance then becomes the primary sense of all beings (1003b 7-8). In Z4, it is also explained that pros hen of being means that being is neither homonymous nor synonymous, and what it expresses is that “definition and essence in the primary and simple sense belong to substances. Here Aristotle’s analysis of essence and essential predication, which focuses on the distinction between what an object is, and how it is remains foundational.
Owen also takes Aristotle’s notion of signification (verb, sèmainein, “to signify) to mean the “sense” or “meaning” of being. The word pollachôs, contains what Matthews calls “sense-kind confusion” and to mitigate such, Owen proposes that to say that a word has a “sense” is to say that it has a distinct “meaning”: a significatum. Moreover, since “Being” has many significata and is thus said in many senses, being can either be the word that is signifying or the things signified. Corresponding to each of these significata, there is a signifying category. The categories “signify” (Cat. 4, lb26), and what they signify are “things that are” (ta onta la20, cf. Topics, 1.9, 103b27). When Aristotle lists “substance,” “quality,” “quantity,” “relation,” and so on, it is often not clear whether he is talking about them as signifying categories, or as the signified extra-linguistic beings. Accordingly, the study of categories is the study of beings.
7. Thinking about Forms Revisited
In these contexts, what focuses our attention is Aristotle’s critique of Plato’s theory of Forms and his “alleged” confusion of the particular and the universal in reified universals: “But those who speak of the Forms in one respect speak correctly in separating the Forms, if they are substances; but in another sense incorrectly, because they say the one in [epi] many is a Form.” In the Metaphysics we find the following complaint: “And to that they [the Forms] are patterns and that the things share them is to use empty words and poetical metaphors.” Three questions generate Aristotle’s critique: 1] are Forms universals; 2] are Forms preconditions for universal predication; and 2] are Forms the basis for an application of predicate terms at all? Three answers emerge from his critique: 3] since Plato’s Forms are ousiai, they are separate in the way substances in his view are separate and cannot be universals; 4] since Forms are separate substances and individual universals existing on their own and not in anything else, they cannot be common to or in a plurality of things and thus cannot be universals; and 5] since Forms are merely properties considered in isolation, they are not capable of sustaining universal predication in any meaningful sense at all. In nuce, Aristotle’s theory of substances [ousiai] is incommensurable with a Platonic theory of Forms [eidè; ideai].
Next Aristotle makes a bold move that requires us to leave aside Platonic habits of thought. However difficult it may be for us to grasp what the perfect knowledge of divine intellect might be like there is in Aristotle’s view no gap between thinking and being. Nous as ousia exhibits numerical identity and a se relation as to ti èn einai [what it is to be] whereas Plato’s claims necessitate a qualitative identity of ousia and Forms and a per se dependence of Nous in relation to Forms.
After Aristotle, a per se demotion of Universals and Forms follows that led later Platonists and Aristotelians to consider whether a numerical / a se identity applies to Forms [intelligibles] and Universals [sensibles] at all. This led later Platonists to consider there was something unsatisfactory with positing Forms a se. Their solution was to place Forms within divine intellect. Since the existence of Nous a se does not depend on any contingent property per se; and the existence of per se properties depends on the a se existence of Nous; a Neo-Aristotelian-Neoplatonic “hierarchy” of forms and universals belonging to different levels of reality emerges where forms are intelligible and universals are sensible. Both reformulations preserve a theory of Forms in two novel ways. First, Forms do not have to withstand judgment as a theory of universals. Secondly, Forms account for the ontological preconditions of universal predication for the application of predicate terms. Perhaps here, in light of the debate on whether or not Platonic ideas are universals, Gerson is correct to argue that Aristotle’s universals are not Plato’s Forms and Wolterstorff that Plato’s Forms are not hypostasized universals – as ante rem universals distinct from post rem universals.
8. The Identity of Thinking and Being Revisited
Aristotle associates the nous/ousia with the highest form of thinking, noèsis via energeia [Met. VI.1072b8]. Nous is identical with pure activity [energeia] which is noèsis. Since this pure activity of thinking is also the highest being – an a se Nous when it thinks itself is numerically identical with being.
And thought thinks itself through participation in the object of thought, for an object of thought it becomes [by the act of] apprehension and thinking, so that they are the same: thought and the object of thought, i.e. being, is thought. And it actually functions [when it] possesses [this object].Met., XII.9.1072b20-23
While there is a distinction between noèsis noèseôs, there is no gap between act and concept, and so no potentiality. Intellect is thought thinking itself as self-reflexive thinking or thought being thought and being thought eternally without interruption. In nuce, with noèsis noeseôs we witness a numerical identity of thought and being and an a se relation of thought to being. A parsing of the identity of thinking and being follows: first, if the object of thinking and being is the identity of self-contemplation, then noèsis is a kind of numerical self-contemplation; and secondly, if Nous is in a a se relation to itself, thinking being is an act of noèsis noèseôs itself.
With Aristotle a pros hen aseity argument begins to emerge – from the term aseitas derived from the prepositional phrase ens a se – where an Intellect / Being ens a se is postulated – completely self-sufficient and independent a se – but in a per se relation with other beings. As an ens a se, Nous is “from itself;” not ens ex se “out of itself.” It does not depend on any necessary property a se or contingent property per se. Its identity, just to itself, is numerical not qualitative, and if there are changes to this a se identity, it is a mere Cambridge change – a claim that emerges again in different forms in Plotinus, Leibniz and Plantinga.
The question of how knowing is identical with being is fundamental. Is the identity of thinking and being numerical or qualitative? Is the relation of thinking to being a se or per se? Aristotle affirms the numerical and a se options. Nous is a self-sufficient archè / principium of all reality; it is a mind a mind whose identity is numerically a unitary whole. Its existence is necessary [a se] and not contingent [per se]. Within a pros hen context Nous is in an a se relation to itself and in a per se relation with other minds and beings.
Is Aristotle’s reading of Parmenides and critique of Plato foundationally and non-inferentially justifiable? Yes – but as an imagined cinema conversation between Ramanujan Hardy and Littlewood began with the question – where are the proofs? So ends our enquiry. Aristotle’s arguments from logical possibility provide acuity to both parsings. He offers a “neo-Eleatic” parsing of claims that “thinking and being are the same” appears in four stages.
Aristotle’s first argument rests on a version of the epistemic regress argument that grounds for any justified true belief involve chains that are: 1] anchored in foundational beliefs [not in chains that are circular, endless, ending in unjustified beliefs or anchored in foundational beliefs that do not derive their justification from other beliefs; and 2] foundational beliefs that can be feasibly justified non-inferentially [i.e. without deriving justification from other beliefs].
1. It would be a non-inferential [or foundational justification];
2. It would be characterized by feasibility.
3. It exhibits a two-tiered structure as described by epistemic foundationalism;
4. It is justified by supporting links or foundational beliefs that are truth-conductive [i.e. it tends to produce true justified beliefs].
Aristotle’s second, third and fourth arguments are based on aseity arguments where an a se and a priori Nous is numerically identical with itself:
1. Nous’s existence is either necessary or logically impossible.
2. It is not impossible for Nous to exist a se [i.e., there is no contradiction in assuming that Intellect exists a se].
[C] Therefore: Nous exists necessarily a se.
1. Nous’s existence is either necessary or logically impossible.
2. It is not impossible for Nous to exist necessarily a se.
Therefore, Nous exists as an abstract entity necessarily a se.
3. It is impossible for Nous to exist a se unless it is uncreated and independent of any other thinking and being object a se or per se.
4. Nous is independent of any other thinking and being object a se or per se.
[C] Therefore, Nous exists as an abstract entity a se.
One of the key problems that remains is the tenet of the numerical identity of Nous in an a se relation to its own thoughts. If we reject 1 we are faced with the option of nominalism and a descent into a loss of sovereignty. The denial of 2 raises the problem of ultimacy. Nous appears to be denied the role as ultimate principle. The dismissal of 3 and 4 raises the problem of dependency.
Aristotle’s answer is Nous’s thinking and being is independent and cannot be numerically identical if it is in a per se relation to itself. Thus:
1. Intellect’s existence is either necessary or logically impossible.
2. It is not impossible for Nous to exist a se [there is no contradiction in assuming that Nous exists a se].
[C] Therefore, Intellect exists a se.
Plato, Theaetetus, 199ab: “when in hunting for some one kind of knowledge, as the various kinds fly about […] so in one example he thought eleven was twelve, because he caught the knowledge of twelve, which was within him, instead of that of eleven, caught a ringdove instead of a pigeon.” Theaetetus, 197de: “Now consider whether knowledge is a thing you can possess in that way without having it about you, like a man who has caught some wild birds […] we might say his “has” them all the time inasmuch as he possesses them […] but in another sense he “has” none of them though he has got control of them, now that he has made them captive in an enclosure of his own; he can take holds of them whenever he likes by catching any bird he chooses, and let them go again and it is open to do that as often as he pleases.”
To transpose as in mathematics – to transfer a term with a changed sign from one side of an algebraic equation to the other so as not to destroy the equality of the members; and as in music – to move a chord, melody, composition upward or downward in pitch while retaining its internal interval structure – as said of players or instruments (cf. Oxford English Dictionary).
The primitive form of noèsis is nôsis, eôs. The words noos, nous, and noein are most probably derived from a root meaning “to sniff” or “to smell.” In Homer noos has several meanings, the most significant being a deeper insight itself. Noos penetrates behind the surface appearance to its real nature. In the Homeric poems Noos and Noein are closely related to the sense of vision – idein and gignôskein. Neither in Homer or the Homeric poems, however, does noos and noein mean propositional/discursive “reasons” or “reasoning.” Nonetheless, each word denotes a thinkable as opposed to a visible disposition. With Xenophanes a different meaning emerges. God is altogether and exclusively noon and is different in noèma from mortal beings. The notion that noos is something exceptional becomes prevalent in the generation after Xenophanes, especially with Heraclitus. In Heraclitus, Noos is still the noun belonging to legein. However, Noos is now what few people possess because it has to do with alètheia legein – to say true things. Saying true things, in turn, is logos, and it has as its focus insight into the divine nomos that governs everything. By inhaling this logos we become noeroi or acquire noos. Again, with Heraclitus, noos is far removed from discursive/propositional “reason” or “reasoning.” Associated by Plato with nous [intelligence, understanding] noesis is not a thinking of extrinsic properties but a thinking of intrinsic properties/forms [eidè]. Any thinking via images, representations, calculations, deductions or discursive propositions is not thinking where thinking and being are numerically the same. See Fritz 1993, pp. 23-85 (esp. pp. 23-43). One will find in the final bibliography the complete reference under the name of the author and the date of publication.
Grammatically to on is a particle and can be used either as a noun or as an adjective with a verbal sense. More precisely, when taken as a noun to on means that which is, a being; taken as a verbal adjective it designates that by which a being “is” or its being. To on can mean Being, beings or both and the interrogation of on hè on can be of either being-in-general [ontology] or on the ultimate ground of being [theology]. Plato designates to on as a metochè/methexis; or as the Latin grammarians took it – a participium. As a grammatical and a philosophical term to on participates in being as a noun, as a verb and as a universal. It exists [einai ti] as thinking and being are the same.
Parmenides, DK, <B> frs. 2-3; 5 and 8.
Informally, identity is a relation each thing bears to itself: the identity of a and b implies and is implied by a and b sharing all their properties. There are two kinds of identity. Numerical identity or isomorphic similarity is distinguished from qualitative identity or exact similarity. Things are numerically identical only if they are one and the same thing [i.e. have the same intrinsic properties in common]: the Evening Star and the Morning Star are the same. Things are qualitatively identical if they look the same [i.e. have the same extrinsic properties in common]: planets, stars, identical twins and Ford automobiles are quantitatively identical. Objects also differ in respect of their intrinsic and extrinsic properties. A thing’s intrinsic or inherent properties never change whereas its extrinsic properties do as in Cambridge properties – a subset of extrinsic properties Cambridge change is non-genuine change. In this sense, an object’s numerical identity is a se or isomorphic identity with no change possible in intrinsic properties while qualitative identity is per se or similar identity where change is possible in intrinsic properties via shifts in an object’s extrinsic properties.
Relation involves special cases of properties. Since relations are indispensable to first philosophy, Platonists and Aristotelians agree on the reality of first principles given that the properties of identity, relation, aseity and perseity exist. Defenders of individual essences [like Plantinga] following Leibniz argue that the framework of possible worlds enables us to make sense of de re modality which identifies the modal status of an objects exemplification of an attribute. Here the haecceity of an object provides a complete concept of that object such that it entails for every possible world W and every property P, either the proposition that the object in question has P in W or the proposition that it fails to have P in W. Thus in relational logic the formal properties of special kinds of relations as among first principles can be examined to establish an epistèmè of first principles. Accordingly an omniscient being could infer from the individual essence of an object a complete account of that object in each possible world in which it exists.
DK <B> frs. 28b1.14ff. and 8.13-15 and 30-31.
DK, <B> frs. 2-3;5. [translation Peter Manchester].
Raven 1948, p. 23; Cornford 1957, pp. 29, 33; Taran 1965, pp. 37-38; Mourelatos 1970, p. 90; Barnes 1986, pp. 155, 163; Owen 1986, pp. 9, 15-16.
Kahn 1966, pp. 700-701, 705; Kahn 1978, pp. 33-35; Kahn 1988, p. 237; Furth 1991, pp. 191, 242-243, 249; Mourelatos 1970, pp. 48-49; Curd 2004, pp. 231-232.
Burnet 1965, p. 178; Popper 1998, p. 69.
On the basis of DK <B> 28. 34-41 see, Sedley 1999, pp. 119-120.
DK <B> fr. 28.8.51-54.
DK <B> fr. 28.8.3-49.
DK <B> fr. 28.6.8-9.
Cherniss 1932, pp. 125-130 and Guthrie 1987, p. 53 claim that the subject of criticism is the first hypothesis and the Eleatic view of ‘one Being.’
See Wood 2005, p. 2; Turnball 1998, p. 19; Ryle 1939, p. 130.
See Harte 2002, p. 83; McCabe 1996, p. 21. Cf. Cornford 1957, pp. 112-114; Schofield 1977, pp. 147-148.
Plato, Parmenides, 137cd.
Plato, Parmenides, 147d.
<DK> B. fr. 8.1-51.
Plato, Sophist, 245d4-6.
Plato, Republic, 509b6-10.
Plato, Republic, 509b6 refers to that which is noeton [cf. 509d4] which are the Forms, which have their archè in the Form of the Good.
Plato, Theaetetus. 188d-189b.
Plato, Sophist, 236d-237e.
Hintikka 1980, p. 17 suggests that Plato’s main proofs for the existence of Forms are forged out of the same materials as Parmenides in that both affirm that “one can only think of what is.”
This knowledge argument, outlined in the Phaedo [79a6-7] complemented by the meaning argument in the Sophist [248a6ff.] show that to pantelos on includes nous – a plurality. Thus soul and life reduces unity to a mental state or activity of knowledge [epistèmè] wherein nous identifies per se with the Forms and the Idea tou agathou.
At Republic [510a9] it is clear that the tois gignôskomenois of [509b6] refers a knower and that which is known [to noèton] – the Demiurge and the Forms.
Although Pepin and Archer-Hind interpret Tim. 37a1 ton noèton aei te ontôn as indicating the identity of the Demiurge with the Forms, Taylor 1928, p. 176 thought little of attempts to turn Plato into an idealist.
Following Roecklein 2011, pp. 136-150.
Aristotle, Metaphysics, I.1 981b29-928a1-3.
Owen 1960, pp. 168-169, 189.
Owen 1960, pp. 163-190; the quotations are from pp. 168-169, 189; Owen 1965, pp. 69-75; Owen 1966, pp. 125-150.
A distinction between kath’auto or a se predications [what universals] and kata symbebekos or per accidens predications [how universals] displays what is necessary to an object; and what is not.
Owen 1965, p. 73. Etymologically, sèmainein is related to the modern word “semantics.” Not surprisingly, it has been a matter of dispute how to understand Aristotle’s conception of signification. While Owen’s understanding (held also by Barnes 1980, p. 205) tends to be intensional, Ferejohn believes that it is extensional (Barnes 1980, p. 118). Kirwan 1993, p. 94 suggests that “to signify” can be either “to mean,” or “to denote” in different texts. Yet Hamlyn 1977-1978, p. 12 (cf. pp. 1-18) claims that Aristotle does not have a distinction between sense and reference. For Aristotle, signifiers include not only name, but also verbs, phrases and sentences (Poetics, 1456b38ff.). For a detailed discussion of this issue, cf. Irwin 1982, pp. 241-266. He concludes that Aristotle’s use is unsystematic.
Ackrill 1963, p. 88 remarks, “It is careless of him to speak as if it were substances (and not names of substances) that signify.” Likely it is both for it is on the conception of signification that Aristotle affirms that there are as many beings as there are categories (Meta Δ 7,1017a 23-28). Indeed, the multi-vocity of being and the theory of categories are so closely associated that Aristotle simply calls substance, quality, quantify, etc. “categories of being.”
Following Gerson 2002, pp. 107-109.
Aristotle, Meta., 1040b28-30.
Aristotle, Meta., 991a20-22.
Aristotle’s solution is universals do not replace Forms [Platonic Ideas are universal properties]; nor are Forms hypostasized universals, as if Plato offered ante rem as opposed to Aristotle’s post rem universals. Moreover, since any dependence of things on the Forms does not fit his account of causation, any such notion dependence is incoherent. This is doubly so because if the Forms are universals [in his sense], substances [in his sense], and objects that cannot be both universals and substances [in his sense] – since a universal is common and a substance individual.
Distinctions among mental acts, their intentional contents, the objects represented or “intended” in these mental acts, and the states [of intellect, perception, sensation, volition, and belief] which underlie them presupposes – are neither the activity of thinking Forms, nor are they bodily actions or behavioral dispositions, but a state or activity of thinking [noèsis] – or in analytic parlance – a mental occurrence alone.
Since properties are a kind of universal, the ontological status of universals has been applied to properties in three ways: 1] nominalism – since only particulars exist either properties do not exist or are reducible to collections of particulars; 2] conceptualism – properties exist but are dependent on the mind; realism – properties exist independently of the mind either in rebus, it has real spatio-temporal instances or ante rem, a property can exist even if it has no real spatio-temporal instances.
Wolterstorff 1970, pp. 263-265.
Analysis of essence and essential predication which focuses on the distinction between what an object is and how it is crucial. Indeed, a distinction between kath’auto or per se predications [what universals] and kata symbebekos or per accidens predications [how universals]. The first displays what necessary to an object; the second what is not.
A primary being ens a se is the greatest conceivable being. If a primary being ens a se depended upon itself, it would cause itself to exist which is a logical contradiction. Thus per se relations are Cambridge properties where Intellect and the One exhibit reciprocal independence a se. Cf. Wolterstorff 1970, pp. 263-265.
Aristotle, Categories, XII. 14a30-45; 14b11-24; Plotinus, VI.8.8.12-15, 11.32. cf. O’Meara 1996, pp. 68-71; Bussanich 1996, pp. 38-65; Leroux 1990.
Berchman 2017, pp. 329-348.
Following Schroeder 2000, pp. 303-313.
Aristotle, Post. An., II.9.93b22-29; II.19. 98b19-100b18.
On arguments from divine aseity see Gould 2011, pp. 305-318.
Following Hedley 2016, pp. 133-137.
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