Categorizing concept predications and participations in Platonic dialogues: An exhaustive analysis of the various types of participation of things and ideas in ideas throughout the Platonic work

The Platonic work, extended to a lot of dialogues, could be used among others as an analytical instruction of the nature of participation given through various types of predication relations. This article focuses on the identification of the implicit and explicit predications (seen as participations) dispersed in the Platonic work. Nine distinct categories have been found and each of them is comprised of certain structures, carrying distinguishable meanings. Ordinary predication, Pauline predication, identity, difference, otherness and definition are included, while the various senses of self-predication and self-participation are presented. Lastly, concept maps of mutual relations between selected ideas are exhibited in a software ontology environment.


INTRODUCTION
Predication is a proposition through which a feature is declared about something (a concrete thing or a number or an idea).The predication has usually the form 'A is B', where A is the subject and B is the predicate, that is, B is predicated of A. At times the copula 'is' and the predicate are united in one term in the form of a verb.Additionally, the predication is not denoted under the form 'A is B' but it is hidden under other expressions such as 'A possesses B', 'B exists in A'.The revelation of the hidden predications in the various Platonic dialogues is one of the main contributions of this article.
Another pole of the current research is the uncovering of the meaning given by Plato to the various prodicative propositions.Predication in Plato implies participation in the most of its occurences.The operation of participation constitutes the kernel of the Platonic philosophical system.The predication 'A is B' implies the participation of A in B; B is an idea in which A participates.Participation is the key process under the Platonic theory of Forms, according to which the sensible things are images or shadows of corresponding ideas, owing to them their existence.In this way the sensibles communicate with the noetic substances.Beyond that Plato provides us with a remarkable extension: not only sensible things but also ideas can participate in ideas.
Allen and Nehamas speak about different levels of reality concerning the ideas and the participating sensibles.They follow the main Platonic view that the ideas are noetic entities that exist by themselves, while the sensibles reside in a lower level as mere reflections of the ideas.
Allen, in his attempt to solve the so called Dilemma of Participation, finds the more detailed description of the participation process in Plato himself, specifically in his dialogue .Platonic Permenides tells of the idea as part of the participant: "If anything partakes of an Idea, a part of the Idea is in it: additionally that part of the Idea is a part of the participant" (Allen, 1998, p. 218).
Ryle looks into the nature of the relation between subject and predicate in a predicative proposition.He supports that our linguistic familiarity of this type of proposition does not allow us to face it in accurate scientific terms.A relation between a particular and a universal (instance-of relation) is implied, a relation which, if we pay attention to, is not a valid relation, since it connects things of different types.Mathematical equation, for example, relates numbers, that is, members of the same class, while predication relation relates sensibles to ideas.Considering the instance-of relation as a pseudo-relation, Ryle concludes to a radical rejection of the whole Platonic theory of ideas (Ryle, 1971, 9-12).
If we identify predication with participation, we should also identify self-predication with self-participation.Nehamas discerns self-predication from self-participation, though.He describes the diference between them as follows: the self-predication 'F is F' must be replaced by the most accurate expression 'F is what it is to be F'; self-predication only tells us what feature it is that the Form constitutes (Nehamas, 1982, p. 355-6).On the other hand, according to Nehamas, the proposition 'F is F' implies 'F participates in F' or equivalently 'F is an F-thing' (Nehamas, 1982, p. 357).Vlastos (1994, p. 479-86) realizes self-predication in the manner Nehamas realizes self-participation: 'F is F' means for him 'F is an F-thing'.As we saw before, Nehamas gives a certain meaning for self-predication and therefore he admits that this could be applied to all ideas.On the contrary, Vlastos considers that self-predication is not valid for all of them.He supports that some -not all-of the ideas are self-predicated, such as the four of the five great genera mentioned in Sophist -the being, the rest, the same and the different-while the fifth one -the motionis not: the being is being (namely it exists), the rest is rest (namely it rests), the same is same (namely it is same with itself) and the different is different (namely it is different from anything else), while the motion is not motion (it cannot move and change, since it is an Idea).Additionally, Vlastos wonders whether Plato identifies self-predication with self-participation and thus if self-predication implies necessarily self-participation.He recites two passages of Platonic Parmenides about the possibility of self-participation of an idea, leading to ambiguous results: In Parm.158a4-6, Parmenides makes clear that "if something participates in the one then it is not the one itself for if not, it would not partake of the one, but would actually be one; but really it is impossible for anything except one itself to be one".Clearly this passage supports the self-predication, excluding at the same time the self-participation.The counter-example is extracted from Parm.162a7-b1: the Being (the idea of being) is to be fully being only through participation in Being; thus in this case Being is required to participate in itself (the Idea of being) in order to be being.Thus, in this case the self-predication 'Being is being' is necessary and sufficient condition of the self-participation 'Being participates in Being'.
In Parm.132a1-b2, Parmenides argues that the Idea of largeness cannot participate in itself since in that case the idea of largeness, considered as large, should participate in a second idea of largeness, leading ad infinitum.This is the first reference to the 'third man argument' (TMA) paradox.Vlastos (1994, p. 489-98) claims that the paradox can be eliminated if one allows self-participation, without introducing the axiom that whatever participates in an idea cannot be the idea itself.
Mutual predication or communication between ideas is the subject of Sophist.Late Plato attempts to reveal how the five great genera-ideas of being, motion, rest, sameness and difference are predicated of each other, if any combination of them is valid and which is the meaning of the valid predications.He is not restricted to the ordinary predication, presenting also the identity-relation and the otherness-relation.
Studying the various predications in Plato in the frame of Fregean Logic and the contemporary Predicate Calculus, we can represent them in the form of two main categories of functions: one-argument functions, such as 'justice is pious' transformed into the function pious (justice) and two-argument functions, such as 'being is-same-as one' transformed into the function same (being, one).
The article is structured as follows: In Chapter 2, the various types of predications are analysed theoretically.In Chapter 3, a number of rich in predications Platonic dialogues is selected, organized in nine main categories, based on the theoretical analysis exhibited in the previous chapter.The chapter is integrated with two concept maps, one of the idea One and the other of the idea Being, by using the drawing environment of the ontology software OWL Protégé.
This article belongs to the interdisciplinary section among humanities, typical logic and informatics, complementing a series of relative articles of the author.In Philosophical Views of the various types of participation of things and ideas in ideas throughout the Platonic work about Digital Information and Relational Schemata a review of old classification schemata is exhibited in the frame of modern relationship types.It is claimed there that the relations mentioned in Platonic Sophist imply the earliest distinction between the two ways of predication: BT/NT (broader term/ narrower term) and identity (equivalence) (Dendrinos, 2006).The process of the extraction of typical predicate relations from a philosophical text and the construction of an analytical concept map concerning the various types of relations of the Idea of One has been presented in detail in Organization of the concepts of the Platonic dialogue Parmenides into a software ontology (Dendrinos, 2015).Predicative propositions presented by Aristotle in Prior Analytics and Topics are examined thoroughy in Concept predications and hierarchies in Aristotelian Organon: A philosophical ontology presented in terms of a software ontology, where one can also see integrated concept maps concerning the three Aristotelian syllogistic schemes (Dendrinos, 2022).

VARIOUS FORMULATIONS OF PREDICATION IN PLATO
Plato interpreted the attribution of a feature to a thing (sensible or number) as participation of the thing to a corresponding Idea.The participation process includes, according to Plato, two interrelated situations: the first is that something has a certain feature (the feature is predicated of a specific thing), constituting the so called predication; the second is that there is a cause of this predication in the form of an independent entity -Idea-in which the thing participates.Let call the above type of predication Plato.type.1.thingparticipating-in-idea.
While in most dialogues Plato presented in detail the predication of sensibles and the equivalent participation of them in Ideasoperating as the ontological analogs of the predicates-one can find in Plato an extended theory of combination of Ideas -Ideas predicated of Ideas-which can be viewed as participation of an Idea in another Idea and in some cases even to itself (self-participation).Such predications are met in great extent in Protagoras, Sophist and Parmenides.Let call this type of predication Plato.type.2.ideaparticipating-in-idea.Passing from the sensibles-participants to the ideas-participants is described in detail in Nehamas 1 .
The participation of a thing (sensible or number) or an idea in an idea is usually denoted through the copula is: subject is* predicate [idea in the form of adjective 2 ] (* ἐστὶν) 3 .An equivalent form for the construct 'is-predicate' is a composite verb-predicate (without is) Predication 'A is B' is denoted sometimes by 'A has B' as follows: The predication 'one has parts' is equivalent to 'one is divided' and the predication 'it has soul' is equivalent to 'it is aminate'.The typical expression is: subject has* predicate [idea] (* ἔχει).The expression is affected [πέπονθεν] is also used as an alternate way to denote the participation in an idea, such as the things participating in unlimited or in limit (Parm.158e4-7), the idea of three participating in the idea of odd (Phd.104a4).The typical expression is: subject is-affected-by* predicate [idea] (* πέπονθεν).Another interesting expression for the participation of a thing (sensible or number) in an Idea is that the Idea possesses the thing (Phd.104d): predicate [idea] possesses* subject [thing] (* κατέχει).
Following the view of Nehamas, I consider self-predication as a specific type of predication and I denote it as Plato.type.3.self-predication.The expression used to denote this predication is: subject [idea] is-what-it-is-to-be predicate [idea], e.g.justice is what it is to be just.
Self-participation belongs to the general category of participations: Plato.type.2.ideaparticipating-in-idea.Following the view of Nehamas, we consider self-participation as the relation 'F is an F-thing'.The expression used to denote this type of predication of an idea to itself is: subject [idea] participates-in-itself, e.g.'the one is one', 'the motion moves', 'the rest rests', 'the being participates in being'.
Phd. 104e-105a presents a very interesting relation between a thing (material thing or number) and an idea, where a thing A brings along [ἐπιφέρει] an idea B, so representing an indirect participation: "as the number three, though it is not the opposite of the idea of even, nevertheless refuses to admit it, but always brings its opposite along against it, and as the number two brings the opposite of the odd along and fire that of cold, and so forth".The meaning of the passage is that number three participates directly in the idea of threeness and indirectly in the idea of oddness, since the set of triads is included within the set of odd numbers; similarly, material fire participates directly in the idea of fire and indirectly in the idea of hotness.Vlastos uses the term implication for the description of this relation: If a thing x is A and A brings along B then x is B. We could consider the above indirect participation as the inclusion relation, where a thing belongs to a class or equivalently a class of things included in a broader set.The first is found in Phil.30e, where Socrates presents the mind as belonging to the class of the causes [ἐστὶ γένους τῆς τοῦ πάντων αἰτίου λεχθέντος].A similar inclusion relation is found, for Vlastos, in Timaeus, where Timaeus describes the intelligible living beings as ideas existing within the Living Being [ἐνούσας ἰδέας τῷ ὃ ἔστιν ζῷον], which contains them [ἐν ἑαυτῷ περιλαβὸν] and of which all other living beings, severally and generically, are portions [καθ᾽ ἓν καὶ κατὰ γένη μόρια] (Tim.30c, 39e).
Let call the above described type of predication Plato.type.4.is-included-in.The expressions used to denote this predication are: subject Besides, Vlastos introduced apart from the typical predication -called ordinary predication (OP), which is the above mentioned Plato.type.2.idea-participating-in-idea-another one predication -called Pauline predication (PP).He presented PP in his text The Unity of Virtues in the Protagoras (Vlastos, 1994, p. 317-402) in order to give meaning to some predications which seem absolutely unreasonable, like 'the Justice is pious' or 'the Piety is just'.He also speaks about PP in his text An Ambiguity in the Sophist (Vlastos, 1994, p. 403-448), where the Stranger sets under consideration the premises 'the Motion rests' and 'the Rest moves'.Pauline predication 'X is y' is meant not with the ordinary meaning 'the entity X has the feature y' but with the meaning 'x has the feature y', where x are sensible of the various types of participation of things and ideas in ideas throughout the Platonic work manifestations of X.Under this interpretation Vlastos can consider the proposition 'the Justice is pious', which is completely nonsense, as 'every just human is pious' which makes sense.In the same way, the proposition 'the Rest moves' should be examined in the frame of the sensible world under the formulation 'the resting things are moving', for Vlastos, since the Stranger does not deal in the specific context in Sophist with the ideas, but with the nature of the sensible things.Vlastos has spent a great effort to categorize the various predications found in Sophist in these two distinct classes.He considers the predications in 256a1, 256c-d as OP, while the predications in 250a11-12, 252d2-11, 255a6-12, 256b7-9 as PP.I do not agree with him, in the sense that all his mentioned predications in Sophist, characterized as PP, are, in my opinion, due to the reference of the idea as idea itself, obviously OP.Among them 255a6-12 is indeed dubious, since, in spite of its apparent OP typical formulation, the logic proof of Vlastos seems indeed to support PP (Vlastos, 1994, p. 438-9).All of them will be presented in detail in Chapter 3.
L et c a l l t h is ex t r aord i na r y t y pe of Pauline predication between ideas: Plato.type.5.Pauline-Predication, and the corresponding expression: subject A similar predication concerns two ideas applied to each other in such a way that their sensible manifestations are in fact related, such as the mastership is mastership of slavery, which can be meant as a master is master of a slave (Parm.133d-e).The expression used to denote this type of predication is: subject [idea-1] is-applied-on-PP predicate [idea-2]  a sensible manifestation of [idea-1] expresses the relative property with regard to a sensible manifestation of [idea-2].
Ackrill contributed a lot to the clear discrimination between predication, identity and idea-to-idea communication, through a deep analysis of a critical passage of Sophist.At first he studies the Platonic phrase in Sophist about Motion: "it (the Motion) is because it shares in being" [ἔστι δέ γε διὰ τὸ μετέχειν τοῦ ὄντος] [Sophist, 256a1].The word because [διὰ] here does not introduce a proof that Motion partakes of being, since this has already been agreed without question before.Therefore, for Ackrill, the term is [ἔστι] in this passage must be taken existentially: "the Motion exists" (Ackrill, 1971(Ackrill, [1957]], p. 211-2).The expression used to denote this predication is: subject [idea] exists* (*ἔστιν).The predicate exists is equivalent to the predicate participates-in being.Therefore, it is a specific case of Plato.type.2.idea-participating-in-idea.
The remaining meanings of is [ἔστιν] are the ordinary copula and the identity-sign.Where the 'is' is being used as copula it is equivalent philosophically to participating [μετέχειν], as we saw it in the beginning of the modes of participation in an idea.When the 'is' is used as identity, it is equivalent to the expression 'shares in sameness' [μετέχειν τοῦ ταυτοῦ], whereas the 'is not' [οὐκ ἔστιν] is equivalent to the expression 'shares in difference' [μετέχειν τοῦ θατέρου] (Ackrill, 1971, p. 213-4).Vlastos also marks the cases where the copula is meant as identity-sign (Vlastos 1994, p. 444): Motion partakes of the same (Soph.256a10), Motion / Rest partake of the same (Soph.255b3), all partake of the same (Soph.256a7-8).Additionally, Ackrill mentions the Fregean identity-role of 'is' versus its copula-role (in predications) via quoting some of Frege's examples: 'something is green' or 'something is mammal' versus 'the morn-ing star is Venus'.The last example denotes identity, where the 'is' is equivalent to 'is no other than' (Ackrill, 1971(Ackrill, [1957]], p. 213).
Identity is a commutative relation, that is, 'A is same as B' and also 'B is same as A'.Let call the identity type of relation between ideas Plato.type.6.identity.The expression used to denote identity is: subject [idea] is-same-as* predicate [idea] (* ταὐτόν ἐστι).The relation is-same-as is equivalent to the relation participates-in sameness to.A specific case of identity is the declaration that an idea is identical to itself, such as 'motion is the same as motion' and 'rest is the same as rest' (mentioned in Sophist).The predication 'idea is-same-as itself' is equivalent to 'idea participates-in sameness to itself ', which can be abbreviated to the formal expression: [idea] participates-in sameness [μετέχει τοῦ ταυτοῦ], following the Platonic text.This predication is included as a specific case of Plato.type.2.idea-participating-in-idea.
Similarly, let call the difference type of relation between ideas Plato.type.7.difference.The expression used to denote the relation of difference is: subject is-different-from* predicate (*ἕτερόν/ θάτερον ἐστι).The relation isdifferent-from is equivalent to not same-as and also equivalent to the relation participates-in difference from.According to the above terminology, an idea A is different from an idea B, when A is not the same as B. This relation could be also named as unlike [ἀνόμοιον], as mentioned in Platonic Parmenides.
Another important relation between two ideas is the relation of otherness, with A and B completely different, not sharing any common characteristic (the term used in Parmenides is ἕτερον).Let call this type of relation between ideas Plato.type.8.otherness.The expression used to denote the relation of otherness is: subject [idea] is other-than* predicate [idea] (*ἕτερόν ἐστι) 5 .
Ackrill mentions a very informative extract of David Ross, where he presents two different textual constructions: the first one with genitive for an idea sharing of/ partaking of an idea [κοινωνεῖν τινὸς, προσκοινωνεῖν τινὸς] (Parm.250b9, 252a2, b9, 254c5, 256b2, 260e2) versus the second one with dative for an idea in combination or communication with an idea [κοινωνεῖν τινὶ, προσκοινωνεῖν τινὶ] (251d9, e8, 252d3, 253a8, 254b8, c1, 257a9, 260e5).Though Ross believes that the two constructions are used by Plato indifferently, Ackrill supports that the usage of the genitive or the dative is used consciously by Plato to differentiate between the non-symmetrical relation of participation and the symmetrical relation of connectedness (Ackrill, 1971, p. 219-220).
These additional expressions belong to the general category 'participation of an Idea in an Idea' (Plato.type.2.idea-participating-in-idea) and they are given as follows: subject [idea] shares-in* predicate (*κοινωνεῖ τινος) and subject [idea] communes-with* predicate [idea] (*προσκοινωνεῖ τινος), where the verbs κοινωνεῖ and προσκοινωνεῖ are followed by genitive.
Another usual practice of arranging ideas, found in the Platonic dialogues, is the attempt for the definition of a term through its genus and the proper differentia.The term to be defined is a species, which is described through a higher term, the genus.Cases of this type have been extracted from Laches, Euthyphro, Theaetetus, Protagoras, Alcibiades I and Hippias Major, where Socrates tries to define certain ideas (usually virtues).Between them an 'is' is intervened.Thus, in this case, an idea (the genus) is the predicate of another idea (the species).Let call this type of predication between ideas: Plato.type.9.Definition-Predication, and the expression used to denote this type of predication: subject [idea-1] is-defined-by predicate [idea-2] of the various types of participation of things and ideas in ideas throughout the Platonic work

CONSTRUCTING THE PLATONIC CONCEPTUAL SCHEME
After the theoretical analysis presented in the previous chapter, certain cases of the various types of predication follow along with the passages of Platonic dialogues they are mentioned in (the translation from ancient Greek to English is based on Perseus Digital Library of Tufts University) 6 .The dialogues used are: Sophist, Parmenides, Timaeus, Phaedo, Philebus, Protagoras, Meno, Alcibiades I, Laches, Lysis, Charmides, Theaetetus, Euthyphro, Hippias Major.

G e n e r a l P r e d i c a t i o n Ty p e P l a t o . type.1.thing-participating-in-idea
Textual expression 1.

G e n e r a l P r e d i c a t i o n Ty p e P l a t o . type.2.idea-participating-in-idea
All the various expressions that follow are categorized under the general expression: participates-in.
Textual expression 2.1: subject [idea] is* predicate [idea in its very form or in the form of adjective] (* ἐστὶν) |Pred Relative passages: "But yet nothing hinders that which has parts from possessing the attribute of unity in all its parts and being in this way one, since it is all [πᾶν] and whole [ὅλον]" (Sophist, 245a1-3)."-Must not the one which exists [ἕν ὄν] be a whole of which the one and being are parts?-Inevitably" (Parm.142d4)."Whatever one, then, exists is a whole and has a part" (Parm.142d8-9). |Pred Relative passages: "-The existent one would be infinite in number?-Apparently" (Parm.143a1-2)."Can the one be in many places at once and still be a whole?Consider that question -I am considering and I see that it is impossible.-Then it is divided into parts, if it is not a whole; for it cannot be attached to all the parts of existence at once unless it is divided" (Parm.144d1-5)."The one, then, split up by existence, is many and infinite in number.-Clearly.-Then not only the existent one is many, but the absolute one divided by existence, must be many.-Certainly.-And because the parts are parts of a whole, the one would be limited by the whole" (Parm.144e4-10).
|Pred Relative passage: "Stranger: Then even if absolute motion partook in any way of rest, it would not be absurd to say it was at rest? Theaetetus: It would be perfectly right, if we are to admit that some of the classes will mingle with one another, and others will not" (Sophist, 256b7-11).
Textual expression 2.4: subject participates-in-itself (the self-participation here is evidently not valid) Relative passage: "Stranger: And in granting that they (motion and rest) exist, do you mean to say that both and each are in motion?Theaetetus: By no means.Stranger: But do you mean that they are at rest, when you say that both exist?Theaetetus: Of course, not" (Sophist, 250b2-7).
|Pred.34| [being] participates-in [being]  [being] participates-in-itself of the various types of participation of things and ideas in ideas throughout the Platonic work Relative passage: "The existence of the existent and the non-existence of the nonexistent would be best assured, when the existent partakes of the existence of being existent and of the non-existence of not being non-existent" (Parm.162a7-b1) Textual expression 2.5: subject [idea] participates-in sameness* (*μετέχει τοῦ ταυτοῦ) Relative passages: "Each of them (being, motion, rest) is, then, different from the remaining two, but the same as itself " (Sophist,."Both (motion and rest) certainly participate in the same and the other" (Sophist,255b3)."But yet we found it (motion) was the same, because all things participate in the same" (Sophist,. |Pred

.38| [one] is-same-as [one]  [one] participates-in [sameness]
Relative passage: "It (the one) must be the same with itself " (Parm.146a9). |Pred Relative passage: "It is, then, also (the one) unlike itself " (Parm.147c1-2).Relative passage: "According to its own nature, then, being is neither at rest nor in motion" (Sophist,. |Pred Relative passage: "Theaetetus: Because motion itself would be wholly at rest, and rest in turn would itself be in motion, if these two could be joined with one another.Stranger: But surely this at least is most absolutely impossible, that motion be at rest and rest be in motion?Theaetetus: Of course" (Sophist,. |Pred
Textual expression 2.8: subject Relative passage: "Why surely that which is really one must, according to right reason, be said to be completely without parts" (Sophist, 245a8-9).
Textual expression 2.9: Relative passage: "Then shall we say that it has mind and life and soul, but, although endowed with soul, is absolutely immovable?"(Sophist, Relative passage: "But yet nothing hinders that which has parts from possessing the attribute of unity in all its parts and being in this way one, since it is all [πᾶν] and whole [ὅλον]" 7 (Sophist, |Pred.56|[the-others] is-affected-by [unlimited] / |Pred.57|[the-others] is-affected-by [limit] Relative passage: "-Inasmuch as they (the others) are all by their own nature unlimited, they are all in that respect affected in the same way -Certainly -And surely inasmuch as they all partake of limitation, they are all affected in the same way in that respect also" (Parm.158e4-7).
Textual expression 2.11: Relative passage: "Whatever living being is near to the good always, altogether, and in all ways, has no further need of anything, but is perfectly sufficient" (Phil.60c).
Textual expression 2.12: predicate Relative passage: " -Suppose some one tinged your golden locks with white lead, would they then be or appear to be white?-Yes, they would so appear, he replied.-And, in fact, whiteness would be present with them?-Yes" (Lysis, 217d Relative passage: "Stranger: Well, then, will either of them (motion and rest) be, if it does not commune with being?Theaetetus: It will not" (Sophist, 252a2-4).
Relative passage: "The thing you named just now, justice, is that itself just or unjust?… then justice is of a kind that is just" (Prot.330c).

|Pred.65| [piety] is-what-it-is-to-be [pious]
Relative passage: "Do you say this thing itself [piety] is of such nature as to be impious, or pious?For my part I should be annoyed at this question, I said, and should answer: Hush, my good sir.It is hard to see how anything could be pious, if piety itself is not to be pious" (Prot.330d-e).

General Predication Type Plato.type.4.isincluded-in
All the various expressions that follow are categorized under the general expression: is-included-in. of the various types of participation of things and ideas in ideas throughout the Platonic work Relative passage: "As the number three, though it is not the opposite of the idea of even, nevertheless refuses to admit it, but always brings its opposite along against it, and as the number two brings the opposite of the odd along and fire that of cold, and so forth" (Phd.104e-105a)."You know of course that those things which the idea of triad possesses must be not only three but also odd" (Phd.104d).
Relative passage: "But we shall affirm that the Cosmos, more than aught else, resembles most closely that Living Being of which all other living beings, severally and generically, are portions 8 " (Tim.30c).

70| [mind] belongs-to-class [cause]
Relative passage: "Mind belongs to that one of our four classes which was called the cause of all.Now, you see, you have at last my answer" (Phil.30e).

|Pred.71| [pleasure] belongs-to-class [infinite]
Relative passage: "Mind was akin to cause and belonged more or less to that class, and that pleasure was itself infinite and belonged to the class which, in and by itself, has not and never will have either beginning or middle or end" (Phil.31a).
Textual expression 4.4: subject Relative passages: "Among the parts of virtue, no other part is like knowledge, or like justice, or like bravery, or like prudence, or like piety" (Prot.330b)."Then it seems that justice or prudence or piety or some other part of virtue must accompany the procuring of these things" (Meno, 78d-e)."Socrates: that it is a part, there being also other parts, which taken all together have received the name of virtue.-Nicias: Why, of course.-Socrates: Besides bravery, I refer to prudence, justice, and other similar qualities" (Laches,198a) Relative passages: "All things immovable and in motion, and must say that being and the all consist of both" (Sophist, 249d)."Being, then, you consider to be something else in the soul, a third in addition to these two, inasmuch as you think rest and motion are embraced by it" (Sophist, 250b8-10) of the various types of participation of things and ideas in ideas throughout the Platonic work whom I call brave?" (Laches,195d)."Socrates: do you say that bravery is knowledge of what is to be dreaded or dared?Nicias: I do" (Laches,. Textual expression 5.2: subject [idea] isapplied-on-PP predicate [idea] |Pred.100|[mastership] is-applied-on-PP [slavery], that is, mastership is mastership of slavery  a master is master of a slave |Pred.101|[slavery] is-applied-on-PP [mastership], that is, slavery is slavery of mastership  a slave is slave of a master Relative passage: "if one of us is master or slave of anyone, he is not the slave of master in the abstract, nor is the master the master of slave in the abstract; each is a man and is master or slave of a man but mastership in the abstract is mastership of slavery in the abstract, and likewise slavery in the abstract is slavery to mastership in the abstract" .Relative passage: "Stranger: And will they say that the whole is other than the one which exists or the same with it?"Theaetetus: "Of course they will and do say it is the same" (Sophist, 244d-e).

G e n e r a l P r e d i c a t i o n
|Pred.104| [one] is-same-as [the other(s)] Relative passage: "And likewise (the one is) the same with the others" (Parm.146b1-2).
|Pred.106| [beautiful] is-same-as [good] Relative passage: "Hence we have seen again that beauty and good are the same thing" (Alcib. I,116c).Relative passages: "Then being is not motion and rest in combination, but something else, different from them" (Sophist,."Each of them (being, motion, rest) is, then, different from the remaining two, but the same as itself " (Sophist,249d)."Then we must not say that motion, or rest either, is the same or different" (Sophist,."Stranger: Take motion first; we say that it is entirely other than rest, do we not?Theaetetus: We do.Stranger: Then it is not rest" (Sophist,."Stranger: Whatever term we apply to rest and motion in common cannot be either of those two.Theaetetus: Why not?Stranger: Because motion would be at rest and rest would be in motion; in respect of both, for whichever of the two became 'different' would force the other to change its nature into that of its opposite, since it would participate in its opposite" (Sophist,

G e n e r a l P r e d i c a t i o n
Relative passages: "But certainly motion and rest are neither different nor the same" (Sophist, 255a3-4)."Now motion again is different from the same… Therefore it is not the same" (Sophist, 256a3-5)."Stranger: Then let us recapitulate: Motion is different from the different, just as we found it to be different from the same and from the rest.Is that true?Theaetetus: Inevitably.Stranger: Then it is in a sense not different and also different, according to our present reasoning" (Sophist, 256a3-5).
|Pred.114| [being] is-different-from [same] Relative passage: "Stranger: But should we conceive of 'being' and 'the same' as one?Theaetetus: Perhaps.Stranger: But if 'being' and 'the same' have no difference of meaning, then when we go on and say that both rest and motion are, we shall be saying that they are both the same, since they are.Theaetetus: But surely that is impossible.Stranger: Then it is impossible for being and the same to be one" (Sophist, Relative passage: "If the other, like being, partook of both absolute and relative existence, there would be also among the others that exist another not in relation to any other; but as it is, we find that whatever is other is just what it is through compulsion of some other… Then we must place the nature of 'the different' as a fifth among the classes in which we select our examples… And we shall say that it permeates them all; for each of them is other than the rest, not by reason of its own nature, but because it partakes of the idea of the other" (Sophist,.Relative passage: "Socrates: do you say that bravery is knowledge of what is to be dreaded or dared?Nicias: I do" (Laches,.

G e n e r a l P r e d i c a t i o n
Pred.124| [prudence] is-defined-by [knowledge] Relative passage: "For if prudence is above all a knowledge of the knowledges, and presides too over the other knowledges, surely she will govern this knowledge of the good, and so benefit us" (Charm.174e).

|Pred.125| [knowledge] is-defined-by [right-opinion]
Relative passage: "Then, it seems, if asked, 'What is knowledge?' our leader will reply that it is right opinion with the addition of a knowledge of difference; for that would, according to him, be the addition of reason or explanation" (Theaet.Figure 2 presents the concept-map of the idea being.

CONCLUSION
This article could help the transformation of the natural language philosophical propositions to typical logical expressions, which is prerequisite for processes, such as automatic deduction and mechanical evaluation of argumentation.Besides, it could contribute to locating similarities among apparently distant philosophical texts and differences among apparently close ones.
Obtaining the accurate form of the philosophical declarations in the various philosophical corpora could help either in the search of identification of orphan or fragmented phrases or in checking the authorship of disputed fragments, based on its content itself rather than its textual expression.
After a detailed analysis of a number of selected Platonic dialogues, where various forms of predication are mentioned, the following cases of predication relations have been extracted: The Platonic types of predication: subject is* predicate [idea in the form of adjective]  Taking into account the various predication relations of significant philosophical terms we can represent them overall in graphical form in ontology software environments.This will increase researchers of philosophy to have a total concise view of the philosophical 'paths' of main concepts within the work of a certain philosopher or extensively in the general frame of philosophy.
Lastly, since predicative propositions constitute a great part of dialectics and rhetoric it is expected that this work could be considered as a guide for standardization of the various freely expressed conceptual schemata and technics, leading to a deeper understanding of the great art of discource.

Figure 1 .
Figure 1.Idea of one: its participations in various Ideas (one rests, one moves, one is being, being is one etc).The relation participates in is depicted by green line.[Drawing environment: Protégé, Ontograf].

Figure 2 .
Figure 2. Idea of being: its participations and identity relations in various ideas (being is the same as one, motion and rest participate in being, but being does not participate in motion or rest, etc).The relations participates in and the same as are depicted by yellow line and grey line, correspondingly.[Drawing environment: Protégé, Ontograf].
You would exclaim loudly that you know no other way by which any thing can come into existence than by participating in the proper essence of each thing in which it participates, and therefore you accept no other cause of the existence of two than participation in duality, and things which are to be two must participate in duality" (Phd.101c).