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Veritative ontology: REINTERPRETING aNCIENT gREEK PHILOSOPHY
PIOTR SWIERCZ Jesuit University Ignatianum in Krakow piotr.swiercz@ignatianum.edu.pl
Abstract. This article proposes a revision of the traditional interpretation of ancient Greek ontology and indicates what consequences this revision may have for political reflection. The basis for the interpretation laid out here lies in classicist Charles H. Kahn's work on the meaning and function of the verb "to be" (einai) in ancient Greek. Kahn asserts that the original and fundamental meaning of einai was veritative (veridical) rather than existential - it was used to signify truth, not existence. Though the significance of Kahn's research has been widely acknowledged, the influence of his analyses on interpretations of Greek ontology seems disproportionately small in comparison. The veritative interpretation remains on the margin of studies dominated by the existential interpretation. My article is meant as a contribution to the project of building a veritative interpretation of Greek ontology. I intend to show, using certain examples, the forms of this interpretation and possibilities it presents. For scholars of ancient Greek philosophy, it is often difficult to distinguish between its onto-logical and epistemological aspects. As I will try to show, this state of affairs results from a post factum imposition of the existential interpretation on Greek thought. The problem is greatly reduced when we use the veritative paradigm in place of the existential paradigm. It also becomes easier to grasp the unity of Greek philosophy, especially the unity of ontology and epistemology. A veritative interpretation of Greek ontology carries with it important consequences for our understanding of Greek political philosophy as well. One of the key consequences is a "formal" (as opposed to "material") understanding of concepts fundamental to Greek political reflection, such as the "good" and "justice." As a result, discussion on ancient Greek political and legal reflection can be conducted from a fruitful new perspective.
Keywords: ontology, epistemology, existence, truth, Greek philosophy, Charles H. Kahn.
Aristotle described first philosophy as the study of "being qua being" and of first causes and principles. The study of being and its causes and principles, or ontology, has since become almost synonymous with philosophy itself, at least with its highest, most fundamental part. Ontology constitutes the basis for ethics, political philosophy, aesthetics, axiology, and other fields. Though such a view of the
ЕХОЛН Vol. 16. 1 (2022) classics.nsu.ru/schole
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relationship between ontology and individual subdisciplines of philosophy has been disputed and has led to attempts to grant these subdisciplines autonomy from ontology, the mere fact that such attempts have been undertaken (regardless of how we judge their outcomes), points to the dominant place and role of ontology. Was the place of ontology as clear and unambiguous in Greek philosophy? Two key issues must be considered.
First, though the primacy of ontology vis-à-vis such fields as ethics and political philosophy seems beyond question, ontology's relationship to epistemology is less certain. Can knowledge about being precede knowledge about knowledge? As Aristotle emphasized, philosophy is not knowledge about simple things - such things that impose themselves on an observer. Philosophy is knowledge about what is difficult to come to know and understand - it is knowledge on the highest, or deepest, level. It is difficult to imagine such knowledge without prior reflection on whether knowledge is possible to attain at all and on how to attain it. If ontology could do without epistemology (i.e. without the primacy of the latter vis-à-vis the former), then epistemology would be unnecessary. This does not seem to be the case: while the ontological question (what is?) may, of course, be posed first, we must take a stance on the epistemological question (in what way can I establish, come to know, and understand what is?) before any attempt at answering the ontological question can be undertaken.
Second, a serious problem is posed by the question, what is being? The answer that has dominated for hundreds, perhaps even thousands, of years seems obvious: being is that, which exists. "To be," or "to be an entity," means the same as "to exist." The matter is much more complicated, however: it is tied with the role and function that the verb "to be" plays in language. As a general rule, we can indicate three basic functions of the verb "to be":
1. the copula function;
2. the existential function;
3. the veritative function.
In the first sense, "to be" is a copula, appearing in sentences of the form, "A is B." This role is most clearly seen in ostensive sentences, such as, "This is a book." In many languages, due to a phenomenon called the zero copula, "to be" in the copula function may be left out altogether.1
The existential function consists in indicating the fact of a given entity's existence, either in a general sense - as in the sentence, "There are whales," which is
1 In the English language, this occurs much more infrequently than it does in other languages, such as Polish or Russian. The most common use of the zero copula in English is in news headlines ("headlinese").
equivalent to "Whales exist," - or in reference to specific circumstances - "There are flowers in this garden," equivalent to "Flowers exist in this garden."
The veritative function, on the other hand, is reflected in the equivalence of "to be" with the truth of that, to which "being" is ascribed, while "not being" is equivalent with its falsehood. This can be clearly seen in the question, "Is that the case, or not?" and in the short answer - "it is" or "it is not." We could have just as well expressed our question in the form, "Is it true that that is the case?" which one could answer with "yes, it is true" or "no, it is not true."
In the following reflections we will leave the copula function aside and concentrate on the existential and veritative functions, as these form the basis for the two fundamental ways of understanding ontology - the existential and the veritative:
1. Existential ontology understands being as that, which exists. In consequence, non-being is that, which does not exist. Paraphrasing Schaffefs statement about the Quinean task for metaphysics, one can say that existential ontology's task is to say what exists, i.e. to list the beings (or what exists).2
2. Veritative ontology understands being as that, which is true, or cognizable to a certain degree. Consequently, non-being is that, which is not true, or not cognizable to a certain degree, only to a probable degree. The task for veritative ontology is to list what is necessary for our cognitive processes to achieve truth and calculate probability.
Here I must refer to Alexander Mourelatos' predicative interpretation of the Parmenidean to eon and how this interpretation relates to veritative ontology. They have much in common. First, they both hold that "akySsia and to sov are "equivalent in Parmenides."3 Mourelatos' main objection concerns the fact that Greek ontology is oriented toward things and objects, rather than facts. In consequence, "the veridical 'is' should be an expression not of the logical (i.e. proposi-tional) structure of the world but of the real identity of things."4 Kahn is convincing in his reply to Mourelatos:
the fundamental division between interpretations of Greek ontology [...] depends upon whether one takes existence or predication as the primary basis for understanding einai. And it is precisely on this question that Alex and I are in agreement [...]. What I call the 'veridical' value of the verb is an isolated focus on the truth claim implicit in any predication. More precisely, the veridical verb may refer either to the in-
2J. Schaffer (2009) 348.
3 A. Mourelatos (2008) 67.
4 Ibid., 60.
tentional content of such a predicative claim [...] or to its objective correlate, the actual fact or state of the world that makes the claim true.5
The Existential Function of the Verb "to Be"
How are we to understand, in commonsense speech, the sentence, "Whales exist"? How does this sentence contribute to our understanding of reality? What are the criteria of "existence"? This sentence seems to mean that the living entities called whales are not fictitious, that they can be seen, touched, etc. - in other words, that we have the ability to observe whales by means of our senses. That is why we say that "werewolves do not exist," since in their case there is no possibility for sensual observation. Of course, drawings and other representations of werewolves do exist. But werewolves themselves are fictitious - they do not exist.
Matters become much more complicated when the entity whose existence we are discussing is one, which may not or cannot be grasped by the senses. An answer to questions such as "Does God exist?" or "Do ghosts exist?" has nothing to do with sensual observation or a lack thereof. Of course, observable "signs" said to stem from the acts of such entities may be discussed, but this does not change the fact that declaring their existence or non-existence does not follow from their ability to be objects of direct sensual observation. How, then, are we to understand the statements "God exists" and "God does not exist"? It would seem that from a cognitive perspective, they are useful only insofar as they give us information about those, who make such statements.
In non-philosophical cognition, expressed by way of common, everyday language, "existence" refers to what is verifiable by means of the senses. Synonyms of "to be" in the existential sense vary depending on the context. "There are (scil. there exist) whales" can be rendered as "whales live on Earth." "There are glasses on the table" can be rendered as "I see glasses on the table," and so on. I will call the existential function so understood the Weak Existential Function [WEF].
Frequently, phrases that exhibit features of the existential use of "to be" are not in fact existential. For example, the question "Will there be sun tomorrow?"6 does not refer to the existence of the sun tomorrow, but is equivalent to the question of whether we can expect good weather and a cloudless sky. I call this function the Pseudo-Existential Function [PEF].
5 C. H. Kahn (2002) 84.
6 This is a direct translation of the Polish Czy bgdzie jutro stonce? Though it is stylistically awkward and unnatural in English, I think it serves as a good example of the PEF of "to be."
The Weak Existential Function
Sentences that use the WEF of "to be" are an important part of the network of statements constituting knowledge. The more complicated the method of observation, requiring advanced technological tools in order to sensually grasp being-existence, the deeper the description and understanding of physical nature reaches. The problem is that since we are talking about the mutable and relative reality that can be sensually grasped, and therefore sensually verified, it is difficult to maintain the idea that we are really dealing with an ontological problem, or even with a problem of fundamental significance for ontology. Aristotle already indicated the separateness of first philosophy from physics and the natural sciences. In this age of rapid growth of the exact sciences, there is no doubt that scientific problems concerning an aspect of reality expressed in language through the WEF of "to be" are merely of secondary importance for philosophy and ontology.
What about the status of mathematical entities?7 This problem was already discussed in Greek philosophy: do mathematical entities have the same status as physical entities? The answer seems obvious: no, as they cannot be sensually grasped and verified. What are mathematical entities, then? Do they exist? From the perspective of the WEF, it is impossible to grant them existence. Should we take them to be fictional, then, like the werewolves mentioned earlier? The problem is that in contrast to werewolves, mathematical entities play an important role in our process of cognition. This was already evident in antiquity, in studies on music, for example. Mathematical entities constituted the foundation of Pythagorean philosophy; they also played an important role in Plato's philosophy and in Platonism. In modern science, on the other hand, they are a necessary tool, without which it would be difficult to imagine not only such disciplines as physics, chemistry, and biology, but also economics or sociology.
In attempting to answer the question of the ontological status of mathematical entities, we must address the problem of how we come to know mathematical entities. Even if we accept that mathematical cognition is derivative in regards to sense cognition, this still does not explain the process thanks to which our minds grasp mathematical entities. Certainly, this is not explained by the process of abstraction, understood as generalizing detachment, though it is possible that the Pythagoreans understood it this way in the context of number as proportion.
7 The case is similar with logical entities. The thing is that though logic can be seen as the laws governing human reasoning, as a necessary condition of reasoning that is not internally contradictory, mathematics touches what is outside of our minds (though we do not understand how exactly this is so).
Thus, though arithmetic entities may be understood as abstractions, geo- and stereometric entities cannot be understood this way. At the basis of the cognition of mathematical entities lies idealization. It is idealization that justifies mathematical entities, not sense cognition. In consequence, the question arises whether contemplating mathematical entities' ontological status, in the sense of their existential status, makes any sense. Does such contemplation add anything to our understanding of reality? Are we able to indicate any standard by which we could evaluate or verify that existential status? Considering what I wrote regarding the WEF and its relation to philosophy, answers to all the above questions must be negative. A difficulty does appear, however. It is clear that mathematical entities do not in any way fall under the WEF. They cannot be examined in that context. Can we indicate a different existential context, which we could call a "Strong Existential Function" [SEF] of the verb "to be"?
The Strong Existential Function
The foundations for a SEF can be found in the philosophy, or rather theology, of Christianity. The notion of creatio ex nihilo creates an intellectual context completely different from the one in which Greek philosophy was born. From this Christian perspective, the world is not eternal, but rather called into being out of nothingness. The act of calling into existence is preceded by (not necessarily chronologically, but logically) ideas in the mind of God, on the basis of which the creator-God executes the calling into existence.
Let us begin with some remarks concerning the etymology of "existence": ex-istere, existo or exsistere, exsisto is a combination of ex and sistere. In the context of interest to us, ex could mean 1. "as a result," "in consequence," "deriving from" "out," "away"; 2. the source, the starting point in space or time, or the state of affairs from which an action is initiated meaning "from," "with," "after"; or 3. as a prefix ex- means "out" or "away". Sisto, sistere means 1. to cause to stand, to set up, to erect; 2. to place firmly, to place, to set; 3. to make firm, fix, stabilize. As a result, exsisto means 1. to come into view, appear, to rise from the dead; 2. to come into being, emerge, arise. It is worth emphasizing that exsisto points to an external source of that process of "coming into being," and the process itself (though this results more from the Christian interpretation, discussed below, than from the concept itself) is not gradual, but immediate, by means of afiat.
I will risk the claim that a fully developed formulation of the problem can be found by referring to two issues in medieval philosophy: 1. The formulation of the problem of universals within the context of universalium ante rem, in re, post rem, and 2. Aquinas' take on essence and existence from De ente et essentia, subsequently developed and modified by Giles of Rome (Aegidius Romanus) in Theo-
remata de Esse et Essentia and later by existential Neothomism (Etienne Gilson8). What is crucial to this understanding is the separation of existence and essence. Of all the beings that preexist in God's mind (all possible individual and general beings preexist in it), only those beings to whom God has explicitly granted existence in the act of coming-into-existence, exist.9 In certain cases (e.g. in Giles of Rome), this real distinction takes on the form of distinctio inter rem et rem. Consequently, this leads to the conclusion that it is possible to come to know the essence of non-existent beings: "now, every essence or quiddity can be understood without anything being understood about its existence. For I can understand what a man is, or what a phoenix is, and yet not know whether they have existence in the real world (et tamen ignorare, an esse habeat in rerum natura)."10 How is it possible to understand non-existent entities? Let us use the example Thomas Aquinas gives - that of a phoenix: I know what a phoenix is regardless of whether phoenixes exist or not.11 This reasoning is flawed, however. Knowledge about the essence of a phoenix is taken from myths about phoenixes, literary descriptions, and other representations, such as illustrations or sculptures. Thus, knowledge of the essence of a phoenix concerns these sources, which do exist! More precisely speaking, I do not know the essence of a phoenix, I know the essence of its various representations: mythological, literary, artistic, and so on.
This is the case for all fictional entities. From the perspective of WEF such entities do not exist, though their representations do. Such representations constitute the basis for alleged knowledge about these nonexistent entities, though this knowledge is precisely knowledge of existing representations. Does the SEF indicate different criteria of existence than the WEF? As Polish existential Neotho-mist M. A. Kr^piec states, everything that exists in some way exists either as a material entity (physical, able to be grasped by the senses; identical with WEF) or as a mental/thought entity (different from the WEF).12 From this perspective, mathematical entities, phoenixes, werewolves, and Sherlock Holmes exist, but as mental/though entities. If so, however, we cannot speak of a real difference between essence and existence, only of a real difference in ways of existence. In consequence, we can ask whether the category of existence is at all useful from a philosophical point of view. Existence in itself does not give us any additional
8 E. Gilson (1948).
9 Giles of Rome points to analogies between essence-existence, matter-form, and potency-act, concluding that actualization, as something "superadded" - superadditum -complements the essence, allowing the latter to attain its proper state of perfection.
10 T. Aquinas, De ente et essentia, IV, 98-100.
11 Ibidem.
12 M. A. Krçpiec (1978) 355.
knowledge allowing us to distinguish entities from one another, as material entities, immaterial entities, and even completely fictitious entities are recognized as existing. Moreover, the criterion distinguishing the material from the immaterial is identical to the criterion characterizing the WEF. This criterion is sensory observation. The ability to perceive something via the senses, to measure it, to subject it to experiments - all these aspects make up the common (colloquial) understanding of what is material. What, in turn, cannot be perceived through the senses, measured, or be made subject to experimentation, is immaterial. I use the phrase "sensory observation" here not in the strictly literal meaning of observation made with the natural senses, but rather to refer to any measurement made using any available technology. In other words, existence in the WEF could be interpreted as "common reason's" version of existence in physics, which may be understood as the "duration of existence in spacetime."13
By the same principle on the basis of which we attempt to emphasize the distinction between essence and existence, we can call into question the status of mathematical entities. In fact, Aquinas consistently considers them only as abstractions of the mind that constitute a generalization of quantitative relations observed by the senses (from ens mobile to ens quantum14 ).
It is at this point in which a great deal of controversy appears. Is it really not possible to distinguish between the existential status of fictional entities and that of mathematical entities? Even if we agree that that is true in the case of Tho-mism, does it necessarily follow that there is no criterion for distinguishing fictional thought entities from non-fictional ones - such a distinction is only possible in colloquial speech and "commonsense" reasoning, but not on the grounds of philosophy - philosophical reflection would have to concern itself equally with the status of mathematical entities and the status of, say, werewolves.15 Let us take a short look at the problem of how to distinguish mythical objects from mathematical objects. Mathematical objects are defined within a structure, with-
13 A. Nikkhah Shirazi (2019) 2.
14 S. Swiezawski (1999) 112. For more on Aquinas and the Thomists' view on mathematics, see e.g.: A. Maurer (1993).
15 It may come as a bit of a surprise that some analytic philosophers take on an approach similar to that represented by Neothomists. Quine's famous statement that "everything" exists and his recognition of the analysis of the existential status of properties, numbers, meanings as the main task of ontology (see: W. V. O. Quine (1964)) leads to consequences similar to those that we encounter in Neothomistic reflection: philosophical analysis becomes a kind of linguistic jugglery, a game consisting in the manipulation of definitions, concepts, and concept extensions.
in an axiomatic system.16 It should be emphasized that mathematical structuralism can be interpreted from two fundamental positions referring to the existential status of mathematical objects: 1. these objects have no intrinsic nature (ante rem structuralism), or 2. these objects do not exist (structuralism without ante rem structures). Consequently, the key in structuralism will be the reference not to "existential status," but to the relationship between "natureless" and "non-existing" "mathematical objects" (S. Shapiro, Mathematical Structuralism, Internet Encyclopedia of Philosophy). It is only on the basis of an analysis of the structure of these relations in ante rem structuralism does the postulate of existence -the existence of the structure - appear. But we can observe something similar with regard to mythical-religious entities. Most religions have certain rules for justifying their claims, and some have an extraordinarily complex system enabling them to distinguish what is "true" (orthodoxy) from what is "untrue" (heresy) within that system. Is it impossible, then, to distinguish the legitimacy of mathematical entities from the legitimacy of mythical-religious entities? Is the only trick needed for legitimization to build a structure, possibly formalize it (at least to some extent), and then define "existence" from the perspective of that structure/system? There seems to be one more important, and perhaps key element. The difference between mathematical entities (structures) and mythical-religious ones lies in the cognitive applicability of mathematical entities to describe physical (natural) objects, or more broadly - in their applicability to many cognitive disciplines. If mathematics could in no way be applied to the description of reality grasped by the senses, its status would be similar to that of religious-theological systems that create their own world - coherent, but not translating into anything outside of itself. Were it not for this applicability of mathematics to the world external to the structure/system, the ontic status (both existential and veritative) of mathematical objects/structures would be indistinguishable from the ontic status of angels - both would be structurally and sys-temically true, whilst being unsuitable for describing and cognizing the world external to the structure/system (no explanatory value). Mathematics would then be nothing more than an extremely complex intellectual exercise or game.17 It is its applicability, i.e. the veritative aspect, that makes the difference. One can, of course, speculate how the status of mathematics would change if we discovered or invented an instrument that described reality more accurately. In that case,
16 For more on mathematical structuralism, see e.g. M.D. Resnik (1997); S. Shapiro (2008)285-309.
17 To be clear: I have nothing against intellectual games. On the contrary, they are fantastic exercises for logical and strategic-tactical thinking, but are not in themselves a literal way of describing and cognizing the world.
mathematics would begin to be regarded as merely an approximation, and its veritative status would be lower than that of the "new instrument." However, this would not in any way change the general conception of veritative ontology. It may be concluded from this that the criterion of "existence" consists precisely in this applicability. In other words, the criterion for the "existential" status would be the "veritative-epistemic" status. On the grounds of language, such a procedure is possible. However, in my opinion, this would be a linguistic misuse, as the concept of existere is historically grounded in the postulate of the necessary distinction between ontology and epistemology, as well as the distinction between esse and essentia (more on this below).18
Consequently, two important questions emerge. 1. What is the status of those aspects of the structure that are not applicable to reality (i.e. not useful in describing what is external, rather than in the sense of being in opposition to what is external)? 2. Since mathematical entities are applicable to reality, can their on-tic status be regarded as being the same in "nature" to the status of what these entities grasp theoretically? Concerning the first point, it can be assumed that the applicability of certain aspects gives truth to the entire structure, and those elements that are not applicable at a given moment constitute a certain "base of possibilities" for a given structure. Concerning the second point, if we consistently hold to the veritative interpretation, the status of mathematical entities/structure should be considered higher than what they describe theoretically, although at this point we are entering the slippery ground of relationships between e.g. physics and mathematics.19 While this relationship may have seemed one-sided some time ago (i.e. mathematics is helpful in physics, but not the other way around), a case can be made for the revision of this point of view.20 I will not
18 The acceptance of such a finding creates another difficulty: does the mere fact that an object is an element of a structure with certain "translatable" aspects mean the same status is given to that object, even if the object itself lacks "translatability" at present? As a result, does it exist or not? While in this context gradability on veritative-epistemological grounds is understandable, it is difficult to fathom how gradability could be possible on existential grounds, based on durability and causality.
19 The main problem here concerns whether mathematics merely describes nature, or whether mathematics is nature, as in the mathematical universe hypothesis; see: M. Tegmark (2014), especially Part III, chapter 10, Physical Reality and Mathematical Reality.
20 As Michael Atiyah puts it: "The mathematical community has benefited from this interaction in two ways. First, and more conventionally, mathematicians have been spurred into learning some of the relevant physics and collaborating with colleagues in theoretical physics. Second, and more surprisingly, many of the ideas emanating from physics have led to significant new insights in purely mathematical problems, and remarkable discoveries have been made in consequence. The main input from physics has come from quantum field theo-
go into this problem here, as neither my competences nor the scope of the article allow for it. Regarding the status of mathematical entities, to simplify greatly: while the confirmation of the reality of a physical object (its "existence") is made through an experiment and results from sensory data (broadly understood "measurement"), the interpretation of this "existence" and its placement in the appropriate area within a given physical theory requires reference to mathematical entities which, by giving them a theoretical meaning, essentially give them a truth value. What sense would it make to solve the problem of mathematical entities' "existential status," especially when there is no universal meaning of "existence"? In consequence, attempts to determine their "existential" status are based on such formulations of the definition of "existence" to which the mathematical structure or mathematical entities could correspond. This approach can be applied to all "thought entities" and, as a result, we obtain many different incompatible "existential" definitions, which form the basis for various "ways of exist-ence".21 The final conclusion to be drawn from accepting such an approach must be a choice between "everything exists" or "nothing exists."
However, existential ontology is not the only possible form of ontology. One alternative proposal has been put forth by neo-Aristotelian philosophers. In it, the central place in ontological reflection is occupied not by existence, but by grounding. Arguing against the existential paradigm, Jonathan Schaffer writes:
the neo-Aristotelian will conceive of the task of metaphysics as: [...] the task of metaphysics is to say what grounds what. That is, the neo-Aristotelian will begin from a hierarchical view of reality ordered by priority in nature. The primary entities form the sparse structure of being, while the grounding relations generate abundant superstructure of posterior entities. The primary is (as it were) all God would need to create. The posterior is grounded in, dependent on, derivative from it. The task of metaphysics is to limn this structure.22
Though this proposal seems more interesting and more fruitful than the existential perspective, it also involves dogmatic and arbitrary solutions. The most significant of these is the understanding and interpretation of ousia, which "grounding" theorists render as "substance," rather than "essence." I am merely signaling this issue here, as it is complicated and would require a comprehensive linguistic and philosophical analysis. For now, I will only note that the concept of
ry. While the analytical foundations of quantum field theory have been intensively studied by mathematicians for many years the new stimulus has involved the more formal (algebraic, geometric, topological) aspects," (Atiyah 1990: 31).
21 For example, Roman Ingarden's four modes of being, or modes of existence - the absolute, the ideal, the real, and the purely intentional.
22 J. Schaffer (2009) 351.
"substance" seems to have an unambiguously ontological-existential reference, while "essence" seems to have a more epistemological-veritative reference. However, I will point out some fundamental issues. "Essence" can, in a way bringing to mind John Locke's distinction between "real essence" and "nominal essence," be understood in an ontological, as well as an epistemological sense. In an ontologi-cal sense, it denotes an alleged feature (or set of features) that is the cause of the observable features of a substance. In an epistemological sense, it signifies our way of knowing (cognizing) a given entity: "essence" - as opposed to accidents -is the aspect of a given entity that we consider important, which we consider to be the reason why a given being is a given being: to ti en einai. It is this feature (set of features), which we consider the most important for the identity of a given entity, that allows us to distinguish that entity from other entities. However, this is always a relative question, and the decision of what constitutes "essence" and what constitutes a mere "accident" is more or less arbitrary. This applies to individual entities as well as species and genera, although on the level of species and genera the "usefulness" (which does not mean adequacy) of using this distinction seems to be more fruitful. This is related to the fact that "species" and "genera" are concepts that in themselves have more veritative-epistemological (they allow us to organize our sense data), than ontological-existential value - their arbitrary "existence" is related to their arbitrary "essence."23 If the definition of a species is to contain what is necessary, then a species trait distinguishing one species of a given genus from another species of the same genus is not the only necessary trait - all the "more general" features that constitute (to use the example of biological systemization) the genus, family, order, class, phylum, kingdom, and so on, are necessary. You cannot be Panthera leo without being Panthera, Felidae, Carnivora, Mammalia, Chordata, Animalia. In the field of ancient philosophy, interesting premises for a discussion on this topic can be found in Sextus Empiricus (to koinos symbebekos/to ou charakteristikon symbebekos vs to charakteristikon symbebekos, PH, III, 173-175) and Porphyry (to choriston symbebekos vs to achoris-ton symbebekos, i.e. "separable accident" and "inseparable accident," and the problem of to athroisma: "such things (scil. Socrates - P.S.) are called individuals (atoma), because each consists of properties of which combination (athroisma) can never be the same in any other" (Porphyry, Isagoga, 2b-3a). To illustrate, let me give a few examples of how arbitrary it is to use "essence" in reference to individual entities. Aristotle's example in the Metaphysics concerning the musician24
23 The real status of "species" in nature is the subject of discussion. In practice, it takes an epistemological-technical form, such as OTU - Operational Technical Unit. What is more, stability and immutability are not part of the nature of biological "species."
24 In the English translation he appears a "cultured" man.
and the builder (1017a 10-11), strongly indicates the relativity (contextuality) of essence (to kath'hauto), whose particular formulation tells more about the cognitive perspective than about what is "objectively" and "ontologically" significant.25 A musician makes music due to his/her essence, a builder builds due to his/her essence, a musician builds accidentally, a builder makes music accidentally. While true, these are but tautologies. Since we define musicians as those who make music and builders as those who build, it cannot be otherwise. However, when we wish to distinguish between two musicians, one of whom could build and others who could not, building would become "essential" to effectively distinguish the two musicians.
The category of "essence" is indeed useful, but only as long as it is not ascribed to entities (especially individuals) as an objective feature of theirs that constitutes the sole and necessary source of their identity, and is not contrasted with non-necessary features - accidents. The usefulness of "essence" as an epistemo-logical instrument proves itself in relative-relational and contextual cognition. On objective, ontological, and existential grounds, I do not see a way to non-arbitrarily distinguish "essence" from "accidents," which in turn leads to the conclusion that "essence" and "being" are the same: all features of a being are essentially constituting for this being; that certain features appear to the cognizing subject as essential or non-essential (more or less essential) is merely a matter of the cognitive goal and perspective. In consequence, "grounding" means existential grounding and though existence itself is not the object of the "ontology of grounding," this ontology functions within the framework of the existential paradigm. I would like to note the possibility of a different sort of "grounding of grounding" - this would be "epistemological grounding." However, such ground-
25 A short digression: the question of Aristotle's understanding of "essence" - whether it is a trait, a set of several traits, or finally a system of all traits - is debatable. The argument for emphasizing a trait, or several traits, but not a system of them, would be to look at the individual through the prism of his/her role, place and significance in the life of polis - here, what counts are the traits an individual possesses that make him/her suitable to hold a certain position (to be a hoplite, for example), not his/her interests. At the same time, however, statements such as he physis ousia, he estin ou stoicheion all'arche (Aristotle, Metaphysics, 1041b 30-31) seem to suggest a system of traits. This problem and the problem of defining species are also connected with the problem of understanding nature, e.g. human nature. We have two opposing positions: the essentialist perspective and the nomological perspective. The essentialist perspective understands "nature" more arbitrarily and selectively, while the nomological perspective understands "nature" holis-tically, as a set of all features. For more on these perspectives, see e.g.: Machery (2008)
321-329.
ing would move the debate from ontology to epistemology. Is a non-existential option available within the framework of ontology itself, as the "study of being"?
The Veritative Function of the Verb "to Be"
Let us now take a look at the veritative function of the verb "to be" and at the proposal of a veritative ontology built on this function. I'd like to start with a very short summary of Kahn's analysis of the meaning of einai in ancient Greek. The main thesis of Kahn's article The Greek Verb "To Be" and the Concept of Being,26 recently elaborated in his famous book, is that "the Greeks did not have our notion of existence."27 Instead, as Kahn convincingly proves, "for the philosophical usage of the verb, the most fundamental value of einai when used alone (without predicates) is [...] 'to be so,' 'to be the case,' or 'to be true.'"28 Very important for the purpose of my thesis are Kahn's remarks about the durative aspect of einai. The verb einai has no aorist and no perfect forms. Kahn pointed out some philosophical consequences of this:
what is the philosophic significance of this morpho-semantic fact? I think it may help us to understand (1) the Greek notion of eternity as a stable present, an untroubled state of duration, (2) the classical antithesis of Being and Becoming, and (3) the incommensurability already noted between the Greek concept of being and the modern-medieval notion of existence.29
Greek Philosophy Through a Veritative Lens As Alexander Mourelatos points out:
Kahn's work gives precision to something that has often been felt as a generalization about Greek philosophy: that Greek ontology is fundamentally concerned with questions not of 'existence' but of 'what-ness' or 'essence.' The point has sometimes been treated as a commonplace, and yet it is very rarely applied to the translation and detailed exegesis of Greek texts. At that level, the rendering 'to exist' for the syntactically absolute use of sivai is still by far the most common.30
The veritative meaning of einai allows us not only to make translational corrections to Greek philosophical texts and to indicate an alternative to the existential conception of ontology; the veritative meaning of einai also allows us to view the whole of Greek philosophy from a completely new perspective. Greek philos-
26 C. H. Kahn (1966) 245-265.
27 Ibid., 248.
28 Ibid., 250.
39 Ibid., 255.
30 A. Mourelatos (2008) 48-49.
ophy's object, its aim would not be to determine what exists and what does not exist. Rather, it would be to gain an understanding of how the kosmos functions, an understanding of its laws. And understanding the kosmos, in itself, would inextricably connect the ontological and epistemological dimensions of Greek thought. In other words: we are talking about perceiving understanding as the only possible way of non-dogmatic philosophizing. Now, let us take a look at a few examples from the history of ancient Greek philosophy.
Pythagorean Unity and Multiplicity
The Pythagoreans are considered to be representatives of ontological dualism. They solve the problem of the origin of opposites, which appears when we accept the idea of one, determined first principle and which Anaximander tried to solve by introducing two opposite principles. These two first principles are peras and apeiron.31 However, there is yet another aporia connected with dualism. This time, the problem is not how opposites are generated, of course (since we have opposite principles), but rather their unity. How are opposites unified? What causes peras and apeiron to interact? What determines the form and principles of this interaction?
In answering these questions, we must consider two possibilities. The first possibility is that the causes and rules regulating peras and apeiron's interaction result from each of their "natures"; that is to say, the rules regulating this interaction are "built-in" to the principles of peras and apeiron. Such an interpretation dominates in research on Pythagorean philosophy. If we consider the fact that these rules cannot be determined by apeiron (because it is apeiron), we have to accept that the rules of interaction are determined by peras. If this were the case, it would be difficult to say that we were dealing with two equal principles. Using Aristotle's terminology, we can speak of apeiron only in the sense of passive matter - hypokeimenon. As a result, this dualism would be a very peculiar dualism -the dualism of two unequal principles.
The second possibility, which appears much more rarely in the secondary literature, adds a third principle, harmony, to the two principles of peras and apeiron. Harmony is not treated as equal to the other two, but as being of higher
31 In the famous table of opposites, relayed by Aristotle in the Metaphysics, the pair peras-apeiron is placed at the beginning of the list. Certain post-Aristotelian commentaries make a correction, moving the pair agathon-kakon to the beginning of the list. Considering the Platonic context, we can risk the thesis that three pairs from the table are closely related to one another. These are peras-hen-agathon and apeiron-plethos-kakon, analogous to the Platonic principles of hen and aoristos dyas. For more on this subject, see: Swiercz (2008) 214-242.
standing, as a meta-principle. This interpretation makes it impossible to continue upholding the thesis that the Pythagoreans were dualists. If harmony were considered equal to peras and apeiron, we would have to speak of a trialism of principles. If, on the other hand, harmony is "above" peras and apeiron, we would either be talking about monism (in the case that harmony generates peras and apeiron), or about a monistic-dualistic conception (in the case that peras and apeiron were not generated by harmony, but united by it).
If we add to these aporias the controversies concerning the status of numbers in Pythagorean philosophy, then we are dealing with a very complicated, hard to order, and very dogmatic system. If we leave traditional ontology aside and look at Pythagorean philosophy from an epistemological-veritative perspective, things become much easier to understand.
What is characteristic for Greek philosophy is the belief (or axiom) that the world is a unity of multiplicity: the multiplicity of perceived elements is organized into one coherent system subject to one law-principle. How should we begin the process of describing and explaining the kosmos so-understood? Since the kosmos is a unity of multiplicity, the cognitive process should encompass both the aspect of unity and the aspect of multiplicity. Multiplicity can be understood in many ways. To simplify a bit, we can say that multiplicity can either be reduced to the eternity of basic, indivisible elements (atomism), or to the first principles of individuation, which are pairs of opposites (dualism). Unity, however, always takes the form of a search for one first arche (monism). None of these positions needs to be understood from the perspective of traditional ontology, a position that ascribes certain cognitive points of departure (atoms, opposites, arche) an ontological-epistemological status. These can be understood simply in the veritative-epistemological context: they are principles-rules of our cognition, of justification, of "truth-making," of legitimization. In his Metaphysics, Aristotle indicates the role of the principles of peras kai apeiron as the highest principles in Pythagorean philosophy, placing them at the top of the ten pairs of opposites. The great ontological and epistemological significance of peras kai apeiron (perainonta kai apeira) is also indicated by Philolaus (DK: B1, B2, B6), and in the treatise Peri archan, which is preserved under the name Archytas of Tarentum (Pseudo-Archytas, Peri Archan).32 Those interpretations of Plato's Timaeus that see in the Demiurge and in his work a symbol of philosophy as the process of cognition (e.g. Jaskola (2004)) perfectly correspond to the perception of peras kai apeiron, especially as cognitive principles. Daniel W. Graham (2014: 50-51) draws attention to the cognitive role of perainonta kai apeira in Philolaus' philosophy,
32 Thesleff (1965) 19-20.
even indicating a resemblance to Kant's transcendentalism. With reference to B3 and B6, Graham notes Philolaus' emphasis on the human character of the cognitive perspective regarding nature, the principles, and harmony, and the fact that the possibility of knowledge and cognition grounds certain ontological theses. Philolaus' approach can be framed from the perspective of veritative ontology (using Kantian terminology) as follows: what "really exists" (noumenon) is a "divine" matter and human cognitive capabilities cannot reach it; human cognition can only capture what appears (phenomenon) and attempt to find a way to describe and justify this phenomenon as accurately as possible.
From this perspective, the debate over the status of Pythagorean philosophy33 is senseless: the Pythagoreans incorporate both unity (monism) and multiplicity (dualism) into their conception of cognition (De Vogel 1966; Burkert 1972; Huffman 1993; Gajda-Krynicka, 2001; Viltanioti 2012, Swiercz 2019). The discussion on whether full unity was first, and then transformed into multiplicity, or whether multiplicity was first, and then was unified-harmonized, is fruitless. If we reject this chronological-genetic-historical perspective and take on a perpetually "actualized" perspective that is fixed-in-mutability and mutable-in-fixity, then the aporias mentioned above lose their power: the kosmos is permanently and simultaneously a unifying multiplicity and a differentiating unity. This unification and individuation are one and the same process. Our cognitive conditions require us to distinguish between these two aspects, but only as an epistemological procedure.
This same problem concerns the status of Plato's Forms. Historically-speaking, the theory of Forms acquires its proper significance within the context of Pythagorean and Eleatic philosophy. It constitutes an attempt at synthesizing these two philosophical conceptions and, at the same time, at overcoming the aporias connected with them.
Parmenides and the Eleatic School
Parmenides plays a special role in the history of philosophy: he was the first philosopher to introduce the terms to eon (to on in Attic dialect), to me eon, meden, to ouk eon.34 How the root meanings of these concepts in Parmenides' philosophy are understood affects our understanding of all of post-Eleatic Greek philosophy.
33 That is, on dualism vs. monism. The problem concerns the status of harmony and its relationship to peras and apeiron. See: De Vogel (1966); Burkert (1972); Huffman (1993); Gajda-Krynicka (2001); Viltanioti (2012); Swiercz (2019).
34 Mourelatos (2008) 75.
Due to space constraints, I will concentrate only on the meaning and relationships between four concepts: being, non-being, truth, and opinion.35
In his treatise Peri physeos, Parmenides writes about two ways of cognition: the way of Truth, whose object is being, and the way of opinion, whose object is non-being. What are being and non-being? If we accept an existential understanding, the whole line of argument loses its significance. How could there be a way of opinion referring to what doesn't exist? The only alternative to the existential interpretation, both in light of the fragments of Parmenides' text and in light of the principles of rational analysis, is the acceptance of a non-existential understanding of the concepts of "being" and "non-being". Being (to eon) is as follows:
1. non-born and indestructible;
2. eternal;
3. immutable;
4. indivisible and complete;
5. full and non-gradational;
6. absolute and identical;
7. necessary and connected to justice and righteousness;
8. authoritative;
9. unified.36
In consequence, non-being does not refer to what is non-existent, but to what is born and perishable, temporal, mutable, divisible and incomplete, gradational, relative and non-identical, unnecessary and unconnected with justice and righteousness, unauthoritative and plural. Non-being (a mixture of being and non-
35 For clarity, it is necessary to emphasize at the start that I am a strong advocate of the two-way interpretation of Parmenides' poem Peri Physeos, which distinguishes the way of Truth and way of opinions. I reject, as completely inconceivable, those interpretations that distinguish a third way - the way of falsehood (e.g. M. Heidegger 1953: 86; English version: M. Heidegger 2000: 119-120. For more on Heidegger's concept of "Nothing," see: M. Heidegger (2018) 733-751). On those interpretations which identified opinions with falsehood, see e.g. A. Drozdek (2011) 9. The reasons for my position will become clear after an analysis of the concepts of being, non-being, truth, and opinion, but I will briefly indicate why accepting a "way of falsehood" is absurd. If truth corresponds to being, and opinion to a mix of being and non-being, we are faced with the fundamental question of what could correspond to falsehood. Being and non-being seem to fill up the entire admissible spectrum. If that is the case, then the way of falsehood is "empty" - in other words, it is not there at all.
36 D. Kubok (2004) 444-445.
being) cannot be grasped by true cognition, only by "probable" cognition.37 The concept of "being" and the ontology at its source are evidently veritative-epistemological in nature, not existential. The problem of how to understand to eon and einai in Parmenides is connected with the interpretation of the adverb hos. How we choose to interpret hos in this context largely influences how we understand to eon and einai. In the context of fragment B2 of Parmenides, I think that the most reasonable interpretation is the synonymous use of hopos and hos.38 The Platonic interpretation of Protagoras' anthropos metron principle is helpful in solving this problem. It seems that in this context, in the use of hos, we are dealing with a shift of emphasis from "that" (existential dimension) to "how/what" (veritative dimension). The method of interpretation presented by Plato/Socrates/Protagoras in the demonstration of how features of a meal are perceived, which illustrates the anthropos metron principle, does not indicate the problem of the "existence" of this meal, but rather of what characteristics can be attributed to it. Man is the measure not "that being is" ("that being exists"), but of "how being is," "what being is" - of course, from his/her perspective. The issue of "existence" is not undertaken by Protagoras in Theaetetus, because it is settled, one could say, on the level of obviousness of sensory perception - "something" evokes these impressions, that is, "something" "exists." The "existence" or "reality" of the meal is not questioned; rather, the problem concerns whether it is tasty or not. There is no need to discuss the problem (or pseudo-problem, in my view) of the status of the object of perception itself within the context of "existence." The really significant question is what it is and what it is like.
Here, one might assert that this cognitive aspect is connected more to the translation of hos than to the veritative meaning of to eon (to on). Let us examine this point. If I take to eon (to on) to mean "a being/something-that-is-true," and to me eon (to me on) to mean "a non-being/something-that-is-probable" (I use "something" not as a synonym for an object, of course), then hos estin means "how [something] is true," and hos ouk estin means "how [something] is not true, but only probable." This idea should be understandable. On the other hand, if I take to eon (to on) to mean "a being/something-that-exists," and to me eon (to me on) to mean "a non-being/something-that-does-not-exist," it is hard to imagine
37 The question arises whether we see a similar distinction between certain knowledge and probably knowledge in Pythagorean philosophy, though no such distinction is explicitly made. Of course, this question is open and debatable. However, I think that in Pythagorean philosophy, the status of certain knowledge can be ascribed to mathematics. Knowledge of entities that can be grasped by the senses would belong to the category of probable knowledge.
38 Kubok (2004) 111, 115-119. Cf. Robinson (2010) 61.
what hos estin, i.e. "how [something] exists" in this context, could mean, and hos ouk estin, i.e. "how [something] does not exist," seems to lack any sense at all.
Is it not possible, however, to interpret "existence" from the perspective of "cognition" or "knowledge"? The problem with this non-source use of the term existere, that is, giving it different meanings from the original one, necessarily leads to misunderstandings. While in the case of post-medieval philosophy it is a certain natural process of the development of philosophy and language, projecting this concept onto earlier conceptions (e.g. Greek philosophy) is dubious. Post-medieval philosophy referred to the already functioning, original notion of existence in Christian theology and philosophy. Greek philosophy could not, of course, refer to this notion. What is more, Greek philosophy lacks a basis for the original Christian notion, because there is no idea of creatio ex nihilo. Therefore, if someone interprets Parmenides' to eon as existence, which s/he defines as an "object of knowledge" (Robinson 2010: 36) and to me eon as "wholly unable ever to become an object of knowledge" (Robinson 2010: 62), then, on the grounds of ver-itative ontology, s/he is using a concept characteristic of existential ontology. Speaking somewhat jokingly: Parmenides is the creator of an ontology, the object of which is the problem of existence, but not existence in the sense that was formulated many centuries later, on the basis of a completely different paradigm.39 Or even more concisely - Parmenides writes about existence, but defined differently than the original [Christian] notion of existence. Is it not simpler to say that Parmenides' notion of being was not existential? To reiterate: at the root of this concept of ontology, "existence" is contrasted with "essence." Therefore, if (1) we understand "essence" as an "object of knowledge," and (2) on the grounds of existential ontology, the possibility of being cognized (being an "object of knowledge") is not a guarantee of existence, then recognizing being an "object of knowledge" as identical with existence is a complete reversal of the original concept of "existence." It would be a bit like someone inventing a new version of philosophy based on "wisdom hatred" - would it not be more accurate to call this conception "anti-philosophy" or something else, just not "philosophy"?
Plato's philosophy, both his theory of Forms and his (likely later) theory of principles, are dependent on Pythagorean and Eleatic philosophy.40 I would go so
39 Thus, it is also difficult to agree with the arguments of Ernst Tugendhat, who agrees with the thesis that Greek ontology was not existential, that e.g. Aristotle does not use the concept of "existence" and that this is not only a matter of terminology, but simultaneously takes the position that the term existentia is appropriate for describing and analyzing Greek ontology (Tugendhat 1975: 15-16).
40 For an excellent synthetic discussion of the influence of Pythagoreanism and Parmenides' philosophy on the work of Plato, see: Kahn (2002) 81-93.
far as to say that the leitmotif of Plato's philosophy is an attempt at overcoming the aporias stemming from Parmenides' philosophy (often formulated in the context of the sophistic "meontic eleatism") by reference to the Pythagorean conception of archai. The problem of politics, in turn, especially the difficulty with establishing the principles of justice, seems to constitute a backdrop for the entire Platonic project.
Simplifying greatly, one consequence of Parmenides' separating the way of Truth-Being from the way of opinion-(non-being) is that all issues connected with the state, including the problem of justice, are reduced to the sphere of opin-ion-(non-being). It seems that the ambition and goal of Plato's philosophy was to formulate a theory allowing for the enjoinment of these two ways, of these two worlds. In consequence, this meant undertaking an attempt at overcoming the philosophy of Parmenides and the sophist philosophy dialectically tied with it, especially the philosophies of Protagoras of Abdera and of Gorgias of Leontinoi. I believe that examining the theory of Forms and the allegory of the cave in this context may turn out to be the most fruitful.
Plato's Allegory of the Cave
The division of being into what is fixed and unchanging and what is permanently mutable had to result in far-reaching consequences in the sphere of political reflection. The sophists expressed this problem the most forcefully: justice as a matter of contract. If we can speak of it, cosmic justice, which would be a model for human justice, is connected with the sphere of being. In consequence, the results of coming to know cosmic justice (if that were possible), could not be translated into human legislative enactments - just as truth-being cannot be translated into opinion-(non-being). In this way, pre-Eleatic-(pre-sophist) political reflection was essentially called into question: coming to know the fixed, unchanging laws of the kosmos, even if there are such, and even if they are cognizable, is useless in the political sphere; since this sphere belongs to non-being, it is the object of opinions, not truth.
In undertaking his discussion with the sophists, Plato begins a great philosophical project, whose aim is the enjoinment of the ways of truth and opinions: only then would it be possible to defend the position that justice is more than a matter of contract and convention. To achieve this goal, Plato introduces Forms, understood as belonging to the sphere of being and as models for what belongs to the sphere of non-being - models for the shadows. However, how are we to understand the status of these Forms? Are we to examine it from an ontological-existential perspective, or rather from a veritative-epistemological perspective? This is certainly an open question. However, when we consider the Pythagorean-
Parmenidean context, the second option seems both more probable and more fruitful.
The allegory of the cave can be seen as an excellent exemplification justifying the above thesis. The description of the two spheres - that within the cave and that outside of it - the grasping of their essence, is done with the help of episte-mological terms, such as eikasia, pistis, dianoia, noesis. The description of the path from the cave to the sun is also expressed through epistemological terminology: the description is a description of a path of cognition. In the cave allegory, Plato seems to combine two traditions: Pythagorean and Parmenidean. The understanding of being and non-being, as well as their relationship with truth and opinions are clearly of Parmenidean origin. On the other hand, the relationship between mathematical entities and entities that can be grasped by sense-perception seem to be rooted in Pythagorean thought. It is these mathematical entities which are to serve as "intermediaries" between being-truth and (non-being)-opinions. The problem is that in Pythagorean epistemology, mathematical entities are seen as properties of entities that are grasped by sense-perception. We come to mathematical entities by investigating phenomena, by finding within them proportions that harmonize the particular elements: these proportions are numbers. Treated this way, however, mathematical entities do not have a separate ontological status (if they do, it is very unclear).
As I mentioned above, mathematical entities are not products of abstraction, but of idealization. In consequence, Plato changes the status of mathematical entities: they become the intermediary between purely rational cognition and cognition based on the senses. In mathematical entities we have the meeting point of the two "ways" mentioned above: the way of opinions, based on sense perception and referring to what is permanently mutable, to non-being, and the way of Truth - the purely rational path of cognizing what is fixed and unchangeable, or being. Only a combination of these two ways can lead to full cognition that integrates various types of experience.41
There is no doubt, however, that noetic cognition is the higher type of cognition. This has traditionally been justified by the thought that on the way of noetic cognition, we come to know those entities that "are" more than phenomena. This is justified from an ontological-existential perspective. However, I believe that
41 There is one "flaw" in the Platonic project, however: it is the fire in the myth of cave. What does the fire symbolize? What is its status? The shadows seen by those in the cave are thrown by the fire, not by the sun. Why, then, do those within the cave need knowledge about what is outside the cave, since their world is filled with shadows that have nothing to do with the sun's light? This is undoubtedly one of the greatest riddles of Plato's philosophy.
the famous expression ousia ontos ousa (Plato, Phaedrus, 247c7) can be understood just as well (or even better) from a veritative-epistemological perspective. Forms "are" more, not because their existence is stronger or more lasting, but because (1) we can come to know them "more truly" and (2) it is on the basis of these forms that we come to know and justify the rest, not the other way around.
According to the above hypothesis, the inspiration for Plato's theory of forms is political reflection, or more precisely meta-political reflection. Was Plato able to achieve his goal of creating an absolute, non-relative foundation for a meta-political conception of justice? I think the answer is both yes, and no. In his analyses in the Politeia (Plato, Politeia, VI, 504b-511e) Plato concludes that the possibility of creating a non-relative conception of justice is conditioned upon the earlier formulation of a non-relative conception of the Good. If such a conception of the Good is not formulated, we are condemned to the sophist path of convention. However, as he himself notes in Book VI, the Good is epekeina tes ousias: the truth about the Good eludes our cognitive capabilities. This thesis is later developed by Neo-Platonic philosophy. On the basis of what we know from Neo-Platonic texts and records concerning the so-called agrapha dogmata, we can however draw a conclusion regarding the status and understanding of the Good in Platonic philosophy.
The Consequences for Political and Ethical Reflection: No Easy Answers
According to Aristoxenus, who cites Aristotle, Plato identified the Good with the One - agathon estin hen (Aristoxenus, Elementa harmonica, II, 30-31; on the translation and interpretation of this formula, see: Taylor 2019: 445). It is hard not to see the influence of Pythagorean philosophy here, especially when we consider the second principle - aoristos dyas. Both the Good-One and the Indeterminate Dyad are in themselves uncognizable, as they are not being-truth. At the same time, they constitute the necessary conditions for all possible cognition. Their veritative-epistemological status can thus be described - in Kantian terms - as purely formal; a material "grasp" or formulation of them is impossible. A "materialization" of the Good can occur only within the context of concrete circumstances. Meta-political reflection, due to its veritative-epistemological nature (analogous to ontology), can thus only be of a formal character, never material. All material formulations (such as specific aspects of political and law systems, e.g. republican or monarchist form of government; or specific ethical postulates, e.g. "do not kill"), both legal-political and ethical, should, in accordance with the above hypothesis, be treated not as extra-contextually, absolutely, and non-relatively established, but as the application of veritative-epistemological cognitive forms to a concrete legal-political or ethical context.
In sum, Greek ontology, based on an understanding of "being" different from the medieval and post-medieval understanding of this concept, is not existential, but veritative. A being's ontic status is tied with the possibility of the certainty of its cognition and with its role in epistemological justification: a being is "more" the more certain the possibility of cognizing it, as well as due to the role it plays in the process of cognition. The justifying entity "is more" than the justified entity.
Humans have only human cognition at their disposal. This cognition can be improved, but the criterion for improvement does not lie in grasping "true existence," but rather the verifiable (by us) consequences of a description and justification, of one theory or another. It can, of course, be argued that with each improvement we come closer to "true existence," but the very notion of "true existence" contributes nothing to our advancement of knowledge. The thesis concerning a judgment's correspondence to reality is clearly naive. We must understand the adequacy of judgments differently. In fact, the only thing that can be discussed in this context is an increasingly better (wider and deeper) explanatory theory, the best criterion of which is its practical application and the growth perspective of a given discipline, and sometimes even many disciplines. The discussion on "existence" is meaningless - firstly, because of the lack of a universal and absolute criterion (and the notion of "existence" is a product of "objective and absolute" thinking), and secondly, because it does not contribute absolutely (sic!) anything to the development of our knowledge or science. A discussion on "existence" only makes sense when it is discussed within a defined scope, with a specific definition, and in relation to a narrow field, e.g. "existence" in physics, in mathematics, or in biology; discussions on "existence" as such are completely unfounded. To undertake the topic of "existence" as such, we would have to be able to look at this problem not from the perspective of various approaches to the issue (e.g. mathematical, logical, physical, theological perspective, and so on) with a subsequent "summing up" of these approaches, but from a meta-perspective which, while not constituting a simple sum, would also include them all. Seemingly, the philosophy of language would be the most suitable for this purpose, after all, all specific perspectives are expressed in language, and perhaps language as such is the only thing that connects them all. The problem is that such an approach in itself would be anti-realistic or arealistic, unless we assume (as in Enuma Elish or Genesis) that a "name" is central to something's "existential status." Moreover, the language of mathematics is not a language in the same sense as the term is applied to everyday language and the technical language derived from it. Attempts to impose the colloquial language (even in its technical version) on scientific data are a frequent source of philosophical and scientific
disputes. These disputes, upon closer examination, are in fact discussions on pseudo-problems, or more precisely - on terminological issues - rather than about real problems in understanding certain phenomena or processes. In the opinion of the writer of these words, an example of such a discussion on pseudoproblems resulting from the mixing up of the levels of colloquial linguistic description with a scientific analysis of a phenomenon and processes is the dispute over determinism/non-determinism in quantum mechanics or the so-called problem of "free will." Without going into detail here, let me suggest that both in these two cases and in relation to the problem of "existence" we are dealing with ideas whose foundations have been formulated within Christian theology (with regard to determinism/non-determinism in quantum mechanics, I mean, of course, not quantum mechanics itself, but rather the problem of determinism/non-determinism within the context of free will), and next, that both the concepts corresponding to these ideas and certain fundamental meanings ("ontic intuitions") associated with them, spread along with the culture and colloquial language into the language of philosophy and science. Although these concepts and ideas have been given various meanings often far-removed from their original meaning, certain "worldview" "residue" within culture (along with the importance of etymology and sources) mean that these concepts cannot (especially in the social environment outside the context of very narrow philosophical and scientific specializations) be separated from the above-mentioned "ontic intuitions." Under these circumstances, the formulation of a uniform definition of being from the perspective of "existence" for all ways of "being" seems impossible. However, it is possible on the grounds of the veritative approach, which focuses on the cognizability of "objects," their internal coherence and the related cognitive perspectives. In this way, the status of mathematical entities can be described as necessary, in contrast to the idea of god, which is only necessary within the system created for its justification. Mathematical entities help to describe, translate and make predictions in many fields of science. The idea of god is not applicable to any field of knowledge other than theological systems.
As a consequence of veritative ontology so understood, ancient Greek meta-political and meta-ethical reflection takes on the form of purely formal reflection. "Filling it" with content is possible only in concrete, determined conditions. Material conclusions are neither absolute nor relative; to the contrary, they are relativized to the circumstances.
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