by Christos Terezis, Professor, University of Patras
Dia-noesis: A Journal of Philosophy 2023, 14
Published: 17 October 2023 (Download here)
Cite: AMA Style: Terezis, A. Aspects of the presence of the Aristotelian Logic in Western Christianity and Eastern Christianity. The “middle places” according to Boethius and Holobolus (1853-1900). Dianoesis-A Journal of Philosophy. 2023, 14.
Chicago/Turabian Style: Athanasios Terezis. 2023. “Aspects of the presence of the Aristotelian Logic in Western Christianity and Eastern Christianity. The “middle places” according to Boethius and Holobolus” Dianoesis: A Journal of Philosophy 14
- Abstract: In this article, we discuss a particular aspect of the presence of the Aristotelian Logic –mainly based on the treatise Topics– in the Christianity of the West as well as in the Christianity of the East, with Boethius and Manuel Holobolus as representatives. As a reference text, we have Boethius’ treatise De topicis differentiis, which was translated into Greek, with certain adaptations and individual comments, by Manuel Holobolus. We approach a concise passage from the Byzantine scholar’s translation, which refers to “middle places”, that is to say, to those which arise neither from the meaning of names per se nor from external factors alone, but from their encounter with each other under particular circumstances. We investigate how “middle places” are distinguished into three categories –a) by πτώσις (case), b) by συστοιχία (co-ordination), and c) by διαίρεσις (division)– and how arguments are structured on the basis of their use. They appear as modalities of nouns, mainly through adjectives and adverbs within prepositional phrases, which do not refer to semantic singulars but to a structure of various kinds of relations between situations and between persons, with evaluative schemes sometimes present. We pay particular attention to how an actual case highlights both morphological and semantic variations so that it is not just a grammatical scheme but also one of philosophical interest. We indicate how through the “middle places” formal Logic is brought into relevance with Ontology, or nominal reflections with pragmatological data, in the perspective of what can be called conceptual realism, which refers to how a meaning adapts to the external conditions it is asked to describe and is transformed accordingly. Finally, we conclude that through Boethius’ original text and Holobolus’s translation, the Aristotelian formal Logic is utilized by the theological and philosophical atmosphere of Christianity, both in the West and in the East, even though there is a gap of about eight centuries between the two thinkers.
- Keywords: Boethius, Holobolus, Logic, “middle spaces”, grammatical case, adverb, argument
Introduction
On the one and, the present study belongs to the systematic philosophical branch of formal Logic and, on the other hand, to the History of Philosophy, since it traces how a detail of the above branch is renewed or updated in later periods than the one in which it first appeared. Thus, its content is also approached in the so-called historical evolutionary light. More specifically, our research draws its motivation from a well-written section of Aristotle’s famous treatise Topics, from how it is received by Boethius, a leading thinker of Western Christianity, and (more importantly) from how it is inscribed in a translational perspective by an important representative of Eastern Christianity, Manuel Holobolus. The Topics owe their fame to how they deal with the foundation of reasoning, argument and proof, but especially for their treatment of “endoxa” and “places”, concepts which have particularly appealed to later scholars, and not only those of the Aristotelian tradition. But certainly, what is said about «ὅρον» (definition), «ἴδιον» (idiom), «γένος» (genus) «συμβεβηκός» (accident) in the course of their development should not be overlooked.[1] Boethius, who is regarded as the “father of Scholastic Philosophy”, attempted to translate the treatise in question into Latin –as well as the rest of the Organon– in the form of what is known as a translation commentary. So, he compiled a systematic treatise De topicis differentiis –composed of four books, each containing several chapters–, which is the so-called authorial archetype of the West for what is characterized as Dialectical Topics, and gradually becomes a textbook for high-level philosophical studies. This study aroused the intense interest of the Byzantine intellectuals and was translated into Greek.[2] Its leading translator –and actually with a critical style and comments– was Holobolus, who, by his choice, made the philosophical quality of this text more widely known in a different cultural context. A translation, however, is not merely an attempt to transfer a text to another tradition, but also reflects the research interests of a scholar and the surrounding atmosphere of the historical period in which he or she is active.[3]
The research objective of our study will concentrate, as far as its grammatical reference is concerned, on the translation of Holobolus, and on his introductory remarks on “middle places”, with “places” generally being understood as argument foundations, which exhibit a wide range of specializations, since arguments as propositional forms vary.[4] It should be noted that this Byzantine thinker is a great Aristotelian, with the consequence that in his translation and especially in his commentaries he accurately traces the Aristotelian imprints of Boethius. However, our main aim will be to bring out, mainly through analytical penetrations and synthetic extensions, certain theoretical propositions concerning how Ontology is connected to formal Logic as well as what role the “middle places” play in this connection to lead to a holistic system of Knowledge. In other words, what possibilities does a well-constructed text provide for us to approach (in a way that is accurate, as far as possible, accurate) an external reality and its conceptual expressions? We believe that, in terms of the development of the history of ideas, such a study can shed light on aspects of the research interests that occupied the academic community in the thirteenth and fourteenth centuries in Byzantium. It should be noted, moreover, that both the Latin text and its Byzantine reproduction lack the scope of the Aristotelian one in terms of the analytical treatment of the terms since an extensive part of their structure has to do with the references to the intermediate tradition, such as, for example, to Themistius, Cicero and Marcus Tullius, while references to other treatises of Aristotle, especially to the Organon, are also evident. However, both are emblematic texts, in the sense that they refer to most of the points of a treatise that decisively found the branch of formal Logic and also taught people how they need to or have the capacity to think accurately, to communicate at a high level with one another, to discourse with external reality, and finally to lead to systematic categorizations in most branches of science.
1. General prolegomena
First, it is pointed out that the middle places arise either from the case or from the array or from the division, that is, a variety of situations-functions-relevancies-methods that are inscribed in the terms of modal causality and highlight through theoretical expressions a highly dynamocratic system of relations, distinctions, and evolutions, inferior to their source with regard to the intrinsic nature of their manifestation. Within this system, the precise clarifications of the factual data depend on the particular presence of the factors constituting or defining them, which can also be described as topical variables. And this threefold specificity is due to the fact that the world of becoming is not one-dimensional and formally reproducible and, therefore, will not be captured in a univocal way either by tautological judgments or by formally repeated reductions. It is a dynamocratic external reality which is one of the capital causes that form what is defined as grammatical-syntactic structuralism.
2. The middle places coming from the cases
In particular, as regards the first case, it is stated that «πτῶσίς ἐστιν ἡ τινὸς ὀνόματος κυριωτάτη κλίσις εἰς ἐπίρρημα», just as, for example, in the case in which «δικαίως» arises as a deviation from «δικαιοσύνην».[5] It needs to be made clear at the outset that the term «κυριωτάτη» refers to the fact that it is not a transfer to another meaning or significance, nor does it refer to external interference in terms of predicates and judgments. The development in predicates, which also includes hierarchy in terms of conceptual intensity, is of an internal order but is also determined by the scope of integration in each case. A case, then, is the signifying alteration, so to speak, in which a particular mode –or modality– of expression emerges from a general concept, which characterizes a specific action, which, due to its constitutional position, will be inscribed –together with its expressive form, of course– in two fields. The first field refers to its topicality, which is clearly specific and unique in terms of the protagonists who shape it and the moment in which it is performed. The second field refers to its reduction to more general signifying regularities, that is, to a natural integrity from which strict justifications and meanings are derived, irrespective of situational adaptations. So, the concept of «δικαιοσύνη» does not essentially change by «δικαίως», but it is inscribed in a particular propositional schema, within which it functions relationally or exegetically or partly definitely. Therefore, the case denotes the transformation of a noun into its feasible modes of linguistic or grammatical utterance, into special fields of situations-relations-reciprocities, compared to the general situation represented by the noun in question as definite and abstract. It is the point at which the literal meaning meets the external conditions, a dialectic which contributes to the formation of the middle places.
In our view, we are in a position to extend and argue modestly that this generality could be characterized as transcendental, as an integral condition of possibility for any particular presence of justice –or any other concept– within the world of becoming, but in such a way that, despite the relativism introduced, its very conceptional identity is not altered. Of course, here the (not easy to deal with) question will be raised –which philosophically refers to the dispute between Platonism and Aristotelianism– regarding whether the abstract refers to a condition that cannot be tangibly proven, and actually at the moment when it has to be clarified whether it has ontological content, an a priori state of existence and presence.[6] However, it is worth noting that the transcendental raises further concerns as to how the abstract is constituted or defined, since, for instance, it is not easily accessible whether it constitutes an a priori analytic or synthetic judgment. The relevant reasoning process could unfold as follows: the abstract would constitute a formal formulation, which would represent a peculiar conceptual realism, i.e. the immanent presence of an inner logical form, under its active or practical manifestation, in a number of specialized behaviours or attitudes of life. Subsequently, the abstract concept will emerge from the synthetic –and certainly comparative in terms of one of their characteristics– reading of the specialized ones. However, under the conditions negotiated here, it will be a concept which will coincide with –or refer directly to– the existent, with the consequence that it is impossible for nominalism to claim the most decisive powers if it is not proved that existence is an initial state and not a posterior state. Moreover, one could not rule out an exclusively mental construction, strictly theoretical in content, but also complex in its constitution, since it would have, as a main basis, or even exclusive, the particular.
However, it cannot be ignored that the noun is the dominant factor in the construction of a sentence, while the adverbial type of noun is a peripheral one, determined by the circumstances of each case, which vary from one to another, based mainly on the intentions, choices and modes of action of the protagonists or the necessities to which they are subject. So, here the adverb will depend on the noun of the sentence as well as on the verb, which reflects its constitutional position as a particular presence (of the noun). Thus, we would note that, in general, the adverb does not bring out a realism of the name, but a name that reflects a realistic view of reality, as a dynamocratic becoming articulated in various or infinite ways. However, the same cannot be argued for the noun, which can stand on its own, and not just in a simple sentence. So, as far as «δικαιοσύνη» is concerned: a) as a noun has a dominant position wherever it is used; b) as an adverb –«δικαίως»– has a secondary or complementary position. Therefore, «δικαίως» is a middle place, inasmuch as it is determined both by the original name and by external circumstances.
3. The middle places as coming from co-ordinates
The second version of the middle places is expressed as follows: «Συνεζευγμένα δὲ λέγονται ἃ ἀπὸ τοῦ αὐτοῦ διαφόρῳ τρόπῳ παραχθέντα ἐχύθησαν». In this case as well, what is being discussed is placed in almost the same categorical axis as the previous ones, since the term «συνεζευγμένα» or «σύστοιχα» (co-ordinates) refers to those which have arisen or have been produced in some way, in a way that is particularly determined by the area of their respective emergence or use, from a common conceptual principle. But the difference is that it is not a derivative adverb. Here too, of course, external conditions play a capital role in the changes of the predicates.[7] For example, «δικαιοσύνη» gave rise to «δίκαιον» and «δικαίως», one-word expressive forms, which do not alter the common conceptual basis but differentiate the semantic, syllogistic or applicative basis, with their affirmations or negations adapted to what has been done. In fact, the function of each of the cognates can be directed to the formulation of particular categorical predicates in relation to any noun in any sentence by the constitution and characterization of a unique argumentative or syllogistic mode of propositional development. So, all these, in their epistemically defined per se condition, together with justice itself as «συνεζευγμένα» or «σύστοιχα», are collectively characterized as jointed in terms of their starting signifying source, since they provide, each in its way, the conditions for direct, topical and explicitly or declaratively expressed arguments of a common range of bases and perspectives, that is, of adaptations to what is happening in the external environment. Those referring to virtuous situations such as justice will also move on to the evaluative scale, based on the quality which is reflected both in their articulation as a structural internal order in a propositional scheme and in their descriptive response to the external data to which they refer and which will obviously have a cathartic and changeable content. At the same time, by having a common conceptual source, they will also have the conditions to lead to the formulation of abstract categorical structures, that is, broader theoretical directions. The fact that they even move with an evaluative determination due to their content, articulated under the intensity that they possess in a propositional scheme, contributes to the formulation of synthetic judgments, with a priori justifications and a posteriori expressions, under foundational and permanently validating places respectively.[8]
Therefore, extending our syllogism, here as well that the initial form of a concept, which is expressed by the abstract noun, is the source of a dynamocratic subsequent articulation of it, or has the requirements to be articulated in multiple ways because external conditions constitute challenges for expressive transformations, which take on the responsibility of responding, as far as possible, to the objective, or even realistic considerations. However, since it is clear that the situations of daily life are multiple, changeable and unpredictable, it is necessary to seek the linguistic terms that will describe them with the proper precision to ensure objective measures for the path to truthfulness, which each time constitutes a perspective of –investigative, analytical and explanatory– targeting. It is a more general condition that reveals not only the intellectual and linguistic capacities of man but also the cultural ones, which are linked to the analytical descriptions and synthetic judgments as they are perceived. Therefore, although two derivatives may have a common semantic source, yet depending on their grammatical type of utterance, they highlight a special conceptual presence and intensity, as well as different worlds of contexts, thus proving the pervasive relativism of becoming. That is, a concept is incorporated into a propositional scheme to describe a strictly particular pragmatological field, which will largely operate in terms of kairos and, therefore, can be of limited duration. However, the degree to which its intentional tendency and relational presences or references are revealed depends on or, more correctly, is specified by the grammatical form in which it is uttered at any given time, which also determines the particular syntactic position in a sentence as a general integral syntactic structure. It is generally understood that the same is true for all concepts included in the articulation of any propositional form in which, in the dominant idiomatic statement or marking, the dominant meets the subordinate terms. It should be noted, however, that as a whole, the terms are necessary for the full structure of the meaning, for its study in terms of its topicality, and for its inclusion, sometimes in axiological ways as well, in a broad system of semantics.
4. The formation and function of the argument
The following descriptions refer to arguments that are inscribed in a categorical perspective. So, it is mentioned that the arguments which follow for validation are formed in a similar way to those mentioned above during their operation within propositional schemes of synthetic content. The particular –but also with clear potential for generalization– example used for the way they are formed is of the following form: «εἰ τοῦτο, ὃ δικαίως ἐστίν, ἀγαθῶς ἐστίν, καὶ ὃ δίκαιόν ἐστιν ἀγαθόν ἐστι· καὶ εἰ ὁ δίκαιος ἀγαθός ἐστι, καὶ ἡ δικαιοσύνη ἀγαθόν ἐστι».[9] That is, the argument has the characteristics of an integral syllogism with direct implications, moving both according to abstract concepts and their bearers, that is, according to their personification. In particular, it is pointed out that the above are inferred in categorical reciprocities according to similarities –or common etymological roots– that a name highlights, with its internal dynamics of adaptation. That is to say, the «δίκαιον» and the «δικαίως» emerge from «δικαιοσύνη» but now these are inscribed in the realm of propositional schemes, simple but clearly belonging to synthetic judgments. This internal relevance certainly leads to an expressive organogram with extensive agreements, in a way that could be argued to have self-evident foundations, specialized analogously to the operationali-zation of the relations, either as objectively feasible or as feasible according to the judgment of the thinking subjects. And in this part we would mention that the argument constitutes a logical process which reflects, on a syntactic-grammatical scale, the actual relations of the external objects or situations. Moreover, it follows that under a general reading by implication that whatever relation exists between nouns and is reflected in terms of reciprocal categorical attributions also exists in the grammatical forms that derive from them as somehow their internal linguistic differentiations, so to speak.
However, the course of the constitution of an argument needs special attention in order to clarify the conceptual –and undoubtedly etymological– emanations. So, the sequence of syntactic-grammatical articulations is as follows: a) mutual categorical reduction between adverbs; b) mutual categorical reduction between adjectives; c) mutual categorical reduction between persons possessing the former particulars, which are mainly indicated by adjectives; d) mutual categorical reduction between abstract concepts. By the above sequence of parallelisms or attributions, we mean that a term-to-term correspondence is brought out, which operates on the basis that if two nouns –and certainly any of their derivatives– are identical, any modification of one brings about a corresponding modification of the other. This transformative synchronicity is carried out, so to speak, by automatisms, in order to preserve syntactic-grammatical relations but also to accurately reflect the pragmatological ones, which, obviously as subject to becoming, are by definition changeable. Thus, the question is inscribed in terms of its generality in the renewed dialectics that develop between the pragmatological and the logical, as well as within each in particular, which are not unidimensional and univocal despite the fact that at a particular moment, they constitute or reflect a tautological situation regarding its existential tone. In addition, we should not exclude the adverbial attribution of a noun to that with which it is in a topical tautological relation, with respect to a pragmatological and logical field. But will this relationship be maintained in continuation? The answer depends on the texture of the factors involved as well as on other external conditions.
In this context, the places described are called mixed or middle places, in the sense that, if the reasoning is directed, for example, to the question of «δικαιοσύνη», the arguments arise either from the case of those places or from their «σύστοιχα», i.e. from those which are topically related to them. Therefore, they do not seem to be attracted to their mode of articulation either by the main and appended expression –for then it would be inflexibility– or by what lies outside of them, but by their case, which is produced by their manifestation on the basis of a short alternation of them. That is, even with an infinitesimal one. It is reasonable, then, the fact that these places are inscribed between the things –which are related to the integral significance of places– and those outside their substance, under any topical encounter between them.[10] However, the intermediate here does not refer to a mixture, but to a statement of identities and differences (or perhaps even heterogeneities). That is, if a mode occurs as a source of encounter, it is necessary to bring middle places to the forefront as speculative intermediates for revealing communications, which can be described as mixed. This possibility moves in the sense that they capture in their communication the different situations between themselves in terms of their source of origin. Each of them, in fact, reveals deviations from its source, which is characterized by its absolute, in fact in its own terms, identity. It is clear that, if the differentiations or alternations –both the pragmatological and linguistic ones– did not arise, there would be no need for the middle places, which are undoubtedly not introduced into propositional schemes as subject to the necessities of world-theoretical schemes. Their mission is defined in describing in detail and explaining, or possibly signifying, evaluating, interpreting, and encouraging since they are expressively inserted into a pulsating becoming. Thus, the previous argument could also be articulated in reverse, but with pragmatological additions, that is, those that make inevitable the cases and alternations that represent the dialectics of nature and history, as well as the approaches by man.
Next, it is pointed out that «ἕπεται ὁ τόπος ἀπὸ διαιρέσεων», which is examined in the following distinct dual role: «πᾶσα διαίρεσις ἢ ἀποφάσει γίνεται ἢ μερισμῷ». More precisely: on the one hand, every division is made by means of negation, as if an analyst has the prerequisites to formulate, for example, this logical-pragmatological schematization from the following two opposing perspectives: «πᾶν ζῶον ἢ ἔχει πόδας ἢ οὐκ ἔχει». This is an expression which does not pass through an intermediate state between the two extremes, the affirmative and the apophatic, a detail that requires attention in terms of the function of the middle places. On the other hand, as far as the separation is concerned, the division can be expressed in the following way: «πᾶς ἄνθρωπος ἢ ὑγιὴς ἐστιν ἢ νοσῶν», where the contrast between the predicates is maintained, but it is expressed in an affirmative mode.[11] Commenting on this, we would point out that the division is based (first and foremost) on the possibility of attributing a negative –in the sense of not possessing– characteristic of a noun or a pragmatological structure. Of course, in each case, it must be made clear if negation is intertwined with deprivation and of what kind, which implies that relativism is inevitable, or that this particular negation removes any pragmatological basis. On the other hand, there is also the opposite case: it is understood that the opposite of the negative can also be attributed, which, in fact, on the basis of the two examples given, is congenial under the pragmatological premises that can be ascertained in a particular case, to the noun, that is, to what objectively determines the constitutional articulations in the grammatical axis. Here, the division refers fundamentally to the distinction of possibilities or to some ontologically feasible formations-states, which are not only opposed to each other. They are also opposed to the modes of being or to the organismicity which they reveal.
The second case of division is the meristic one, according to the processes in which we separate the possible states which could occur in a being and which are permanently attributed categorically with a positive expressive sign but which are opposed to each other and, therefore, not coincidental at the same time in the same being, or in the same wider substantive field in a strictly concrete spacetime, which constitutes an individual topical identity. Here, a division emerges that has clearly pragmatological characteristics, which do not absolutely and exclusively determine a noun, but move in the region of possibility, which can arise from a variety of circumstances and, therefore, can be reflected in expressive cases. Generalizing, however, we could discuss the dialectics of nature, on the possibility of the existence of opposites, in the form of succession, of course, and not synchronicity, under the synthetic scheme that causes the observation of a subject on the basis of its idiosyncratic presence, which is characterized by its findings and by the historicity of its formation, which however is not typically linear. Ηowever, this presence could be generalized by the abstractive method on the proven representations and in their co-examination with other presences. In comparison, however, with «απόφασιν» it is clearly more comprehensible, since it refers to data which are, as a whole, subject to sensory experience.
Subsequently, the following sentence is formulated by means of specific reductions: «Γίνεται δὲ πᾶσα διαίρεσις ἢ ἀπὸ γένους εἰς εἴδη ἢ ὅλου εἰς μέρη ἢ φωνῆς εἰς οἰκεῖα σημαινόμενα ἢ συμβεβηκότος εἰς οὐσίαν ἢ συμβεβηκότων εἰς συμβεβηκότα».[12] The latter specification probably refers to the division of general accidents into individual ones, or their successive occurrence in a subject, with similarities that fit with it, which could also lead to their categorization as determinations. Thus, regarding the ways in which the division is carried out, the following are mentioned: A) T he transition from genus to species, with its process constituting a general categorical determination in the individual second, which will either appear simultaneously or successively, on the basis of either natural evolution, divine design, or divine plan, which directs evolution. B) From the whole to the parts of which it is composed or with which it manifests itself in terms of the organismicity proper to it, while also on the coexistence of the whole of them depends on its maintenance in existence or at least on its functional presence. C) From a verbal reference to those semantic elements, operating of course by references of a clearly non-neutral order, which are connected with it. This is an extension that reflects the potentialities of linguistic utterances, which are not, however, understood, here too, as merely expressive forms which would only aim at understanding, but also as responding to modes of existence of external reality. D) From the accident to the essence to which it is added, with the division clearly referring to a dynamocratic opening, to its multiple and multimodal presence according to the conditions or to the organismic absorptions each time, which form a new manifestation of the general ontic field, added to its infinite variety. E) From the essence to the accidents that are added to its substance or by which it reveals itself, a relation which refers to the open character of its presence, with what it contains, or what happens to it reflecting individual states of its structure or its inner richness. F) From accidents to accidents, a situation that will mainly be observed either under the type of succession or under the type of addition, with possibly both together or with variations accompanying and having the conditions apparently to be included in the structure of a categorical logical scheme, in all probability also renewable or open, provided that the evolutionary mode of operation of the becoming is taken into account.
Epilogue
According to what we have examined, we believe that we can come to the following three conclusions, one concerning the historical and two concerning the systematic branch of Philosophy, in a cultural environment –that of Christianity– where the theological tone is pervasive.
Ι] The translation of Boethius’ treatise De topicis differentiis by Manuel Holobolus highlights a tendency in the intellectual atmosphere of the late Byzantine world. This point takes on further meaning, since the treatment of topics of formal Logic is not merely inscribed in a perspective of theoretical philosophical performance, but also in the way of presenting properly and accurately its relationship to the external reality. That is, it is a matter of responsibility since the strictly structured reason attempts to remove surface approaches and to bring out the conditions which constitute situations, processes, communi-cations, valuations, interpretations, etc. As such, it penetrates the inner depths of daily life and explains it in terms of its actual facts. Thus, it is a theoretical work, which refers to broader cultural contexts.
II] Regardless of the variety of their versions, the middle places are founded expressively by what is defined as a case, which constitutes or forms both a morphological and a semantic category; the former referring to the competence of grammar and the latter to that of philosophy, without, however, this distinction being of absolute order and without excluding the inclusion of the former in the structural articulation of the latter as a subsystem of it. Either way, however, the case captures a leading intellectual attempt, which aims at projecting objectivity with regard to the descriptions performed. In fact, the flexibility that it presents with regard to its specializations also highlights the exodus from the strictly nominal or even authentically essential relationship between the subject, the predicate, and the emergence of those feasible relations that reflect particular pragmatological and theoretical contexts; that is, the case reveals the dialectical possibilities of the names in their encounter with those of things, from the perspective of an external environment with endless changes, both historical and physical.
III] The middle places are one of the “super weapons” of argumentation since they also refer to how methods –or constitutional structures within a propositional scheme– must be chosen and operated to provide the springboards to validate or refute a position. In their structure, they apply to both individual and universal scales of meaning and constitute wholes of meaning and signification of comparable intensity. In order for all these to take place, however, not only the artful functions of the human mind are required, but also their response to what philosophically belongs to the branch of Ontology –which includes being, becoming, and the representation of things. However, they must reflect on something similar in their reference to historical events. Thus, by using adverbs and adjectives, we can refer to the investigation of the categorical scale, which is not excluded from being polyvalent, even in a short sentence.
Our study was concise and followed the perspective of showing the interests of Western and Eastern Christianity, at least on a microcosmic scale. Boethius’ treatise has been shown by research and by its historical renewal to be of great philosophical importance, with the translation of Holobolus confirming it. Of course, both texts show how Christian thought has received Aristotelianism, which has fed it crucially, at least at the level of conceptual formulations, and in theologically oriented treatises. To confirm this, the writings of Leontius of Byzantium, John of Damascus and Thomas Aquinas should not be ignored as some leading examples.
[1] The Topics constitute a treatise which also specifies the ways of understanding the differences between terms and propositional schemes, while their contribution to the formation of categories is also noteworthy. For a systematic approach, we refer to the edition published by “Les Belles Lettres”, Paris 1967, with an introduction, French translation and commentary by M. J. Brunschwig.
[2] Boethius’ treatise De topicis differentiis has been published by the Academy of Athens in collaboration with the publishing houses “J. Vrin” and “Ousia” in 1990, with an introduction and a critical edition by Dimitrios Z. Nikitas, in the series “Corpus Philosophorum Medii Aevi”, vol. 5.
[3] The translation by Manuel Holobolus has been published in the same volume together with the translation by Prochoros Kydones. It should be noted that the research project of Dimitrios Z. Nikitas is of immense importance, both for its history and for its systematic approach. Apart from the great grammatical edition, his work is also characterized for its critical argumentation, which sheds light on particular aspects concerning the philosophical encounters of Eastern Christianity with Western Christianity.
[4] Cf. A. M. Severini Boetii, De topicis differentiis, II, 4, pp. 28-29 of the above. Manouel Holobolus, Βοετίου, περῖ τόπων διαλεκτικῶν, ΙΙ, 4, p. 115, of the above, where we read the following: «Πάντας τοίνυν τοὺς τόπους, ἤγουν τὰς τῶν μεγίστων προτάσεων διαφοράς, ἢ ἀπ’ αὐτῶν ἀγεσθαι τῶν ὄρων ἀνάγκη ἐστὶ τῶν ἐν τῷ προβλήματι κειμένων, ἢγουν τοῦ κατηγορουμένου τε καὶ ὑποκειμένου, ἢ ἔξωθεν λαμβάνεσθαι ἢ τούτων μέσον, αἱ καὶ ἐν αμφοτέροις στρέφονται» (115.22-26). Regarding the general content of the places, we refer to the following passage: : «Τόπος γοῦν ἐστιν, ὡς τῷ Μάρκῳ Τουλλίῳ δοκεῖ, ἐπιχειρήματος ἕδρα. Τοῦ γὰρ ἐπιχειρήματος ἕδρα ποτέ μέν ἡ μεγίστη πρότασις νοεῖσθαι πέφυκε, ποτὲ δὲ ἡ τῆς μεγίστης προτάσεων διαφορά» (112.27-30).
[5] Βοέτιου, περὶ τόπων διαλεκτικών (124.2-5). Cf. Aristotle, Topics, 106b29-107a2.
[6] It is a subject which has been extensively discussed by the Hellenistic, Neoplatonic and Neo-Aristotelian philosophical tradition that follows, as well as by contemporary research. We shall refer to the great study of L. Robin, La Théorie platonicienne des Idées et des Nombres d’apres Aristote: Étude Histoire et Critique, Heidelscheim 1998, originally written in 1906. It is a work which was a milestone in the Platonism-Aristotelianism relations-differences during the first period of their emergence, and which also highlighted the starting points of the constitution of Mathematics during that period, which –remarkably– included a famous personality, Eudoxus, who had a crucial influence on Euclid. It would not be an exaggeration if we said that with his impressive synthetic use of the sources and the excellent categorization of them –as well as with his emblematic articulations of interdisciplinarity–the above-mentioned researcher sealed the relevant scientific course up to modern times.
[7] Note that in his comments, Holobolus criticizes Boethius’ use of the relational adjective «συνεζευγμένα» and argues that Aristotle uses «σύστοιχα», a term which more accurately describes the emanation or multiplication of words of the same route from a common source. On the other hand, the former term refers to a process of meeting presumably a posteriori, which is not justified by the context here. Furthermore, the Byzantine thinker clarifies that in his references here Boethius has as his basis the passage 114a27-b2 of the Topics, where he specifies with further examples the «σύστοιχα», as with those derived from «ανδρείαν» and «υγείαν».
[8] This is a detail which is found in the above passage of the Topics, where Aristotle includes in the evaluative category of that which deserves to be praised the «δικαιοσύνη», the «δίκαιος», the «δίκαιον» and the «δικαίως», with the additional aim of showing that any predicate is attributed to the noun is also attributed to its etymological derivatives, with similar adaptations within the various prepositional schemes.
[9] Βοετίου, περὶ τόπων διαλεκτικῶν, 124.8-12. We should note that on the whole the development between the cognate words is characterized as «ὁμοίωσις» –and in Boethius we find it as “similitudis” in relation to the original name from which they come. Perhaps it would be more correct to use the term “similitudis”, which denotes the emanation from an original source, while «ὁμοίωσις» refers to the equalization which certain derivatives achieve with their common conceptual source. It is, to a great degree, a distinction between the a priori descending and the a posteriori ascending.
[10] Cf. Βοετίου, περὶ τόπων διαλεκτικῶν, 124.12-18.
[11] Βοετίου, περὶ τόπων διαλεκτικῶν, 124.18-22. The «ἀπόφασις» refers not so much to a denial but to the impossibility of attributing a predicate due to certain pragmatological necessities.
[12] Βοετίου, περὶ τόπων διαλεκτικῶν, 124.22-25. In other words, descending developments and ascents are included here, obviously determined each time by the way in which the specific pragmatological data are examined.
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