Category of being

In ontology, the different kinds or ways of being are called categories of being or simply categories. To investigate the categories of being is to determine the most fundamental and the broadest classes of entities. A distinction between such categories, in making the categories or applying them, is called an ontological distinction.

Introduction

The categories of being, or simply "the categories", are defined as the highest classes under which all elements of being whether material or conceptual can be classified. These categories belong to the realm of philosophy and the difference between categories and classes was described by the philosopher C.I. Lewis as that of a hierarchical tree or pyramid where the most general categories such as those of logic are to be found at the top and the least general classes such as species of animal at the bottom.[1] There are therefore two main areas of interest (i) at the top of the tree - how being first divides into discrete or overlapping subentities, and (ii) at the bottom of the tree - how the different elements can be correlated into higher classes. The structure may consist of a simple list such as the one produced by Aristotle[2] or it may be composed of headings and subheadings such as the tables produced by Immanuel Kant.[3] The elements of being are commonly seen as "things", whether objects or concepts, but most systems will also include as elements the relations between the objects and concepts. The distinction is also made between the elements themselves and the words used to denote such elements. The word "category" itself is derived from the Greek κατηγορία (katigoría), meaning to predicate, and therefore the categories may also be thought of as kinds of predicate which may be applied to any particular subject or element, and by extension to the concept of being itself.

If we take any subject and with it form a sentence "the subject is…" then in a valid system of categorisation all the different things we can say about the subject should be classifiable under one of the categories within the system. Aristotle listed ten categories amongst which we find, for example, the three categories of Substance, Quality and Quantity. In Heidegger’s example "This is a house. It is both red and tall" the word "house" can be classified under Substance, "red" under Quality and "tall" under Quantity.[4] The subject, the house, gathers around it what was called in the 19th century a "colligation of concepts"[5] or in the 20th century a "bundle of properties"[6] all of which serve to define the house. By extension we can say that all being consists of nothing but Substance, Quality, Quantity and the rest because nothing else can be said of the subject. Categorisation has raised many problems throughout the history of philosophy, including those of the number and types of category, how the categories interrelate with one another and whether they are real in some way or just mental constructs, and to introduce the many different solutions that have arisen it is worth considering the history of the categories in brief outline.

Early development

The process of abstraction required to discover the number and names of the categories has been undertaken by many philosophers since Aristotle and involves the careful inspection of each concept to ensure that there is no higher category or categories under which that concept could be subsumed. The scholars of the twelfth and thirteenth centuries developed Aristotle’s ideas, firstly, for example by Gilbert of Poitiers, dividing Aristotle's ten categories into two sets, primary and secondary, according to whether they inhere in the subject or not:

Secondly, following Porphyry’s likening of the classificatory hierarchy to a tree, they concluded that the major classes could be subdivided to form subclasses, for example, Substance could be divided into Genus and Species, and Quality could be subdivided into Property and Accident, depending on whether the property was necessary or contingent.[8] An alternative line of development was taken by Plotinus in the second century who by a process of abstraction reduced Aristotle’s list of ten categories to five: Substance, Relation, Quantity, Motion and Quality.[9] Plotinus further suggested that the latter three categories of his list, namely Quantity, Motion and Quality correspond to three different kinds of relation and that these three categories could therefore be subsumed under the category of Relation.[10] This was to lead to the supposition that there were only two categories at the top of the hierarchical tree, namely Substance and Relation, and if relations only exist in the mind as many supposed, to the two highest categories, Mind and Matter, reflected most clearly in the dualism of René Descartes.[11]

Modern development

An alternative conclusion however began to be formulated in the eighteenth century by Immanuel Kant who realised that we can say nothing about Substance except through the relation of the subject to other things.[12] In the sentence "This is a house" the substantive subject "house" only gains meaning in relation to human use patterns or to other similar houses. The category of Substance disappears from Kant’s tables, and under the heading of Relation, Kant lists inter alia the three relationship types of Disjunction, Causality and Inherence.[13] The three older concepts of Quantity, Motion and Quality, as Peirce discovered, could be subsumed under these three broader headings in that Quantity relates to the subject through the relation of Disjunction; Motion relates to the subject through the relation of Causality; and Quality relates to the subject through the relation of Inherence.[14] Sets of three continued to play an important part in the nineteenth century development of the categories, most notably in G.W.F.Hegel’s extensive tabulation of categories,[15] and in C.S.Peirce’s categories set out in his work on the logic of relations. One of Peirce’s contributions was to call the three primary categories Firstness, Secondness and Thirdness[16] which both emphasises their general nature, and avoids the confusion of having the same name for both the category itself and for a concept within that category.

In a separate development, and building on the notion of primary and secondary categories introduced by the Scholastics, Kant introduced the idea that secondary or "derivative" categories could be derived from the primary categories through the combination of one primary category with another.[17] This would result in the formation of three secondary categories: the first, "Community" was an example that Kant gave of such a derivative category; the second, "Modality", introduced by Kant, was a term which Hegel, in developing Kant’s dialectical method, showed could also be seen as a derivative category;[18] and the third, "Spirit" or "Will" were terms that Hegel[19] and Schopenhauer[20] were developing separately for use in their own systems. Karl Jaspers in the twentieth century, in his development of existential categories, brought the three together, allowing for differences in terminology, as Substantiality, Communication and Will.[21] This pattern of three primary and three secondary categories was used most notably in the nineteenth century by Peter Mark Roget to form the six headings of his Thesaurus of English Words and Phrases. The headings used were the three objective categories of Abstract Relation, Space (including Motion) and Matter and the three subjective categories of Intellect, Feeling and Volition, and he found that under these six headings all the words of the English language, and hence any possible predicate, could be assembled.[22]

Twentieth century development

In the twentieth century the primacy of the division between the subjective and the objective, or between mind and matter, was disputed by, among others, Bertrand Russell[23] and Gilbert Ryle.[24] Philosophy began to move away from the metaphysics of categorisation towards the linguistic problem of trying to differentiate between, and define, the words being used. Ludwig Wittgenstein’s conclusion was that there were no clear definitions which we can give to words and categories but only a "halo" or "corona"[25] of related meanings radiating around each term. Gilbert Ryle thought the problem could be seen in terms of dealing with "a galaxy of ideas" rather than a single idea, and suggested that category mistakes are made when a concept (e.g. "university"), understood as falling under one category (e.g. abstract idea), is used as though it falls under another (e.g. physical object).[26] With regard to the visual analogies being used, Peirce and Lewis,[27] just like Plotinus earlier,[28] likened the terms of propositions to points, and the relations between the terms to lines. Peirce, taking this further, talked of univalent, bivalent and trivalent relations linking predicates to their subject and it is just the number and types of relation linking subject and predicate that determine the category into which a predicate might fall.[29] Primary categories contain concepts where there is one dominant kind of relation to the subject. Secondary categories contain concepts where there are two dominant kinds of relation. Examples of the latter were given by Heidegger in his two propositions "the house is on the creek" where the two dominant relations are spatial location (Disjunction) and cultural association (Inherence), and "the house is eighteenth century" where the two relations are temporal location (Causality) and cultural quality (Inherence).[30] A third example may be inferred from Kant in the proposition "the house is impressive or sublime" where the two relations are spatial or mathematical disposition (Disjunction) and dynamic or motive power (Causality).[31] Both Peirce and Wittgenstein[32] introduced the analogy of colour theory in order to illustrate the shades of meanings of words. Primary categories, like primary colours, are analytical representing the furthest we can go in terms of analysis and abstraction and include Quantity, Motion and Quality. Secondary categories, like secondary colours, are synthetic and include concepts such as Substance, Community and Spirit.

Categorical distinctions

The common or dominant ways to view categories as of the end of the 20th century.

  1. via bundle theory as bundles of properties—categories reflect differences in these
  2. via peer-to-peer comparisons or dialectics—categories are formed by conflict/debate
  3. via value theory as leading to specific ends—categories are formed by choosing ends
  4. via conceptual metaphors as arising from characteristics of human cognition itself—categories are found via cognitive science and other study of that biological system

Any of these ways can be criticized for...

In process philosophy, this last is the only possibility, but historically philosophers have been loath to conclude that nothing exists but process.

Categorization of existence

As bundles of properties

Bundle theory is an ontological theory about objecthood proposed by the 18th century Scottish philosopher David Hume, which states that objects only subsist as a collection (bundle) of properties, relations or tropes. In an epistemological sense, bundle theory says that all that can be known about objects are the properties which they are composed of, and that these properties are all that can be truly said to exist.

For example, if we take the concept of a black square, bundle theory would suggest that all that can be said to exist are the properties of a black square.

The properties of a black square are: Black, Regular, and Quadrilateral.

However, from these properties alone, we cannot deduce any kind of underlying essence of a "black square", or some object called a "black square", except as a bundle of properties which constitute the object that we then go on to label as a "black square", but the object itself is really nothing more than a system of relations (or bundle) of properties. To defend this, Hume asks us to imagine an object without properties, if we strip the black square of its properties (being black, regular and quadrilateral) we end up reducing the object to non-existence.

Intuition as evasion

A seemingly simpler way to view categories is as arising only from intuition. Philosophers argue this evades the issue. What it means to take the category physical object seriously as a category of being is to assert that the concept of physical objecthood cannot be reduced to or explicated in any other terms—not, for example, in terms of bundles of properties but only in terms of other items in that category.

In this way, many ontological controversies can be understood as controversies about exactly which categories should be seen as fundamental, irreducible, or primitive. To refer to intuition as the source of distinctions and thus categories doesn't resolve this.

Ideology, dogma, and theory

Modern theories give weight to intuition, perceptually observed properties, comparisons of categories among persons, and the direction of investigation towards known specified ends, to determine what humanity in its present state of being needs to consider irreducible. They seek to explain why certain beliefs about categories would appear in political science as ideology, in religion as dogma, or in science as theory.

As metaphors

A set of ontological distinctions related by a single conceptual metaphor was called an ontological metaphor by George Lakoff and Mark Johnson, who claimed that such metaphors arising from experience were more basic than any properties or symbol-based comparisons. Their cognitive science of mathematics was a study of the embodiment of basic symbols and properties including those studied in the philosophy of mathematics, via embodied philosophy, using cognitive science. This theory comes after several thousand years of inquiry into patterns and cognitive bias of humanity.

Categories of being

Philosophers have many differing views on what the fundamental categories of being are. In no particular order, here are at least some items that have been regarded as categories of being by someone or other:

Physical objects

Physical objects are beings; certainly they are said to be in the simple sense that they exist all around us. So a house is a being, a person's body is a being, a tree is a being, a cloud is a being, and so on. They are beings because, and in the sense that, they are physical objects. One might also call them bodies, or physical particulars, or concrete things, or matter, or maybe substances (but bear in mind the word 'substance' has some special philosophical meanings).

Minds

Minds—those "parts" of us that think and perceive—are considered beings by some philosophers. Each of us, according to common sense anyway, "has" a mind. Of course, philosophers rarely just assume that minds occupy a different category of beings from physical objects. Some, like René Descartes, have thought that this is so (this view is known as dualism, and functionalism also considers the mind as distinct from the body), while others have thought that concepts of the mental can be reduced to physical concepts (this is the view of physicalism or materialism). Still others maintain though "mind" is a noun, it is not necessarily the "name of a thing" distinct within the whole person. In this view the relationship between mental properties and physical properties is one of supervenience – similar to how "banks" supervene upon certain buildings.

Classes

We can talk about all human beings, and the planets, and all engines as belonging to classes. Within the class of human beings are all of the human beings, or the extension of the term 'human being'. In the class of planets would be Mercury, Venus, the Earth, and all the other planets that there might be in the universe. Classes, in addition to each of their members, are often taken to be beings. Surely we can say that in some sense, the class of planets is, or has being. Classes are usually taken to be abstract objects, like sets; 'class' is often regarded as equivalent, or nearly equivalent, in meaning to 'set'. Denying that classes and sets exist is the contemporary meaning of nominalism.

Properties

The redness of a red apple, or more to the point, the redness all red things share, is a property. One could also call it an attribute of the apple. Very roughly put, a property is just a quality that describes an object. This will not do as a definition of the word 'property' because, like 'attribute', 'quality' is a near-synonym of 'property'. But these synonyms can at least help us to get a fix on the concept we are talking about. Whenever one talks about the size, color, weight, composition, and so forth, of an object, one is talking about the properties of that object. Some—though this is a point of severe contention in the problem of universals—believe that properties are beings; the redness of all apples is something that is. To deny that universals exist is the scholastic variant of nominalism.

Note that the color red is an objective property of an object. The intrinsic property is that it reflects radiation (including light) in a certain way. A human perceives that as the color red in his or her brain. An object thus has two types of properties, intrinsic (physical) and objective (observer specific).

Relations

An apple sitting on a table is in a relation to the table it sits on. So we can say that there is a relation between the apple and the table: namely, the relation of sitting-on. So, some say, we can say that that relation has being. For another example, the Washington Monument is taller than the White House. Being-taller-than is a relation between the two structures. We can say that that relation has being as well. This, too, is a point of contention in the problem of universals.


Space and time

Space and time are what physical objects are extended into. There is debate as to whether time exists only in the present or whether far away times are just as real as far away spaces, and there is debate (among who?) as to whether space is curved. Many (nearly all?) contemporary thinkers actually suggest that time is the fourth dimension, thus reducing space and time to one distinct ontological entity, the space-time continuum.

Propositions

Propositions are units of meaning. They should not be confused with declarative sentences, which are just sets of words in languages that refer to propositions. Declarative sentences, ontologically speaking, are thus ideas, a property of substances (minds), rather than a distinct ontological category. For instance, the English declarative sentence "snow is white" refers to the same proposition as the equivalent French declarative sentence "la neige est blanche"; two sentences, one proposition. Similarly, one declarative sentence can refer to many propositions; for instance, "I am hungry" changes meaning (i.e. refers to different propositions) depending on the person uttering it.

Events

Events are that which can be said to occur. To illustrate, consider the claim "John went to a ballgame"; if true, then we must ontologically account for every entity in the sentence. "John" refers to a substance. But what does "went to a ballgame" refer to? It seems wrong to say that "went to a ballgame" is a property that instantiates John, because "went to a ballgame" does not seem to be the same ontological kind of thing as, for instance, redness. Thus, events arguably deserve their own ontological category.

Properties, relations, and classes are supposed to be abstract, rather than concrete. Many philosophers say that properties and relations have an abstract existence, and that physical objects have a concrete existence. That, perhaps, is the paradigm case of a difference in ways in which items can be said to be, or to have being.

Many philosophers have attempted to reduce the number of distinct ontological categories. For instance, David Hume famously regarded Space and Time as nothing more than psychological facts about human beings, which would effectively reduce Space and Time to ideas, which are properties of humans (substances). Nominalists and realists argue over the existence of properties and relations. Finally, events and propositions have been argued to be reducible to sets (classes) of substances and other such categories.

History

Aristotle

One of Aristotle’s early interests lay in the classification of the natural world, how for example the genus "animal" could be first divided into "two-footed animal" and then into "wingless, two-footed animal".[33] He realised that the distinctions were being made according to the qualities the animal possesses, the quantity of its parts and the kind of motion that it exhibits. To fully complete the proposition "this animal is…" Aristotle stated in his work on the Categories that there were ten kinds of predicate where...

"…each signifies either substance or quantity or quality or relation or where or when or being-in-a-position or having or acting or being acted upon".[34]

He realised that predicates could be simple or complex. The simple kinds consist of a subject and a predicate linked together by the "categorical" or inherent type of relation. For Aristotle the more complex kinds were limited to propositions where the predicate is compounded of two of the above categories for example "this is a horse running". More complex kinds of proposition were only discovered after Aristotle by the Stoic, Chrysippus,[35] who developed the "hypothetical" and "disjunctive" types of syllogism and these were terms which were to be developed through the Middle Ages[36] and were to reappear in Kant’s system of categories.

Category came into use with Aristotle's essay Categories, in which he discussed univocal and equivocal terms, predication, and ten categories:[37]

Plotinus

Plotinus in writing his Enneads around AD 250 recorded that "philosophy at a very early age investigated the number and character of the existents… some found ten, others less…. to some the genera were the first principles, to others only a generic classification of existents".[38] He realised that some categories were reducible to others saying "why are not Beauty, Goodness and the virtues, Knowledge and Intelligence included among the primary genera?"[39] He concluded that such transcendental categories and even the categories of Aristotle were in some way posterior to the three Eleatic categories first recorded in Plato's dialogue Parmenides and which comprised the following three coupled terms:

Plotinus called these "the hearth of reality"[41] deriving from them not only the three categories of Quantity, Motion and Quality but also what came to be known as "the three moments of the Neoplatonic world process":

Plotinus likened the three to the centre, the radii and the circumference of a circle, and clearly thought that the principles underlying the categories were the first principles of creation. "From a single root all being multiplies". Similar ideas were to be introduced into Early Christian thought by, for example, Gregory of Nazianzus who summed it up saying "Therefore Unity, having from all eternity arrived by motion at duality, came to rest in trinity".[43]

Kant

In the Critique of Pure Reason (1781), Immanuel Kant argued that the categories are part of our own mental structure and consist of a set of a priori concepts through which we interpret the world around us.[44] These concepts correspond to twelve logical functions of the understanding which we use to make judgements and there are therefore two tables given in the Critique, one of the Judgements and a corresponding one for the Categories.[45] To give an example, the logical function behind our reasoning from ground to consequence (based on the Hypothetical relation) underlies our understanding of the world in terms of cause and effect (the Causal relation). In each table the number twelve arises from, firstly, an initial division into two: the Mathematical and the Dynamical; a second division of each of these headings into a further two: Quantity and Quality, and Relation and Modality respectively; and, thirdly, each of these then divides into a further three subheadings as follows.

Table of Judgements

Mathematical

  • Quantity
    • Universal
    • Particular
    • Singular
  • Quality
    • Affirmative
    • Negative
    • Infinite

Dynamical

  • Relation
    • Categorical
    • Hypothetical
    • Disjunctive
  • Modality
    • Problematic
    • Assertoric
    • Apodictic

Table of Categories

Mathematical

Dynamical

Criticism of Kant’s system followed, firstly, by Arthur Schopenhauer, who amongst other things was unhappy with the term "Community", and declared that the tables "do open violence to truth, treating it as nature was treated by old-fashioned gardeners",[46] and secondly, by W.T.Stace who in his book The Philosophy of Hegel suggested that in order to make Kant’s structure completely symmetrical a third category would need to be added to the Mathematical and the Dynamical.[47] This, he said, Hegel was to do with his category of Notion.

Hegel

G.W.F. Hegel in his Science of Logic (1812) attempted to provide a more comprehensive system of categories than Kant and developed a structure that was almost entirely triadic.[48] So important were the categories to Hegel that he claimed "the first principle of the world, the Absolute, is a system of categories… the categories must be the reason of which the world is a consequent".[49] Using his own logical method of combination, later to be called the Hegelian dialectic, of arguing from thesis through antithesis to synthesis, he arrived, as shown in W.T.Stace's work cited, at a hierarchy of some 270 categories. The three very highest categories were Logic, Nature and Spirit. The three highest categories of Logic, however, he called Being, Essence and Notion which he explained as follows:

Schopenhauer’s category that corresponded with Notion was that of Idea, which in his "Four-Fold Root of Sufficient Reason" he complemented with the category of the Will.[51] The title of his major work was "The World as Will and Idea". The two other complementary categories, reflecting one of Hegel’s initial divisions, were those of Being and Becoming. Interestingly, at around the same time, Goethe was developing his colour theories in the Farbenlehre of 1810, and introduced similar principles of combination and complementation, symbolising, for Goethe, "the primordial relations which belong both to nature and vision".[52] Hegel in his Science of Logic accordingly asks us to see his system not as a tree but as a circle.

Peirce

Charles Sanders Peirce, who had read Kant and Hegel closely, and who also had some knowledge of Aristotle, proposed a system of merely three phenomenological categories: Firstness, Secondness, and Thirdness, which he repeatedly invoked in his subsequent writings. Like Hegel, C.S.Peirce attempted to develop a system of categories from a single indisputable principle, in Peirce’s case the notion that in the first instance he could only be aware of his own ideas. "It seems that the true categories of consciousness are first, feeling… second, a sense of resistance… and third, synthetic consciousness, or thought".[53] Elsewhere he called the three primary categories: Quality, Reaction and Meaning, and even Firstness, Secondness and Thirdness, saying, "perhaps it is not right to call these categories conceptions, they are so intangible that they are rather tones or tints upon conceptions":[54]

Although Peirce’s three categories correspond to the three concepts of relation given in Kant’s tables, the sequence is now reversed and follows that given by Hegel, and indeed before Hegel of the three moments of the world-process given by Plotinus. Later, Peirce gave a mathematical reason for there being three categories in that although monadic, dyadic and triadic nodes are irreducible, every node of a higher valency is reducible to a "compound of triadic relations".[56] Ferdinand de Saussure, who was developing "semiology" in France just as Peirce was developing "semiotics" in the USA, likened each term of a proposition to "the centre of a constellation, the point where other coordinate terms, the sum of which is indefinite, converge".[57]

Others

Edmund Husserl (1962, 2000) wrote extensively about categorial systems as part of his phenomenology.

For Gilbert Ryle (1949), a category (in particular a "category mistake") is an important semantic concept, but one having only loose affinities to an ontological category.

Contemporary systems of categories have been proposed by John G. Bennett (The Dramatic Universe, 4 vols., 1956–65), Wilfrid Sellars (1974), Reinhardt Grossmann (1983, 1992), Johansson (1989), Hoffman and Rosenkrantz (1994), Roderick Chisholm (1996), Barry Smith (ontologist) (2003), and Jonathan Lowe (2006).

See also

References

  1. ↑ Lewis C.I. Mind and the World Order 1929, pp.233-234
  2. ↑ Aristotle Categories in Aristotle’s Categories and De Interpretatione (tr. Ackrill J.L. Clarendon Press, Oxford, 1963) Ch.4
  3. ↑ Kant I. Critique of Pure Reason 1781 (tr. Smith N.K., Macmillan, London, 1968)
  4. ↑ Heidegger M. What is a Thing 1935 (tr. Barton W. & Deutsch V. Henry Regnery, Chicago, 1967) pp.62,187
  5. ↑ Peirce C.S. Collected Papers of Charles Sanders Peirce (Hartshorne C. & Weiss P. (eds) Harvard University Press, 1931) Vol.2, p.267
  6. ↑ cf Locke J. Essay concerning Human Understanding (J.F.Dove, London, 1828) p.371 on “coexistence of qualities”
  7. ↑ Reese W.L. Dictionary of Philosophy and Religion (Harvester Press, 1980)
  8. ↑ Ibid. cf Evangelou C. Aristotle’s Categories and Porphyry (E.J.Brill, Leiden, 1988)
  9. ↑ Plotinus Enneads (tr. Mackenna S. & Page B.S., The Medici Society, London, 1930) VI.3.3
  10. ↑ Ibid. VI.3.21
  11. ↑ Descartes R. The Philosophical Works of Descartes (tr. Haldane E. & Ross G., Dover, New York, 1911) Vol.1
  12. ↑ Op.cit.3 p.87
  13. ↑ Ibid. pp.107,113
  14. ↑ Op.cit.5 pp.148-179
  15. ↑ Stace W.T. The Philosophy of Hegel (Macmillan & Co, London, 1924)
  16. ↑ Op.cit.5 pp.148-179
  17. ↑ Op.cit.3 p.116
  18. ↑ Hegel G.W.F. Logic (tr. Wallace W., Clarendon Press, Oxford, 1975) pp.124ff
  19. ↑ Op.cit.15
  20. ↑ Schopenhauer A. On the Four-Fold Root of the Principle of Sufficient Reason 1813 (tr. Payne E., La Salle, Illinois, 1974)
  21. ↑ Jaspers K. Philosophy 1932 (tr. Ashton E.B., University of Chicago Press, 1970) pp.117ff
  22. ↑ Roget P.M. Roget’s Thesaurus: The Everyman Edition 1952 (Pan Books, London, 1972)
  23. ↑ Russell B. The Analysis of Mind (George Allen & Unwin, London, 1921) pp.10,23
  24. ↑ Ryle G. The Concept of Mind (Penguin, Harmondsworth, 1949) pp.17ff
  25. ↑ Wittgenstein L. Philosophical Investigations 1953 (tr. Anscombe G., Blackwell, Oxford, 1978) pp.14,181
  26. ↑ Ryle G. Collected Papers (Hutchinson, London, 1971) Vol.II: Philosophical Arguments 1945, pp.201,202
  27. ↑ Op.cit.1 pp.52,82,106
  28. ↑ Op.cit.9 VI.5.5
  29. ↑ Op.cit.5 Vol I pp.159,176
  30. ↑ Op.cit.4 pp.62,187
  31. ↑ Kant I. Critique of Judgement 1790 (tr. Meredith J.C., Clarendon Press, Oxford 1952) p.94ff
  32. ↑ Op.cit.25 pp.36,152
  33. ↑ Aristotle Metaphysics 1075a
  34. ↑ Op.cit.2
  35. ↑ Long A. & Sedley D. The Hellenistic Philosophers (Cambridge University Press, 1987) p.206
  36. ↑ Peter of Spain (alias John XXI) Summulae Logicales
  37. ↑ Categories, translated by E. M. Edghill. For the Greek terms, see The Complete Works of Aristotle in Greek (requires DjVu), Book 1 (Organon), Categories Section 4 (DjVu file's page 6). Archived November 2, 2013, at the Wayback Machine.
  38. ↑ Op.cit.9 VI.1.1
  39. ↑ Ibid. VI.2.17
  40. ↑ Plato Parmenides (tr. Jowett B., The Dialogues of Plato, Clarendon Press, Oxford, 1875) p.162
  41. ↑ Op.cit.9 Op.cit.1.4
  42. ↑ Ibid. III.8.5
  43. ↑ Rawlinson A.E. (ed.) Essays on the Trinity and the Incarnation (Longmans, London, 1928) pp.241-244
  44. ↑ Op.cit.3 p.87
  45. ↑ Ibid. pp.107,113
  46. ↑ Schopenhauer A. The World as Will and Representation (tr. Payne A., Dover Publications, London, New York, 1966) p.430
  47. ↑ Op.cit.15 p.222
  48. ↑ Ibid.
  49. ↑ Ibid. pp.63,65
  50. ↑ Op.cit.18 pp.124ff
  51. ↑ Op.cit.20
  52. ↑ Goethe J.W. von, The Theory of Colours (tr. Eastlake C.L., MIT Press, Cambridge, Mass., 1970) p.350
  53. ↑ Op.cit.5 p.200, cf Locke
  54. ↑ Ibid. p.179
  55. ↑ Ibid. pp.148-179
  56. ↑ Ibid. p.176
  57. ↑ Saussure F. de,Course in General Linguistics 1916 (tr. Harris R., Duckworth, London, 1983) p.124

Selected bibliography

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