One hundred years ago, Edmund Husserl was perhaps the first philosopher to pay any interest to the formal treatment of some of the most fundamental questions of ontology. Powerful tools of logic were developed in those days, and this new development inspired in a natural way various attempts to use these techniques within this prestigious area of philosophical inquiry. Through Husserl's younger colleague, Roman Ingarden, and in the light of related ideas of Leśniewski and other members of Lwow-Warsaw School, these ideas spread rapidly, particularly in the Polish scientific community.

 

Philosophical inquiries into ontology in an advanced formal setting were put forward first by Stanislaw Leśniewski. Inspired by the contemporary discussion on the foundations of mathematics, Leśniewski was interested in finding a formal framework appropriate for the ontological grounding of both mathematics and logic. The basic system was Mereology, i.e. the general theory of collective sets. Ontology itself arises from Protothetic. All his axiomatic systems came about in an elegant yet somewhat exotic notation. (1) Leśniewski's mereology was intended to play the part of an alternative to set theory. Later -- as an axiomatic 'calculus of individuals' -- it appears to be a proper extension of set theory rather than a competitive calculus.

 

Thomas Mormann's article Topological Representations of Mereological Systems (2) can be seen as a recent example of that line of research. He shows that nothing is lost when a reasonable mereological system is substituted by its topological model. That brings mereology into contact with well developed mathematical theories and may help mereology, as Mormann concludes, "to leave its present state of theoretical immaturity". In any case, mereology can be treated as a contribution to formal ontology only if it carries a meaningful theory of (the construction of) universes. The same holds for (pure) set theory itself, which is sometimes taken to be the most usable and convenient base for any formal ontological system (cf. Quine's discussion of this topic in various places, and for several other approaches see e.g. Poli and Simons (eds.), Formal Ontology Dordrecht: Kluwer, 1996; Scheffler and Urchs, "Ontologic. Essays on Formal Ontology", Logic and Logical Philosophy, Torun, Copernicus University Press, vol. 2, 1995)." (p. 11)

 

Notes

(1) Tadeusz Kotarbinski served as a faithful translator of Leśniewski's rather esoteric writings for the broader public. Most of Leśniewski's successors both within and outside the Lwow-Warsaw School set out their own considerations on formal ontology in the spirit of his systems. They often, however, use Kotarbinski's explication of these ideas.

(2) [Same volume, pp. 463-486].

 

From: Jan Faye, Uwe Scheffler and Max Urchs, Philosophical Entities. An Introduction, in: Jan Faye, Uwe Scheffler and Max Urchs (eds.), Things, Facts and Events, Amsterdam: Rodopi 2000, pp. 1-64.

 

There are three occurrences of the term ontologia in Leibniz:

Ontologiam seu scientiam de Aliquo et Nihilo, Ente et Non ente, Re et modo rei, Substantia et Accidente (Ontology or the science of something and of nothing, of Being and not-being, of the thing and the mode of the thing, of substance and accident.)

 

From: Louis Couturat, Opuscules et fragments inédits de Leibniz, Paris: Alcan 1903. Reprinted Hildesheim: Georg Olms 1961, p. 512 (Introductio ad Encyclopaediam Arcanam) (Now in: G. W. Leibniz Sämtliche Schriften und Briefe, VI Sektion: Philosophische Schriften, Band IV, Text n. 126 p. 527.)

 

In a fragment titled by the Editors De duobus systematis scientiarum (1693?) on the classification of books in a library Leibniz in a deleted paragraph wrote: Philosophici doppelt unterstr. (aaaa) Dida (bbbb) Logicam, Mnem (cccc) Didacticam, (aaaaa) Mnemonicam, (bbbbb) Logicam (aaaaaa) Rhet (bbbbbb) oratoriam seu (aaaaaaa) Persuasoriam (bbbbbbb) partem Rhetoricae persuasoriam, Mnemonicam; (aaaaaaaa) Metaphysicam, (bbbbbbbb) Ontologiam. (Sämtliche Schriften und Briefe, Akademie Verlag, Berlin 2004, Reihe IV, Bd. V, p. 592, ad. l. 25.

 

The third occurrence was published by Nicholas Jolley, An Unpublished Leibniz MS on Metaphysics, Studia Leibnitiana, 7 (1975), 2, p. 179, l. 81 and var. ad l. 81: Scientiam autem genera lis quam vulgo Ontolog (But the science of genera is a matter which is commonly called Ontolog), but he later altered his text to read: Scientia autem generalis quam dicam Metaphysicam vocant (But the general science which I shall call Metaphysics).

 

(See: Michaël Devaux, Marco Lamanna, The Rise and Early History of the Term Ontology (1606-1730), Quaestio. Yearbook of the History of the Metaphysics, 9, 2009, pp. 173-208 (on Leibniz see pp. 197-198).

 

If you wish to study philosophy fruitfully, then logic must be given the very first place. Logic treats the rules which direct the cognitive faculty to the knowledge of truth. Now we should study philosophy in such a way as to acquire complete certitude. Hence, he who studies philosophy should know how to proceed in the knowledge of truth. Consequently, he should be acquainted with logic. Hence, logic must be given the very first place.

 

It might also be mentioned that those who are beginning in philosophy overcome their inexperience by studying logic. We have already given the reason for this. He who is unacquainted with logic does not know how to examine definitions and demonstrations with rigor. Therefore, he easily admits as certain things which greatly disagree with evidence. And he often thinks he understands things which he has not examined.

 

However, if everything in logic is to be demonstrated, then principles must be borrowed from ontology and psychology. Logic treats of the rules which direct the intellect in the knowledge of all Being, for the definition of logic does not restrict it to any species of Being; therefore, it ought to teach us what to look for in order to know things. Now that which pertains to the general knowledge of Being is derived from ontology. Hence it is clear that, in order to demonstrate the rules of logic, principles must be taken from ontology.

 

Furthermore, since logic explains how to direct the intellect in the knowledge of truth, it ought to teach how the operations of the intellect are used in knowing truth. Now we must learn from psychology what the cognitive faculty is and what its operations are. Hence it is also clear that, in order to demonstrate the rules of logic, principles must be taken from psychology.

 

This will be clearer when you have learned logic and have compared it with ontology and psychology. We have experienced this many times while carefully investigating the rules of logic and their reasons.

 

If all things in logic are to be rigorously demonstrated with genuine proofs, then logic must come after ontology and psychology. Logic derives its principles from ontology and psychology. Now the parts of philosophy should be ordered in such a way that those parts come first which provide principles for other parts. Therefore, ontology and psychology should precede logic if everything in logic is to be rigorously demonstrated and if its rules are to be genuinely proven.

 

Demonstrative method requires that logic be treated after ontology and psychology. However, the process of learning requires that logic precede all the other parts of philosophy, including ontology and psychology. Both methods cannot be observed. Weighing this more carefully, we should realize that he who does not know logic cannot be usefully acquainted with ontology and psychology. However, the principles of ontology and psychology which pertain to logic can be easily explained in logic. Therefore, we choose the method of learning in preference to the method of demonstration.

 

Another reason why this approach is preferable is that ontological principles are definitions and psychological principles are established from experience. Consequently, ontological principles can be understood and admitted as true, even though the other things which are treated in ontology have not yet been examined. And the presuppositions of logic which can be demonstrated in psychology can be grasped a posteriori. (p. 17)

 

Philosophy is the science of the possibles insofar as they can be. (ibid., pp. 39-40)

 

There are some things which are common to all beings and which are predicated both of souls and of natural and artificial bodies. That part of philosophy which treats of Being in general and of the general affections of Being is called ontology, or first philosophy. Thus, ontology, or first philosophy, is defined as the science of Being in general, or insofar as it is Being.

 

Such general notions are the notions of essence, existence, attributes, modes, necessity, contingency, place, time, perfection, order, simplicity, composition, etc. These things are not explained properly in either psychology or physics because both of these sciences, as well as the other parts of philosophy, use these general notions and the principles derived from them. Hence, it is quite necessary that a special part of philosophy be designated to explain these notions and general principles, which are continually used in every science and art, and even in life itself, if it is to be rightly organized. Indeed, without ontology, philosophy cannot be developed according to the demonstrative method. Even the art of discovery takes its principles from ontology. (ibid., pp. 45-46)

 

From: Christian Wolff, Preliminary Discourse on Philosophy in General 1728), translated, with an introduction and notes, by Richard J. Blackwell, Indianapolis: The Bobbs-Merrill Company, Inc. 1963.

 

Prolegomena to Metaphysics [ 1-3]

1. METAPHYSICS is the science of first principles in human cognition.

2. Ontology, cosmology, psychology, and natural theology belong to metaphysics.

3. NATURAL METAPHYSICS is the cognition of matters treated in metaphysics that are attained through the mere use of these matters. If artificial [metaphysics] explained in 1 is also added to it, then it is useful (1) for the development of its concepts, (2) for the determination and conception of its first principles, and (3) for the continuation and certainty of its proofs, etc.

 

PART ONE: ONTOLOGY [ 4-35c]

Prolegomena [ 4-6]

4. ONTOLOGY (ontosophy, metaphysics, cf. 1, universal metaphysics, architectonic, first philosophy) is the science of the general predicates of a thing.

5. The predicates of a thing that are more general are the first principles of human cognition, thus ontology belongs ( 2), with reason, to metaphysics ( 1, 4).

6. Ontology contains the predicates of a thing ( 4), (I) [that are] internal, (I) universal, which are in each thing, (2) disjunctive, one of which is in each thing; (II) relative.” (p. 89)

 

Translated from Alexander Baumgarten, Metaphysica (Frankfurt, 1757, 4th ed., 1739 1st ed.), reprinted at 15:4-54 and 17:23-226 of Immanuel Kant's Gesammelte Schriften (Berlin: Königlich-Preussischen Akademe der Wissenschaften zu Berlin, 1902-).

 

From: Eric Watkins, Kant's Critique of Pure Reason. Background Sources Materials, Cambridge: Cambridge University Press 2009.

 

In the course of the present semester which has just begun, I propose to hold private lectures on the following science, which I intend to handle in an exhaustive fashion.

 

1. Metaphysics. (...) I hope that I shall be able in the near future to present a complete account of what may serve as the foundation of my lectures in the aforementioned science. Until that time, however, I can easily, by applying gentile pressure, induce A. G. Baumgarten, the author of the text book on which this course will be based [the Metaphysica (1739)] -- and that book has been chosen chiefly for the richness of its contents and the precision of its method -- to follow the same path. Accordingly, after a brief introduction, I shall begin with empirical psychology, which is really the metaphysical science of man based on experience. (...)The second part of the course will discuss corporeal nature in general. (...) Since everything in the world can be subsumed under these two classes [organic and inorganic], I shall then proceed to ontology, the science, namely, which is concerned with the more general properties of all things. (pp. 294-295)

 

From: M. Immanuel Kant's Announcement of the Programme of His Lectures for the Winter Semester 1765-1766, translated and edited by David Walford in collaboration with Ralf Meerbote in: Immanuel Kant, Theoretical Philosophy 1755-1770, Cambridge: Cambridge University Press 1992.

---

The Transcendental Analytic accordingly has this important result: That the understanding can never accomplish a priori anything more than to anticipate the form of a possible experience in general, and, since that which is not appearance cannot be an object of experience, it can never overstep the limits of sensibility, within which alone objects are given too us. Its principles are merely principles of the exposition of appearances, and the proud name of an ontology, which presumes to offer synthetic a priori cognitions of things in general in a systematic doctrine (e.g., the principle of causality), must give way to the modest one of a mere analytic of the pure understanding. ( A 247 / B 303)" (p. 345)

 

From: Immanuel Kant, Critique of Pure Reason, translated and edited by Paul Guyer and Allen W. Wood, Cambridge: Cambridge University Press 1998.

---

Thus all pure a priori cognition, by means of the special faculty of cognition in which alone it can have its seat, constitutes a special unity, and metaphysics is that philosophy which is to present that cognition in this systematic unity. Its speculative part, to which this name has been especially appropriated, namely that which we call metaphysics of nature and which considers everything insofar as it is (not that which ought to be) on the basis of a priori concepts, is divided in the following way. (a)

 

Metaphysics in this narrower sense consists of transcendental philosophy and the physiology of pure reason. The former considers only the understanding and reason itself in a system of all concepts and principles that are related to objects in general, without assuming objects that would be given (Ontologia); the latter considers nature, i.e., the sum total of given objects (whether they are given by the senses or, if one will, by another kind of intuition), and is therefore physiology (though only rationalis). (A 845 / B 873)"

 

(a) Inserted in Kant's copy of the first edition:

 

I would divide it in accordance with the classes of the categories, so that in the third category, which contains the other two, yields the idea of the science:

 

1. General ontology [Allgemeine Wesenlehre]; 2. Theory of nature; 3. Cosmology [Weltwissenschaft]; 4. Theology." (E CLXXXIII, p. 54; 23:43). This is the last emendation Kant made in his copy of the first edition.

 

Accordingly, the entire system of metaphysics consists of four main parts. 1. Ontology. 2. Rational Physiology. 3. Rational Cosmology. 4. Rational Theology. The second part, namely the doctrine of nature of pure reason, contains two divisions, physica rationalis and psychologia rationalis. (A 847 / B 875)" (pp. 698-699)

 

From: Immanuel Kant, Critique of Pure Reason (1781), translated and edited by Paul Guyer and Allen W. Wood, Cambridge: Cambridge University Press 1998.

---

We now begin the science of the properties of all things in general, which is called ontology. One easily comprehends that it will contain nothing but all basic concepts and basic propositions of our a priori cognition in general: for if it is to consider the properties of all things, then it has as an object nothing but a thing in general, i.e., every object of thought, thus no determinate object. Thus nothing remains for me other than the cognizing, which I consider. (The science that deals with objects in general, will deal with nothing but those concepts through which the understanding thinks, thus of the nature of the understanding and of reason, insofar as it cognizes something a priori. - That is transcendental philosophy, which does not say something a priori of objects, but rather investigates the faculty of the understanding or of reason for cognizing something a priori; thus with regard to content it is a self-cognition of the understanding or of reason, just as logic is a self-cognition of the understanding and of reason with regard to form; the critique of pure reason belongs necessarily to transcendental philosophy.

 

But since one used to treat ontology without a critique - what was ontology then? An ontology that was not a transcendental philosophy. Thus one philosophized back and forth without asking: can one do that? Transcendental philosophy is the result of critique, for if I can represent the extent and the sources in a connection then the connected representation of the a priori principles is transcendental philosophy, and if I take all the consequences that flow from that, then that is metaphysics; without critique I do not know whether the concepts of pure reason and pure understanding are all there or whether some are still missing - because I have no principles. One set no boundaries to reason, and thereby went as far as one was able. They indeed comprehend that in matters of experience they cannot mix everything together, but a priori they can comprehend everything, and that because no one can refute them)." (pp. 140-141)

 

From: Immanuel Kant, Lectures on Metaphysics, Part III Metaphysik Mrongovius (1782-1783), translated and edited by Karl Ameriks and Steve Naragon, Cambridge: Cambridge University Press 1997.

---

Philosophy, like mathematics as well, can be divided into two parts, namely into the pure and into the applied. Metaphysics is the system of pure philosophy. The word "metaphysics" means a science which goes beyond the boundaries of nature. (Nature is the summation of all objects of experience.)

 

A principle principium is a general rule, which again contains other rules under it. If we take together all pure concepts which can be entirely separated from the empirical ones, then we attain thereby a science.

 

Philosophical cognition consists of mere concepts a priori.

 

Physics is the philosophy of nature insofar as it depends on principles from experience; but metaphysics is the philosophy of nature insofar as it depends on a priori principles. Moral philosophy teaches us the practical principles of reason. The concepts toward which everything seems to be aimed is the concept of a highest being and of another world.

 

Metaphysics is necessary. Its ground is reason, which is never to be satisfied by empirical concepts. Reason finds satisfaction neither in the consideration of things, nor in the field of experience, i.e, in the sensible world. The concepts of God and of the immortality of the soul, these are the two great incentives on whose account reason went out beyond the field of experience.

 

A major question is: how are a priori cognitions possible? The whole pure mathematics is a science which contains only a priori concepts, without its supporting their ground on empirical concepts. That there are thus actual a priori cognitions is already proved; indeed, there is a whole science of sheer pure concepts of the understanding. But the question arises: how are the a priori cognitions possible? The science that answers this question is called critique of pure reason. Transcendental philosophy is the system of all our pure a priori cognitions; customarily it is called ontology. Ontology thus deals with things in general, it abstracts from everything particular. It embraces all pure concepts of the understanding and all principles of the understanding or of reason.

 

The main sciences that belong in metaphysics are: ontology, cosmology, and theology.

 

Ontology is a pure doctrine of elements of all our a priori cognitions, or: it contains the summation of all our pure concepts that we can have a priori of things. (pp. 307-308)

 

From: Immanuel Kant, Lectures on Metaphysics, Part V. Metaphysik L2 (1790-1791?), translated and edited by Karl Ameriks and Steve Naragon, Cambridge: Cambridge University Press 1997.

---

Ontology is the first part that actually belongs to metaphysics. The word itself comes from the Greek, and just means the science of beings, or properly according to the sense of the words, the general doctrine of Being.

 

Ontology is the doctrine of elements of all my concepts that my understanding can have only a priori.

 

ON THE POSSIBLE AND THE IMPOSSIBLE. The first and most important question in ontology is: how are a priori cognitions possible? This question must be solved first, for the whole of ontology is based on the solution of this question. Aristotle decided the proposition in that he rejected all a priori cognitions, and said that all cognitions were empirical, or that they were based on the first principles of experience. For his main proposition was: nothing is in the intellect that was not first in the senses. Through this he overturned all a priori cognitions. But Plato said that all our a priori cognitions arose from an original intuition.

 

We have no innate concepts at all, but rather we attain them all, or we receive acquired concepts. The understanding acquires concepts by its paying attention to its own use. All that can be said of that is this: that there are certain a priori cognitions, even when it seems that they are taken from experience, or that they are used beyond the boundaries of experience. There is in our reason a certain dialectic, that is: a certain art of illusion, which shows me either something true or false. A good dialectician must maintain at the same time and with the same facility thesis and antithesis of a matter, or he must at the same time prove the truth and falsity of a matter, or be able to say yes or no. Dialectic contains a conflict which indicates that it is impossible to proceed dogmatically here in metaphysics. (p. 309)

 

From: Immanuel Kant, Lectures on Metaphysics - Part V. Metaphysik L2 (1790-1791?), translated and edited by Karl Ameriks and Steve Naragon, Cambridge: Cambridge University Press 1997.

---

Ontology is that science (as part of metaphysics) which consists in a system of all concepts of the understanding and principles, but only so far as they refer to objects that can be given to the senses, and thus confirmed by experience. It makes no allusion to the super-sensible, which is nevertheless the final aim of metaphysics, and thus belongs to the latter only as a propaedeutic, as the hallway or vestibule of metaphysics proper, and is called transcendental philosophy, because it contains the conditions and first elements of all our knowledge a priori.

 

In this field there has not been much progress since the days of Aristotle. For as grammar is the resolution of a speech-form into its elementary rules, and logic a resolution of the form of thought, so ontology is a resolution of knowledge into the concepts that lie a priori in the understanding, and have their use in experience; a system whose troublesome elaboration we may very well be spared, if only we bear in mind the rules for the right use of these concepts and principles, for purposes of empirical knowledge; for experience always confirms or corrects it, which does not happen if our design is to progress from the sensible to the super-sensible, for which purpose an assessment of the powers of understanding and its principles must indeed be carried out with thoroughness and care, in order to know from whence, and with what props and crutches, reason can venture upon its transition from the objects of experience to those that are not of this kind.

 

Now the celebrated Wolf has rendered an incontestable service to ontology, by his clarity and precision in analysing these powers; but not by any addition to our knowledge in that area, since the subject matter was exhausted.

 

However, the above definition, which merely indicates what is wanted of metaphysics, not what there needs to be done in it, would simply mark it out from other doctrines as a discipline belonging to philosophy in the specific meaning of the term, to the doctrine of wisdom, and prescribe its principles to the absolutely necessary practical use of reason; though that has only an indirect relation to metaphysics considered as a scholastic science and system of certain theoretical cognitions a priori, which are made the immediate topic of concern. Hence the explanation of metaphysics according to the notion of the schools will be that it is the system of all principles of purely theoretical rational knowledge through concepts; or in brief, that it is the system of pure theoretical philosophy. (p. 354)

 

From: Immanuel Kant, What Real Progress Has Metaphysics Made in Germany Since the Time of Leibniz and Wolff? (1793/1804) in: Theoretical Philosophy After 1781, edited by Henry Allison and Peter Heath, Cambridge: Cambridge University Press 2002.

---

The first stage of metaphysics can be called that of ontology, since it does not teach us to investigate the essence of our concepts of things by a resolution into their elements, which is the business of logic; it tells us, rather, what concepts of things we frame to ourselves a priori, and how, in order to subsume thereunder whatever may be given to us in intuition generally; which in turn could not happen save insofar as the form of a priori intuition in space and time makes these objects knowable to us merely as appearances, not as things-in-themselves. In this stage, reason sees itself obliged, in a series of conditions, subordinated one to another and each in turn conditioned without end, to progress incessantly towards the unconditioned, since every space and every time can never be represented as anything but part of a still larger given space or title, in which the conditions for what is given to us in each intuition must still be sought, in order to attain to the unconditioned." (p. 376)

 

From: Immanuel Kant, What Real Progress Has Metaphysics Made in Germany Since the Time of Leibniz and Wolff? (1793/1804), in: Theoretical Philosophy After 1781, edited by Henry Allison and Peter Heath, Cambridge: Cambridge University Press 2002.

 

After what has already been said, it is easy to think that I associate a quite different concept with the word ontology than the concept usually associated with it. That is to say, for me ontology is not a science that is applicable to the thing-in-itself, but only to appearances. It cannot have a wider domain. Here I will deal specifically with those points where I differ from the Wolffians, and hence also from Kant; for to say what others have already said would be superfluous. My exposition follows Baumgarten's paragraph ordering, so that the reader may more easily grasp the difference between our approaches). (1)

 

Ontology is the science of the most general properties of things; that is to say, not the properties of a thing in general (of a thing determined through no condition), but the properties of every a priori determined thing. As a part of metaphysics, it differs from logic as much as from the doctrine of nature as follows: logic relates merely to the form of thinking, without relation to any determined object whether determined a priori or a posteriori, while the doctrine of nature relates itself only to an object determined a posteriori. For example, the form of hypothetical propositions in logic is expressed like this: if one thing is supposed then another thing must necessarily be supposed. Here the subject (thing) is determined only by the predicate (relation of antecedent to consequent). In physics the form is expressed like this; 'heat expands air': here the subject of the relation ([between] heat and air) is determined by means of a posteriori conditions. In metaphysics, on the other hand, it is expressed like this: if A comes first, and B follows it according to a I rule, then the supposition of A makes it necessary to suppose B. In this case the subject of the relation of cause and effect is determined by means of a time-determination (succession according to a rule) that is a priori. So the concept or principle of cause belongs to metaphysics. The objects of logic can be compared to transcendental magnitudes (which are not determined in relation to one another by any algebraic equation), while the objects of metaphysics can he compared to variable magnitudes (which are determined only by means of their relation to one another), and the objects of physics to continuous magnitudes. (pp. 126-127)

 

Notes

(1) Maimon's paragraph numbering in fact follows not the original Latin text of Baumgarten's Metaphysica but that of Georg Friedrich Meter's abridged German translation: Alexander Gottlieb Baumgarten, Metaphysica trans. G. F. Meier, (Halle: 1783).

 

From: Salomon Maimon, Essay on Transcendental Philosophy (1790), translated by Nick Midgley et. al., London-New York: Continuum 2010.

 

I therefore think that mathematics could best be defined as a science which deals with the general laws (forms) to which things must conform in their existence. By the word 'things', I understand here not merely those which possess an objective existence independent of our awareness, but also those which simply exist among our ideas, either as individuals i.e. intuitions, or simply as general concepts, in other words, everything at all which can be an object of our perception. Furthermore, if I say that mathematics deals with the laws to which these things conform in their existence, this indicates that our science is concerned not with the proof of the existence of these things, but only with the conditions of their possibility. When I call these laws general, I mean it to be understood that mathematics never deals with a single thing as an individual, but always with whole genera. These genera can of course be higher or lower, and on this will be based the classification of mathematics into individual disciplines.

 

The definition given here will certainly not be found too narrow, for it clearly covers everything that has previously been counted in the domain of mathematics. But I am more afraid that it might be found rather too wide, and the objection might be made that it leaves too little for philosophy (metaphysics), as the latter will be limited by my definition to the single concern of proving, from a priori concepts, the real existence of certain objects. Mathematics and metaphysics, the two main parts of our a priori knowledge, would, by this definition, be contrasted with each other so that the first deals with the general conditions under which existence of things is possible; the latter, on the other hand, seeks to prove a priori the reality of certain objects (such as the freedom of God and the immortality of the soul). Or, in other words, the former concerns itself with the question, how must things be made in order that they should be possible? The latter raises the question, which things are real -- and indeed (because it is to answered a priori) -- necessarily real? Or still more briefly, mathematics would deal with hypothetical (1) necessity, metaphysics with absolute necessity." (p. 183)

 

Notes

(1) However, not all its propositions have this hypothetical form, because the condition, especially in chronometry and geometry, where it is the same for all propositions, is tacitly assumed.

 

From: Bernard Bolzano, Contributions to a Better-Grounded Presentation of Mathematics (1810), translated by William Ewald in: From Kant to Hilbert: A Source Book in the Foundations of Mathematics, vol. I, Oxford: Clarendon Press 1996.

 

The Fourfold Distinction of Being.Being is a homonym. Its several senses fit into the fourfold distinction of accidental being: being in the sense of being true, being of the categories, and potential and actual Being.

 

'Being is said in various ways' [to de on legetai men pollachos], says Aristotle in the beginning of the fourth book of his Metaphysics (Met. IV. 2 1003a33). He repeats this in Books VI and VII and several more times in other places. In these passages he enumerates a number of concepts, each of which, in different ways, is called a being. In Met. IV. 2 1003b6 he says "one thing is said to be because:

For this reason we also say that non-being is non-being.

 

The various sorts of Being which are here enumerated can be reduced to four kinds:

 

Another enumeration of concepts to which the appellation Being is attached in different ways is given in Met. VI. 2 1026a33. In that passage, one kind of Being is said to be accidental Being, another Being in the sense of being true, whose opposite is non-being in the sense of being false. Besides, there is said to be another kind of Being which divides into the categories, and, in addition to all of them, potential and actual Being. It will be noted that this division, too, is fourfold, but does not consistently correspond to that in Book IV.

Thus the distinction of Being given in Book VI will provide the organization of our investigation. We shall deal, first of all, with the accidental Being, then with the Being in the sense of being true and non-being in the sense of being false, then with potential and actual Being and finally with the categories. In his Metaphysics Aristotle dealt with the last two in opposite order. He first had to acquaint us with substance [ousia] and with its form and matter (Met. VIII) in order to be able to speak afterwards of potential and actual Being. Since our essay is not intended to become a complete ontology, the first order is more suitable to our purposes, and the subsequent development itself will justify its adoption. (pp. 3-5)

From: Franz Brentano, On the Several Senses of Being in Aristotle (1862), translated by Rolf George, Berkeley: University of California Press 1975.

---

 

A metaphysical theory may begin with the following explication of words: By that which is, when the expression is used in the strict sense, we understand a thing; for example, a body, a mind, or a topoid of more or fewer than 3 dimensions. A part of a body or of a topoid may also be called a thing. And so a number of things taken together may also be called a thing. But it would be wrong to suppose that the two parts of a thing taken together constitute an additional third thing. For where we have an addition the things that are added must have no parts in common. Thus we may say, for example, that a triangle has three angles, but not that it has three pairs of angles: angles A and B form a pair, as do B and C, and also C and A, but each of these pairs has a part in common with each of the others.

 

The expression 'that which is' is also used in various extended senses:* (a) The resources of language enable us to form an abstractum for every concretum. For the concretum, that which is, there is the abstractum, Being; for body, there is the abstractum corporeality, for mind, there is spirituality or mentality, for lover, there is love; for which knows, there is knowledge; for that which is formed, there is form; and so on. What do these abstracta denote? Obviously not the same things as do the corresponding concreta; this would be a pointless duplication of names. Sometimes the relation between the concrete and abstract terms is explained by saying: "That which is formed is formed in virtue of its form. For example, that which is round is round in virtue of its roundness; and whatever is a body is a body in virtue of its corporeality or its corporeal nature." It has also been said that the roundness is in that which is round and that the corporeal nature is in the body. This seems to suggest that the concretum is related to the abstractum as part to whole. Indeed, the abstractum has been called the formal part of the concretum; the concretum is then said to be that which is denoted by the concrete term because it contains the abstractum as part.

 

(a) If abstracta were in fact thus parts of concreta there would be no objection to including abstracta among those things which are in the proper sense. But actually they are not parts. A division of the concretum into two parts one of which is the form corresponding to the abstractum is plainly impossible. This division is purely fictive: it amounts to saying that a thing has as many parts as there are predicates that apply to it. Using abstracta in this way, one says that a thing is round because roundness is included among its parts just as one says that an animal is hairy because hair is included among its parts. But whereas an animal's hair is a real thing which can be separated from the animal both in fact and in thought, the contrary is true of the so-called roundness, which can neither exist by itself nor be thought of by itself. Fictions of this sort are often harmless, and they may even be useful, as when mathematicians treat circle as a regular polygon with an infinite number of sides or assume that parallel lines meet in infinity. If such fictions served no purpose whatever, they would hardly have come into use. But what has been expressed by abstract terms can always be expressed by concrete ones, without recourse to fictions. Leibniz pointed out that by such rephrasing a number of difficulties that baffled the Scholastic philosophers are easily disposed of. So far as linguistic usage is concerned, we can say, not only that there is something round, but also that there is such a thing as roundness; but we must bear in mind that the "is" in the latter statement is used in an extended sense, and that the only thing that can properly be said to be here is the thing which is round.

 

(b) Instead of saying that a thinker is thinking of something, one can also say that there is something which is thought about by him. Here, again, we are not dealing with what may be said to be in the proper sense - indeed, the person in question may himself deny that what he is thinking about is something that there is. Even a contradiction in terms, something that is plainly impossible. can be something that is thought about. We have just said that not roundness but that which is round is in the strict sense; similarly, not the contemplated round thing, but the person contemplating it is what is in the strict sense. This fiction, that there is something which exists as a contemplated thing, may also prove harmless, but unless one realizes that it is a fiction, one may be led into the most glaring absurdities. Things which exist as objects of thought do not constitute a subspecies of genuine Being, as some philosophers have assumed. Once we have translated statements about such fictive objects into other terms, it becomes clear that the only thing the statement is concerned with is the person who is thinking about the object. What I have said here with general reference to that which is contemplated or thought about also applies, of course, to that which is affirmed.

 

(c) If one says, something is past or something is future, one is making an affirmation. But one is not thereby affirming or accepting something as Being. One is making an affirmation in the temporal mode of the past or the future instead of the temporal mode of the present. If one were to say "The past Caesar is," instead of saying "Caesar is past" he would be using "is" in an extended sense. The case would be analogous to that in which, instead of saying that there can be no such thing as a round square, one says that a round square is an impossibility. Once again, a different phrasing would be a suitable way of showing that we are not dealing with a strict interpretation of Being.

 

(d) Many other examples of improper use of the "is" could be cited. Consider, for example, the statement that there is a time that has neither beginning nor end or the statement that there is a three-dimensional space indefinitely in all directions. It is easy to see on the basis of what has been said already that such statements do not refer to anything than can be in the strict sense. Time and space seem to belong to the abstracta. This means that what is in the strict sense, is not space or time, but rather that which is spatial and that which is temporal. Instead of speaking of space and time, we should speak of things that are spatial, things that are spatially different, things that are temporal, things that are simultaneous, and so on. Those philosophers who say that there is an infinite space as precondition of everything spatial conceive of this space as a thing. But this doctrine has no basis; indeed it is demonstrably false and absurd. Similarly, what philosophers have called time would be a thing if it actually existed. But time, thus considered as a thing, is a philosophical aberration. And this is so even if it is true that there is a thing that had no beginning and will always be, a thing that is continuously undergoing changes and producing changes in everything outside itself, thus making indirectly necessary the uniformity of the temporal process in things. Such an entity would not correspond to the thing that philosophers have thought of as being time. (pp. 16-19 notes omitted)

 

From: Franz Brentano, The Theory of Categories (1933), translated by Roderick M. Chisholm and Norbert Guterman, The Hague: Martinus Nijhoff 1981.

 

We must turn, in the first place, to a philosophical discipline which is not as yet part of the tradition, which is therefore in a certain sense new, and about which I have said some things which were intended to be of a fundamental nature. To begin with, it is impossible to give a regular definition of entity [Gegenstand]; for genus and differentia are lacking, since everything is an entity. However, the etymology of the word 'gegenstehen' yields at least an indirect characteristic, since it points to the experiences which apprehend entities; but these experiences must not be thought of as somehow constituting the entities. Every inner experience, at least every sufficiently elementary one, has such an entity; and insofar as the experience finds an expression - hence first of all in the words and sentences of language - this expression has a meaning [Bedeutung], and this meaning is always an entity. All knowledge, too, deals therefore with entities.

 

But large and important groups of entities have found no home in the traditional sciences; these sciences, moreover, are for the most part exclusively concerned with a knowledge of reality [Wirklichen], while even unreal things with Being, things without Being, possibilities, and even impossibilities can be objects of knowledge, namely, of a knowledge which is of interest to the as yet theoretically naive person only, as it were, when it promises to serve as a means for knowledge of reality. In contrast to such a preference for reality, which, in fact, has been overcome so far in no science, there exists the obvious need for a science which deals with entities without any restriction, especially without restriction to the special case of existence, so that it can be called existence-free [daseinsfrei].This science about entities as such, or about pure entities, I have called the theory of entities.

 

Much of what belongs to this theory has already been studied under the title 'Logic' (especially: 'Pure Logic'); and that modem mathematical logic belongs completely to the realm of the theory of entities is only concealed by its goal of being a calculus, which seems to favor an extensive externalization [Veräusserlichung] in the sense of the logic of extensions, while it is just a complete internalization [Verinnerlichung] which the theory of entities strives for and makes possible. People have dealt with topics from the theory of entities since antiquity under the heading of 'Metaphysics,' and, especially, under the heading of 'Ontology' as a part of metaphysics; and they have not always failed to recognize the characteristic feature of freedom from existence. But as a goal in itself, the concept of a theory of what is free from existence has, so far as I can see, never been espoused. According to this concept, there belongs to the theory of entities everything that can be made out about entities irrespective of their existence (for example, whatever it is that holds for the class of all colors which make up the 'color space,' as distinguished from the 'color body' which is restricted to the psychologically given); hence, everything that is a matter of a priori knowledge, so that the a priori can be treated as a defining characteristic of the kind of knowledge of which the theory of entities consists.

 

What belongs to the theory of entities is thus what is rational. Insofar [as it is that], it is therefore anything but a newly discovered country, but rather, in regard to one of its most important parts, mathematics, the justly admired standard of scientific precision. What is new is, perhaps, an insight into the peculiarity of this country and into the nature of its boundaries - unless one should rather speak of its boundlessness. In this respect, it is a kind of companion piece to metaphysics which tries to comprehend the totality of reality, while the theory of entities, because of its freedom from existence, tries to encompass also everything that is not real. Naturally, this freedom from existence does not mean that entities as such cannot have existence in the true sense. The fact that the kind of consideration and knowledge peculiar to the theory of entities therefore also appears where it can be applied to existents, constitutes one of the main values of the postulation of the new science.

 

Just as the concept of an entity in general is to be determined, at least cum grano salis (with a grain of salt), with an eye on apprehension, so are the main groups of entities characterized in regard to the main groups of apprehending experiences; and apprehensions are, as mentioned, all elementary experiences. Corresponding to the four main groups of the latter - to presentation [Vorstellen], thought [Denken], emotion [FühIen], and desire [Begehren] - there are, therefore, four main groups of entities: objects [Objekte], objectives [Objektive], dignitatives [Dignitative], and desideratives [Desiderative]. However, the characteristics of the latter are not derived from the characteristics of the apprehending experiences. For this reason, nothing stands in the way of assigning to the immeasurable realm of objects, for example, also the inner experiences, even though these inner experiences cannot be given through presentations, but can only be apprehended through self-presentation or with the help of imagination." (Appendix I, pp. 224-225)

 

From: Alexius Meinong, Self-Presentation (1921), translated in: Reinhardt Grossmann, Meinong, London: Routledge & Kegan Paul 1974.

 

In order to explain the meaning of the word 'object' further, one can also - as we have done already - point to the linguistic designation and assert that everything which is designated is an object. Such designation uses either nomina (to name) understood in a grammatical sense, or it uses phrases consisting of nomina and other expressions, or, finally, it uses other parts of speech, assuming that they have been converted into nouns. One can, therefore, say that everything which is designated by a noun or by an expression which is used as a noun is an object in the sense here adopted.

 

Now, since everything can be object - object of presentation - the subject of the presentation itself not excluded, those who conceive of the object as the summum genus (of the highest kind) are justified. Everything which is is an object of a possible presentation; everything which is is something. And here, therefore, is the point where the psychological discussion of the difference between content and object of presentations turns into metaphysics.

 

The objects of presentations have indeed been viewed from a meta-physical point of view up to the present time. In calling them onta [in Greek], entia [in Latin], one revealed the way which led to them. However, that the Aristotelian on - like the ens of medieval philosophy - is nothing else but the object of presentations is shown by the fact that all doctrines about the ens, as far as they are correct, hold for the object of presentations. We shall confine ourselves here to the most famous of these doctrines.

 

1. The object is something different from the existent; some objects have existence in addition to their objecthood [Gegenständlichkeit], that is, in addition to their property of being presented (which is the real sense of the word 'essentia'); others do not. What exists is an object (ens habens actualem existentiam), as is also what merely could exist (ens possibile); even what never can exist but what can only be conceived of (ens rationis) is an object; in short, everything which is not nothing, but which in some sense is "something," is an object. (1) In fact, the majority of scholastics maintain that aliquid is synonymous with ens, in contrast to those who conceive of the former as an attribute of the latter.

 

2. Object is summum genus. Scholastics express this by the statement that the concept of ens is not a generic concept, but is a transcendental concept, because it omnia genera transcendit (transcends all kinds).

 

3. Every object of a presentation can be object of a judgment and object of an emotion. This is the meaning of the scholastic doctrine that every object of a presentation is "true" and "good." The (metaphysical) truth of an object does not consist in being judged in a (logically) true judgment; as little as its "goodness" depends on whether the feeling concerning it is good in the ethical sense or not. Rather, an object is called true inasmuch as it is object of a judgment, and it is called good inasmuch as it is related to an emotion. (...)

 

4. An object is called true with regard to its ability to be judged; it is called good with regard to its ability to be the object of an emotion. The question could be raised whether the object has, in an analogical manner, an attribute which expresses its conceivability and which, therefore, would be a name of the object inasmuch as it is presented. Now, medieval philosophy knows of a third attribute of the object; every ens, according to this philosophy, is not only verum and bonum, but also unum. We shall investigate in a different context - since this question will arise there quite naturally - what this unity means for the presentation of an object, especially whether we may see in it the analogue in the sphere of presentations to truth in the sphere of judgments and goodness in the sphere of emotions.

 

5. If the object of presentations, judgments, and feelings is nothing else but the Aristotelian-scholastic ens, then metaphysics must be definable as the science of objects in general, taking this word in the sense here proposed. And this is indeed the case. The particular sciences, too, deal with nothing else but the objects of our presentations, their changes, their properties, as well as the laws according to which objects affect each other. Only, the particular sciences always deal with a more or less limited group of objects, a group which is formed by the natural context or a certain purpose. The natural sciences, in the widest sense of the word, for example, are concerned with the peculiarities of those objects which one calls inorganic and organic bodies; psychology investigates the properties and laws characteristic of mental phenomena, of mental objects. Metaphysics is a science which considers all objects, physical - organic and inorganic - as well as mental, real as well as non-real, existing objects as well as non-existing objects; investigates those laws which objects in general obey, not just a certain group of objects. What we here mean is expressed by the venerable definition of metaphysics as the science of Being [Seienden] as such.(2) The backward glance at some of the points of the scholastic doctrine of ens is supposed to characterize as precisely as possible the meaning which we connect, in the present investigation, with the word 'object'. Summarizing what was said, we can describe the object in the following way. Everything that is presented through a presentation, that is affirmed or denied through a judgment, that is desired or detested through an emotion, we call an object. Objects are either real or not real; they are either possible or impossible objects; they exist or do not exist. What is common to them all is that they are or that they can be the object (not the intentional one!) of mental acts, that their linguistic designation is the name, (...) and that considered as genus, they form the summum genus which finds its usual linguistic expression in the word 'something.' Everything which is in the widest sense "something" is called "object," first of all in regard to a subject, but then also regardless of this relationship." (pp. 34-37)

 

Notes

(1) Some philosophers, like Suárez, withhold the name ens from what has merely a "ficta" or "chimaerica essentia" and give it only to the "essentia realis." However, this restriction seems to involve an inconsistency. Suárez, Disputationes metaphysicae II, sect. 4.

(2) Compare Brentano, On the Several Senses of Being in Aristotle vol. I, chapter 1, par. 1.

 

From: Kazimierz Twardowski, On the Content and Objects of Presentations (1894), translated and with an introduction by Reinhardt Grossmann, The Hague: Martinus Nijhoff Publishers 1977.

 

Section 5. The concept of Pure logic as MATHESIS UNIVERSALIS (the unity of the "analytic doctrine of forms for that which can be an object on the one hand with the categories of meaning on the other). The "Positivity" of logic and the philosophical problem of its phenomenological elucidation. - Positive science in general and phenomenology.

 

I turn now to the misinterpretations having to do with my idea of a "pure logic": which present themselves in various ways depending on the standpoint from which the philosophical reader approaches the Logical Investigations. It might be best here if I meet these misinterpretations by pointing out positively what is essential to my position with special emphasis upon the points which have not received enough attention.

 

"Pure logic", in its most comprehensive extension characterizes itself by an essential distinction as "mathesis universalis." It develops through a step-by-step extension of that particular concept of formal logic which remains as a residue of pure ideal doctrines dealing with "propositions" and validity after the removal from traditional logic of all the psychological misinterpretations and the normative-practical goal positings [Zielgebungen]. In its thoroughly proper extension, it includes all of the pure "analytical" doctrines of mathematics (arithmetic, number theory, algebra, etc.) and the entire area of formal theories, or rather, speaking in correlative terms, the theory of manifolds [Mannigfaltigkeitslehre] in the broadest sense. The newest development of mathematics brings with it that ever new groups of formal-ontological laws are constantly being formulated and mathematically treated which earlier had remained unnoticed. "Mathesis universalis" as an idea includes the sum total of this formal a priori. It is, in the sense of the "Prolegomena," directed toward the entirety of the "categories of meaning" [Bedeutungskategorien] and toward the formal categories for objects correlated to them or, alternatively, the a priori laws based upon them. It thus includes the entire a priori of what is in the most fundamental sense the "analytic" or "formal" sphere - a sense which receives a strict specification and clarification in the third and sixth investigations. (pp. 28-29)

 

From: Introduction to the Logical Investigations. A Draft of a Preface to the Logical Investigations (1913), edited by Eugen Fink, translated with introductions by Philip J. Bossert and Curtis H. Peters, The Hague: Martinus Nijhoff 1975.

---

Region and Category. The Analytic Region and its Categories

 

Let us start from formal ontology (always as pure logic in its full extent as mathesis universalis) which, as we know, is the eidetic science (exact science) of any object whatever. Anything and everything is an object in the sense proper to formal ontology, and an infinity of various truths, distributed among the many disciplines of mathesis, can be established for it. But they all lead back to a small stock of immediate or "fundamental" truths which function as "axioms" in the disciplines of pure logic. We define now as logical categories or categories of the logical region, any object whatever: the fundamental concepts of pure logic which occur in those axioms - the concepts by means of which, in the total set of axioms, the logical essence of any object whatever becomes determined, or the concepts which express the unconditionally necessary, and constituent determinations of an object as object, of anything whatever in so far as it can be something at all. Because the purely logical, in the sense delimited by us with absolute exactness, determines that concept of the "analytic" (25) as contrasted with the "synthetic," which alone is important (but which is important fundamentally) to philosophy, we may also designates these categories as analytic." (pp. 21-22)

 

(...) "apophantic logic," although it makes statements exclusively about significations, is nevertheless part of formal ontology in the fully comprehensive sense. Still one must set the signification-categories apart as a group by themselves and contrast them with the others as the formal objective categories in the pregnant sense. (26)" (p. 22)

 

Notes

(25) AUTHOR FOOTNOTE: cf. Logische Untersuchungen, Vol. II, “Third Investigation,” §§ 11 ff.

(26) AUTHOR FOOTNOTE: On the division of logical categories into signification-categories and formal-ontological categories, cf. Logische Untersuchungen vol. I 67 [Logical Investigations pp. 236f.] The entire "Third Investigation" specifically concerns the categories of whole and part. A that time I did not venture to take over expression "ontology" which was objectionable on historical grounds; rather I designated this investigation (p. 222 of the first edition) as part of an “apriorische Theorie der Gegenstande als solcher"" [“apriori theory of objects as objects”] a phrase contracted by Alexius Meinong to make the word "Gegenstandtheorie" ["object-theory"]. Now that times have changed, however, I consider it more correct to rehabilitate the old expression, "ontology".

 

From: Edmund Husserl, Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy. First Book: General Introduction to a Pure Phenomenology (1913), translated by F. Kersten, The Hague: Martinus Nijhoff 1982.

 

All ontology has to do with fundamental assertions about Being as such. Assertions of this sort are precisely what we call categories of Being. Like the Kantian categories - which, as far as content is concerned, are also precisely this: fundamental assertions about Being - they have the character of universal constitutive principles comprising all more specialized ontological assertions. Hence, the new ontology might be expected to provide a transcendental deduction also of these ontological assertions. Otherwise, it is argued, it could not guarantee their objective validity. That, however, would mean that this ontology in its turn was in need of an epistemological foundation which would have to provide the justification of a priori principles of an even wider scope.

 

Thereby a way for ontology is traced, and this way once more follows the scheme of the old deductivity. But it is here that the roads of the old and the new ontology part. Just as in regard to the problem of Being, it is today no longer a question of substantial forms and of the teleological determination of actual processes by these forms, so also the problem at issue is no longer that of a post factum justification of a priori principles. The categories with which the new ontology deals are won neither by a definition of the universal nor through derivation from a formal table of judgments. They are rather gleaned step by step from an observation of existing realities. And since, of course, this method of their discovery does not allow for an absolute criterion of truth, here no more than in any other field of knowledge, it must be added that the procedure of finding and rechecking is a laborious and cumbersome one. Under the limited conditions of human research it requires manifold detours, demands constant corrections, and, like all genuine scholarly work, never comes to an end.

 

Here one may truly and literally speak of new ways of ontology. The basic thesis can possibly be formulated like this: The categories of Being are not a priori principles. Only such things as insights, cognitions, and judgments can be a priori. In fact the whole contrast between a priori and a posteriori is only an epistemological one. But ontology is not concerned with knowledge, much less with mere judgments, but with the object of knowledge in so far as this object is at the same time "transobjective", that is, independent of whether or to what extent Being is actually transformed into an object of knowledge. The principles of the object in its very Being are in no way eo ipso (by that fact alone) also cognitive principles. In some fields they can be quite heterogeneous, as the manifold admixtures of the unknowable in nearly all basic problems of philosophy amply prove. From this alone it follows that the principles of Being cannot be a priori principles of our intellect, that they, as a matter of fact, are just as indifferent to the dividing line between the knowable and the unknowable as the Being whose principles they are. (pp. 13-14)

 

From: Nicolai Hartmann, New Ways of Ontology (1949), translated by Reinhard C. Kuhn, Chicago: Henry Regnery Company 1953.

---

The true characteristics of reality do not depend on the categories of space and matter but on those of time and individuality. Ontologically considered, time and space are not categories of equal worth: Time is by far more fundamental than space. Only material things and living beings, including the processes through which their existence flows, are spatial. But spiritual and psychic processes, as well as material processes, are temporal. For everything real is in time and only a part of it in space --we might say, only one half of the real world, its lower forms.

 

Inseparably joined with temporality is individuality. This consists in nothing but singleness and uniqueness. The real is perishable and thereby also unrepeatable. The same sort of thing recurs, never the same identical thing. This holds true of historical events as well as of cosmic motions, of persons as well as of things. Only the universal recurs, for, considered by itself, it is timeless, always existing, eternal. This timelessness was once considered in the old ontology to be a being of a higher order, indeed, even the only true Being. But, in truth, it is rather a dependent, a merely ideal being, and the universal has reality nowhere else but in the real particulars which are both temporal and individual. What once was considered a kingdom of perfection, the kingdom of essences, whose faint copies things were supposed to be, has proved itself to be a kingdom of incomplete Being which becomes independent only through abstraction. In the recognition of this lies perhaps the most striking contrast of the new ontology to the old.

 

That is why the new ontology can very well grapple with the deep problems of German idealism, why it can deal with the spirit and freedom, social life and history, just as well as with the cosmos and the organism. Hence new light may be expected to be shed by it on the characteristic situation and activity of man as a spiritual being within a non-spiritual, law-determined world.

 

These reflections are but a small section from a chapter on categorial analysis. Here they are only sketched. They justly demand a much more exact discussion of space, time, process, psychic act, reality, and so forth. Particularly reality, the pure mode of Being of the structures and processes which form the world, is a very difficult subject for analysis. In order to understand reality, the philosopher must start with an examination of the relationship of possibility and actuality -- for centuries the fundamental problem of ontology. And the revolution in the whole problem of Being extends even to these very foundations of Being. For what the old ontology teaches about potency and act -- a relationship according to which everything real is a realization of a pre-existing disposition and all Being is destined to become what it is by disposition -- proves to be far from adequate in view of the broadened problem of reality. It is incumbent upon us to introduce a new concept of 'real possibility' (Realmöglichkeit) which no longer coincides with essential possibility but which signifies the totality of conditions present at a given time within the real context. To this must correspond just as novel a concept of 'actual reality' (Realwirklichkeit) which is no longer thought of as the goal of an anthropomorphically conceived tendency, as if the processes in the cosmos were tied to the activity of an intelligence. Rather such actual reality must in every case be considered to be the complex result of a far-flung context of determinants. A whole science concerns itself with these inner relationships of reality considered as a mode of Being. It forms the core of the new ontology, and, in contrast to an analysis of categories directed toward the structural content, it may be called modal analysis. (pp. 25-27)

 

From: Nicolai Hartmann, New Ways of Ontology (1949), translated by Reinhard C. Kuhn, Chicago: Henry Regnery Company 1953.

 

Leśniewski's system of logic consists of two theories, which he called Protothetic and Ontology. Of these, the former is perhaps the most comprehensive Logic of Propositions which has ever been devised. It goes beyond the classical Calculus of Propositions in several respects. It allows for instance for functorial variables for which constant functors of the Calculus of Propositions can be substituted. It provides for the use of the universal quantifier to bind both the propositional and the functorial variables. It has a rule of definitions, which enables us to extend at will the variety of semantical categories within the field of the Logic of Propositions, and, in addition, it has a rule of extensionality; but the most significant point about Protothetic is that, with its aid, we can derive theses which enable us to dispose of the usual rules for operating with the universal quantifier in any deductive theory of lower generality. In the edifice of the possible deductive theories, Protothetic forms the very base. It requires no more fundamental theory than itself whereas other deductive theories, not included in it, have to be built on it or on a part of it. This is the case with Ontology.

 

If Protothetic is the most comprehensive Logic of Propositions then Ontology is the most comprehensive Logic of Names. Roughly speaking, it comprises the traditional logic in its modernized form and has counterparts of the Calculus of Predicates, the Calculus of Classes, and the Calculus of Relations including the Theory of Identity.

 

At first sight Leśniewski's use of the term Ontology may seem curious and daring, but it should become clearer as we proceed that he was eminently justified. In fact his whole conception of logic was ontological through and through in a truly classical sense. Contrary to the widely accepted practice, Leśniewski intended his logic to be an interpreted system. He attached definite meanings to his constants and regarded the theses of his deductive theories as true propositions in the sense in which propositions of empirical sciences are accepted as true. It is with this in mind that we should approach his theories. Ontology has been described as the most comprehensive Logic of Names because its most characteristic expressions belong to the semantical category of names, just as the most characteristic expressions of Protothetic belong to the semantical category of propositions. If, however, we take into account the contents of Ontology then it would be more appropriate to describe it as a theory of what there is. Just as astronomy tells us something about heavenly bodies, the theses of ontology tell us something about things, or objects if one prefers, or individuals. Since in accordance with Leśniewski's intentions theses of ontology are to be regarded not as mere 'well formed formulae' but as meaningful propositions which can be examined for their truth or falsity, it is essential that we should understand as clearly as possible the ontological vocabulary. Only when we have mastered this vocabulary can a further step be made, namely the one which consists of a critical study of those ontological theses which are already at our disposal. Finally, we may try to discover new truths, which we can formulate in terms of the ontological vocabulary, and assign them their proper places in the theory by deducing them from the axiom or establishing their independence." (pp. 124-126 of the reprint, note omitted)

 

From: Czeslaw Lejewski, On Leśniewski's Ontology, in: Ratio vol. I, n. 2, 1958, pp. 150-176 (Reprinted in: Jan T. J. Srzednicki, V. F. Rickey (eds.), Leśniewski' Systems. Ontology and Mereology, The Hague: Martinus Nijhoff 1984, pp. 123-148.

 

The ontological analyses of works of art affected Ingarden's entire ontology. Its best elaboration is contained in Spór o istnienie swiata (The controversy over the existence of the world, 1947-48). A being, i.e., an object, can be considered in three different respects:

 

Ingarden understands ontology as based on eidetic insight and intuitive analyses of the contents of ideas, i.e., upon the Eidetic Method, which enables one to discover the necessary and purely possible relations between the pure ideal qualities. Ontology is for him the most general theory of objects. He distinguishes it from metaphysics, which fulfills the role of an applied theory of objects and which, being based on ontology, considers the nature and essence of factual beings. The eidetic character distinguishes metaphysics from the so-called real sciences.

 

Ontology aims at obtaining a general spectrum of eidetic possibilities and necessities with reference to any objects whatever. In the frame of an existential ontology, which has nothing to do with Martin Heidegger's Fundamental Ontology, Ingarden distinguishes and clearly defines four mutually exclusive pairs of moments of Being - something can be:

 

Considerations connected with the analysis of the second pair has led Ingarden to an original interpretation of the relation of causality. His analysis of time has brought some additional pairs of existential moments, such as actuality and non-actuality; persistence and fragility; and fissuration and non-fissuration. These differentiations enables him to distinguish and describe four basic modes of Being (consisting of non-contradictory combinations of existential moments). These are:

 

We cannot experience any existing object without its mode of Being.

 

In epistemology Ingarden distinguishes:

 

From: Andrzej Przylebski, Roman Ingarden, In: Lester Embree, and alii (eds.), Encyclopedia of Phenomenology, Dordrecht: Kluwer 1997, pp. 348-350.

 

ONTOLOGY: The serious secular version of metaphysics. The branch of philosophy that studies the most pervasive features of reality, such as real existence, change, time, chance, mind, and life. Ontology does not study constructs, i.e., ideas in themselves. These are studied by the formal sciences and epistemology. Hence the expression 'ontology of mathematics' makes sense only in the context of objective idealism (such as Pythagoras's and Plato's). By contrast, the question 'What is the ontological status of mathematical objects?' is meaningful in all contexts, and in a fictionist philosophy of mathematics it has a simple answer: None.

 

Ontology can be classed into general and special (or regional). General ontology studies all existents, whereas each special ontology studies one genus of thing or process-physical, chemical, biological, social, etc. Thus, whereas general ontology studies the concepts of space, time, and event, the ontology of the social investigates such general sociological concepts as those of social system, social structure, and social change. Whether general or special, ontology can be cultivated in either of two manners: speculative or scientific. The ontologies of Leibniz, Wolff, Schelling, Hegel, Lotze, Engels, Mach, W. James, H. Bergson, A. N. Whitehead, S. Alexander, L. Wittgenstein, M. Heidegger, R. Carnap, and N. Goodman are typically speculative and remote from science. So is the contemporary possible worlds metaphysics. Warning: the expression 'the ontology of a theory' is sometimes misleadingly employed to designate the reference class or universe of discourse of a theory. The expression is misleading because ontologies are theories, not classes." (pp. 200-201)

 

From: Mario Bunge, Dictionary of Philosophy, Amherst: Prometheus Books 1999.

 

The main object of the ensuing analysis is to tie together several seemingly disparate topics. These include: (a) a theory of types (that is, a theory describing the way terms are conjoined to form category correct statements in a natural language); (b) a formal theory of ontological categories and ontological features; (c) a theory of predication (that is, a theory accounting for the subject-predicate distinction and one which provides certain formal characteristics of the binary relation 'is predicable of'); (d) a procedure for enforcing ambiguity.

 

The results of the analysis support the main features of the Russell program. I take these to be that (a) a clarification of natural language is ontologically revealing and discriminatory of the sorts of things there are; (b) linguistic structures and ontological structures are isomorphic. The meaning of 'ontology' in what immediately follows is 'the science of categories.'

 

The ontologist is interested in categories; he is, qua ontologist, not interested in whether a thing is red or whether it is green but in whether it is colored. Even this is not altogether accurate: he is interested in its character of being colored or colorless. For the ontologist 'colored' means | red | which is the same thing as colored or colorless. A toothache is neither, but water can be either red or not red or colored or colorless.

 

We speak as ontologists when, for example, we say that points belong to the category of extension even though they belong to the class of extensionless things. The category of extension is defined by the predicate | extended | and points belong to it. Concepts do not belong to it since they are neither extended nor extensionless. Space (spatial) is another category word since it has no complement which is not categorial. And if the word 'color' is taken to include that 'color' we call 'colorless,' it too is a category word. (pp. 351-352).

 

From: Fred Sommers, Types and Ontology: The Philosophical Review, 72, 1963, pp. 327-363.

---

Sommers defines 'ontology' as the 'science of categories' ('Types and Ontology,' p. 351). More specifically, it is the systematic attempt to say what categories are, how they are determined, and how they are related to one another. Ontology is, of course, nothing new. Plato's theory of forms, Aristotle's Categories, Russell's theory of types are three quite obvious examples of attempts at a science of categories. But it is Sommers' own theory which comes closest to a complete, workable theory of categories.

 

So what is a category? It is a group of things, a class -- but a special kind of class. We saw above that a class consists of all those things of which some given term is true. The notion "true of" is the source of one of the problems with classes. Consider how we negate. Modern logicians take all the kinds of negation which can occur in a natural language sentence as amounting to the negation of the entire sentence.

(...)

 

Let us make a distinction between what a term is true of and what it spans ('Types and Ontology,' p. 329). A term spans whatever either it or its negation could be used to sensibly characterize. And all the things spanned by a given term constitute the category with respect to that term. Thus, while the lowest prime is in the counter-class of 'married', it is not in the category determined by 'married'. While a term and its negation exclusively and exhaustively divide the world, a term and its negation both determine the same category, which need not exhaust the world. This is because whatever can be sensibly characterized by a term can be sensibly characterized by its negation. Spanning is not defined in terms of truth. While a term and its negation are never true of the same things, they both span the same things. For example, whatever can be sensibly characterized as married can equally well be characterized (though perhaps falsely) as unmarried. It would be false, but nonetheless sensible, to characterize Queen Elizabeth as unmarried. On the other hand, neither 'married' nor 'unmarried' can be used to characterize the lowest prime number. To characterize it in either way would be senseless, nonsense, category mistaken.

 

While classes are defined in terms of truth, categories are defined in terms of spanning (which in turn is defined in terms of sense). A category with respect to a term 'X' will include the class of X things and some (usually not all) of the counter-class of X things. The class of married things has in it me, the Queen, my wife, etc. The counter-class has my son, the Pope, the Moon, Mars, etc. (viz. anything of which 'married' is not true). The category with respect to 'married' has me, the Queen, my wife, my son, the Pope, etc., but not the Moon, Mars, etc. For, while 'married' is false of, say, both my son and Mars, it spans only the former and not the latter. (pp. 4-5)

 

From: George Englebretsen, A Reintroduction to Sommers' Tree Theory, in Essays on the Philosophy of Fred Sommers, Lewiston: The Edwin Mellen Press 1990, pp. 1-32.

 

Lecture 3. Ontology and Semantics.

 

It is at the beginning of Book IV of his Metaphysics that Aristotle first introduces his new conception of philosophy. There is a science which studies being as being. Indeed the special character of this science vis-à-vis the other sciences is supposed to consist in the fact that whereas the latter investigate a particular sphere of Being, philosophy investigates being as being. (1) What distinguishes the concept of Being, for Aristotle, is that it is the most general concept. (2) For of everything and anything one can say that it is. Everything and anything, therefore, can be called Being.

 

Clearly Aristotle arrives at his new conception of philosophy by dropping the aspect of justification from the preliminary conception developed at the beginning and settling exclusively for the aspect of highest generality. The highest, pre-eminent science, called philosophy, is universal, but does not have a justificatory role in relation to the particular sciences. This conception, since it is orientated towards the concept of Being (on), leads to the conception of philosophy as ontology. An explicitly semantic enquiry was, however, unknown to Aristotle. This is why he called predicative determinations both onta (beings) and legomena (something said). (3) In the Middle Ages this undecidedness became the starting-point of the nominalism controversy. Aristotle refused to follow Plato in treating the meaning of predicates as an independent object. However, because he failed to perceive the semantic dimension he inevitably objectified their meaning. The result is a peculiar extension of the concept of Being (on). It is - together with the concepts of the one and of something - more comprehensive than that of an object (tode ti).

 

The title 'ontology' now begins to iridesce. It would have an unequivocal sense if one were to define it, as I initially did, and as is usual in analytical philosophy, in terms of the concept of an object, or, which amounts to the same thing, in terms of the concept of Being in the sense of existence; 'ontology' would then mean 'theory of objects'. In contrast to this the introduction of ontology by Aristotle, which became standard in the tradition, contains a tension which was not resolved in the tradition. This tension is a consequence of Aristotle's dual orientation: on the one hand, to the - objectual - formula being as being; on the other hand, to the verbal form 'is'. He lets himself be guided by this verbal form even where it does not connote Being in the sense of existence, i.e. where the 'is' is not the 'is' of a being; and since the formula being as being nonetheless remains the guiding principle, the formalizing approach, which in itself would have led away from the restriction to the problem of objects, is again being cast into an objectual terminology. Aristotelian ontology transcends the formal theory of objects in the direction of a formal semantics, but in such a way that what emerges is misinterpreted in terms of an object-oriented perspective, owing to the lack of awareness of the semantic dimension.

 

Thus if one views the traditional elaboration, essentially determined by Aristotle, of the idea of a philosophical fundamental discipline as ontology from a language-analytical perspective (one of reflection on the meaning of words) it turns out to be unsatisfactory in regard to both of the aspects in Aristotle's preliminary conception of philosophy. Firstly, in regard to its justification: the object-orientated Aristotelian formal discipline lacks a foundation in a method of reflection; such a foundation would be provided by a formal semantics (though whether this is the only possible foundation we do not yet know). Secondly, in regard to its scope: its claim to universality could only seem convincing so long as one remained orientated to objects. But the orientation to everything (and that means: to all objects) appears itself restricted as soon as one focusses on the realm of the formal itself. The perspective on objects then corresponds to just one semantic form among others. (p. 21)

 

Notes

(1) 1003 a22-25, 1025 b7-10.

(2) 998 b220f.

(3) cf. e.g. 1045 b30 f.

 

From: Ernst Tugendhat, Traditional and Analytical Philosophy. Lecture on the Philosophy of Language, translated by P. A. Gorner, Cambridge: Cambridge University Press 1982.

 

Ontology asks and tries to answer two related questions. What are the categories of the world? And what are the laws that govern these categories? In chemistry, by comparison, we search for chemical elements and the laws which they obey; and in physics we try to discover the elementary particles and their laws. But ontology is not a science among sciences. Its scope is larger; its viewpoint, fundamentally different.

 

When Anaximander [perhaps Empedocles?] speculated that everything is made up from the four elements -- fire, earth, air, and water -- he proposed, in effect, a rudimentary theory of chemistry. And so did Anaximenes when he maintained that everything consists of various densities of air. Ontology was born when someone realized that any view of this sort implies a distinction between individual things, on the one hand, and their properties, on the other. Ontology was born when someone realized that there are, not only different kinds of individual thing, but also different kinds of entity. This realization must have led almost immediately to a number of distinctly ontological questions. How, precisely, do individuals and properties differ? How are they related to each other? Are there perhaps any other kinds of entity? And so on. Plato's theory of forms deals with just these sorts of questions, and we think of it, therefore, as one of the first ontological inquiries.

 

But properties are not the only kind of abstract entity, as we shall see. There are numbers and, hence, there is arithmetic. There are sets and, hence, there is set theory. There are several kinds of abstract entity and, hence, several further kinds of inquiry, distinct both from the natural sciences and from ontology. And this fact raises a number of new questions for ontology. How do these kinds of abstract entity differ from each other? How are they connected with each other? And how are they related to individual things? What looks at the beginning of the ontological enterprise like the fundamental dichotomy, namely, the distinction between individuals and properties, turns out to be just one of many equally basic distinctions.

 

A particular ontological theory must of course strive to accommodate all of these differences and connections. It must attempt to present us with a complete list of categories. Everything there is must find a place in the system. The theory is unsatisfactory if it is incomplete, that is, if there are entities which are not categorized. It may be argued, for example, that classes have no place within the Aristotelian framework of substance and modification of substance. But it is not enough that everything should find a category in the theory. Everything must be fitted to the proper category. An ontological theory is also faulty if it assigns entities to the wrong categories. For example, a Cartesian would contend that Aristotelians misplace the mind: A mind is a substance in its own right and not, as Aristotelians claim, a mere modification of a substance. Or it might be argued, to turn to the present, that natural numbers are, not classes of classes, but quantifiers of a certain kind. Nor, finally, must the ontology contain distinctions that make no differences. Categorial distinctions must not be made capriciously. Categories are not to be multiplied arbitrarily. Aristotelian ontology may be accused of introducing a spurious distinction by separating so-called essential from accidental properties.

 

Hand in hand with the discovery of categories goes the discovery and formulation of categorial laws. To discern the former is, in a sense, to find the latter; for these laws specify how the categories differ from each other and resemble each other. There is again a similarity to the natural sciences. In physics, the fundamental laws describe the behavior of elementary particles. In ontology, similarly, the fundamental laws describe the behavior of categories. For example, individuals are subject to change, while properties are not. Individuals, furthermore, even though they exemplify properties, are never exemplified by anything. Laws of this nature distinguish between different categories; and the second law mentioned also shows how they establish connections between categories. Properties are connected with entities by means of what I shall call "the nexus of exemplification." Classes, on the other hand, are connected with entities by the membership relation. And it may be thought, mistakenly as we shall see, that properties and classes determine each other mutually. (pp. 3-5)

 

From: Reinhardt Grossmann, The Categorial Structure of the World, Bloomington: Indiana University Press 1983.

 

Metaphysics consists of the separate disciplines of ontology and cosmology, each with their respective methodologies. Formal ontology connects logical categories -- especially the categories involved in predication -- with ontological categories. The goal of a formal ontology is the construction of a lingua philosophica, or characteristica universalis, as explicated in terms of an ars combinatoria and a calculus ratiocinator as part of al formal theory of predication. A formal ontology should serve as the framework of a characteristica realis, and hence as the basis of a formal approach to science and cosmology. It should also serve as a framework for our commonsense understanding of the world. (p. 23)

 

From: Nino Cocchiarella, Formal Ontology and Conceptual Realism, New York: Springer 2007.

---

Comparative formal ontology is the study of how different informal ontologies can be formalized and compared with one another in their overall adequacy as explanatory frameworks. One important criterion of adequacy of course is consistency, a condition that can be satisfied only by formalization. Formalization also makes explicit the commitments of an ontology.

 

There are other important criteria of adequacy as well, however, in addition to consistency and transparency of ontological commitment. One major such criterion is that a formal ontology must explain and provide an ontological ground for the distinction between Being and existence, or, if the distinction is rejected, an adequate account of why it is rejected. Put simply, the problem is: Can there be things that do not exist? Or is Being the same as existence? Different formal ontologies will answer these questions in different ways.

 

The simplest account of the distinction between Being and existence is that between actualism and possibilism, where by existence we mean physical existence, i.e., existence as some type of physical object; and by Being we mean possible physical existence, i.e., physical existence in some possible world. According to possibilism, there are objects that do not now exist but could exist in the physical universe, and hence Being is not the same as existence. In actualism Being is the same as existence.

---

---

Possibilism: There are objects (i.e., objects that have Being or) that possibly exist but that do not in fact exist.

Therefore: Existence = Being.

---

---

Actualism: Everything that is (has Being) exists.

Therefore: Existence = Being.

---

---

 

Now the implicit understanding in formal ontology of both possibilism and actualism is that the objects that the quantifier phrases in these statements range over are values of the variables bound by the first-order quantifiers ∀ and ∃ (for the universal and existential quantifiers, respectively), and hence that what has Being (on the level of objects) is a value of the (object) variables bound by these quantifiers. In other words, to be (an object, or thing) in both actualism and possibilism is to be a value of the bound object variables of first-order logic. This means that in possibilism, where Being is not the same as existence, existence must be represented either by different quantifiers or by a predicate, e.g., E!, which is the predicate usually chosen for this purpose.

 

Another criterion of adequacy for a formal ontology is that it must explain the ontological grounds, or nature, of modality, i.e., of such modal notions as necessity and possibility, and in particular the meaning of possible physical existence. If the modalities in question are strictly formal, on the other hand, as is the case with logical necessity and possibility, then it must explain the basis of that formality.

 

This criterion cannot be satisfied by a set-theoretic semantics alone, especially one that allows for arbitrary sets of possible worlds (models) and so-called accessibility relations between those worlds. Such a semantics may be useful for showing the consistency of a modal logic, or perhaps even as a guide to our intuitions in showing its completeness; but it does not of itself provide an ontological ground for modality, or, in the case of logical modalities, explain why those modalities are strictly formal.

 

We restrict our considerations here to how physical existence, both actual and possible, is represented in a formal ontology. This does not mean that the formal ontologies considered here cannot be extended so as to include an account of how abstract objects might be represented as well, if allowed at all. (pp. 105-106)

 

Nino Cocchiarella, Actualism versus Possibilism in Formal Ontology, in: Roberto Poli, Johanna Seibt (eds.), Theory and Applications of Ontology. Vol 1: Philosophical Perspectives., Dordrecht: Springer 2010, pp. 105-118.

 

2. Ontology and its Parts

 

Ontology is the theory of what there is, the theory of Being. It considers the full ontological universe, all items that are possible, describing and classifying them and searching for the principles of this universe, principles of taking together the plurality of ontic objects, particular beings, into one -- the Being.

 

Thus two questions govern ontological investigations: what is possible and why? The second question, concerning the Being's principles, may be strengthened to the deepest -- last in logical order -- question: how that which is given, or rather what there is, is possible? The question about principles of Being, i.e. general laws of nature, plus the question that makes possible what there is and renders impossible what there isn't? Because of its matter and problematic, ontology is the most general discursive discipline. It is the general theory of possibility. By the nature of its questions it is also very modal.

 

3. Ontology has two sides: descriptive -- phenomenological, and theoretical -- formal. Hence, it is divided into three parts: onto-ontics (In brief: ontics), ontomethodology and ontologic.

 

4. Ontics is devoted to the selection of ontological problems and notions, their differentiation, classification and analysis. Doing ontics we construe the conceptual net of a given ontological theory, i.e. its categories. It is also one of the tasks of ontics to state ontological hypotheses, based on the previous analysis of concepts.

 

Ontics, being a part of ontology, is itself complex. Its further description depends on the general idea of ontology, on accepted classification of ontological concepts. For example, Ingarden has distinguished three parts of ontology: the material ontics, the formal ontics and the existential one. Notice that his ontology is, in our terms, ontics!

 

5. Ontomethodology concerns ways of doing ontology, methods and types of ontological constructions as well as principles of choice between ontological statements and theories. Examples of such ontomethodic principles are: tine principle of non-contradiction, the principle of sufficient reason, and Ockham's razor.

 

Indication and discussion of the appropriate principles is necessary for sure for any critique of ontological theories, particularly the critique of the logical means used in ontology.

 

6. Ontologic is a logic of the ontic realm. It is an investigation of ontological connections, concerning particularly logical relations between pieces of optic information. Also, it is a theory of the fundament of ontic relations.

 

Ontologic considers the organization of the ontological universe, trying to describe its mechanism. It describes the complexity of the Being, looking for its laws and base - the Logos.

 

7. Ontics is a purely descriptive and analytical discipline, ontologic is speculative and formal. They are, however, closely connected and interrelated disciplines, affecting one another. The product of ontics is a description, usually complex, of the ontological universe, whereas ontologic supplies different theories of this universe.

 

Certainly, at present ontic considerations are more common. In ontology we have many descriptions and claims, but not as many theories. Among Polish ontologists, for instance, Ingarden may be regarded as a typical ontics reasoner, while Leśniewski should be treated as a typical ontologician." (pp. 23-24)

 

From: Jerzy Perzanowski, Ontologies and Ontologics in: Ewa Zarnecka-Bialy (ed.), Logic Counts, Dordrecht: Kluwer 1990, pp. 23-42.

---

2. Beings, the Being and Being.

 

2.1 Ontology is the discipline of Being. It is the theory of what there is, why and how.

 

As the tradition makes clear, the verb 'to be' used here is ambiguous. It refers either to the domain of existing objects, depending therefore on an appropriate theory of existence, or to what really exists (in a metaphysical sense) - to logos which is behind existing items and behind the facts. The latter realm emerges when emphasis is placed on the second part of the above definition, i.e., on the questions: why and how? The answer we are looking for is of the form: there is x because x is possible and in addition for existing objects x satisfies certain specific conditions of existence. Possibility is frequently explained as a matter of consistency or coherence, whereas existence conditions are specified in terms of stability, homeostasis, actualization, etc.

 

2.2 Ontology is distinguished by its extreme generality and by the richness and fertility of its basic notions. The most basic ontological notions are notions of a particular being and the Being. Both notions can be approached in at least three ways: possibilistically, connectionally (or qualitatively), and through what we shall call verb-type-ontologies.

 

2.3 In the verb-type-approach both notions - of a being and the Being - are obtained from the verb 'to be' by transformations and nominalizations.

 

The theory behind the latter is quite complicated, much more than is the grammar of the verb 'to be' itself, and this is complicated enough. In most Indo-European languages we must distinguish at least eleven variants of the verb 'to be', which leads to a rather rich variety of verb-type-ontologies.

 

A being here is defined as any item which is in a sense specified according to an appropriate variant of the verb 'to be'.

 

The verb 'to be' has its basic form in the context 'S is P', where it denotes a binary relation. The most general verb-type-ontology is therefore the general theory of relations. By specification of variants of the verb 'to be' we obtain variants of the verb-type-ontology, for example the ontology of things and properties and the set-theoretic ontology.

 

2.4 In the possibilistic approach, a being is defined as any possible object, hence the ontological universe is understood as the space of all possibilities. Its ontology is therefore the general theory of possibility.

 

2.5 The qualitative or connectional approach deals with the most traditional concept of a being, defined as any item having some quality (or as a subject of qualities).

 

Here at least three topics need further elaboration: the ontological connection itself and the items connected: qualities and subjects. In consequence, there are four variants of this type of ontology: the qualitative one, stressing qualities, the subjective one, putting emphasis on subjects (individuals); the connectional one, stressing the formal side of the ontological connection, and the eclectic one, which tries to develop all three factors in unison.

 

From: Jerzy Perzanowski, The Way of Truth, in: Roberto Poli, Peter Simons (eds.), Formal Ontology, Dordrecht: Kluwer 1996, pp. 61-130.

 

I must now make a few brief comments about the principal parts of metaphysics. This is necessary because often particular authors confuse metaphysics with some of its parts, thus unnecessarily restricting the scope of the discipline. The discussion of such a taxonomy, then, prevents confusions which may obscure the nature of metaphysics.

 

Some of the parts of metaphysics with which it is most frequently confused are ontology, etiology, philosophical anthropology, theology, and philosophy of language. There are many others, but for the sake of brevity I shall use only these as examples.

 

Consider those philosophers who identify metaphysics with ontology. Ontology is concerned with the study of the most fundamental categories of Being and with the relations among them. This naturally explains the use of the term "ontology" and suggests that the discipline deals with Being, a traditional description of the object of metaphysics. The use of the term "ontology" to refer to metaphysics appears in early modern philosophy and is still with us. Indeed many contemporary metaphysicians speak of their discipline as ontology.

 

Yet, if ontology involves only the subject matter mentioned, it is clear that it excludes much that metaphysicians discuss. For example, much of what is discussed in the philosophy of mind falls outside ontology, for it does not concern the development of the fundamental categories of Being and the exploration of the relations among them. It concerns rather the categorization of the mind and the description of its relations to various categories, and this does not seem to be a part of ontology." (pp. 147-148, notes omitted)

 

From: Jorge J. E. Gracia, Metaphysics and Its Task. The Search for the Categorial Foundation of Knowledge, Albany: State University of New York Press 1999.

 

An ontology consists of all those items which are, in an appropriate sense, accepted. There are different views as to what it is for an item to be accepted into an ontology. For some, it is merely a matter of existence or Being; for others, it is a matter of real existence or Being, where this is something which stands in contrast to ordinary existence or Being. This is an issue which, important as it is, will not concern me here; for most of what I have to say will remain correct under any reasonable understanding of the term. However, it is perhaps worth pointing out that I do not require the term to have any psychological connotations. An item is accepted into an ontology because it should be there, not necessarily because someone puts it there. It is, if you like, the ontology which accepts the item and not the person who endorses the ontology.

 

An ontology is total; it includes everything that is accepted. By contrast, we may talk of a partial ontology or of a sub-ontology, which includes some, but perhaps not all, of what is accepted.

 

An ontology is actual; it includes everything that it is correct to accept. By contrast, we may talk of a possible ontology, which consists of everything that might be accepted (as the total ontology).

 

One might take a sceptical stand on either of these two distinctions. One might hold that there is no such thing as a total, as opposed to a partial, ontology; for any ontology there is always a larger ontology within which it is contained. (The paradoxes have led some to hold such a view for the ontology of sets). And one might also hold that there is no such thing as an actual, as opposed to a possible, ontology. There is nothing which counts as the correct ontological stand; there are merely different, equally legitimate, stands.

 

I shall not engage with the first form of scepticism, though what I have to say can, to some extent, be made to accommodate it. However, I shall engage with the second form. I shall attempt to see how absolutist notions might be eschewed in the description of an ontology.

 

This is not because I endorse the second form of scepticism. It is more that I am interested in the distinction on which the position rests rather than with the position itself. The sceptic draws a line. But one may be interested in the line without accepting it as a boundary. (p. 265)

 

From: Kit Fine, "A Study of Ontology", Noûs 25, 1991, pp. 263-294.

 

The word ontology has four established meanings in philosophy.

 

There are two intersecting sets of distinctions. Pure philosophical ontology is different from applied scientific ontology, and ontology in the applied scientific sense can be understood either as a discipline or a domain.

 

Ontology as discipline is a method or activity of enquiry into philosophical problems about the concept or facts of existence. Ontology as a domain is the outcome or subject matter of ontology as a discipline. Applied scientific ontology construed as an existence domain can be further subdivided as the theoretical commitment to a preferred choice of existent entities, or to the real existent entities themselves, including the actual world considered as a whole, also known as the extant domain. Ontology as a theoretical domain is thus a description or inventory of the things that are supposed to exist according to a particular theory, which might but need not be true. Ontology as the extant domain, in contrast, is the actual world of all real existent entities, whatever these turn out to be, identified by a true complete applied ontological theory. As a result, we must be careful in reading philosophical works on ontology, when an author speaks of "ontology" without qualification, not to confuse the intended sense of the word with any of the alternatives. (pp. 2-3)

 

From: Dale Jacquette, Ontology, Montreal: McGill-Queen's University Press 2002.

 

Ontology is the theory of objects. And it is so of every type of object, concrete and abstract, existent and non-existent, real and ideal, independent and dependent. Whatever objects we are or might be dealing with, ontology is their theory. Object is used in this sense as synonymous with the traditional term Being.

 

THESIS 1. An ontology is not a catalogue of the world, a taxonomy, a terminology or a list of objects, things or whatever else. If anything, an ontology is the general framework (= structure) within which catalogues, taxonomies, terminologies may be given suitable organization. This means that somewhere a boundary must be drawn between ontology and taxonomy.

 

THESIS 2. An ontology is not reducible to pure cognitive analysis (in philosophical terms, it is not an epistemology or a theory of knowledge). Ontology represents the 'objective' side (= on the side of the object), and the theory of knowledge the subjective side (= on the side of the knowing subject) of reality. The two sides are obviously interdependent, but this is not to imply that they are the same (exactly like the front and rear of a coin). In order to conduct ontological analysis, it is necessary to 'neutralize', so to speak, the cognitive dimension, that is, to reduce it to the default state. I assume that the default state is the descriptive one, where the dimensions of attention, of interest, etc., are as neutral as possible (= natural attitude). It is of course possible to modify the default state and construct ontologies of the other cognitive states as well, but this involves modifications of the central structure.

 

THESIS 3. There is nothing to prevent the existence of several ontologies, in the plural. In this case too, ontological study is useful because, at the very least, it renders the top categories explicit and therefore enables verification of whether there are reasonable translation strategies and of which categorization can serve best to achieve certain objectives. (p. 313)

 

From: Roberto Poli, "Ontology for Knowledge Organization", in Rebecca Green (ed.), Knowledge Organization and Change, Indeks, Frankfurt, 1996, pp. 313-319.