Theory and History of Ontology
by Raul Corazzon - e-mail: raul.corazzon[at]formalontology.it
For an overview see the Index of the Pages, the SITE MAP or the Alphabetical Index of the Philosophers: A-F - G-O - P-Z; You can also download this page as 
Table of Contemporary Ontologists 
(click on the image to see the PDF file)
Index of the Section: "The Rediscovery of Ontology in Contemporary Thought"
Table of Formal and Descriptivists Ontologists (PDF - from Bernard Bolzano to present time)
Ontologists of the 19th and 20th Centuries (a selection of critical judgments about some of the greatest philosophers of the recent past)
Living Ontologists (a list of authors with an interest in ontology, with synthetic bibliographies)
Selected bibliography on Bolzano's Logic and Ontology: A-G
Selected bibliography on Bolzano's Logic and Ontology: H-Z
INTRODUCTION
"[The Wissenschaftslehre] in its treatment of the logical 'theory of elements' far surpasses anything that world-literature has to offer in the way of a systematic sketch of logic. Bolzano did not, of course, expressly discuss or support any independent demarcation of pure logic in our sense, but he provided one de facto in the first two volumes of his work, in his discussions of what underlay a Wissenschaftslehre or theory of science in the sense of his conception; he did so with such purity and scientific strictness, and with such a rich store of original, scientifically confirmed and fruitful thoughts, that we must count him as one of the greatest logicians of all time.
He must be placed historically in fairly close proximity to Leibniz, with whom he shares important thoughts and fundamental conceptions, and to whom he is also philosophically akin in other respects."
Edmund Husserl - Logical Investigations - vol. I - Prolegomena to a pure logic § 61 (Appendix) (1900).
"It is as logician, methodologist and epistemologist that Bolzano, after a long period of neglect, has regained philosophical attention in twentieth century. Mainly in order to combat radical skepticism, he found it necessary to base his teachings in these fields on certain ontological conceptions. He was convinced that there exist truth-in-themselves (Wharheiten an sich) prior to and independent of language and man. These truths he carefully distinguished from truths expressed in words and conceived truths. The set of truths-in-themselves is a subset of the set of propositions (in-themselves) (Sätze an sich), again to be distinguished from propositions expressed in words and conceived propositions. Propositions consists of terms (ideas-in-themselves, Vorstellungen an sich). These are likewise to be distinguished, on the one hand, from the words or word sequences by which they are denoted and, the other, from subjective ideas that occur in our mind. Although linguistic entities and conceived entities exist concretely, terms, propositions, and truths do not. Terms were equally carefully distinguished from their objects, whether or not these objects themselves existed concretely. Though Bolzano was a Platonist (in the modern sense), his ontology was rather remote from that of Plato or, for that matter, from that of Kant, in spite of the common an sich terminology."
Yehoshua Bar-Hillel - "Bolzano, Bernard" in: Paul Edwards (ed.) - The Encyclopedia of Philosophy, vol. II p. 337-338 (1967).
"While the idealists were removing every trace of objectivity from Kant's semantics, there was in a corner of the Austro-Hungarian empire, ignored by the leaders of German philosophy, a Czech priest by the name of Bernard Bolzano, who was engaged in the most far-reaching and successful effort to date to take semantics out of the swamp into which it had been sinking since the days of Descartes. Bolzano was the first to recognize that transcendental philosophy and its idealistic sequel were a reductio ad absurdum of the semantics of modem philosophy. He was also the first to see that the proper prolegomena to any future metaphysics was a study not of transcendental considerations but of what we say and its laws and that consequently the prima philosophia was not metaphysics or ontology but semantics. The development of these ideas in his monumental Wissenschaftslehre and in a variety of other writings established Bolzano as the founder of the semantic tradition. Bolzano's philosophy was the kind that takes from and then gives life to science. His approach to semantics was developed in dialectical interplay with the decision to solve certain problems concerning the nature of mathematical knowledge. Kant had not even seen these problems; Bolzano solved them. And his solutions were made possible by, and were the source of, a new approach to the content and character of a priori knowledge."
J. Alberto Coffa - The semantic tradition from Kant to Carnap. To the Vienna station - Edited by Linda Wessels - Cambridge, Cambridge University Press 1991
"Bernard Bolzano was a lone forerunner both of analytical philosophy and phenomenology.
Born in Prague in the year when Kant's first Critique ;appeared, he became one of the most acute critics both of Kant and of German Idealism. He died in Prague in the same year in which Frege was born; Frege is philosophically closer to him than any other thinker of the nineteenth or twentieth century.
Bolzano was the only outstanding proponent of utilitarianism among German-speaking philosophers, and was a creative mathematician whose name is duly remembered in the annals of this discipline. His Wissenschaftslehre (Theory of Science) of 1837 makes him the greatest logician in the period between Leibniz and Frege.
The book was sadly neglected by Bolzano's contemporaries, but rediscovered by Brentano pupils: its ontology of propositions and ideas provided Husserl with much of his ammunition in his fight against psychologism and in support of phenomenology, and through Twardowski it also had an impact on the development of logical semantics in the Lwow-Warsaw School."
Wolfgang Künne - "Bolzano, Bernard" in: Edward Craig (ed.) - Routledge Encyclopedia of Philosophy, vol. II p. 823-827 (1998).
THE IMPORTANCE OF BOLZANO'S LOGIC
"Why look back now? Let me start by stating my non-historian's view of the modem history of logic. Like many scientific disciplines, flourishes while being ill-defined. Despite textbook orthodoxy, the issue what logic should be about is a legitimate topic of discussion, and one to which answers have varied historically. One key topic is reasoning: its valid laws for competent users, and perhaps also its sins: mistakes and fallacies. But the modern core also includes independent concerns such as formal languages, their semantic meaning and expressive power. Moreover, the modem research literature, much of it still in a pre-textbook stage, reveals a wide range of topics beyond reasoning and meaning, dealing with general structures in information, and many-agent activities other than reasoning, such as belief revision or communication. Thus, the agenda of logic keeps evolving, as it should. In this light, going back to the pioneers is not just a matter of piety, but also of self-interest.
One striking feature of older literature is its combination of issues in logic with general methodology of science. One sees this with Bolzano, Mill, or Peirce, but also with major modem authors, such as Tarski, Carnap, or Hintikka. The border line between logic and philosophy of science seems arbitrary. Why have 'confirmation', 'verisimilitude', or 'theory structure' become preserves for philosophers of science, and not for logicians? This separation seems an accidental feature of a historical move, viz. Frege's 'contraction of concerns', which tied up logic closely with the foundations of mathematics, and narrowed the agenda of the field to a point where fundamentalists would say that logic is the mathematics of formal systems. Admittedly, narrowing an agenda and focusing a field may be hugely beneficial. Frege's move prepared the ground for the golden age of logic in the interbellum, which produced the core logic curriculum we teach today. At the same time, broader interests from traditional logic migrated, and took refuge in other disciplines. But as its scientific environment evolved in the 20th century, logic became subject to other influences than mathematics and philosophy, such as linguistics, computer science, AI, and to a lesser degree, cognitive psychology and other experimental disciplines.
Compared with Frege, Bolzano's intellectual range is broad, encompassing general philosophy, mathematics, and logic. This intellectual span fits the above picture. Even so, I am not going to make Bolzano a spokesman for any particular modern agenda. The current professional discussion speaks for itself. But I do want to review some of his themes as to contemporary relevance. Incidentally, the main sources for the analysis in my 1985 paper, besides reading Bolzano himself, have been Kneale & Kneale 1962, and Berg 1963. After the Vienna meeting this autumn of 2002, I learnt about Rusnock 2000, whose logic chapters turned out sophisticated and congenial.
A short summary of Bolzanian themes:
We quickly enumerate those points in Bolzano's logical system that are the most unusual and intriguing to logicians. These will return at lower speed in later sections.
All these themes do, or should, occur in modern logic! Let's take them up now one by one."
From: Johann van Benthem - Is there still logic in Bolzano's key? - in: Edgar Morscher (ed.) - Bernard Bolzanos Leistungen in Logik, Mathematik und Physik - Sankt Augustin, Academia Verlag, 1999, pp. 12-14.
BOLZANO'S CONTRIBUTION TO LOGIC
"The Wissenschaftslehre (1837) by Bernard Bolzano (1781-1848) is one of the masterpieces in the history of logic. In this encyclopedic work Bolzano intended to construct a new and philosophically satisfactory foundation of mathematics. The search for such a foundation brought forth valuable by-products in logical semantics and axiomatics. For example, Bolzano introduced the notion of abstract, non-linguistic proposition and described its relations to other relevant notions such as sentence, truth, existence and analyticity. Furthermore, he studied relations among propositions and defined highly interesting notions of validity, consistency, derivability and probability, based on the idea of "replacing" certain components in propositions. In set theory, he stated the equivalence of reflexivity and infiniteness of sets and considered isomorphism as a sufficient condition for the identity of powers of infinite sets. He conceived of a natural number as a property characterizing sets of objects, even though he did not base his development of arithmetic on this notion, and analyzed sentences about specific numbers in a way reminiscent of Frege and Russell. In a posthumous manuscript from the 1830's (recently published) he developed a theory of real numbers, which differs from those of Dedekind, Weierstrass, Méray and Cantor. Bolzano's real numbers may be identified with certain sequences of rational numbers.
Logic in Bolzano's sense is a theory of science, a kind of metatheory, the objects of which are the several sciences and their linguistic representations. This theory is set forth in Bolzano's monumental four-volumes work Wissenschaftslehre (hereafter referred to as WL). Bolzano's very broad conception of logic with its strong emphasis on methodological aspects no doubt accounts for the type of logical results which he arrived at. The details of his theory of science proper are given in the fourth volume of the WL and belong to the least interesting aspects of his logic. On the other hand, Bolzano's search for a solid foundation for his theory of science left very worthwhile by-products in logical semantics and axiomatics. His theory of propositions in the starting-point of these results.
Bolzano became more and more aware of the profound distinction between the actual thoughts of human beings and their linguistic expressions on the one hand, and the abstract propositions and their components which exist independently of these thoughts and expressions on the other hand. Furthermore, he imagined a certain fixed deductive order among all true propositions. This idea was intimately associated with his vision of a realm of abstract components of propositions constituting their logically simple parts.
For the following presentation of Bolzano's theory of propositions I have to define some terms. A concrete sentence occurrence is a sequence of particles existing in space and time, arranged according to the syntactic rules of a grammar, and contrasting with its surroundings. A simple sentence shape, on the other hand, is a class of similar concrete occurrences of simple sentences. A compound sentence shape is built up recursively from simple sentence shapes by means of syntactic operations. Not every compound sentence shape has a corresponding concrete sentence occurrence. Two compound sentence shapes may be considered identical if they are built up from identical simple sentence shapes in the same way. Two simple sentence shapes are identical if they contain the same sentence occurrences.
Now consider the compound sentence containing the following concrete sentence occurrence: 'a simple sentence shape is a class of similar sentence occurrences or it is not the case that a simple sentence shape is a class of similar sentence occurrences'. In another sense one could say that this sentence shape, which is an abstract logical object outside of space and time, contains two sentence occurrences, i.e., two abstract "occurrences" of the simple sentence shape containing the following concrete inscription: 'a simple sentence shape is a class of similar sentence occurrences'. In the following, I will use the expression 'sentence occurrence' exclusively in the first, concrete sense.
Bolzano's notion of abstract non-linguistic proposition (Sätz an sich) is a keystone in his philosophy and can be traced in his writings back to the beginnings of the second decade of the 19th century. I shall try to characterize Bolzano's conception of propositions by means of certain explicit assumptions. These assumptions also give information about the relation between propositions and other logically interesting objects.
In his logic Bolzano utilizes a concept which is an exact counterpart of the modern logical notion of existential quantification. Therefore, he could have stated that (1) There exist entities, called 'propositions', which fulfill the following necessary conditions (2) through (15). (Cf. WL §§ 30 ff.)
Thus, propositions possess the kind of logical existence developed in modern quantification theory. However, (2) A proposition does not exist concretely in space and time (WL § 19).
According to Bolzano, both linguistic and mental entities such as thoughts and judgments are concrete (WL, §§ 34, 291). Hence, propositions could not be identified as concrete linguistic or mental occurrences. Furthermore,(3) Propositions exist independently of all kinds of mental entities (WL § 19).
Therefore the identification between propositions and mental dispositions sometimes made in medieval nominalism cannot be applied to propositions in Bolzano's sense.
A proposition in Bolzano's sense is a structure of ideas-as-such. Hence, an idea-as-such (Vorstellung an sich) is a part of a proposition which is not itself a proposition (WL § 48). But to he able to generate propositions we have to characterize ideas-as-such independently of propositions. This is in fact implicit in Bolzano. He worked extensively with the relation of being an object of an idea as-such, which corresponds in modern logic to the relation of being an element of the extension of a concept. In terms of this relation, taken as a primitive by Bolzano, certain postulates may be extracted from his writings which concern the existence and general properties of ideas-as-such.
Independently of human minds and of linguistic expressions there exists a collection of absolutely simple ideas-as-such. As examples Bolzano mentions the logical constants expressed by the words 'not', 'and', 'some', 'to have', 'to be', 'ought' (WL, 78); but he admits being unable to offer a more comprehensive list. He seems to mean that each complex idea A can be analyzed into a sequence S(A) of simple ideas which would probably include certain logical constants.
I shall call this sequence S(A) the 'primitive form' of A. The manner in which a complex idea is built up from simple ones may be expressed by a chain of definitions. So it appears that some complex ideas behave somewhat like the open formulas of a logical calculus. Bolzano assumes that two ideas are strictly identical if and only if they have the same primitive form (WL §§ 92, 119, 557).
From: Jan Berg - Bolzano's contribution to logic and philosophy of mathematics - in: R. O. Gandy, J. M. Hyland - Logic Colloquium '76, Amsterdam, North Holland, pp. 147-150.
BOLZANO'S CONTRIBUTION TO SEMIOTIC
"The Prague philosopher, Bernard Bolzano, in his major work The Theory of Science (1837), mainly in the last two of the four volumes, reserves much space for semiotics. The author frequently cites Locke's Essay and the Neues Organon, and discovers in Lambert's writings "an semiotics many very estimable remarks", though these are of little use "for the development of the most general rules of scientific discourse", one of the aims Bolzano sets himself (paragraph 698).
The same chapter of The Theory of Science bears two titles, one of which --Semiotik -- appears in the table of contents (vol. IV, p. XVI), the other of which -- Zeichenlehre -- heads the beginning of the text (p. 500); paragraph 637, which follows, identifies both designations -- the theory of signs or semiotics (Zeichenlehre Oder Semiotik). If, in this chapter and in several other parts of the work, the author's attention is held above all by the testing of the relative perfection of signs (Vollkomenheit oder Zweckmässigkeit) and particularly of signs serving logical thought, then it is in the beginning of the third volume that Bolzanο tries to introduce the reader to the fundamental notions of the theory of signs throughout paragraph 285 (pp. 67-84) which overflows with ideas and is titled "the designation of our representations" (Bezeichnung unserer Vorstellungen).
This paragraph begins with a bilateral definition of the sign, "An object through whose conception we wish to know in a renewed fashion another conception connected therewith in a thinking being, is known to us as a sign". A whole chain of geminate concepts follows, some of which are very new, while others, referring back to their anterior sources, are newly specified and enlarged. Thus Bolzano's semiotic thoughts bring to the surface the difference between the meaning (Bedeutung) of a sign as such and the significance (Sinn) that this sign acquires in the context of the present circumstance, then the difference between the sign (1) produced by the addresser (Urheher) and (2) perceived by the addressee who, himself, oscillates between understanding and misunderstanding (Verstehen und Missverstehen). The author makes a distinction between the thought and expressed interpretation of the sign (gedachte und sprachliche Auslegung), between universal and particular signs, between natural and accidental signs (natürlich und züfallig), arbitrary and spontaneous ( willkürlich und unwillkürlich), auditory and visual (hörbar und sichtbar), simple (einzeln) and composite (zusamengestzt, which means "a whole whose parts are themselves signs"), between unisemic and polysemic, proper and figurative, metonymical and metaphorical, mediate and immediate signs; to this classification he adds lucid footnotes on the important distinction to be made between signs (Zeichen) and indices (Kennzeichen) which are devoid of an addresser, and finally on another pressing theme, the question of the relationship between interpersonal (an Andere) and internal (Sprechen mit selbst) communication." pp. 202-203 of the reprint.
From: Roman Jakobson - A Glance at the Development of Semiotics, in The Framework of Language – Translated from the French by Patricia Baudoin - Ann Arbor, Michigan Studies in the Humanities, Horace R. Rackham School of Graduate Studies, 1980 and reprinted in: R. Jakobson – Selected writings. Contributions to comparative mythology. Studies in linguistics and philology – Berlin, Walter de Gruyter, 1985 pp. 199-218
EXCERPTS FROM THE Theory of Science (Wissesnschaftslehre)
The main work of Bolzano, Wissenschaftslehre, was first published in four volumes: Wissenschaftslehre: Versuch einer ausführlichen und grösstetheils neuen Darstellung der Logik, mit steter Rücksicht auf deren bisherige Bearbeiter. Herausgegeben von mehren seiner Freunde. Mit einer Vorrede von Dr. J. Cr. Heinroth. - Sulzbach 1837.
Critical edition edited by Jan Berg: Gesamtausgabe - Voll.11-14 (1985-2000).
Vol. I XVI+571 [3], vol. II VIII+568+[2], vol. III VIII+575 and vol. IV XX+683 pages; the work is composed of five book in 718 paragraphs.
Summary (from the editions of Rolf George and Jan Berg - citations by Bolzano are from Introduction, § 15):
Introduction (§ 1-16). Logic as a theory of science
Book One: Theory of Fundamentals Truths (§§ 17-45)"including the proof that there are truths in themselves and that we humans also have the capacity to know them
Purpose, Contents and Divisions of this Book (§ 17)
Refutation of some Objections (§ 18)
Part One: Of the Existence of Truths in Themselves (§§ 19-33)
Part Two: Of the Recognizability of Truth (§§ 34-45)
Book Two: Theory of Elements "or the theory of ideas, propositions, true propositions and inferences in and of themselves"
Purpose, Contents, and Sections of this Book (§ 46)
Part One: Of Ideas in Themselves (§§ 47-114)
Appendix: Earlier Treatment of the Subject Matter of this Part (§§ 115-120)
Part Two: Of Propositions in Themselves (§§ 121-184)
Appendix: Earlier Treatment of the Subject Matter of this Part (§§ 185-194)
Part Third: Of True Propositions (§§ 195-222)
Part Fourth: Of Arguments (§§ 223-253)
Appendix: Earlier Treatment of the Subject Matter of this Part (§§ 254-268)
Book Three: Theory of Knowledge "or concerning the conditions underlying the possibility of knowing the truth, particularly among us humans"
Purpose, Content, and Divisions of this Book (§ 269)
Part One: Of Ideas (§§ 270-289)
Part Two: Of Judgments (§§ 290-306)
Part Third: Of the Relation between Judgments and Truth (§§ 307-316)
Part Fourth: Of Certainty, Probability and Confidence in Judgments (§§ 317-321)
Book Four: The Art of Invention (§§ 322-391) "or rules to be observed in the enterprise of thought when it is aimed at discovering the truth"
Book Five: Theory of Science proper (§§ 392-718) "or rules that must be observed in dividing up the domain of truth generally into particular sciences and in presenting those sciences in specialized scholarly treatises."
§1. What the Author Understands by Theory of Science
Suppose that all truths which are now, or eve were, known to any man were somehow collected together, e.g. compiled in a single book; I would call such an aggregate the sum of all human knowledge. Compared to the immense domain of truths in themselves, most of which are altogether unknown, this sum is very small; but it is large, ever too large a sum for the mental capacity of any man.(...)4. It should be possible through some reflection t find the rules which we must follow in dividing the total domain of truth into individual sciences and which must govern the writing of the respective treatises. There can also be no doubt that the sum of these rules itself deserves to be called a science, since it is clearly worth while to collect the most important part of the in a special book, and to order the and provide proofs for them so that everyone can understand and accept them with conviction. I allow myself to call it the theory of science [Wissenschaftslehre], since it is the science which teaches us to represent other sciences (actually only their treatises) (...) [Berg 1973]
§ 15. General Outline of this Treatise
It is desirable that the theory of science proper should be preceded by a discussion of rules to be followed in the discovery of truths: heuretic. Heuretic seems to require an antecedent discussion of the general conditions of human knowledge: epistemology. Epistemology can be fruitfully developed only if it is preceded by the theory of ideas, propositions and deductions: the theory of elements. The latter will be preceded by a theory of fundamentals in which it is proved that there are truths and propositions in themselves. [George 1972].
§ 19. What the author Means by a Proposition in Itself
In order to indicate as clearly as possible to my readers what I mean by a proposition in itself (Satz an sich), I shall begin by explaining first what I call as assertion or a proposition expressed in words. I use this term to designate a verbal statement (most often consisting f several, but at times of just a single word) if it is an instrument of asserting or maintaining something, if it is therefore always either true or false, on of the two, in the ordinary sense of these words, if it (as can also say) must be either correct or incorrect (...) But I also call the following sequence of words a proposition: 'Squares are round'. For through this form of words something is also stated or asserted, although something false and incorrect. On the other hand, I do not call the following expressions propositions: 'The omnipresent God', 'A round square'. For though these expressions something is indeed represented but nothing is stated or asserted. Consequently one can, strictly speaking, neither say that there is anything thru, nor that is anything false in them. [Berg 1973].
§ 67. Ideas without Referents
It is true that most ideas have some, or even infinitely many, referents. Still, there are also ideas that have no referent at all, and thus do not have an extension. The clearest case seems to be that of the concept designated by the word 'nothing'. It seems absurd to me to say that this concept, has an object too, i.e. a something that it represents. Somebody might in turn find it absurd that an idea or representation should have no object at all, and thus represent nothing, but the reason for this is in all likelihood that he means by ideas merely mental ideas, i.e. thoughts, and that he identifies the content of these mental ideas (i.e. the ideas in themselves) with their objects. It is reasonable to say that the thought 'nothing' has a content, namely the objective concept 'nothing' itself; but that the latter should also refer to a certain object, is an assertion that can hardly be justified. The same holds of the ideas 'a round square', 'green virtue', etc. We do and must think something by these expressions, but this is not the object of these ideas, but the ideas in themselves. Incidentally, it is evident from these ideas themselves that no object can correspond to them, since they would attribute contradictory properties to it. However, there are probably also ideas that lack reference, not because they attribute contradictory properties to their objects, but for some other reason. Thus the ideas 'golden mountain', 'a presently blooming vine' are perhaps without object, although they do not contain a contradiction.
NOTE. It might be objected that ideas of which I have said that they lack reference must nonetheless have extensions, since they are occasionally compared with respect to their extensions, and some of them called wider than others. For example we find it quite proper to say that a person who shows the impossibility of round polygons achieves more than one who merely shows the impossibility of round squares, since the latter follows from the former, but not conversely. This conclusion seems to be valid only if it is assumed that the concept of a round polygon is wider than that of a round square. I admit that the impossibility of round squares can be inferred from the possibility of round polygons in general. I deny, however, that for this inference we need the minor premise 'round squares are a kind of round polygon', and that we thus have to attribute an extension to these two concepts in order to draw the above conclusion. It is after all the case that the assertion that no round polygons are possible follows from the proposition 'No polygon is round'. (Or every polygon is something that is not round.) Hence the conclusion that no square is round, and thus that round squares are impossible, follows from the minor premise that all squares (not only the round ones that do not exist) are also polygons. Moreover, in § 108 I shall discuss a sense in which the relation of subordination can also be applied to ideas that do not have reference. [George 1972]
The main features of Bolzano's ontology
(click to enlarge the image)
(From: Jan Berg - Ontology without ultrafilters and possible worlds. An examination of Bolzano's ontology - Sankt Augustin - Academia Verlag 1992 - p. 32)
Last modified: Tuesday, March 09, 2010