"An initial reference-point in this area is provided by Leibniz's distinction between two components of his ambitious project in mathematical logic or, rather, project to create a mathematical logic. On the one hand, Leibniz proposed to develop a characteristica universalis or lingua characteristica which was to be a universal language of human thought whose symbolic structure would reflect directly the structure of the world of our concepts. On the other hand, Leibniz's
ambition included the creation
of a calculus ratiocinator which was conceived of by him as a method of symbolic calculation which would mirror the processes of human reasoning.
When Leibniz's project began to be realized in the nineteenth century, its two components were taken up by different research traditions. The "algebraic' school represented by Boole, Peirce, and Schröder sought to develop in the spirit of Leibniz's calculus ratiocinator mathematical techniques by means of which different kinds of human reasoning could be mastered. In contrast, Frege himself noted, his Begriffsschrift was to be primarily a characteristica universalis
in Leibniz's sense, a Formelsprache
des reinen Denkens (cf. here Sluga, Frege against the Booleans, Notre Dame Journal of Formal Logic, 28, 1987, pp. 80-98). Admittedly, Frege made claims for it also as a calculus ratiocinator, but those claims were not met with enthusiasm. Husserl contradicted them, apparently thinking (as Tarski did later) that a lingua universalis cannot be purely formal. In any case, as Jourdain snidely noted, Frege's formalism was singularly clumsy as a means of actual reasoning: "... using Frege's symbolism as a calculus
would be rather like using a three-legged stand-camera for what is called 'snap-shot' photography" (Jourdain, "Preface" to Louis Couturat, The algebra of logic, 1914 pp. III-X). Subsequent attempts to find specific help for the purpose of concrete work in logic or in the foundations of mathematics have tended to confirm rather than to disconfirm Jourdain's judgment. The theoretical interest of Frege's ambitious project is due to its being an attempted characteristica universalis or at least lingua
characteristica mathematicae, not to its being a viable calculus ratiocinator."
From: Jaakko Hintikka - Lingua Universalis vs. Calculus Ratiocinator. An ultimate presupposition of Twentieth-century philosophy. Dordrecht: Kluwer 1997 pp. IX-X.
"Answering Schröder's criticisms of Begrifsschrift, Frege states that, unlike Boole's, his logic is not a calculus ratiocinator, or not merely a calculus ratiocinator, but a lingua characterica.(1) If we come to understand what Frege means by this opposition, we shall gain a useful insight into the history of logic. The opposition between calculus ratiocinator and lingua characterica has several connected but distinct aspects. These various aspects, most of
the time not stated by Frege, have to be
brought out by a study of his work. From Frege's writings a certain picture of logic emerges, a conception that is perhaps not discussed explicitly but nevertheless constantly guides Frege. In referring to this conception I shall speak of the universality of logic.
This universality of Frege's lingua characterica is, first, the universality that quantification theory has in its vocabulary and that the propositional calculus lacks. Frege frequently calls Boole's logic an 'abstract logic' (2), and what he means by that is that in this logic the proposition remains unanalyzed. The proposition is reduced to a mere truth value. With the introduction of predicate letters, variables, and quantifiers, the proposition becomes articulated
and can express a meaning. The new
notation allows the symbolic rewriting of whole tracts of scientific knowledge, perhaps of all of it, a task that is altogether beyond the reach of the propositional calculus. We now have a lingua, not simply a calculus. Boole's logic, which cannot claim to be such a lingua, remains the study, in ordinary language, of algebraic relations between propositions. This study is carried out in ordinary language and is comparable to many branches of mathematics, say group theory. In Frege's system the propositional
calculus subsists embedded in quantification theory; the opposition between lingua and calculus is, in this respect, not exclusive, and that is why Frege writes that his own logic is not merely a calculus ratiocinator.(3)However, the opposition between calculus ratiocinator and lingua characterica goes much beyond the distinction between the propositional calculus and quantification theory. The universality of logic expresses itself in an important feature of Frege's system. In that system the quantifiers binding
individual variables range over all objects. As is well known, according to Frege, the ontological furniture of the universe divides into objects and functions. Boole has his universe class, and De Morgan his universe of discourse, denoted by '1'. But these have hardly any ontological import. They can be changed at will. The universe of discourse comprehends only what we agree to consider at a certain time, in a certain context. For Frege it cannot be a question of changing universes. One could not even say that
he restricts himself to one universe. His universe is the universe. Not necessarily the physical universe, of course, because for Frege some objects are not physical. Frege's universe consists of all that there is, and it is fixed."
(1) Schröder's criticisms are contained in his review of Begriffsschrift, published in Zeitschrift für Mathematik und Physik 25 (1880), Historisch-literarische Abtheilung, 81-94. Frege's reply was an address to a learned society, delivered on 27 January 1882 and published in its proceedings, 'Über den Zweck der Begriffsschrift', Sitzungs-berichte der Jenaischen Gesellschaft für Medicin und Naturwissenschaft fur das Jahr 1882 (Jena 1883), pp. 1-10,
reprinted in Gottlob Frege, Begriffsschrift
und andere Aufsatze, Hildesheim 1964, pp. 97-106. [English translation by Terrell Ward Bynum in: Gottlob Frege - Conceptual notation, and related articles - Oxford, Clarendon Press, 1972, reprinted 2000, pp. 90-100] On the origin of the expression 'lingua characterica' see Günther Patzig's footnote 8, on p. 10 of Gottlob Frege, Logische Untersuchungen, Göttingen 1966.
(2) See, for instance, Frege's comments on Boole in 'Über den Zweck der Begriffsschrift' (mentioned in footnote 1), pp. 1-2.
(3) In 'Ober die Begriffsschrift des Herr Peano and meine eigene', Berichte über die Verhandlungen der Königlichen Sächsischen Gesellschaft der Wissenschaften zu Leipzig, Mathematisch-physische Classe 48 (1897), 361-378, [English translation in: Gottlob Frege - Collected papers on mathematics, logic and philosophy - Edited by Brian McGuinness - Oxford, Basil Blackwell, 1984, pp. 234-248]. Frege writes on p. 371: "Boole's logic is a calculus ratiocinator,
but no lingua characterica;
Peano's mathematical logic is in the main a lingua characterica and, subsidiarily, also a calculus ratiocinator, while my Begriffsschrift intends to be both with equal stress." Here the terms are used with approximately the meanings given in the present paragraph: Boole has a propositional calculus but no quantification theory; Peano has a notation for quantification theory but only a very deficient technique of derivation; Frege has a notation for quantification theory and a technique of derivation.
From: Jean van Heijenoort - "Logic as calculus and logic as language," Synthese 17: 324-330 (1967) pp. 324-325.
"Sir Isaiah Berlin has shown how to understand Tolstoi on the basis of the insight that Tolstoi was a fox who believed that he was a hedgehog (1). It is time we realize similarly what Frege was: a semanticist who did not believe in semantics. This insight we owe largely to van Heijenoort, who describes it by speaking of two conceptions of language and logic (2). He called them conceptions of logic as language and logic as calculus. More generally, and perhaps a shade
more aptly, we might label them conceptions
of language as the inescapable medium of communication (in brief, "language as medium") and language as calculus.
The most general form of the former I can think of is that we cannot according to this view get "outside" our language, as it were look on it from outside. The reason is that the results of all such "viewing" must be expressible in our language. Now this language presupposes in all its uses certain semantical relations (relations of representation) between language and reality. (Otherwise we could not use language in our transactions with reality.)
But since these semantical relations are
presupposed in each and every use of language, they cannot be expressed in language. Any attempt to do so involves a circularity and hence results in nonsense or tautology.
I am not putting forward these views as being unchallengeable. Indeed, they are challenged by the view of language and its logic as calculus. According to this view we can do all or most of the things the contrary opinion deemed impossible. Among other things, we can think of the representative relationships between language and the world as being varied radically and in a large scale. The point of using the term "calculus" is hence not to compare language to
an uninterpreted calculus, a mere game
with characters, but to emphasize that language, including our very own home language, is in principle freely reinterpretable like a calculus, at least for the purposes of a semanticist.
As van Heijenoort already pointed out, the development of all systematic logical semantics (model theory) thus presupposes some variant of the view of language as calculus. For one of the leading ideas of all model theory is to vary the interpretation of some part of the language in question in a way the view of language as medium does not countenance. As we saw, the stronger forms of this view even forbid saying anything significant and nonvacuous about the basic semantical
relationships (relationships of
naming, reference, or otherwise named representation)."
(I) Isaiah Berlin. The Hedgehog and the Fox. London, 1957.
(2) Jean Van Heijenoort, "Logic as Language and Logic as Calculus". Synthese. vol. 17 (1967). pp. 324-330.
From: Jaakko Hintikka "Frege's hidden semantics," Revue Internationale de Philosophie 33: 716-722 (1979). pp. 716-717
SELECTED BIBLIOGRAPHY
Banchetti-Robino Marina, "Husserl's theory of language as calculus ratiocinator," Synthese 112: 303-321 (1997).
Abstract: "This paper defends an interpretation of Husserl's theory of language, specifically as it appears in the Logical Investigations, as an example of a larger body of theories dubbed `language as calculus'. Although this particular interpretation has been previously defended by other authors, such as Hintikka and Kusch, this paper proposes to contribute to the discussion by arguing that what makes this interpretation plausible are Husserl's distinction between the notions of meaning-intention and meaning-fulfillment, his view that meaning is instantiated through meaning-intending acts of transcendental consciousness, and his view that the content of meaning-intending acts is ideal meaning simpliciter. As well, the paper argues that the phenomenological method of reduction itself presupposes the notion that reality as such can be reached by subtracting the influence of the language of the natural attitude and its ontological commitments and it, thus, presupposes the conception of language as a reinterpretable calculus."
Bar-Hillel Yehoshua, "Husserl's conception of a purely logical grammar," Philosophy and Phenomenological Research 17: 362-369 (1956).
Reprinted in: Aspects of language. Essays and lectures on philosophy of language, linguistic philosophy and methodology of linguistics - Jerusalem - The Magnes Press - The Hebrew University, 1970 pp. 89-97.
Reprinted also in: Jitendra Nath Mohanty - Readings on Husserl's Logical Investigations - The Hague - Martinus Nijhoff 1977 pp. 128-137.
Blanché Robert. La logique et son histoire d'Aristote à Russell. Paris: Armand Colin 1970.
See Chapter VIII. Leibniz 1. Situation de Leibniz 189; 2. Logique classique 193; 3. Lingua characteristica universalis 201; 4. Calculus ratiocinator 208-219.
Burkhardt Hans. Logik und Semiotik in der Philosophie von Leibniz. München : Philosophia Verlag 1980.
See in particular: 3.04 Die Charakteristik pp. 186-205.
Cocchiarella Nino, "Predication versus membership in the distinction between logic as language and logic as calculus," Synthese 77: 37-72 (1988).
Cohen Jonathan L., "On the project of a universal character," Mind 63: 49-63 (1954).
Reprinted as Chapter 1 in: Knowledge and language. Selected essays of L. Jonathan Cohen - Edited and with an introduction by James Logue - Dordrecht, Kluwer, 2002, pp. 1-14.
Couturat Louis. La logique de Leibniz: d'aprés des documents inédits. Paris: Felix Alcan 1901.
Reprinted: Hildesheim, Olms, 1961 e 1985.
Dresner Eli, "Hintikka's 'language as calculus vs. language vs. universal medium' distinction," Pragmatics and Cognition 7: 405-421 (1999).
Ferriani Maurizio, "Boole, Frege e la distinzione leibniziana lingua-calculus," Annali di Discipline Filosofiche dell'Università di Bologna 3 (1984).
Reprinted in: Maurizio Ferriani - Logica e filosofia della logica. Studi su Boole e Peirce - Bologna, CLUEB, 1999 pp. 3-26.
Goldfarb Warren, "Logic in the Twenties: the nature of the quantifier," Journal of Symbolic Logic 44: 351-368 (1979).
Goldfarb Warren. Frege's conception of logic. In Future pasts. The analytic tradition in Twentieth century philosophy. Oxford: Oxford University Press 2001. pp. 25-41
"The first task is that of delineating the differences between Frege's conception of logic and the contemporary one. I shall start with the latter. Explicit elaborations of it are surprisingly uncommon. (In most writing on issues in philosophical logic,
it is implicitly assumed; yet many textbooks gloss over it, for one pedagogical reason or another.) There are various versions; I will lay out the one formulated by Quine in his textbooks (1) as it seems to me the clearest.
On this conception, the subject matter of logic consists of logical properties of sentences and logical relations among sentences. Sentences have such properties and bear such relations to each other by dint of their having the logical forms they do. Hence, logical properties and relations are defined by way of the logical forms; logic deals with what is common to and can be abstracted from different sentences. Logical forms are not mysterious quasi-entities, à la Russell. Rather, they are simply schemata: representations of the composition of the sentences, constructed from the logical signs (quantifiers and truth-functional connectives, in the standard case) using schematic letters of various sorts (predicate, sentence, and function letters). Schemata do not state anything and so are neither true nor false, but they can be interpreted: a universe of discourse is assigned to the quantifiers, predicate letters are replaced by predicates or assigned extensions (of the appropriate r-ities) over the universe, sentence letters can be replaced by sentences or assigned truth-values. Under interpretation, a schema will receive a truth-value. (pp. 25-26)
(...)
Such a schematic conception is foreign to Frege (as well as to Russell). This comes out early in his work, in the contrast he makes between his Begriffsschrift and the formulas of Boole: "My intention was not to represent an abstract logic in formulas, but to express a content through written signs in a more precise and clear way than it is possible to do through words." (2) And it comes out later in his career in his reaction to Hilbert's Foundations of Geometry: "The word 'interpretation' is objectionable, for when properly expressed, a thought leaves no room for different interpretations. We have seen that ambiguity [Vieldeutigkeit] simply has to be rejected." (3) There are no parts of his logical formulas that await interpretation. There is no question of providing a universe of discourse. Quantifiers in Frege's system have fixed meaning: they range over all items of the appropriate logical type (objects, one place functions of objects, two place functions of objects, etc.). (p. 27)
(...)
On Frege's universalist conception, then, the concern of logic is the articulation and proof of logical laws, which are universal truths. Since they are universal, they are applicable to any subject matter, as application is carried out by instantiation. For Frege, the laws of logic are general, not in being about nothing in particular (about forms), but in using topic-universal vocabulary to state truths about everything. (p. 28)
(...)
My central aims in this paper have been to delineate Frege's universalist conception of logic and contrast it with a more familiar one, to show that this conception connects with many other points in Frege's philosophy, and to suggest that the conception is a well-motivated one, given the nature of Frege's project. Of course, today most of us would find the schematic conception (or some variant of it) far more natural, if not unavoidable. But I hope to have caused us to reflect on how much else has to shift in order to make it." (p. 41)
(1) Elementary Logic (Boston: Ginn, 1941) and Methods of Logic (New York: Holt, 1950).
(2) "Über den Zweck der Begriffsschrift," Jenaische Zeitschrift far Naturwissenschaft 16, Supplement (1882): 1-10, p. 1
(3) "Über die Grundlagen der Geometrie," Jahresbericht der Deutschen Mathematiker Vereinigung 15 (1906): 293-309, 377-403, 423-430, p. 384
Haaparanta Leila, "Analysis as the method of logical discovery: some remarks on Frege and Husserl," Synthese 77: 73-98 (1988).
Heinekamp Albert, "Ars characteristica und natürliche Sprache bei Leibniz," Tijdschrift voor Filosofie 34: 446-488 (1972).
"One can distinguish two different approaches toward language in Leibniz's work. On one hand, he considers natural language insufficient and would like to replace it by a 'rational' language (lingua philosophica), while on the other hand, he is an empirical researcher of language who collects phenomena from the most diverse languages in order to compare them with other languages. The literature about Leibniz highlights only these two aspects of his work, and usually considers them to be incompatible. The relationship between Leibniz's remarks about 'characteristica universalis' and his theories about natural language is explored. Even though Leibniz did not produce an explicit theory about this relationship, a difference between these two is clearly implied in his remarks. Natural language and characteristica are to Leibniz, basically different in their existence, their function, and their performance. Nevertheless, they both form integral components of Leibniz's monad theory."
Hernández Márquez Victor Manuel, "Leibniz y la lingua characterica," Diánoia.Anuario de Filosofía 45: 35-63 (1999).
Hintikka Jaakko, "Frege's hidden semantics," Revue Internationale de Philosophie 33: 716-722 (1979).
"From my observations, several corollaries follow for the recent discussions concerning Frege in the literature.
For instance, the truly interesting historical problem is not to find anticipations of Frege on sense and reference in earlier philosophers or, more generally, to study Frege's theory in its relation to his predecessors. The fascinating novelty which I for one would very much like to understand better is how Frege came upon his ideas about extensional logic, ideas which were radically different from the great majority of traditional philosophers. Furthermore, the deep objects of comparison and contrast in twentieth-century philosophy are not later theories of senses (or their partial dispensability as in Kripke) or other theories of intensional contexts but those recent findings which challenge Frege's treatment of first-order logic.
Among these targets of challenge, the most important ones are probably the paucity of Frege's ontology (set of categories represented by his primitive symbols), the so-called Frege principle (1), and the Frege-Russell claim that ordinary-language words like the English "is" and the German "ist" are ambiguous between the "is" of existence, identity, predication, and subsumption (2). In some ways, the true import of Frege's tacit first-order semantics is best seen from the criticisms to which these three cornerstones of Frege's semantics have been subjected." p. 722
(1) See here my paper "Theories of Truth and Learnable Languages" (forthcoming).[Stig Kanger and Sven Öhman (eds.) - Philosophy and grammar: papers on the occasion of the Quincentennial of Uppsala University - Dordrecht, D. Reidel Publishing Company, 1981 pp. 37-58]
(2) See my paper, "'Is', Semantical Games, and Semantical Relativity." Journal of Philosophical Logic. vol. 8 ( 1979), 433-468.
Hintikka Jaakko. Semantics: a revolt against Frege. In Contemporary philosophy. Vol. I. Philosophy of language. Edited by Floistad Guttorm. The Hague: Martinus Nijhoff 1981. pp. 57-82
Hintikka Jaakko. Wittgenstein's semantical Kantianism. In Ethics: Proceedings of the Fifth International Wittgenstein Symposium, 25-31 August 1980, Kirchberg am Wechsel, Austria. Edited by Morscher Edgar and Stranzinger Rudolf. Wien: Hölder-Pichler Tempsky 1981. pp. 375-390
Hintikka Jaakko, "A hundred years later: the rise and fall of Frege's influence in language theory," Synthese 59: 27-49 (1984).
Hintikka Jaakko and Hintikka Merrill. Wittgenstein and language as the Universal Medium. In Investigating Wittgenstein. Oxford: Blackwell 1986. pp. 1-29
Reprinted in: Lingua Universalis vs. Calculus Ratiocinator. An ultimate presupposition of Twentieth-century philosophy pp. 162-190.
Hintikka Jaakko, "On the development of the model-theoretic viewpoint in logical theory," Synthese 77: 1-36 (1988).
Hintikka Jaakko. Lingua Universalis vs. Calculus Ratiocinator. An ultimate presupposition of Twentieth-century philosophy. Dordrecht: Kluwer 1997.
Contents: Origin of the essays VII; Introduction IX-XXII; 1. Contemporary philosophy and the problem of truth 1; 2. Is truth ineffable? 20; 3. Defining truth, the whole truth and nothing but the truth 46; 4. On the development of the model-theoretic viewpoint in logical theory 104; 5. The place of C. S. Peirce in the history of logical theory 140; 6. (with Merrill B. Hintikka): Wittgenstein and language as the universal medium 162; 7. Carnap's work in the foundations of logic and mathematics in a historical perspective 191; 8. Quine as a member of the tradition of the universality of language 214; Appendixes. 1. Jean van Heijenoort: Logic as calculus and logic as language 233; 2. Martin Kusch: Husserl and Heidegger on meaning 240-268.
"Of these essays, 1 and 5 are being published elsewhere at the same time but have not been published before. Essays 2, 4 and 6-8 are published without any changes. For technical reasons, it has not been feasible to make them completely uniform typographically or to bring their references completely up to date. Essay 3, which is the mainstay of the argumentation of this volume, has been revised for republication. In particular, its sections 9 and 12 have been thoroughly rewritten."
Hintikka Jaakko. The place of C. S. Peirce in the history of logical theory. In The rule of reason. The philosophy of Charles Sanders Peirce. Edited by Brunning Jacqueline and Forster Paul. Toronto: Toronto University Press 1997. pp. 13-33
Kluge Eike Henner W., "Frege, Leibniz "et alii"," Studia Leibnitiana 9: 266-274 (1977).
"Patzig has argued that Frege's use of the phrase 'lingua characterica' constitutes an insufferable pleonasm that no-one with first-hand knowledge of Leibniz's writings would have committed. On this he bases an argument to show that Frege's knowledge of Leibniz was weak and garnered from secondary sources. I show that this claim ignores certain crucial Leibniz quotes by Frege which he could have found only in the Gerhardt edition of Leibniz's mathematical works and his correspondence, and lay the foundation for an analysis of the historical influence of Leibniz on the development of Frege's thought."
Kluge Eike Henner W., "Frege, Leibniz and the notion of an ideal language," Studia Leibnitiana 12: 140-154 (1980).
"This paper examines the question, whether and to what degree Leibniz's project of an ideal language -- of a "lingua characterica" which at the same time can also function as a "calculus ratiocinator" -- had an influence on Frege's project of a "Begriffsschrift". It concludes that not only are there sufficient conceptual similarities to warrant an hypothesis of historical connection, but that there are also historical indications in Frege's own writings to that effect."
Kusch Martin, "Husserl and Heidegger on meaning," Synthese 77: 99-127 (1988).
Reprinted in: Jaakko Hintikka - Lingua Universalis vs. Calculus Ratiocinator. An ultimate presupposition of Twentieth-century philosophy - Dordrecht, Kluwer, 1997, pp. 240-268.
Kusch Martin. Language as calculus vs. language as universal medium. A study in Husserl, Heidegger, and Gadamer. Dordrecht: Kluwer 1989.
Contents: Preface IX-XI; Part I. Introduction: Language as calculus vs. language as the universal medium 1; Part II. Husserl's phenomenology and language as calculus 11; Part III. Heidegger's ontology and language as the universal medium 135; Part IV. Between Scylla and Charybdis -- Gadamer's hermeneutics 229; Notes to Part I 259; Notes to Part II 260; Notes Part III 290; Notes to Part IV 310; Bibliography 315; Index of names 343; Index of subjects 353.
Lenzen Wolfgang. Calculus universalis. Studien zur Logik von G. W. Leibniz. Paderborn: Mentis Verlag 2004.
O'Briant Walter. Leibniz's Europeanism and the characteristica universalis. In Leibniz und Europa. VI. Internationaler Leibniz-Kongress. Vorträge. 1. Teil. Hannover: Gottfried-Wilhelm-Leibniz-Gesellschaft 1994. pp. 541-543
Patzig Günther, "Leibniz, Frege und die sogennante 'lingua characteristica universalis'," Studia Leibnitiana.Supplementa: 103-112 (1969).
Akten des Internationale Leibniz-Kongresses Hannover 14-19 November 1966 - Vol. 3: Erkenntnislehre, Logik, Sprachphilosophie, Editionsberichte
Peckhaus Volker. Logik, Mathesis universalis und allgemeine Wissenschaft: Leibniz und die Wiederentdeckung der formalen Logik im 19. Jahrhundert. Berlin: Akademie Verlag 1997.
Contents: Vorwort VII-VIII; 1. Einleitung 1; 2. Die Idee der mathesis universalis bei Leibniz 25; 3. Die frühe Rezeption Leibnizscher mathesis universalis und Logik 64; 4. Die "logische Frage" und die Entdeckung der Leibnizschen Logik 130; 5. Leibniz und die englische Algebra der Logik 185; 6. Ernst Schröder: "Absolute Algebra" und Leibnizprogramm 233; 7. Schluss 297; Verzeichnisse 309-412.
Peckhaus Volker, "Calculus ratiocinator versus characteristica universalis? The two traditions in logic, revisited," History and Philosophy of Logic 25: 3-14 (2004).
Peregrin Jaroslav. Formal logic and the pursuit of meaning. 1996.
Proops Ian, "Russell and the Universalist conception of logic," Noûs 41: 1-32 (2007).
Rossi Paolo. The twisted roots of Leibniz' Characteristic. In The Leibniz Renaissance. Firenze: Leo S. Olschki 1989. pp. 271-289
Schneider Martin, "Leibniz' Konzeption der "characteristica universalis" zwischen 1677 und 1690," Revue Internationale de Philosophie 48: 213-236 (1994).
Schõfer Erasmus. Heidegger's language: metalogical forms of thought and grammatical specialities. In On Heidegger and language. Edited by Kockelmans Joseph J. Evanston: Northwestern University Press 1972. pp. 281-301
Translated from German by Joseph J. Kockelmans
Scholz Heinrich. Concise history of logic. New York: Philosophical Library 1961.
Translated from: Abriss der Geschichte der logik (1931) by Kurt F. Leidecker
Sluga Hans, "Frege against the Booleans," Notre Dame Journal of Formal Logic 28: 80-98 (1987).
Smith Barry. Characteristica Universalis. In Language, truth and ontology. Edited by Mulligan Kevin. Dordrecht: Kluwer 1990. pp. 50-81
"Our task will be to construct portions of a directly depicting language which will enable us to represent the most general structures of reality. We shall draw not on standard logical treatments of the contents of epistemic states as these are customarily conceived in terms of propositions. Rather, we shall turn to a no less venerable but nowadays somewhat neglected tradition of formal ontology: not sentences or propositions, but maps, diagrams or pictures, shall serve as the constituents of our mirror of reality."
Swanson J.W., "On the calculus ratiocinator," Inquiry 8: 315-331 (1965).
Van Heijenoort Jean, "Logic as calculus and logic as language," Synthese 17: 324-330 (1967).
Reprinted in:
R.S. Cohen & M.W. Wartofsky (editors) - Boston Studies in the Philosophy of Science - vol. 3 (1967), In Memory of Norwood Russell Hanson, Proceedings of the Boston Colloquium on Philosophy of Science, 1964/1965 (Dordrecht, Reidel, 1967), pp. 440-446
Jean van Heijenoort - Selected essays - Napoli, Bibliopolis, 1985, pp. 11-16
and in: Jaakko Hintikka - Lingua Universalis vs. Calculus Ratiocinator. An ultimate presupposition of Twentieth-century philosophy - Dordrecht, Kluwer, 1997, pp. 233-239.
Van Heijenoort Jean. Set-theoretic semantics. In Logic Colloquium '76. Edited by Gandy Robin O. and Hyland John Martin Elliott. Amsterdam: North-Holland 1977. pp. 183-190
Vilkko Risto. A hundred years of logical investigations: reform efforts of logic in Germany 1781-1879. Paderborn: Mentis Verlag 2002.
Wolenski Jan, "Husserl and the development of semantics," Philosophia Scientiae 3: 151-158 (1998).
"This paper investigates the role of Edmund Husserl in the development of formal or model-theoretic semantics through glasses of the distinction of language as calculus vs. language as universal medium, introduced by Jaakko Hintikka and Martin Kusch. In particular, the paper raises the question of possible Husserl's influence on the conception of language accepted in Polish philosophy, in particular by Lesniewski and Tarski."
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