The theory of form logic

Wolfgang Freitag, Alexandra Zinke



We investigate a construction schema for first-order logical systems, called “form logic”. Form logic allows us to overcome the dualistic commitment of predicate logic to individual constants and predicates. Dualism is replaced by a pluralism of terms of different “logical forms”. Individual form-logical systems are generated by the determination of a range of logical forms and of the formbased syntax rules for combining terms into formulas. We develop a generic syntax and semantics for such systems and provide a completeness proof for them. To illustrate the idea of form logic, and the possibilities it facilitates, we discuss three particular systems, one of which is the form-logical reconstruction of standard first-order predicate logic.


form logic; particular-universal distinction; three-valued logic; logical form; Wittgenstein

Full Text:



Armstrong, David, 1989, A Combinatorial Theory of Possibility, Cambridge University Press, Cambridge.

Frege, Gottlob, 1960/1891, “Function and Concept”, pages 21–41 in: Translations of the Philosophical Writings of Gottlob Frege, 2nded, Peter Geach and Max Black (eds.), Basil Blackwell, Oxford.

Freitag, Wolfgang, 2009, Form and Philosophy. A Topology of Possibility and Representation, Synchron, Heidelberg.

Hintikka, Jaakko, 1956, “Identity, variables, and impredicative definitions”, The Journal of Symbolic Logic 21: 225–45.

Kearns, John T., 1979, “The Strong Completeness of a System for Kleene’s Three-Valued Logic”, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 25: 61–68.

Macbride, Fraser, 2005, “The Particular-Universal Distinction. A Dogma of Metaphysics?”, Mind 114: 565–614.

Ramsey, Frank P., 1925, “Universals”, Mind 136: 401–17.

Russell, Bertrand, 1903, Principles of Mathematics, Cambridge University Press, Cambridge.

Skyrms, Brian, 1981, “Tractarian Nominalism”, Philosophical Studies 40: 199–206.

Stenius, Eric, 1976, “The Sentence as a Function of its Constituents in Frege and in the Tractatus”, pages 71–84 in: Essays on Wittgenstein in Honour of G.H. von Wright, Acta Philosophical Fennica, vol. 28, Jaakko Hintikka (ed.), North-Holland, Amderstam.

Wehmeier, Kai F., 2004, “Wittgensteinian Predicate Logic”, Notre Dame Journal of Formal Logic 45/1: 1–11.

Wehmeier, Kai F., “How to Live Without Identity — and Why”, Australasian Journal of Philosophy (forthcoming).

Wittgenstein, Ludwig, 1922, Tractatus Logico-Philosophicus, Routledge, London and New York.

Wittgenstein, Ludwig, 1980/1964, Philosophical Remarks, University of Chicago Press, Chicago.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism