Universal Logic

Logical Forms

Pontifical Catholic University, Rio de Janeiro - PUC-RJ
and Brazilian Research Council - CNPq

Frege generalized the basic intuition of traditional logic that every sentence is of subject-predicate form through two main moves: the analysis of sentences in terms of function and arguments, and the analysis of quantification as higher-order predication. Combining these two ideas, every linguistic assertion, and every logical formula, can be interpreted in different ways as a predication involving one or more subjects. This has important applications to theories of truth and falsity, theories of description, as well as to other logical and philosophical issues. In the three tutorials I will discuss the following subjects:

I. Predicates and properties. States of affairs. Truth and falsity.

II. Logical properties. Logical forms. Logical truth and logical states of affairs.

III. Descriptive terms and descriptive properties. Senses and propositions. Truth as instantiation.

Main references

Chateaubriand, O. Logical Forms: Truth and Description. CLE – Unicamp, 2001.
______ “Descriptions: Frege and Russell Combined”. Synthese, v. 130, 2002.
______ “Deconstructing “On Denoting””. In G. Imaguire & B. Linsky (eds.) “On Denoting” 1905-2005. Philosophia Verlag, 2005.
_______ “The truth of thoughts: variations on fregean themes”. Grazer Philosophische Studien, v. 75, 2007.
______ “Senses: Response to Marco Ruffino”. Manuscrito, v. 31, 2008.

Frege, G. “On Sense and Reference”. Translations from the Philosophical Writings of Gottlob Frege. P. Geach & M. Black (eds.). Blackwell, 1960.
______ “Thoughts”. Collected Papers on Mathematics, Logic, and Philosophy. B. McGuinness (ed.). Blackwell, 1984.
Kripke, S. Naming and Necessity. Harvard University Press, 1980.
Russell, B. “On Denoting”. Logic and Knowledge, Essays 1901-1950. R.C. Marsh (ed.). Allen and Unwin, 1956.
______ “The Philosophy of Logical Atomism”. Logic and Knowledge, Essays 1901-1950. R.C. Marsh (ed.). Allen and Unwin, 1956.
Tarski, A. “What are Logical Notions?” History and Philosophy of Logic, 7, 1986.