Logic 3

Mirko Jakić, Ph.D.
full professor

 Programme

2+1 (3^rd year of philosophy study)

 Goals:

• precise application of symbollic means of contemporary logic in philosophical texts analysis;

• symbolic grasp of subsentential structural relations in logical and linguistic research of natural languages;

• application of symbollically expressed subsentential structure relations in philosophical researches in the philosophy of science (deductive basis of natural sciences);

• developing of more precise means of contemporary symbollic method on example pf basic first-order logic model: predicate logic model;

• logic as a distinct applied scientific discipline: research methods and object;

• philosophy of logic.

 Content:

Predicate logic and natural languages. Basic terms definition. Single terms. Reference and denotation. Predicates. Variables. Constants. Domain. Quantifyers. Instantiation. Translating object language sentences in predicate logic symbollic language. Predicate logic model's formulae. Context and scope of a proceeding. Complex sintactic characteristics of subsentential relations. Identity. Symbollic semantics of predicate logic model. Extension. Interpreting quantified formulae. Truth-functional conditions of quantified formulae. Truth-functional relations of predicate logic symbollised sentencies considering interpretation pattern. Quantifying truth of logical forms. Quantifying identity. Quantifying consistency. Quantifying deducibility. Quantifying argument validity. Validity of logical form as the necessary condition of truth. Predicate logic model with identity. Truth-tree of predicate logic model. Predicate logic model axiomatisation. Fifteen theorems of predicate logic model with corresponding proof constructions. Philosophy of logic and some applications of deductive logic model in mathematics. Exercises.

 Literature:

A) Obligatory

• Kleene, Stephen C., Mathematical Logic, Wiley, New York 1967.

• Quine, W.V., Philosophy of Logic, Prentice-Hall, Englewood Cliffs 1970.

• Šikić, Z. Novija filozofija matematike [New philosophy of mathematics], Sazvežđa 101, Nolit, Beograd 1987.

B) Additional

• Tarski, A., Logic, Semantics, Metamathematics, Hackett Publishing Company, Indianapolis 1984.

• D' Agostino, Marcello, etc. (ed.), Handbook of Tableau Methods, Kluwer Academic Publishers, Dordrecht, Boston, London, 1999.

• Dummett, M., The Logical Basis of Metaphysics, Harvard University Press Cambridge, Massachusetts 1991.