Logic as a Tool

The main objective of the course is to familiarize audience with basic concepts of logic and applications of logic in analysis of natural language. I will start from presentation of fundamental notions such as truth, consistency, validity, logical constant and truth functionality in the first part of the course. The second will be devoted to more advanced topics such as formalization of arguments and logical interpretations of conditionals. Philosophical motivations and perspective of the problems presented during the course will serve as a referring point for aforementioned topics.

The objective of the course is presentation of logic that locates its subject in historical and philosophical context as this branch of knowledge which provides tools for solving problems which human thought have faced since antiquity until contemporary times.

Particular emphasis will be on the role of logic in analysis of deductive sciences, their philosophy and methodology.

Complete course embraces the following topics.

1. The subject of logic, logic as theory of reasoning.

2. Branches of logic and their characteristics: semantics, syntacticts, methodology of sciences, formal logic.

3. Logical fallacies: equivocation, amphiboly, inconsistency.

4. Reasonings, models of reasonings.

5. Consequence, analytical consequence, logi cal consequence.

6. Justification of sentences, deductive justifications, proofs.

7. Notions of a true sentence, logical value and logical proposition/sentence.

8 Logical constans: negation, conjunction, disjunction, material implication, material equivalence. Extensional and intensional connectives. De Morgan’s laws. Conditionals and material implication. Quantifiers.

9. Foundations of the theory of logical consequence.

10. Formal proofs.

1. D. Hofstadter Gödel, Escher, Bach: an Eternal Golden Braid, Penguin, 1999

2. M. Sainsbury Logical Forms: An Introduction to Philosophical Logic, Wiley-Blackwell, 2000

3. W.V.O. Quine Philosophy of logic, Harvard University Press, 2009 (2nd edition)

The criteria for the evaluation of students:

1. multiple-choice test plus problems and exercises to solve,

2. one larger homework after first five meetings,

3. activity,

4. class attendance – one absence is accepted.

Final grade will be estimated according to the following criteria: Final test graded according to the standard scale.

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