Logic

Elementary logic

Logical arguments, uses of language, definition and meaning, fallacies, categorical propositions and immediate inferences, categorical syllogisms and their validity, syllogisms in ordinary language, logical symbols, rules of inference, proofs, basics of quantification theory, analogical inferences, causal reasoning.

Syllogism evaluator

Java applet for evaluating all categorical syllogisms.

Aristotle's Logic

A detailed analysis of Aristote's works on logic.

Traps of Traditional logic and Dialectics by R.E.Horn

Symbolic logic by Peter Suber

Handouts for the course. Truth and validity, terms, propositional logic, paradoxes, derivations, predicate logic.

Critical logic by Michael Lynch

Brief samples of the course handouts: reasoning and pseudo-reasoning, fallacies, categorical syllogisms, propositional logic, famous logicians

Logical Analysis by W.J.Talbott

Handouts for a philosophy course.

Dialectical logic
(most of these texts discuss special aspects of dialectical logic, in specific interpretations; some of them may have rather distant relation to dialectical logic proper)

• E. Ilyenkov:
  • Dialectical Logic (in Russian)
  • Dialectical Logic
  • The Problem of Contradiction (in Russian)
• Notes on Dialectical Logic (The Critical project)
• Introduction to Dialectical Logic: Fallacies of Discreteness by J.C.Mickelsen
• Dialectical Logic by J.Klumpp
• The ABC of Materialist Dialectics by Leon Trotsky
• The Formal Structure of Dialectical Psychology by W.C.Hoffman
• Introduction to the Logic of Marxism by G.Novack
• A Mathematical Model of Relational Dialectical Reasoning by M.Wrede
• Dialectical-Thinking Model

Logic in mathematics

Practical Foundations of Mathematics by Paul Taylor.

Online book. First Order Reasoning, types and induction, posets and lattices, Cartesian closed categories, limits and colimits, structural recursion, adjunctions, algebra with dependent types, the quantifiers.

Mathematical logic and foundations

From The mathematical Atlas by D.Rusin.

A Problem Course in Mathematical Logic by Stefan Bilaniuk

A freeware course. Vol.I: Propositional and First-Order Logic. Vol.II: Computability and Incompleteness.

Introduction to mathematical Logic by Vilnis Detlovs and Karlis Podnieks

Hyper-textbook for students. Riga, University of Latvia.

Around Goedel's Theorem by Karlis Podnieks

Hyper-textbook for students. Riga, University of Latvia.

Dialectics in Mathematics by Brendan Larvor

A talk for the Centre for Philosophical Studies at KCL 20th October 1999

Vorlesungsskript Mathematische Logik by Martin Ziegler

A number of texts in German (.pdf, .ps, .dvi). Model theory, recusrsion theory, algebra, mathematical logic.

Alternative logics

Logical systems by Peter Suber

Handouts for the course. Map of some logical systems, the shadow problem, Hunter-Hofstadter map, formal systems and machines, infinite sets, the quirk problem, non-standard logics, mathematical induction, mid-term review, satisfaction, three levels of truth, Löwenheim-Skolem theorem, Gödel's proof, recursive function theory.

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