General Logic Resources

  • A note on mathematical logic and philosophical logic: A common misconception is that mathematical logic is a synonym for formal or symbolic logic, while philosophical logic is a less rigorous version of such. It may be true that philosophical logic is often taught in a less formal manner, but the difference between the two actually concerns their object of study - philosophical logic is restricted to the use of logic - for example, proving propositions about things using a logical framework, whether propositional, first-order, modal, or something else. Mathematical logic, on the other hand, deals largely with metalogic - the investigation and proof of statements about logic - is it complete? What is the strength of a particular system?, and so on.
  • A Modern Formal Logic Primer (1989), by Paul Teller, has generously been made available free online.
  • Notes for an introductory course on (largely philosopical) logic, by Peter Suber (Earlham College), are online here.
  • Notes for by Peter Smith's (Cambridge, retired) lecture series on mathematical logic entitled 'Gödel Without (Too Many) Tears' , online here.
  • Philpaper's Category for Logic and the Philosophy of Logic is here

Fundamental Logical Concepts

What is 'Logic'?
  • Encyclopedia entries:
    • Internet Encyclopedia of Philosophy on what an argument is: Argument
  • Online tutorials:
What is a 'Statement'?
  • Online tutorials:
    • Statements from Critical Thinking Web (with test quiz).
What is an 'Argument'?
Validity and Soundness
Deduction versus Induction
  • Encyclopedia entries:
    • Deductive and Inductive Arguments: IEP
    • Confirmation and Induction: IEP
  • Online tutorials:
  • This wiphi clip by Greg Ganssle of Yale is about the idea that a deductive argument will fail to prove its conclusion with complete certainty if its premises have themselves been established using an inference to the best explanation:

Logical Consequence
  • Encyclopedia entries:
    • Logical Consequence: SEP and IEP
    • Deductive-Theoretic Conceptions of Logical Consequence: IEP
    • Model-Theoretic Conceptions of Logical Consequence: IEP. See also the later section on model theory
Necessary and Sufficient Conditions
Contradiction and Inconsistency
  • Encyclopedia entries:
    • Contradiction: SEP
Reductio ad Adsurdum
  • Encyclopedia entries:
    • Reductio ad Absurdum: IEP
  • Encyclopedia entries:
    • Logical Constants: SEP
    • Propositional Function: SEP
    • Logical Pluralism: SEP

The History of Logic

Logical strength

    Kevin deLaplante explains the notion of logical strength in the next clip:

Non-Classical Logic

Paraconsistent Logic
  • Encyclopedia entries:
    • Paraconsistent Logic: SEP and IEP
    • Dialetheism: SEP
    • Impossible Worlds: SEP
    • Inconsistent Mathematics: SEP and IEP
    • Relevance Logic: SEP
  • Podcasts:
    • Rationally Speaking: in the following podcast (audio only) Graham Priest talks about paraconsistent logic and dilethism:
Intuitionistic Logic
  • Encyclopedia entries:
    • Intuitionistic Logic: SEP
    • Constructive Mathematics: IEP
Other Non-Classical Logics

Predicate Logic

  • Also called several variations on 'First-Order'/'Lower'/'Quantifier'/'Predicate' 'Logic'/'Calculus', and the most common referent of 'classical logic'
  • SEP article
  • Wolfram Mathworld's briefer summary here
  • The Philpapers subcategory for predicate logic

Propositional Logic

Model Theory

Proof Theory


Higher-Order Logic

Completeness and Incompleteness