Logic

## 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 'GĂ¶del 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:
- The nature of logic from philosophy.lander.edu (with test quiz).
- What is logic? from Critical Thinking Web (with test quiz).
## What is a 'Statement'?- Online tutorials:
- Statements from Critical Thinking Web (with test quiz).
## What is an 'Argument'?- Encyclopedia entries:
- Argument: IEP
- Online tutorials:
- The Structure of Arguments from philosophy.lander.edu.
- Explanations and Non-arguments from philosophy.lander.edu.
- Identifying arguments from Critical Thinking Web (with test quiz).
- The standard format from Critical Thinking Web (with test quiz).
- Argument mapping from Critical Thinking Web (with test quiz).
- Michael Palin explains what an "argument" is the following Monty Python skit:
## Validity and Soundness- Encyclopedia entries:
- Validity and Soundness: IEP
- Online tutorials:
- Truth, Validity and Soundness from philosophy.lander.edu (with test quiz).
- Validity from Critical Thinking Web (with test quiz).
- Soundness from Critical Thinking Web (with test quiz).
- Valid patterns from Critical Thinking Web (with test quiz).
- More valid patterns from Critical Thinking Web.
- A simple 10-question quiz on validity from the University of Hong Kong.
- Logic 101: Validity and Soundness from the (un)Enlightened Academy (with a nice explanation of why validity does not entail truth).
- For a really fine example of a bad argument, that is both glaringly invalid and strewn with false premises, there is no surpassing the witch argument (from
*Monty Python and the Holy Grail*):
## Deduction versus Induction- Encyclopedia entries:
- Online tutorials:
- Deductive and Inductive Arguments from philosophy.lander.edu (with test quiz).
- Inductive reasoning from Critical Thinking Web.
- Good arguments from Critical Thinking Web (with test quiz).
- Analogical arguments from Critical Thinking Web (with test quiz).
- 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:
## Translation- Online tutorials:
- Deductive and Inductive Arguments from philosophy.lander.edu (with test quiz)
- Hidden assumptions from Critical Thinking Web (with test quiz)
## Necessary and Sufficient Conditions- Online tutorials:
- Necessary and sufficient conditions from Critical Thinking Web (with test quiz).
- Types of possibility from Critical Thinking Web.
- The distinction is explained by Kelly Schiffman (grad student at Yale) in the following wiphi clip:
## Contradiction and Inconsistency- Encyclopedia entries:
- Contradiction: SEP
## Reductio ad Adsurdum- Encyclopedia entries:
- Reductio ad Absurdum: IEP
## Miscellaneous## The History of Logic- The SEP has entries on:
- The IEP has entries on:
## Logical strength-
Kevin deLaplante explains the notion of logical strength in the next clip:
## Non-Classical Logic## Paraconsistent Logic- Encyclopedia entries:
- Podcasts:
- Rationally Speaking: in the following podcast (audio only) Graham Priest talks about paraconsistent logic and dilethism:
- Rationally Speaking: in the following podcast (audio only) Graham Priest talks about paraconsistent logic and dilethism:
## Intuitionistic Logic## Other Non-Classical Logics- The SEP has entries on:
- Informal Logic
- Second-order and Higher-order Logic
- Modal Logic
- Temporal Logic
- Many Valued Logic
- Fuzzy Logic
- Logic and Probability
- Epistemic Logic
- Defeasible Reasoning
- Free Logic
- Provability Logic
- Proof-Theoretic Semantics
- Deontic Logic
- Linear Logic
- Justification Logic
- The Logic of Action
- Connexive Logic
- Propositional Consequence Relations and Algebraic Logics
- Independence Friendly Logic
- Substructural Logics
- Propositional Dynamic Logic
- Dialogical Logic
- Combining Logics
- Hybrid Logic
- The IEP has entries on:
## 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- The IEP entry onPropositional Logic
- The philpapers propositional logic subcategory
## Model Theory- SEP on Model Theory
- SEP on First-Order Model Theory
- Proofwiki's category for Model Theory
## Proof Theory## Computability## Higher-Order Logic## Completeness and Incompleteness |