Philosophy of logic
Following the developments in formal logic with symbolic logic in the late nineteenth century and mathematical logic in the twentieth, topics traditionally treated by logic not being part of formal logic have tended to be termed either philosophy of logic or philosophical logic if no longer simply logic.
Compared to the history of logic, the demarcation between philosophy of logic and philosophical logic is of recent coinage and not always entirely clear. Characterisations include:
- Philosophy of logic is the area of philosophy devoted to examining the scope and nature of logic.
- Philosophy of logic is the investigation, critical analysis and intellectual reflection on issues arising in logic. The field is considered to be distinct from philosophical logic.
- Philosophical logic is the branch of study that concerns questions about reference, predication, identity, truth, quantification, existence, entailment, modality, and necessity.
- Philosophical logic is the application of formal logical techniques to philosophical problems.
Introduction
This article makes use of the following terms and concepts:Aristotle said To say that that which is, is not or that which is not is, is a falsehood; and to say that which is, is and that which is not is not, is true
This apparent truism has not proved unproblematic.
Truthbearers
Logic uses such terms as true, false, inconsistent, valid, and self-contradictory. Questions arise as Strawson writesTarski's definition of truth
See:- Semantic theory of truth § Tarski's Theory
- T-schema
-
Analytic truths, logical truth, validity, logical consequence and entailment
- A necessary truth is one that is true no matter what the state of the world or, as it is sometimes put, in all possible worlds.
- Logical truths are those necessary truths that are necessarily true owing to the meaning of their logical constants only.
- In formal logic a logical truth is just a "statement" which is true under all possible interpretations.
- An analytic truth is one whose predicate concept is contained in its subject concept.
- If q is a logical truth, then p therefore q will be a valid argument.
- If p1, p2, p3... pn therefore q is a valid argument then its corresponding conditional will be a logical truth.
- If p1 & p2 & p3... pn entails q then If then q is a logical truth.
- If q is a logical consequence of p1 & p2 & p3... pn if and only if p1 & p2 & p3... pn entails q and if and only if If then q is a logical truth
- If there are truths that must be true, what makes them so?
- Are there analytic truths that are not logical truths?
- Are there necessary truths that are not analytic truths?
- Are there necessary truths that are not logical truths?
- Is the distinction between analytic truth and synthetic truth spurious?
Paradox
Meaning and reference
See- Sense and reference
- Theory of reference
- Mediated reference theory
- Direct reference theory
- Causal theory of reference
- Descriptivist theory of names
- Saul Kripke
- Frege's Puzzle
- Gottlob Frege
- Failure of reference
- Rigid designator
- Philosophy of language
- Index of philosophy of language articles
- Supposition theory
- Referring expression
- Meaning
- Denotation and Connotation
- Extension and Intension
- Extensional definition
- Intensional definition
- Metacommunicative competence
Names and descriptions
- Failure to refer
- Proper name
- Definite description
- Descriptivist theory of names
- Theory of descriptions
- Singular term
- Term logic § Singular terms
- Empty name
- Bas van Fraassen § Singular Terms, Truth-value Gaps, and Free Logic
- The Foundations of Arithmetic § Development of Frege's own view of a number
- Philosophy of language § references
- Direct reference
- Mediated reference theory
Formal and material consequence
- The problem of the material conditional: see Material conditional
Logical constants and connectives
Quantifiers and quantificational theory
Modal logic
Deviant logics
Classical v. non-classical logics
Philosophical theories of logic
- Conceptualism
- Constructivism
- Dialetheism
- Fictionalism
- Finitism
- Formalism
- Intuitionism
- Logical atomism
- Logicism
- Nominalism
- Realism
- Platonic realism
- Structuralism
- Nyaya Epistemology
Other topics
- Leibniz's Law: see Identity of indiscernibles
- Vacuous names
- Do predicates have properties?: See Second-order logic
- Sense, Reference, Connotation, Denotation, Extension, Intension
- The status of the Laws of Logic
- Classical Logic
- Intuitionism
- Realism: see Platonic realism, Philosophical realism
- The Law of Excluded Middle: see Law of excluded middle
- Modality, Intensionality and Propositional Attitude
- Counter-factuals
- Psychologism
Important figures
- Noriko H. Arai
- Aristotle
- George Boole
- George Boolos
- John Buridan
- Agata Ciabattoni
- Alonzo Church
- Gordon Clark
- Michael Dummett
- Augustus De Morgan
- Gottlob Frege
- Kurt Gödel
- Georg Hegel
- William of Ockham
- Peter of Spain
- Rudolf Carnap
- Immanuel Kant
- Gottfried Leibniz
- David Lewis
- John Stuart Mill
- Charles Sanders Peirce
- Valeria de Paiva
- Alvin Plantinga
- Arthur Prior
- Willard Van Orman Quine
- Bertrand Russell
- Alfred Tarski
- Ludwig Wittgenstein
Philosophers of logic
- W.V.O. Quine
- Bertrand Russell
- Ludwig Wittgenstein
- Michael Dummett
- Hilary Putnam
- Saul Kripke
- Charles Sanders Peirce
- Alfred Tarski
- Donald Davidson
- Augustus De Morgan
- Gordon Clark
- Aristotle