# Analytic / synthetic (1783)

Distinction first formulated by the German philosopher Immanuel Kant (1724-1804), adopted as a fundamental principle in linguistic semantics.

An analytic or necessary truth (‘sentence’ in linguistics) is true by virtue of its meaning: ‘All bachelors are unmarried men’.

A synthetic or contingent truth is true by virtue of empirical fact: ‘Grass is green’ is not necessarily true, but only if grass is green.

Source:
T M Olshewsky, ed., Problems in the Philosophy of Language (New York, 1969), ch. 5

## Natural sciences

### Chemistry

• Analytical chemistry, the analysis of material samples to learn their chemical composition and structure
• Analytical technique, a method that is used to determine the concentration of a chemical compound or chemical element
• Analytical concentration

### Mathematics

• Abstract analytic number theory, the application of ideas and techniques from analytic number theory to other mathematical fields
• Analytic capacity, a number that denotes how big a certain bounded analytic function can become
• Analytic combinatorics, a branch of combinatorics that describes combinatorial classes using generating functions
• Analytic continuation, a technique to extend the domain of definition of a given analytic function
• Analytic expression, a mathematical expression using well-known operations that lend themselves readily to calculation
• Analytic function, a function that is locally given by a convergent power series
• Analytic geometry, the study of geometry using the principles of algebra
• Analytic number theory, a branch of number theory that uses methods from mathematical analysis
• Analytic solution: a solution to a problem that can be written in “closed form” in terms of known functions, constants, etc.
• Analytic variety, the set of common solutions of several equations involving analytic functions

#### Set theory

• Analytical hierarchy, an extension of the arithmetical hierarchy
• Analytic set, if it is a continuous image of a Polish space. These sets were first defined by Luzin (1917) and his student Souslin (1917)
• Lightface analytic game, a game whose payoff set A is a subset of Baire space; that is, there is a tree T on which is a computable subset of, such that A is the projection of the set of all branches of T

#### Proof theory

• Analytic proof, in structural proof theory, a proof whose structure is simple in a special way
• Method of analytic tableaux, a fundamental concept in automated theorem proving

#### Miscellaneous mathematical disciplines

• Analytic element method, a numerical method used to solve partial differential equations
• Analytic manifold, a topological manifold with analytic transition maps

### Computer science

• Analytic or reductive grammar, a kind of formal grammar that works by successively reducing input strings to simpler forms
• Analytics, to find meaningful patterns in data
• Online analytical processing, interactive version of above

### Miscellaneous natural scientific disciplines

• Analytic signal, a particular representation of a signal
• Analytical mechanics, a refined, highly mathematical form of classical mechanics
• Analytical balance, a very high precision (0.1 mg or better) weighing scale

## Philosophy

• Analytic philosophy, a style of philosophy that came to dominate English-speaking countries in the 20th century
• Analytic proposition, a statement whose truth can be determined solely through analysis of its meaning
• Analytical Thomism, the movement to present the thought of Thomas Aquinas in the style of modern analytic philosophy
• Postanalytic philosophy, describes a detachment from the mainstream philosophical movement of analytic philosophy, which is the predominant school of thought in English-speaking countries

## Social sciences

### Psychology

• Analytical psychology, part of the Jungian psychology movement
• Cognitive analytic therapy, a form of psychological therapy initially developed in the United Kingdom by Anthony Ryle
• Psychoanalysis, a set of psychological and psychotherapeutic theories and associated techniques

### Sociology

• Analytic induction, the systematic examination of similarities between various social phenomena to develop concepts or ideas
• Analytic frame, a detailed sketch or outline of some social phenomenon, representing initial idea of a scientist analyzing this phenomenon

### Politics

• Analytical Marxism, an interpretation of Marxism

### Linguistics

• Analytic language, a natural language in which most morphemes are free (separate), instead of fused together

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