Principle of distributivity

Principle of distributivity

The principle of distributivity states that the algebraic distributive law is valid for classical logic, where both logical conjunction and logical disjunction are distributive over each other so that for any logical propositions "A", "B" and "C" the equivalences:A land (B lor C) iff (A land B) lor (A land C)and:A lor (B land C) iff (A lor B) land (A lor C)hold.

The principle of distributivity is valid in classical logic, but invalid in quantum logic. The article "Is logic empirical?" discusses the case that quantum logic is the correct, empirical logic, on the grounds that the principle of distributivity is inconsistent with a reasonable interpretation of quantum phenomena.

Operational definitions and distributivity

The principle of distributivity is generally challengeable when an operational method of empirical observation to establish the truth of a proposition is introduced. For example, if "true" is operationally defined as "it can proved in a court of law", then cases will arise where it can be proved that Smith or Jones must have committed a crime, but it cannot be sufficiently proved that Smith committed it and it cannot be proved that Jones committed it. It is, in general, sometimes possible observational operations to result in sufficient evidence to establish a composite, but not to result in sufficient evidence to establish any of the underlying component propositions.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Distributivity — In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra.For example:: 2 • (1 + 3) = (2 • 1) + (2 • 3).In the left hand side of the… …   Wikipedia

  • Is logic empirical? — is the title of two articles that discuss the idea that the algebraic properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about quantum phenomena may provide grounds …   Wikipedia

  • Logic — For other uses, see Logic (disambiguation). Philosophy …   Wikipedia

  • List of mathematics articles (P) — NOTOC P P = NP problem P adic analysis P adic number P adic order P compact group P group P² irreducible P Laplacian P matrix P rep P value P vector P y method Pacific Journal of Mathematics Package merge algorithm Packed storage matrix Packing… …   Wikipedia

  • Boolean algebra — This article discusses the subject referred to as Boolean algebra. For the mathematical objects, see Boolean algebra (structure). Boolean algebra, as developed in 1854 by George Boole in his book An Investigation of the Laws of Thought,[1] is a… …   Wikipedia

  • Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …   Wikipedia

  • Distributive property — In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalizes the distributive law from elementary algebra. For example: 2 × (1 + 3) = (2 × 1) + (2 × 3). In the left hand side of the… …   Wikipedia

  • Boolean algebra (logic) — For other uses, see Boolean algebra (disambiguation). Boolean algebra (or Boolean logic) is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of… …   Wikipedia

  • Boolean algebra (introduction) — Boolean algebra, developed in 1854 by George Boole in his book An Investigation of the Laws of Thought , is a variant of ordinary algebra as taught in high school. Boolean algebra differs from ordinary algebra in three ways: in the values that… …   Wikipedia

  • Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”