Law of identityIn logic, the law of identity states that each thing is identical with itself, or symbolically a = a. It applies to singular terms, and is a tautology. HistoryAncient and Medieval philosophyIdentity was discussed since antiquity in philosophy, but as a principle in logic was not discussed until much later. William Hamilton offers a history of the so called "laws of thought".
Logical conjunctionRelated conceptsPropositional calculusPredicate logicBoolean algebraTruth tableTruth functionBoolean functionFunctional completenessScope (logic) ApplicationsDigital logicProgramming languagesMathematical logicPhilosophy of logicIn logic, mathematics and linguistics, and (∧{\displaystyle \wedge }) is the truth-functional operator of conjunction or logical conjunction.
Logical disjunctionRelated conceptsPropositional calculusPredicate logicBoolean algebraTruth tableTruth functionBoolean functionFunctional completenessScope (logic) ApplicationsDigital logicProgramming languagesMathematical logicPhilosophy of logicIn logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as ∨ and read aloud as "or".
Law of excluded middleIn logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true. Symbolically expressed, the law is p∨¬p{\displaystyle p\lor eg p}. The law of the excluded middle is also known as the law/principleof the excluded third, in Latinprincipium tertii exclusi. Another Latin designation for the law is tertium non datur or "no third [possibility] is given".Identity of indiscerniblesThe identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. That is, entities x and y are identical if every predicate possessed by x is also possessed by y and vice versa. It states that no two distinct things (such as snowflakes) can be exactly alike, but this is intended as a metaphysical principle rather than one of natural science.
LogicStudy of correct reasoningLogic studies valid forms of inference like modus ponens.Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory.
George BooleGeorge Boole ( BOOL; 2 November 1815 – 8 December 1864) was an English mathematician and philosopher often credited with revolutionizing logic by transforming it from a philosophical study of language into a mathematical system of algebraic equations using binary values and logical operators. Boole was the son of a shoemaker. He received a primary school education and learned Latin and modern languages through various means. At 16, he began teaching to support his family.
Law of noncontradictionIn logic, the law of noncontradiction (LNC; also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that for any given proposition, the proposition and its negation cannot both be simultaneously true, e.g., the proposition "the house is white" and its negation "the house is not white" are mutually exclusive.Singular termSingular terms are as expressions that purport to denote or designate particular individual people, places, or other objects. They contrast with general terms (such as "car" or "chair") which can apply to more than one thing.
The Laws of ThoughtAn Investigation of the Laws of Thought: on Which are Founded the Mathematical Theories of Logic and Probabilities by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic. Boole was a professor of mathematics at what was then Queen's College, Cork, now University College Cork, in Ireland.
IdealismPhilosophical positionIdealism in philosophy, also known as philosophical idealism or metaphysical idealism, is the set of metaphysical perspectives asserting that, most fundamentally, reality is equivalent to mind, spirit, or consciousness; that reality or truth is entirely a mental construct; or that ideas are the highest type of reality or have the greatest claim to being considered "real".
PhilosophyStudy of general and fundamental questionsThe statue The Thinker by Auguste Rodin is a symbol of philosophical thought.
NegationIn logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P {\displaystyle P} to another proposition "not P {\displaystyle P} ", written ¬ P {\displaystyle \neg P} , ∼ P {\displaystyle {\mathord {\sim }}P} , P ′ {\displaystyle P^{\prime }} or P ¯ {\displaystyle {\overline {P}}} . It is interpreted intuitively as being true when P {\displaystyle P} is false, and false when P {\displaystyle P} is true.*As an Amazon Associate I earn from qualifying purchases.