Logic

Saturday, 18 August 2012

logic \Log"ic\, n. [OE. logike, F. logique, L. logica, logice, Gr. logikh` (sc. te`chnh), fr. logiko`s belonging to speaking or reason, fr. lo`gos speech, reason, le`gein to say, speak. See Legend.] 1. The science or art of exact reasoning, or of pure and formal thought, or of the laws according to which the processes of pure thinking should be conducted; the science of the formation and application of general notions; the science of generalization, judgment, classification, reasoning, and systematic arrangement; the science of correct reasoning. [1913 Webster]
Logic is the science of the laws of thought, as thought; that is, of the necessary conditions to which thought, considered in itself, is subject. --Sir W. Hamilton. [1913 Webster]
Note: logic is distinguished as pure and applied. "Pure logic is a science of the form, or of the formal laws, of thinking, and not of the matter. Applied logic teaches the application of the forms of thinking to those objects about which men do think." --Abp. Thomson. [1913 Webster]
2. A treatise on logic; as, Mill's logic. [1913 Webster]
3. correct reasoning; as, I can't see any logic in his argument; also, sound judgment; as, the logic of surrender was uncontestable. [PJC]
4. The path of reasoning used in any specific argument; as, his logic was irrefutable. [PJC]
5. (Electronics, Computers) A function of an electrical circuit (called a gate) that mimics certain elementary binary logical operations on electrical signals, such as AND, OR, or NOT; as, a logic circuit; the arithmetic and logic unit. [PJC]
logic n 1: the branch of philosophy that analyzes inference 2: reasoned and reasonable judgment; "it made a certain kind of logic" 3: the principles that guide reasoning within a given field or situation; "economic logic requires it"; "by the logic of war" 4: the system of operations performed by a computer that underlies the machine's representation of logical operations 5: a system of reasoning [syn: logic, logical system, system of logic]
logic
1. <philosophy, logic> A branch of philosophy and mathematics that deals with the formal principles, methods and criteria of validity of inference, reasoning and knowledge.
Logic is concerned with what is true and how we can know whether something is true. This involves the formalisation of logical arguments and proofs in terms of symbols representing propositions and logical connectives. The meanings of these logical connectives are expressed by a set of rules which are assumed to be self-evident.
Boolean algebra deals with the basic operations of truth values: AND, OR, NOT and combinations thereof. Predicate logic extends this with existential and universal quantifiers and symbols standing for predicates which may depend on variables. The rules of natural deduction describe how we may proceed from valid premises to valid conclusions, where the premises and conclusions are expressions in predicate logic.
Symbolic logic uses a meta-language concerned with truth, which may or may not have a corresponding expression in the world of objects called existance. In symbolic logic, arguments and proofs are made in terms of symbols representing propositions and logical connectives. The meanings of these begin with a set of rules or primitives which are assumed to be self-evident. Fortunately, even from vague primitives, functions can be defined with precise meaning.
Boolean logic deals with the basic operations of truth values: AND, OR, NOT and combinations thereof. Predicate logic extends this with existential quantifiers and universal quantifiers which introduce bound variables ranging over finite sets; the predicate itself takes on only the values true and false. Deduction describes how we may proceed from valid premises to valid conclusions, where these are expressions in predicate logic.
Carnap used the phrase "rational reconstruction" to describe the logical analysis of thought. Thus logic is less concerned with how thought does proceed, which is considered the realm of psychology, and more with how it should proceed to discover truth. It is the touchstone of the results of thinking, but neither its regulator nor a motive for its practice.
See also fuzzy logic, logic programming, arithmetic and logic unit, first-order logic,
See also Boolean logic, fuzzy logic, logic programming, first-order logic, logic bomb, combinatory logic, higher-order logic, intuitionistic logic, equational logic, modal logic, linear logic, paradox.
2. <electronics> Boolean logic circuits.
See also arithmetic and logic unit, asynchronous logic, TTL.
(1995-03-17)
logic, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion -- thus: _Major Premise_: Sixty men can do a piece of work sixty times as quickly as one man. _Minor Premise_: One man can dig a posthole in sixty seconds; therefore -- _Conclusion_: Sixty men can dig a posthole in one second. This may be called the syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.

“	Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy: Do not block the way of inquiry.	”
—Charles Sanders Peirce, "First Rule of Logic")

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Maverick Sabre
Birth name	Michael Stafford
Born	(1990-07-12) 12 July 1990 (age 21) Hackney, London, England
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Name	Sabre, Maverick
Alternative names	Michael Stafford
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Date of birth	12 July 1990
Place of birth	Hackney, London, England
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	Book: Logic
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Branches of Mathematics

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