37
edits
Changes
Jump to navigation
Jump to search
Line 1:
Line 1: − Logic was invented by Greek philosopher [[Aristotle]]. No other civilization can lay claim to its invention. The rules of logic were codified by Aristotle several centuries before the coming of Christ, and were used by St. Paul in his theological discussions. Logic was very appealing to Jewish scholars, and many instances of logical reasoning appear in the Old Testament. + − Logic helps discern truth, which helps lead a person to the saving grace of a relationship with God:+ − *Come, let us reason together. − *You shall know the truth, and the truth shall set you free. − The forms and methods of logic are codified as ''[[formal logic]]'', a highly structured set of rules for ''deductive'' reasoning. Formal logic depends totally on ''mutual agreement between and among parties to any discussion'' on fundamental premises and other facts asserted as evidence. If the parties cannot agree on fact, then formal logic is unavailing. Some [[logical fallacies]] are formal-logical failures.+ − + + + + + + + + + + − + Line 19:
Line 26: − ==Logic and common sense== − − Informal logic consists of "common sense" and other, rather loose rules that people employ while making most decisions and even in debate. It is unstructured, and depends largely on one's view of "the reasonable"--which in turn is that body of facts that one ''reasonably'' expects to exist. Informal logic also includes ''inductive'' reasoning. The thresholds of what is "reasonable" and what is not, are inexact and subject to change with the receipt of sufficient contrary evidence--and again, what constitutes "sufficiency" in this context might vary from person to person. Most [[logical fallacies]] are failures in informal logic. − + − + + + +
expand history; remove irrelevant material; still needs expansion and cleanup.
[[Logic]] ([[Greek]] λογίζω I reckon, I count, from λόγος a word) is a branch of [[philosophy]] that deals with and attempts to guide the faculty of human reason.
[[Logic]] ([[Greek]] λογίζω I reckon, I count, from λόγος a word) is a branch of [[philosophy]] that deals with and attempts to guide the faculty of human reason.
[[Aristotle]] was the first to formalize the practice of reasoning. In particular, Aristotle developed a formalization of the [[syllogism]] and the [[Square of Opposition]]. While [[Modus ponens]] and its complement [[Modus tollens]] were known to the Medievals, it is not clear when these central laws of deduction were first formalized.{{fact}}
The next easily-identifiable major development in logic comes from [[Boole]] in 1847 with the creation of [[Boolean algebra]]. In the 1870's, Peirce introduces a logic of quantifiers, followed by [[Gottlob Frege]]'s 1879 ''Begriffsschift'', which contains the first complete formalization of the propositional calculus. Frege's work was developed in service of his [[logicism|logicist]] project, which was shown to be inconsistent by [[Bertrand Russell]] in 1903 with what is famously called [[Russell's paradox]].
By the 1950's, with the work of many logicians including [[Hilbert]], [[Emile Post]], [[Alfred Tarski]] and [[Kurt Goedel]], most of the major results in first-order logic had been proved, and in the 1960's [[Saul Kripke]] added a completeness proof for [[modal logic]].
[[Symbolic logic]] is formal logic expressed in an abstract language, similar to the language of [[algebra]]. It uses variable names for propositions and various symbolic operators to stand for formal logical processes like conjunction (p and q), disjunction (p or q or both), and implication (p implies q or if p, then q). Symbolic logic does not differ from formal logic, except that in that the latter is written in the same language in which human beings regularly write and speak, whereas symbolic logic uses a language of its own.
Most logical systems are [[bivalent]]; that is, they admit only two truth-values. However, there is a fair amount of work done on non-bivalent systems of logic, especially [[intuitionist logic]] and [[relevance logic]]. In intuitionist logic, "true" and "false" are replaced with "proven true", "proven contradictory", and "not proven". In relevance logic, "neither true nor false" and "both true and false" are added to the standard two truth values. There is some debate about the value of these systems in philosophical circles, and [[Timothy Williamson]] claims to have a proof that any non-bivalent logic can be converted into a bivalent logic.
Formal logic requires, since Frege, a distinction between the [[object language]] and the [[metalanguage]]. The metalanguage is ordinarily a natural language like English or German, while the object language is a symbolic language with a limited alphabet and syntax.
== Informal Logic ==
The art of [[rhetoric]] is sometimes called "informal logic", and the classic [[logical fallacies|fallacies]] are often described as "logical fallacies", though, strictly speaking, most of them are simply emotionally effective ways to build an invalid argument. Generally speaking, "informal logic" consists of "common sense" and a collection of other rather loose rules that people employ while making most decisions and even in debate. It is unstructured, and depends largely on one's view of "the reasonable". The thresholds of what is "reasonable" and what is not, are inexact and subject to change with the receipt of sufficient contrary evidence--and again, what constitutes "sufficiency" in this context might vary from person to person.
== Deduction and Induction ==
Deductive logic is characterized by certainty: in a valid argument, when the premises are true, the conclusion '''must''' be true. Inductive logic is famously less certain; in a good inductive argument, even when the premises are true, it is still possible for the conclusion to be false. [[David Hume]]'s 18th-century critique of induction remains a very pressing problem for disciplines like [[science]] which rely on inductive reasoning.
== Uses of logic in other disciplines ==
== Uses of logic in other disciplines ==
Logic is a necessary discipline in [[philosophy]], because it deals with how we study and interact with the world and with other people in it. Logic is also an integral part of [[mathematics]], dealing as it does with why certain mathematical facts follow from other, more basic facts. For example, given a standard definition of the area of a [[rectangle]] as "a measure of the interior of the rectangle, expressed as the product of the lengths of any two adjacent sides of it," one can use logic to prove area formulas for the [[parallelogram]], the [[triangle]], and the [[circle]], to name three examples. All of these formulas follow, directly or indirectly, from that initial definition of the area of a rectangle.
Logic is a necessary discipline in [[philosophy]], because it deals with how we study and interact with the world and with other people in it. Logic and [[mathematics]] are also closely connected, and much of mathematics can be reduced to first-order logic, though Goedel's [[Incompleteness theorem]] shows that not all of mathematics can be so reduced.
In [[computer science]], logic dictates how a machine will follow a set of instructions, including how to test its "world," evaluate it, and act according to that evaluation. Every computer language includes its own version of the language of symbolic logic, except that instead of establishing propositions, a computer following a program is usually choosing between and among different commands to execute.
In [[computer science]], logic dictates how a machine will follow a set of instructions, including how to test its "world," evaluate it, and act according to that evaluation. Every computer language includes its own version of the language of symbolic logic, except that instead of establishing propositions, a computer following a program is usually choosing between and among different commands to execute.
Logic, and especially formal logic, inform the discipline of [[critical thinking]]--which, by no coincidence, takes its name from the [[Greek]] word for a judge. Indeed, judges and juries in courts of [[law]] must apply logic, both formal and informal, to arrive at their decisions. Formal logic will usually serve to state what obedience to a given body of law requires; informal logic must usually serve a trier of fact charged with deciding whether a given person was in obedience or in violation. The latter principle holds primarily because plaintiff and defendant in a court of law quite often ''do not'' agree on matters of fact.
Logic, and especially formal logic, inform the discipline of [[critical thinking]]--which, by no coincidence, takes its name from the [[Greek]] word for a judge. Indeed, judges and juries in courts of [[law]] must apply logic, both formal and informal, to arrive at their decisions. Formal logic will usually serve to state what obedience to a given body of law requires; informal logic must usually serve a trier of fact charged with deciding whether a given person was in obedience or in violation. The latter principle holds primarily because plaintiff and defendant in a court of law quite often ''do not'' agree on matters of fact.
== See Also ==
== See Also ==
* [[Aristotle]], "Organon"
* [[Aristotle]], "Organon"
* [[Nathaniel Branden|Branden, Nathaniel]], ''The Benefits and Hazards of the Philosophy of Ayn Rand''
* [[Gottlob Frege]], "Begriffsschrift"
* [[Ayn Rand|Rand, Ayn]], ''The Virtue of Selfishness'' and other collections of essays
* [[Gottlob Frege]], "The Foundations of Arithmetic"
* [[Bertrand Russell]] and [[Albert N Whitehead]], "Principia Mathematica"
* [[Bas van Fraassen]] and [[J C Beall]], "Possibility and Paradox"
* Geoffrey Hunter, "Metalogic"
[[Category:Philosophy]]
[[Category:Philosophy]]