Difference between revisions of "Logic"
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| − | [[Logic]] ([[Greek]] λογίζω I reckon, I count, from λόγος a word) | + | [[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 was invented by Greek philosopher [[Aristotle]]. No other civilization can lay claim to its invention. The rules of logic | + | 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 | + | Logic helps discern truth, which helps lead a person to the saving grace of a relationship with God: |
*Come, let us reason together. | *Come, let us reason together. | ||
*You shall know the truth, and the truth shall set you free. | *You shall know the truth, and the truth shall set you free. | ||
| − | The forms and methods of logic | + | 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. |
| − | [[Symbolic 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. |
== Uses of logic in other disciplines == | == Uses of logic in other disciplines == | ||
| − | Logic | + | 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. |
| − | 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 | + | 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. | ||
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==Logic and common sense== | ==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 | + | 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. |
== See Also == | == See Also == | ||
Revision as of 23:25, July 14, 2007
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 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.
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.
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.
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 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.
See Also
- Aristotle, "Organon"
- Branden, Nathaniel, The Benefits and Hazards of the Philosophy of Ayn Rand
- Rand, Ayn, The Virtue of Selfishness and other collections of essays