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*2. [[Logic]]. A proposition (whether true or false). *3. Logic and [[Mathematics]]. ‘A self-evident proposition, requiring no [[formal]]

:b : to [[assume]] as a postulate or axiom (as in [[logic]] or [[mathematics]]) In [[traditional]] [[logic]], an axiom or '''postulate''' is a [[proposition]] that is not proved or

...erm_logic Aristotelian logic], although in contemporary [[mathematical]] [[logic]] the term satisfiable is used instead. The [[syntactic]] definition states ...cs, such as [https://en.wikipedia.org/wiki/Second-order_logic second-order logic], are not complete.

In [[logic]] and [[philosophy]], the term '''proposition''' (from the [[word]] "propos ...the term "statement", and this is the current usage in [[mathematical]] [[logic]].[https://en.wikipedia.org/wiki/Proposition]

...age:Visualization_of_algorithm.jpg|right|frame|<center>"Visualization of a mathematical [[algorithm]]."</center>]] ...,’ from Old French ''mathematique'', from [[Latin]] ''(ars) mathematica'' ‘mathematical (art),’ from [[Greek]] ''mathēmatikē'' (''tekhnē''), from the base of

...ed in [[logic]]. See [https://en.wikipedia.org/wiki/Syntax_(logic) Syntax (logic)]; [https://en.wikipedia.org/wiki/Computer_programming Computer-programming

...dy of abstract structures. [[Mathematical structure]] on a set, additional mathematical objects that in some manner attach to the set, making it easier to visualiz ...e leaves at the bottom. In mathematical logic, a [[Structure (mathematical logic)|structure]] is an object that gives semantic meanings to the symbols in a

...predominantly concerned with abstract [[formal systems]], for instance, [[logic]], [[mathematics]], and the theoretical branches of [[computer science]], [ ...science and the invention of [[scientific method]], with the most ancient mathematical texts available dates back to 1500BC-500 BC ([[ancient India]]), 1300-1200

In [[logic]] and [[mathematics]], a '''formal system''' consists of two components, a ...er science, a [[formal language]] is a language that is defined by precise mathematical or machine processable formulas. Like languages in [[linguistics]], formal

==Logic== In [[logic]] a statement is a declarative sentence that is either true or false. A sta

*3 a : the operation of finding a converse in [[logic]] or [[mathematics]] :b : reduction of a mathematical [[expression]] by clearing of [[fractions]]

...tural and social) and the other used in [[philosophy]], [[mathematics]], [[logic]], and across other fields in the [[humanities]]. There is considerable [[d ...e generally expected to follow principles of [[rational]] [[thought]] or [[logic]].

*2: to free (a mathematical expression) from irrational parts <rationalize a denominator> In [[psychology]] and [[logic]], '''rationalization''' (or making excuses) is an informal [[fallacy]] of

...], [[data]] collection and [[analysis]] including the [[development]] of [[Mathematical model|statistical models]] to test hypotheses and the documentation of resu

* [[Logic]] studies the laws of valid inference. ...century, has built numerous [[formal system]]s that embody [[Aristotelian logic]] (or variants thereof).

...en.wikipedia.org/wiki/Graph_(mathematics) graphs], and [[statements]] in [[logic]] – do not vary smoothly in this way, but have distinct, separated [[valu

=== Logic === In logic an [[infinite regress]] argument is "a distinctively philosophical kind of

...kipedia.org/wiki/Church%E2%80%93Turing_thesis Church–Turing thesis] is a [[mathematical]] [[statement]] of this [[versatility]]: any computer with a certain minimu ...nents: the [https://en.wikipedia.org/wiki/Arithmetic_logic_unit arithmetic logic unit] (ALU), the [https://en.wikipedia.org/wiki/Control_unit control unit],

...ps://en.wikipedia.org/wiki/Mathematical_notation mathematical notation], [[logic]], UML), which are used worldwide regardless of how they are pronounced in

Study of abstract [[formal systems]],i.e. [[logic]], [[mathematics]], & theoretical [[computer science]], [[information theor ==== [[Logic]][https://nordan.daynal.org/wiki/index.php?title=Category:Logic] ====

...that of the initial theorem; B is unlikely to be termed a corollary if its mathematical [[consequences]] are as significant as those of A. Sometimes a corollary ha [[Category: Logic]]

...rgues that it is impossible to prove any [[truth]] with certainty, even in logic and mathematics. This argument is called the [https://en.wikipedia.org/wiki

*1: a [[formula]], [[proposition]], or [[statement]] in [[mathematics]] or [[logic]] deduced or to be deduced from other formulas or propositions ...ons, depending on the [[meanings]] of the derivation rules. The proof of a mathematical theorem is a [[logical]] [[argument]] demonstrating that the [[conclusions]

...flective]] [[conclusions]] based on [[cosmic]] [[response]]. This is the [[mathematical]] [[form]] of the [[cosmic]] [[discrimination]]. ...evelation]]. [[Matter]]-[[energy]] is recognized by the [[mathematical]] [[logic]] of the [[senses]]; [[mind]]-[[reason]] [[intuitively]] knows its [[moral]

...y]], [[ethics]] and [[aesthetics]] (which together comprise [[axiology]]). Logic is sometimes included as another main branch of philosophy, sometimes as a ...with [[modal qualifier]]s like "possibly" and "necessarily", or [[temporal logic]], which deals with the logical relationships established by the ''[[tense]

'''Logic''' (from [[Ancient Greek|Classical Greek]] λόγος [[logos]]; meaning wo ...reasoning using [[probability]] and to arguments involving [[causality]]. Logic is also commonly used today in [[argumentation theory]]. J. Robert Cox and

...nt of deduction as it is understood in [[mathematics]], see [[mathematical logic]]. ==Deductive logic==

...equality and inequality, are studied by mathematics. The essential part of mathematical quantities is made up with a collection variables each assuming a set of va ==Quantity in logic and semantics==

...[individual]] [[personality]] in the [[motions]] and [[tensions]] of the [[mathematical]] level of the [[energy]] [[universe]]. Nor can man ever [[discern]] [[spir ...[[personality]]. Nor will the [[exhaustion]] of the [[possibilities]] of [[logic]] and [[reason]] ever [[reveal]] to the logician or to the reasoner the [[e

...rly usage, scholars often referred to a clever [[idea]] or to a convenient mathematical approach that simplified cumbersome calculations as a ''hypothesis''; when ...ome a theory itself. Normally, scientific hypotheses have the form of a [[mathematical model]]. Sometimes, but not always, one can also formulate them as existen

...essors. As it became clear that computers could be used for more than just mathematical calculations, the field of computer science broadened to study [[computatio ...view, as opposed to the more declarative point of view taken by classical mathematical subjects.

...t.html#mod), but popularized much later, represents propositions and basic logic, and can derive conclusions from known premises. [[KL-ONE]] (1980s) is more ...ions, such as [[truth table]]s, which were used to study and model Boolean logic, for example. [[Spreadsheet]]s are yet another tabular representation of kn

...f linear algebra. Other types of entries, such as elements in more general mathematical fields or even |rings are also used. Matrices consisting of only one column ...tics [[text]] from between 300 BC and AD 200, ''[[The Nine Chapters on the Mathematical Art]]'' (''Jiu Zhang Suan Shu''), is the first example of the use of matrix

..., he excludes [[mathematical]] thought, which operates primarily through [[logic]]. Totems are chosen [[arbitrarily]] for the sole [[purpose]] of making the

...at is, intuition that is not empirical (''Prolegomena, p.7''). Intuitistic logic was devised by Arend Heyting to accommodate this position (and has been ado

...in Book I of his [[Sum of Logic|Summa Totius Logicae]] (''Treatise on all Logic'', written some time before 1327) that Categories are not a form of Being i

..., and then you grow in insight and are able to use that insight in another mathematical situation. If you have behaviors that are erratic it will not prevent the i

Theory of Computation attempts to grasp the patterns that appear within the [[logic]] of [[computer science]]. Since efficiency is extremely important when exe [[Fractals]] are mathematical patterns that are scale invariant. This means that the shape of the patter

You who are [[creative]] [[writers]] have neglected to cultivate the [[mathematical]], [[analytical]] and [[logical]]. You who are [[scientists]] have emphasiz Q: How are the terms [[masculine]] and [[feminine]] applicable to [[logic]] and [[intuition]].

...anger]] that the purely physical [[scientist]] may become afflicted with [[mathematical]] [[pride]] and [[statistical]] [[egotism]], not to mention [[spiritual]] [ 133:5.5 [[Logic]] is valid in the [[material]] world, and [[mathematics]] is reliable when

...mplex ''codomain'' or ''target'', using all of these words in the sense of mathematical category theory. ...[literary theory]], and specializations within [[philosophy]] outside of [[logic]], speaks of a mapping from what is typically the more familiar area of exp

...mpirical methods. Formal science, which also includes [[statistics]] and [[logic]], is vital to the empirical sciences. Major advances in formal science hav ...of nature or the behavior of the subject of the field of study. Unlike a mathematical proof, a scientific theory is [[empirical]], and is always open to [[falsif

...a system in an environment. On the other hand cybernetic factory can be [[mathematical model|modeled]] as a control system. ...s of control systems, electrical network theory, mechanical engineering, [[logic]] modeling, evolutionary [[biology]], neuroscience, [[anthropology]], and [

...oduced the method of basing claims about [[pheonomena|appearances]] on a [[logic]]al concept of Being, he is considered one of the founders of metaphysics. ...[law]] of noncontradiction and the status it holds in non-paraconsistent [[logic]]s.

...mpirical methods. Formal science, which also includes [[statistics]] and [[logic]], is vital to the empirical sciences. Major advances in formal science hav ...of nature or the behavior of the subject of the field of study. Unlike a mathematical proof, a scientific theory is [[empirical]], and is always open to [[falsif

...d society, and from the [[formal science]]s, such as [[mathematics]] and [[logic]], which use a different [[methodology]]. Aside from the logical and mathematical sciences, there are three great branches of ''natural science'' which stand

...r it should be noted that roughly parallel concepts within mathematics and logic go back beyond [[Aristotle]]. It has been variously been ascribed to [[Desc * [[Mathematics|Mathematical]] analysis, the generic name given to any branch of mathematics that depend

...ctly from subjects taught at the original universities, such as [[law]], [[logic]], [[philosophy]], and [[medicine]]. But the university’s main role in th ...Although at first glance the seven liberal arts appear to be limited to [[mathematical]] and [[language]] studies, the process of teaching and expounding them fur

===='''''[[Logic]]''''', '''''[[Faith]]'''''==== ...paragraphs]] for similar [[argument]]] So one can not find the answer in [[logic]].

...4._THE_ANDITES Andite] successors who first attempted to [[divorce]] the [[mathematical]] from the [[volitional]]. Increasingly has civilized man followed in the f ...its [[interpretations]] of [[reality]] in the [[linear]] [[fashion]] of [[logic]]; it must never fail to reckon with the [[elliptic]] [[symmetry]] of reali

...ists have proposed that the mind contains such mental representations as [[Logic|logical]] propositions, rules, [[concepts]], images, and analogies, and tha ===Formal logic===

...and significant developments in the field of Philosophy of [[religion]], [[Logic]] and [[Metaphysics]]. The three principles that underlie all their work are the use of [[logic]], [[dialectic]] and [[analysis]] to discover the [[truth]], known as ratio

In [[philosophy]] and [[logic]], [[contingency]] is the status of propositions that are not necessarily t ...Though Gerolamo Cardano and Galileo wrote about games of chance, the first mathematical treatments were given by [[Blaise Pascal]], Pierre de Fermat and Christiaan

...[wisdom]]. Man's [[conceit]] often outruns his [[reason]] and eludes his [[logic]]. ...entist who thus [[observes]] universe [[phenomena]] and [[classifies]] the mathematical [[facts]] inherent in the mechanistic [[phases]] of the material side of [[

...tem]]s come into being starting from a small set of axioms and rules. In [[logic]], the time that an algorithm requires to complete cannot be measured, as i ...guage or implementation. In this sense, algorithm analysis resembles other mathematical disciplines in that it focuses on the underlying properties of the algorith

An alternative, [[qualitative]], mathematical description is to say that there is an iterative process through (m+n)-dime ...objection to the [https://en.wikipedia.org/wiki/Game Theory game theory] [[logic]] of mutual assured destruction during the Cold War. Peace activists, objec

...t]] project of [[attaining]] all [[truth]] by reason alone. Mathematical [[logic]] showed that fundamental choices of [[axioms]] were essential in [[deducti ...relativized into something that is only "true for them". [[Subjective]] [[logic]] is a belief reasoning formalism where beliefs explicitly are subjectively

...true. The [[scientific method]] is built on testing assertions which are [[logic]]al consequences of scientific theories. This is done through repeatable [[ [[Mathematical models]] and computer models are frequently used to both describe the [[beh

...of [[history]], [[poetry]] or [[politics]]. Only with the development of [[mathematical proof]] did there gradually arise a perceived difference between "scientifi ...Pascal]], [[Gottfried Leibniz]] and [[Johannes Kepler]], each of whom took mathematical examples as models for human behavior directly. In Pascal's case, the [[Pas

...he publication in 1948 of an influential paper by [[Claude Shannon]], "[[A Mathematical Theory of Communication]]." This paper provides the foundations of [[infor Micheal Reddy noted that "'signals' of the [[mathematical theory]] are 'patterns that can be exchanged'. There is no message contain

...thods of verification and testing of hypotheses may involve less stringent mathematical and statistical interpretations of these elements within the respective dis William Stanley Jevons, ''The principles of science: a treatise on logic and scientific method''

...of [[religion]] [[transcends]] the [[reason]] of the [[mind]], even the [[logic]] of [[philosophy]]. [[Religion]] is [[faith]], [[trust]], and [[assurance] ...ithin, it is altogether reasonable. [[Religion]] is not derived from the [[logic]] of [[human]] [[philosophy]], but as a [[mortal]] [[experience]] it is alt

.... In the book ''[[Sex, Ecology, Spirituality]]'', Wilber describes vision-logic as a planetary awareness. He uses it to translate the term ''vernunft'' as ...ing to [[Ervin László]], a ''Theory of Everything'' would include not just mathematical formulas and quantum physics, but life, mind, and culture as well. He poin

...4._THE_ANDITES Andite] successors who first attempted to [[divorce]] the [[mathematical]] from the [[volitional]]. Increasingly has civilized man followed in the f ...its [[interpretations]] of [[reality]] in the [[linear]] [[fashion]] of [[logic]]; it must never fail to reckon with the [[elliptic]] [[symmetry]] of reali

[[Logic]]al determinism is the notion that all propositions, whether about the past ===Determinism in mathematical models===

...uld not be confused with [[information theory]], the study of a particular mathematical concept of information, or with [[library science]], a field related to [[l ...to Laws of Thought...,’’ which lays the foundations for [[Boolean algebra (logic)|Boolean algebra]], which is later used in [[information retrieval]].<ref>

==Logic== ...statement has the combination of a true antecedent and false consequent. [[Logic]] requires only that [[truth]] not be deceptive.

...lluminating power of scientific reason. However, once these scientific and mathematical principles had been objectified they could encompass all of reality, and it ...mgarten, in the context of defining sensuous knowledge as a counterpart to logic as a theory of intellectual knowledge, thus denoting a special domain of co

...flective]] [[conclusions]] based on [[cosmic]] [[response]]. This is the [[mathematical]] [[form]] of the [[cosmic]] [[discrimination]]. ...evelation]]. [[Matter]]-[[energy]] is recognized by the [[mathematical]] [[logic]] of the [[senses]]; [[mind]]-[[reason]] [[intuitively]] knows its [[moral]

...[[certitude]] because it is not wholly [[supported]] by [[intellectual]] [[logic]]. To every such doubter the believer only replies, "How do you know that I ...question [[faith]], faith can always [[supplement]] both [[reason]] and [[logic]]. [[Reason]] creates the [[probability]] which [[faith]] can [[transform]]

"Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything ...seen by two different observers in motion relative to each other produce a mathematical concept of time that works pretty well for describing the everyday phenomen

...s the minus signs in place of plus signs. The consequences of that small [[mathematical]] difference are [[profound]]. ...ays positive, and the only zero distance is between a point and itself. In mathematical terms, the Euclidean metrical structure is positive definite. But in the Mi

...fection|affective]], [[Music|musical]], spatial, [[logic]]al-[[Mathematics|mathematical]], [[karma|karmic]], etc. One can be highly developed cognitively (cerebral ...nsions). What he calls "broad science" would include evidence from [[Logic|logic]], [[Mathematics|mathematics]], and from the [[symbol]]ic, [[hermeneutics|h

(152) ‘Today, mathematical models proclaim access to the origins of the present [[universe]]. ...[[Utopia]] of the Sunday, the aesthetic will, presumably, no longer have [[logic]]

...his [[immediate]] or remote interest; [[self-interest]] largely obscures [[logic]]. The [[difference]] between the [[minds]] of savage and civilized men is ...] puts an [https://en.wikipedia.org/wiki/Actuarial_science actuary] with [[mathematical]] reckoning in the place of fictitious spirits and whimsical gods.

...hanasius_of_Alexadria Athanasius], and but for the [[eloquence]] and the [[logic]] of this believer, the [[persuasions]] of [https://en.wikipedia.org/wiki/A ...im merely an [[arithmetical]] [[symbol]] finding a helpless place in the [[mathematical]] [[formula]] of an unromantic and [https://en.wikipedia.org/wiki/Mechanism

...authors who identify [[language]] and [[cognition]], he describes his own mathematical thinking as largely wordless, often accompanied by [[mental images]] that r ...xpression, one can postulate a continuum extending from "[[interpretation (logic)|interpretation]]" to "innovation". Established [[art movements|artistic mo

thought to be a more tranquil society to be dominated by logic and reason through education. ...a of scientific empiricism by showing in print that there is a fundamental logic

...place without the psychological phenomenon of fusion. Whether, in terms of logic, a chord presents an entity, and not merely a combination of intervals, dep ...eness of the imaginary fundamental bass that was essential to the harmonic logic. Those theorists who in the 17th century formulated the principle of chorda

...dels describing collapse of agrarian civilizations. For example, the basic logic of Turchin's "fiscal-demographic" model can be outlined as follows: during

...anger]] that the purely physical [[scientist]] may become afflicted with [[mathematical]] [[pride]] and [[statistical]] [[egotism]], not to mention [[spiritual]] [ 133:5.5 [[Logic]] is valid in the [[material]] world, and [[mathematics]] is reliable when

...the twenty-third chamber of the site. It contained text, symbol pictures, mathematical equations, and what turned out to be music files. ...e a literal translation, there would be no sentence structure--more like a logic syntactical approach--which simply means an abstracted language flow which

...mind what or whom to [[trust]]. Is it man who designs the universe with [[mathematical]] immutability, or is it a [[Creator]]’s mind which knows matter so well ...ton, and like God it exists as an [[absolute]] [[quality]] rather than a [[mathematical]] certainty.

...need the taking or giving of life. Again I say, [[primitive]] [[ideas]], [[logic]] and [[emotions]]. Many wars have been fought in [[God]]'s [[name]]. This It is almost [[mathematical]], but that is not [[simplicity]]. You all still work within your [[limitat

...f your being. You who are creative writers have neglected to cultivate the mathematical, analytical and logical. You who are scientists have emphasized these trait ...mental attitudes are essential in this love growth. The strength of man is logic, and the logical thought pattern is somewhat inimical to the strength of wo