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...=liHivlUYWcUC&pg=PA34 p. 34.]</ref><ref>{{Cite web|title=Truth-value {{!}} logic|url=https://www.britannica.com/topic/truth-value|access-date=2020-08-15|web ...9 p. 199.]</ref><ref>[[Graham Priest]], ''An Introduction to Non-Classical Logic: From If to Is'', 2nd ed, Cambridge University Press, 2008, {{ISBN|0-521-85 ...

{{Short description|Term in logic and deductive reasoning}} ...proven in the system is logically valid with respect to the [[Semantics of logic|logical semantics]] of the system. ...

...ise]]s to be [[truth|true]] and the conclusion nevertheless to be [[False (logic)|false]].<ref>[http://www.iep.utm.edu/val-snd/ Validity and Soundness – Int ...ment terminology used in logic (en).svg|thumb|Argument terminology used in logic]] ...

...dity (logic)|validity]]",<ref>[[Oxford Dictionary of English]], sense 1 of logic.</ref> while they are rational according to the broader requirement that th ...e doctrine that mathematical concepts, among others, are reducible to pure logic. ...

...n many cases, a lemma derives its importance from the theorem it aims to [[mathematical proof|prove]]; however, a lemma can also turn out to be more important than {{Mathematical logic}} ...

The '''language of mathematics''' or '''mathematical language''' is an extension of the [[natural language]] (for example [[Engl The main features of the mathematical language are the following. ...

...a field of study that investigates topics such as [[number]], [[space]], [[Mathematical structure|structure]], and change.<!--Please, do not link "change", as it h ...cs]] is the system used by [[mathematician]]s to communicate [[Mathematics|mathematical]] ideas among themselves, and is distinct from natural languages in that it ...

A '''calculation''' is a deliberate [[mathematical]] process that transforms one or more inputs into one or more outputs or '' ...ion. Extracting the [[square root]] or the [[cube root]] of a number using mathematical models is a more complex algorithmic calculation. ...

...inguistics]]. While philosophers since [[Aristotle]] have discussed modal logic, and [[Medieval Philosophy|Medieval philosophers]] such as [[Avicenna]], [[ ...[dynamic logic (modal logic)|dynamic logic]] to create [[dynamic epistemic logic]], which can be used to specify and reason about information change and exc ...

...e in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or deception in the presenta ...hese fallacies, for pedagogic reasons, usually take the form of spurious [[Mathematical proof|proofs]] of obvious [[contradiction]]s. Although the proofs are flawe ...

|title = Paradoxes and Contemporary Logic |url-id = paradoxes-contemporary-logic ...

* logical unknowability — arising from abstract considerations of epistemic logic. ...is a prominent example of an unknowability associated with the established mathematical field of [[computability theory]]. In 1936, [[Alan Turing]] proved that the ...

{{About|the subject as it is studied in logic and philosophy}} ...|first=Walter |title=Understanding arguments: an introduction to informal logic |last2=Fogelin |first2=Robert J. |date=2015 |publisher=Cengage Learning |is ...

== Mathematical == {{Main|Mathematical structure}} ...

...itle=The Death of Argument |date=2004 |isbn=978-9048167005 |series=Applied Logic Series |volume=32 |pages=3–23 |chapter=Who Cares About the Fallacies? |doi= ...</ref> Arguments containing informal fallacies may be formally [[Validity (logic)|valid]], but still fallacious.<ref name="Downden">{{Cite web |last=Dowden ...

...le are able to remember, [[gestaltism]]s or failure of the principles of [[logic]], etc.; ...Gray%20et%20al%20Mental%20Modeler%202013.pdf|title=Mental Modeler: A Fuzzy-Logic Cognitive Mapping Modeling Tool for Adaptive Environmental Management|websi ...

{{Short description|Academic field of logic and rhetoric}} ...ple of an early [[argument map]], from [[Richard Whately]]'s ''Elements of Logic'' (1852 edition)]] ...

...tain certain mathematical truths that human minds can.<ref>Roger Penrose, "Mathematical Intelligence," in Jean Khalfa, editor, ''What is Intelligence?'', chapter 5 ...48–179.)|url=http://dx.doi.org/10.2307/2271581|journal=Journal of Symbolic Logic|volume=36|issue=1|pages=177|doi=10.2307/2271581|jstor=2271581|issn=0022-481 ...

...e was viewed primarily as a way of making factual [[Judgment (mathematical logic)|assertions]], and the other uses of language tended to be ignored, as Aust ...|classical]] semantics) and illocutionary force (given by [[intuitionistic logic|intuitionistic]] semantics). Up to now the main basic formal applications o ...

...vel, information pertains to the interpretation (perhaps [[Interpretation (logic)|formally]]) of that which may be [[sense]]d, or their [[abstraction]]s. A ...]], [[pattern theory|pattern]], [[perception]], [[Proposition#Treatment in logic|proposition]], [[knowledge representation|representation]], and [[Entropy ( ...