en>Yobot: clean up, References after punctuation per WP:REFPUNC and WP:CITEFOOT using AWB (8792)

2012-12-11T13:01:52Z

clean up, References after punctuation per WP:REFPUNC and WP:CITEFOOT using AWB (8792)

← Older revision		Revision as of 15:01, 11 December 2012
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	~~Hello. Let me introduce the author. Her~~ title is ~~Refugia Shryock~~. ~~Doing ceramics is what her family and her enjoy~~. ~~South Dakota is exactly where I~~'~~ve usually been living~~. ~~He used~~ to ~~be unemployed~~ but ~~now he~~ is a ~~computer operator~~ but ~~his promotion by no means arrives~~.<br><br>~~Feel free~~ to ~~surf to my page ::~~ [~~http~~:~~//torontocartridge~~.~~com/uncategorized/~~the-~~ideal-way-to-battle-a-yeast-infection~~/ ~~http~~:~~//torontocartridge~~.~~com~~]		{{Italic title}}
			{{Refimprove\|date=November 2006}}

			'''''Consequentia mirabilis''''' ([[Latin]] for "admirable consequence"), also known as '''Clavius's Law''', is used in [[traditional logic\|traditional]] and [[classical logic]] to establish the truth of a proposition from the [[Consistency proof\|inconsistency]] of its negation.<ref>Sainsbury, Richard. ''Paradoxes''. Cambridge University Press, 2009, p. 128.</ref> It is thus similar to ''[[reductio ad absurdum]]'', but it can prove a proposition true using just its negation. It states that if a proposition is a consequence of its negation, then it is true, for consistency. It can thus be demonstrated without using any other principle, but that of consistency.

			In formal notation:
			<math> (\neg A \rightarrow A) \rightarrow A </math>
			which is equivalent to <math> (\neg \neg A \or A) \rightarrow A </math>.

			''Consequentia mirabilis'' was a pattern of argument popular in 17th century Europe that first appeared in a fragment of Aristotle's ''[[Protrepticus (Aristotle)\|Protrepticus]]:'' "If we ought to philosophise, then we ought to philosophise; and if we ought not to philosophise, then we ought to philosophise (i.e. in order to justify this view); in any case, therefore, we ought to philosophise."<ref name="Kneale1957">{{cite journal \|last=Kneale \|first=William \|journal=The Journal of Hellenic Studies \|title=Aristotle and the Consequentia Mirabilis \|volume=77 \|number=1 \|year=1957 \|pages=62-66 \|jstor=628635}}</ref>

			The most famous example is perhaps the Cartesian ''cogito ergo sum'': Even if one can question the validity of the thinking, no one can deny that they are thinking.

			==See also==
			*''[[Ex falso quodlibet]]''
			*''[[Tertium non datur]]''

			==References==
			{{Reflist}}

			{{DEFAULTSORT:Consequentia Mirabilis}}
			[[Category:Theorems in propositional logic]]
			[[Category:Latin logical phrases]]

90.62.153.63 at 17:15, 8 April 2012

2012-04-08T17:15:48Z

New page

Hello. Let me introduce the author. Her title is Refugia Shryock. Doing ceramics is what her family and her enjoy. South Dakota is exactly where I've usually been living. He used to be unemployed but now he is a computer operator but his promotion by no means arrives.<br><br>Feel free to surf to my page :: [http://torontocartridge.com/uncategorized/the-ideal-way-to-battle-a-yeast-infection/ http://torontocartridge.com]

Maximal pair - Revision history

en>Yobot: clean up, References after punctuation per WP:REFPUNC and WP:CITEFOOT using AWB (8792)

90.62.153.63 at 17:15, 8 April 2012