|
|
Line 1: |
Line 1: |
| {{Other uses|Closure (disambiguation){{!}}Closure}}
| | Andera is what you can call her but she by no means truly favored that name. Since I was 18 I've been operating as a bookkeeper but [http://kjhkkb.net/xe/notice/374835 online psychic] soon my wife and I will [http://www.octionx.sinfauganda.co.ug/node/22469 love psychic readings] start our own company. I've always loved residing in Kentucky but now I'm considering other options. To climb is something I really enjoy performing.<br><br>my web page ... real psychics ([http://gcjcteam.org/index.php?mid=etc_video&document_srl=696611&sort_index=regdate&order_type=desc click the next internet page]) |
| | |
| '''Deductive closure''' is a [[property (philosophy)|property]] of a [[set (mathematics)|set]] of [[object (philosophy)|objects]] (usually the objects in question are [[statement (logic)|statement]]s). A [[set (mathematics)|set]] of objects, <var>O</var>, is said to exhibit ''closure'' or to be ''closed'' under a given [[closure operator|operation]], <var>R</var>, provided that for every object, <var>x</var>, if <var>x</var> is a member of <var>O</var> and <var>x</var> is <var>R</var>-related to any object, <var>y</var>, then <var>y</var> is a member of <var>O</var>.<ref>[[Peter D. Klein]], ''Closure'', ''[[The Cambridge Dictionary of Philosophy]] (second edition)</ref> In the context of statements, a deductive closure is the set of all the statements that can be [[Deductive reasoning|deduced]] from a given set of statements.
| |
| | |
| In [[propositional calculus|propositional logic]], the set of all true propositions exhibits '''deductive closure''': if set <var>O</var> is the set of true propositions, and operation <var>R</var> is [[logical consequence]] (“<math>\vdash</math>”), then provided that proposition <var>p</var> is a member of <var>O</var> and <var>p</var> is <var>R</var>-related to <var>q</var> (i.e., p <math>\vdash</math> q), <var>q</var> is also a member of <var>O</var>.
| |
| | |
| == Epistemic closure == | |
| {{main|Epistemic closure}}
| |
| | |
| In [[epistemology]], many philosophers have and continue to debate whether particular subsets of [[proposition]]s—especially ones ascribing [[knowledge]] or [[Theory of justification|justification]] of a [[belief]] to a subject—are closed under deduction.
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| [[Category:Concepts in logic]]
| |
| [[Category:Deductive reasoning|Closure]]
| |
| [[Category:Logical consequence]]
| |
| [[Category:Propositional calculus]]
| |
| [[Category:Set theory]]
| |
Revision as of 20:24, 28 February 2014
Andera is what you can call her but she by no means truly favored that name. Since I was 18 I've been operating as a bookkeeper but online psychic soon my wife and I will love psychic readings start our own company. I've always loved residing in Kentucky but now I'm considering other options. To climb is something I really enjoy performing.
my web page ... real psychics (click the next internet page)