Quantifier (definition) - Revision history

AndrewCarnie at 06:13, 16 June 2012

2012-06-16T06:13:09Z

2012-06-16T06:12:25Z

2012-06-16T06:11:58Z

2009-09-28T02:48:11Z

‎References

2009-09-24T23:30:37Z

‎Kinds of Quantifiers

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‎External Links

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‎External Links

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 # [[Numerals]]
 # [[Articles]]
 == See Also ==

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 == Kinds of Quantifiers ==
-. '''Universal Quantifier (&forall;)''': given some object ''x'', &forall;''x'' can be interpreted as: "for all ''x''...", "all ''x''...", "any ''x''..."<br>
+# '''Universal Quantifier (&forall;)''': given some object ''x'', &forall;''x'' can be interpreted as: "for all ''x''...", "all ''x''...", "any ''x''..."
-. '''Existential Quantifier (&exist;x)''', given some object ''x'', &exist;''x'' can be interpreted as: "for some ''x''...", "some ''x''...", "there exists (at least one) ''x''..."
+# '''Existential Quantifier (&exist;x)''', given some object ''x'', &exist;''x'' can be interpreted as: "for some ''x''...", "some ''x''...", "there exists (at least one) ''x''..."
-. [[Numerals]]
+# [[Numerals]]
-. [[Articles]]
+# [[Articles]]
 == Example ==

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-[[Category: Technical Definitions]]
+Quantifiers are elements of quantity that are used to define the selection (essentially, ''all'' or ''some'') of tokens within the set of the abstract target object type (e.g., a noun such as 'rock').  For instance, quantifiers allow the referent of a certain type of object (e.g., table, turtle, rock) to point to ''all'' tokens of that type (e.g., "all rocks") or ''some'' tokens of that type (e.g., "some rocks").
 == Kinds of Quantifiers ==
 . '''Universal Quantifier (&forall;)''': given some object ''x'', &forall;''x'' can be interpreted as: "for all ''x''...", "all ''x''...", "any ''x''..."<br>
 . '''Existential Quantifier (&exist;x)''', given some object ''x'', &exist;''x'' can be interpreted as: "for some ''x''...", "some ''x''...", "there exists (at least one) ''x''..."
 == Example ==
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 == See Also ==
-[http://gaelicgrammar.org/~gaelic/mediawiki/index.php/Semantics_%28definition%29 Semantics]
+[[Article (definition)]]
 == External Links ==
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 == References ==
-Discrete Mathematics and Its Applications. Kenneth H. Rosen.
+Partee, B., A. ter Meulen, and R. E. Wall. (1990) Mathematical Methods in Linguistics. Springar.
-<br>
-Mathematical Methods in Linguistics. Barbara H. Partee, Alice ter Meulen, and Robert E. Wall.
+[[Category: Technical Definitions]]

← Older revision		Revision as of 02:48, 28 September 2009
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	== References ==		== References ==
−	~~TBD~~	+	Discrete Mathematics and Its Applications. Kenneth H. Rosen.
		+	<br>
		+	Mathematical Methods in Linguistics. Barbara H. Partee, Alice ter Meulen, and Robert E. Wall.

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 == Kinds of Quantifiers ==
-Given some object ''x'':<br>
+. '''Universal Quantifier (&forall;)''': given some object ''x'', &forall;''x'' can be interpreted as: "for all ''x''...", "all ''x''...", "any ''x''..."<br>
-. '''Universal Quantifier (&forall;x)''' can be interpreted as: "for all x..." "all x..." "any x..."<br>
+. '''Existential Quantifier (&exist;x)''', given some object ''x'', &exist;''x'' can be interpreted as: "for some ''x''...", "some ''x''...", "there exists (at least one) ''x''..."
 == Example ==

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 == External Links ==
-[http://en.wikipedia.org/wiki/Quantification ''Quantification'' on Wikipedia]
+[http://en.wikipedia.org/wiki/Quantification ''Quantification'' on Wikipedia]<br>
 [http://www.philosophypages.com/dy/q.htm#qfrs ''Quantifiers'' from Philosophy Pages]
 == References ==
 TBD

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 [[Category: Syntax]]
 [[Category: Parts of Speech]]
 == General Definition ==
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 == Kinds of Quantifiers ==
 Given some object ''x'':<br>
-. '''Universal Quantifier (Ax)''' can be interpreted as: "for all x..." "all x..." "any x..."<br>
+. '''Universal Quantifier (&forall;x)''' can be interpreted as: "for all x..." "all x..." "any x..."<br>
-. '''Existential Quantifier (Ex)''' can be interpreted as: "for some x..." "some x..." "there exists (at least one) x..."
+. '''Existential Quantifier (&exist;x)''' can be interpreted as: "for some x..." "some x..." "there exists (at least one) x..."
 == Example ==
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 G(t) = "turtles are green"<br>
 Now, this does not express what we may really intend when making this proposition. What we may really be stating is "the property of being green can be attributed to all turtles" or "with respect to all turtles, it is the case that the property of being green is attributed to turtles."  Quantifiers are used to express this perhaps non-overt statement using symbols:<br>
-At[G(t)]
+&forall;t[G(t)]

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 == Kinds of Quantifiers ==
 Given some object ''x'':<br>
-. Universal Quantifier (interpreted as: "for all x..." "all x..." "any x...")<br>
+. '''Universal Quantifier (A)''' can be interpreted as: "for all x..." "all x..." "any x..."<br>
-. Existential Quantifier (interpreted as: "for some x..." "some x..." "there exists (at least one) x...")
+. '''Existential Quantifier (E)''' can be interpreted as: "for some x..." "some x..." "there exists (at least one) x..."
 == Example ==
 One can make a proposition such as "turtles are green." Now, this certainly ''can'' be true ''given that certain conditions are met''. What are these conditions? One type of condition is that of quantity; quantifiers allow for defining this condition. For instance, "turtles are green" can be divided into symbolic representations as follows:<br>
 Given some object ''x'':<br>
-T = "turtles" <br>
+t = "turtles" <br>
 G(x) = "x is/are green"<br>
-G(T) = "turtles are green"<br>
+G(t) = "turtles are green"<br>
 Now, this does not express what we may really intend when making this proposition. What we may really be stating is "the property of being green can be attributed to all turtles" or "with respect to all turtles, it is the case that the property of being green is attributed to turtles."  Quantifiers are used to express this perhaps non-overt statement using symbols:<br>
-A(T)[G(T)]
+At[G(t)]