Directory:Jon Awbrey/Papers/Introduction to Inquiry Driven Systems - Revision history

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Jon Awbrey: ('''Note to Self.''' Some parts of this page need to be updated. — JA, Sep 2010)

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('''Note to Self.''' Some parts of this page need to be updated. — JA, Sep 2010)

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Jon Awbrey: /* Toward a Functional Conception of Quantificational Logic */

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Toward a Functional Conception of Quantificational Logic

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 ===Secondary sources===
-* Awbrey, Jon, and Awbrey, Susan (1995), "Interpretation as Action:  The Risk of Inquiry", ''Inquiry:  Critical Thinking Across the Disciplines'', 15, 40–52.  [http://www.chss.montclair.edu/inquiry/fall95/awbrey.html Eprint]
+* Awbrey, S.M., and Awbrey, J.L. (May 2001), &ldquo;Conceptual Barriers to Creating Integrative Universities&rdquo;, ''Organization : The Interdisciplinary Journal of Organization, Theory, and Society'' 8(2), Sage Publications, London, UK, pp. 269&ndash;284.  [http://org.sagepub.com/cgi/content/abstract/8/2/269 Abstract].
-* [[Susan Haack|Haack, Susan]] (1993), ''Evidence and Inquiry:  Towards Reconstruction in Epistemology'', Blackwell Publishers, Oxford, UK.
+* Awbrey, S.M., and Awbrey, J.L. (September 1999), &ldquo;Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next Century&rdquo;, ''Second International Conference of the Journal &lsquo;Organization&rsquo;'', ''Re-Organizing Knowledge, Trans-Forming Institutions : Knowing, Knowledge, and the University in the 21st Century'', University of Massachusetts, Amherst, MA.  [http://cspeirce.com/menu/library/aboutcsp/awbrey/integrat.htm Online].
-* [[William Kneale|Kneale, William]], and [[Martha Kneale|Kneale, Martha]], ''The Development of Logic'', Oxford University Press, London, UK, 1962.
+* Awbrey, J.L., and Awbrey, S.M. (Autumn 1995), &ldquo;Interpretation as Action : The Risk of Inquiry&rdquo;, ''Inquiry : Critical Thinking Across the Disciplines'' 15(1), pp. 40&ndash;52.  [http://web.archive.org/web/19970626071826/http://chss.montclair.edu/inquiry/fall95/awbrey.html Archive].  [http://independent.academia.edu/JonAwbrey/Papers/1302117/Interpretation_as_Action_The_Risk_of_Inquiry Online].
 ==See Also==

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 <br><sharethis />
 [[Category:Artificial Intelligence]]
 [[Category:Critical Thinking]]
 [[Category:Cybernetics]]

← Older revision		Revision as of 21:24, 21 September 2010
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	{{DISPLAYTITLE:Introduction to Inquiry Driven Systems}}		{{DISPLAYTITLE:Introduction to Inquiry Driven Systems}}
		+	('''Note to Self.''' Some parts of this page need to be updated. — JA, Sep 2010)
		+
	The following essay is intended to provide readers with background on the pragmatic theory of [[inquiry]] and its relationship to the pragmatic [[theory of signs]].		The following essay is intended to provide readers with background on the pragmatic theory of [[inquiry]] and its relationship to the pragmatic [[theory of signs]].

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-{{aficionados}}<sharethis />
+<br><sharethis />
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 ==Toward a Functional Conception of Quantificational Logic==
-Up till now quantification theory has been based on the assumption of individual variables ranging over universal collections of perfectly determinate elements.  Merely to write down quantified formulas like <math>\forall_{x \in X} Fx</math> and <math>\exists_{x \in X} Fx</math> involves a subscription to such notions, as shown by the membership relations invoked in their indices.  Reflected on pragmatic and constructive principles, however, these ideas begin to appear as problematic hypotheses whose warrants are not beyond question, projects of exhaustive determination that overreach the powers of finite information and control to manage.  Therefore, it is worth considering how we might shift the scene of quantification theory closer to familiar ground, toward the predicates themselves that represent our continuing acquaintance with phenomena.
+Up till now quantification theory has been based on the assumption of individual variables ranging over universal collections of perfectly determinate elements.  Merely to write down quantified formulas like <math>\forall_{x \in X} F(x)</math> and <math>\exists_{x \in X} F(x)</math> involves a subscription to such notions, as shown by the membership relations invoked in their indices.  Reflected on pragmatic and constructive principles, however, these ideas begin to appear as problematic hypotheses whose warrants are not beyond question, projects of exhaustive determination that overreach the powers of finite information and control to manage.  Therefore, it is worth considering how we might shift the scene of quantification theory closer to familiar ground, toward the predicates themselves that represent our continuing acquaintance with phenomena.
 ===Higher Order Propositional Expressions===
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 <br>
-I am going to put off explaining Table 8, that presents a sample of what I call "Interpretive Categories for Higher Order Propositions", until after we get beyond the 1-dimensional case, since these lower dimensional cases tend to be a bit "condensed" or "degenerate" in their structures, and a lot of what is going on here will almost automatically become clearer as soon as we get even two logical variables into the mix.
+I am going to put off explaining Table&nbsp;8, that presents a sample of what I call ''interpretive categories'' for higher order propositions, until after we get beyond the 1-dimensional case, since these lower dimensional cases tend to be a bit ''condensed'' or ''degenerate'' in their structures, and a lot of what is going on here will almost automatically become clearer as soon as we get even two logical variables into the mix.
 {| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:90%"
-|+ '''Table 8.  Interpretive Categories for Higher Order Propositions (n = 1)'''
+|+ '''Table 8.  Interpretive Categories for Higher Order Propositions (''n'' = 1)'''
 |- style="background:paleturquoise"
 |Measure||Happening||Exactness||Existence||Linearity||Uniformity||Information
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 <br>
-====Higher Order Propositions and Logical Operators (n <nowiki>=</nowiki> 2)====
+====Higher Order Propositions and Logical Operators (''n'' = 2)====
 By way of reviewing notation and preparing to extend it to higher order universes of discourse, let us first consider the universe of discourse ''X''° = [''X''] = [''x''<sub>1</sub>, ''x''<sub>2</sub>] = [''x'', ''y''], based on two logical features or boolean variables ''x'' and ''y''.

@@ Line 906: / Line 906: @@
 ==Toward a Functional Conception of Quantificational Logic==
-Up till now quantification theory has been based on the assumption of individual variables ranging over universal collections of perfectly determinate elements.  Merely to write down quantified formulas like "&forall;<sub>''x''&isin;''X''</sub>&nbsp;''Fx''" and "&exist;<sub>''x''&isin;''X''</sub>&nbsp;''Fx''" involves a subscription to such notions, as shown by the membership relations invoked in their indices.  Reflected on pragmatic and constructive principles, however, these ideas begin to appear as problematic hypotheses whose warrants are not beyond question, projects of exhaustive determination that overreach the powers of finite information and control to manage.  Therefore, it is worth considering how we might shift the scene of quantification theory closer to familiar ground, toward the predicates themselves that represent our continuing acquaintance with phenomena.
+Up till now quantification theory has been based on the assumption of individual variables ranging over universal collections of perfectly determinate elements.  Merely to write down quantified formulas like <math>\forall_{x \in X} Fx</math> and <math>\exists_{x \in X} Fx</math> involves a subscription to such notions, as shown by the membership relations invoked in their indices.  Reflected on pragmatic and constructive principles, however, these ideas begin to appear as problematic hypotheses whose warrants are not beyond question, projects of exhaustive determination that overreach the powers of finite information and control to manage.  Therefore, it is worth considering how we might shift the scene of quantification theory closer to familiar ground, toward the predicates themselves that represent our continuing acquaintance with phenomena.
 ===Higher Order Propositional Expressions===
-By way of equipping this inquiry with a bit of concrete material, I begin with a consideration of "higher order propositional expressions" (HOPE's), in particular, those that stem from the propositions on 1 and 2 variables.
+By way of equipping this inquiry with a bit of concrete material, I begin with a consideration of ''higher order propositional expressions'' (HOPE's), in particular, those that stem from the propositions on 1 and 2 variables.
-====Higher Order Propositions and Logical Operators (''n'' <nowiki>=</nowiki> 1)====
+====Higher Order Propositions and Logical Operators (''n'' = 1)====
-A "higher order proposition" is, very roughly speaking, a proposition about propositions.  If the original order of propositions is a class of indicator functions {''F'' : ''X'' &rarr; '''B'''}, then the next higher order of propositions consists of maps of the type ''m'' : (''X'' &rarr; '''B''') &rarr; '''B''', where, as usual, '''B''' = {0,&nbsp;1}.
+A ''higher order proposition'' is, very roughly speaking, a proposition about propositions.  If the original order of propositions is a class of indicator functions {''F'' : ''X'' &rarr; '''B'''}, then the next higher order of propositions consists of maps of the type ''m'' : (''X'' &rarr; '''B''') &rarr; '''B''', where, as usual, '''B''' = {0,&nbsp;1}.
 For example, consider the case where ''X'' = '''B'''<sup>1</sup> = '''B'''.  Then there are exactly four propositions of the form ''F'' : '''B''' &rarr; '''B''', and exactly sixteen higher order propositions, all of the type ''m'' : ('''B''' &rarr; '''B''') &rarr; '''B'''.  Table 7 lists the sixteen higher order propositions about propositions on one boolean variable, organized in the following fashion:

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 [[Category:Information Systems]]
 [[Category:Inquiry]]
 [[Category:Intelligence Amplification]]
 [[Category:Learning Organizations]]