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<font size="3">☞</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
'''Inquiry''' is any proceeding or process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.
'''Inquiry''' is any proceeding or process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.
For ease of reference, Figure 1 and the Legend beneath it summarize the classical terminology for the three types of inference and the relationships among them.
For ease of reference, Figure 1 and the Legend beneath it summarize the classical terminology for the three types of inference and the relationships among them.
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<pre>
<pre>
The converging operation of all three reasonings is shown in Figure 2.
The converging operation of all three reasonings is shown in Figure 2.
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<pre>
<pre>
The common proposition that concludes each argument is AC. Introducing the symbol "⇒" to denote the relation of logical implication, the proposition AC can be written as C ⇒ A, and read as "C implies A". Adopting the parenthetical form of Peirce's alpha graphs, in their ''existential interpretation'', AC can be written as (C (A)), and most easily comprehended as "not C without A". In the context of the present example, all of these forms are equally good ways of expressing the same concrete proposition, namely, "contributing to charity is wise".
The common proposition that concludes each argument is AC. Introducing the symbol "⇒" to denote the relation of logical implication, the proposition AC can be written as C ⇒ A, and read as "C implies A". Adopting the parenthetical form of Peirce's alpha graphs, in their ''existential interpretation'', AC can be written as (C (A)), and most easily comprehended as "not C without A". In the context of the present example, all of these forms are equally good ways of expressing the same concrete proposition, namely, "contributing to charity is wise".
:* Deduction could have obtained the Fact AC from the Rule AB, 'benevolence is wisdom', along with the Case BC, 'contributing to charity is benevolent'.
:* Deduction could have obtained the Fact AC from the Rule AB, "benevolence is wisdom", along with the Case BC, "contributing to charity is benevolent".
:* Induction could have gathered the Rule AC, after a manner of saying that 'contributing to charity is exemplary of wisdom', from the Fact AE, 'the act of earlier today is wise', along with the Case CE, 'the act of earlier today was an instance of contributing to charity'.
:* Induction could have gathered the Rule AC, after a manner of saying that "contributing to charity is exemplary of wisdom", from the Fact AE, "the act of earlier today is wise", along with the Case CE, "the act of earlier today was an instance of contributing to charity".
:* Abduction could have guessed the Case AC, in a style of expression stating that 'contributing to charity is explained by wisdom', from the Fact DC, 'contributing to charity is done by this wise man', and the Rule DA, 'everything that is wise is done by this wise man'. Thus, a wise man, who happens to do all of the wise things that there are to do, may nevertheless contribute to charity for no good reason, and even be known to be charitable to a fault. But all of this notwithstanding, on seeing the wise man contribute to charity we may find it natural to conjecture, in effect, to consider it as a possibility worth examining further, that charity is indeed a mark of his wisdom, and not just the accidental trait or the immaterial peculiarity of his character — in essence, that wisdom is the 'cause' of his contribution or the 'reason' for his charity.
:* Abduction could have guessed the Case AC, in a style of expression stating that "contributing to charity is explained by wisdom", from the Fact DC, "contributing to charity is done by this wise man", and the Rule DA, "everything that is wise is done by this wise man". Thus, a wise man, who happens to do all of the wise things that there are to do, may nevertheless contribute to charity for no good reason, and even be known to be charitable to a fault. But all of this notwithstanding, on seeing the wise man contribute to charity we may find it natural to conjecture, in effect, to consider it as a possibility worth examining further, that charity is indeed a mark of his wisdom, and not just the accidental trait or the immaterial peculiarity of his character — in essence, that wisdom is the ''cause'' of his contribution or the ''reason'' for his charity.
As a general rule, and despite many obvious exceptions, an English word that ends in '-ion' denotes equivocally either a process or its result. In our present application, this means that each of the words 'abduction', 'deduction', 'induction' can be used to denote either the process of inference or the product of that inference, that is, the proposition to which the inference in question leads.
As a general rule, and despite many obvious exceptions, an English word that ends in ''-ion'' denotes equivocally either a process or its result. In our present application, this means that each of the words ''abduction'', ''deduction'', ''induction'' can be used to denote either the process of inference or the product of that inference, that is, the proposition to which the inference in question leads.
One of the morals of Peirce's illustration can now be drawn. It demonstrates in a very graphic fashion that the three kinds of inference are three kinds of process and not three kinds of proposition, not if one takes the word 'kind' in its literal sense as denoting a ''genus'' of being, essence, or substance. Said another way, it means that being an abductive Case, a deductive Fact, or an inductive Rule is a category of relation, indeed, one that involves at the very least a triadic relation among propositions, and not a category of essence or substance, that is, not a property that inheres in the proposition alone.
One of the morals of Peirce's illustration can now be drawn. It demonstrates in a very graphic fashion that the three kinds of inference are three kinds of process and not three kinds of proposition, not if one takes the word ''kind'' in its literal sense as denoting a ''genus'' of being, essence, or substance. Said another way, it means that being an abductive Case, a deductive Fact, or an inductive Rule is a category of relation, indeed, one that involves at the very least a triadic relation among propositions, and not a category of essence or substance, that is, not a property that inheres in the proposition alone.
This category distinction between the absolute, essential, or monadic predicates and the more properly relative predicates constitutes a very important theme in Peirce's architectonic. There is of course a parallel application of it in the theory of sign relations, or semiotics, where the distinctions among the sign relational roles of Object, Sign, and Interpretant are distinct ways of relating to other things, modes of relation that may vary from moment to moment in the extended trajectory of a sign process, and not distinctions that mark some fixed and eternal essence of the thing in itself.
This category distinction between the absolute, essential, or monadic predicates and the more properly relative predicates constitutes a very important theme in Peirce's architectonic. There is of course a parallel application of it in the theory of sign relations, or semiotics, where the distinctions among the sign relational roles of Object, Sign, and Interpretant are distinct ways of relating to other things, modes of relation that may vary from moment to moment in the extended trajectory of a sign process, and not distinctions that mark some fixed and eternal essence of the thing in itself.
Now let any two of these statements be Givens (their order not mattering), and let the remaining statement be the Conclusion. The result is an ''argument'', of which three kinds are possible:
Now let any two of these statements be Givens (their order not mattering), and let the remaining statement be the Conclusion. The result is an ''argument'', of which three kinds are possible:
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! !! Deduction !! Induction !! Abduction
! !! Deduction !! Induction !! Abduction
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| ''Given'' || Rule || Case || Rule
| ''Premiss'' || Rule || Case || Rule
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| ''Given'' || Case || Result || Result
| ''Premiss'' || Case || Fact || Fact
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| ''Conclusion'' || Result || Rule || Case
| ''Conclusion'' || Fact || Rule || Case
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====Deduction====
====Deduction====
====Analogy====
====Analogy====
The classic description of analogy in the syllogistic frame comes from Aristotle, who called this form of inference by the name ''paradeigma'', that is, reasoning by way of example or through the parallel comparison of cases.
The classic description of [[analogy]] in the syllogistic frame comes from Aristotle, who called this form of inference by the name ''paradeigma'', that is, reasoning by way of example or through the parallel comparison of cases.
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Figure 3 gives a graphical illustration of Aristotle's example of 'Example', that is, the form of reasoning that proceeds by Analogy or according to a Paradigm.
Figure 3 gives a graphical illustration of Aristotle's example of 'Example', that is, the form of reasoning that proceeds by Analogy or according to a Paradigm.
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<pre>
<pre>
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o-----------------------------------------------------------o
o-----------------------------------------------------------o
Figure 3. Aristotle's 'War Against Neighbors' Example
Figure 3. Aristotle's "War Against Neighbors" Example
</pre>
</pre>
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==Example of inquiry==
==Example of inquiry==
Examples of inquiry, that illustrate the full cycle of its abductive, deductive, and inductive phases, and yet are both concrete and simple enough to be suitable for a first (or zeroth) exposition, are somewhat rare in Peirce's writings, and so let us draw one from the work of fellow pragmatician [[John Dewey]], analyzing it according to the model of zeroth-order inquiry that we developed above.
Examples of inquiry, that illustrate the full cycle of its abductive, deductive, and inductive phases, and yet are both concrete and simple enough to be suitable for a first (or zeroth) exposition, are somewhat rare in Peirce's writings, and so let us draw one from the work of fellow pragmatician John Dewey, analyzing it according to the model of zeroth-order inquiry that we developed above.
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Figure 4 gives a graphical illustration of Dewey's example of inquiry, isolating for the purposes of the present analysis the first two steps in the more extended proceedings that go to make up the whole inquiry.
Figure 4 gives a graphical illustration of Dewey's example of inquiry, isolating for the purposes of the present analysis the first two steps in the more extended proceedings that go to make up the whole inquiry.
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<pre>
<pre>
Figure 5 schematizes this way of viewing the 'analogy of experience'.
Figure 5 schematizes this way of viewing the 'analogy of experience'.
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<pre>
<pre>
==References==
==References==
* [[Dana Angluin|Angluin, Dana]] (1989), "Learning with Hints", pp. 167–181 in David Haussler and Leonard Pitt (eds.), ''Proceedings of the 1988 Workshop on Computational Learning Theory'', MIT, 3–5 August 1988, Morgan Kaufmann, San Mateo, CA, 1989.
* [[Dana Angluin|Angluin, Dana]] (1989), "Learning with Hints", pp. 167–181 in David Haussler and Leonard Pitt (eds.), ''Proceedings of the 1988 Workshop on Computational Learning Theory'', MIT, 3–5 August 1988, Morgan Kaufmann, San Mateo, CA, 1989.
* [[Aristotle]], "[[Prior Analytics]]", [[Hugh Tredennick]] (trans.), pp. 181–531 in ''Aristotle, Volume 1'', [[Loeb Classical Library]], [[Heinemann (book publisher)|William Heinemann]], London, UK, 1938.
* [[Aristotle]], "[[Prior Analytics]]", [[Hugh Tredennick]] (trans.), pp. 181–531 in ''Aristotle, Volume 1'', [[Loeb Classical Library]], [[Heinemann (book publisher)|William Heinemann]], London, UK, 1938.
* 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), "Conceptual Barriers to Creating Integrative Universities", ''Organization : The Interdisciplinary Journal of Organization, Theory, and Society'' 8(2), Sage Publications, London, UK, pp. 269–284. [http://org.sagepub.com/cgi/content/abstract/8/2/269 Abstract].
* Awbrey, S.M., and Awbrey, J.L. (September 18, 1999), "Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next Century", ''Second International Conference of the Journal ''Organization'' '', ''Re-Organizing Knowledge, Trans-Forming Institutions : Knowing, Knowledge, and the University in the 21st Century'', University of Massachusetts, Amherst, MA. [http://www.cspeirce.com/menu/library/aboutcsp/awbrey/integrat.htm Online].
* Awbrey, J.L., and Awbrey, S.M. (Autumn 1995), "Interpretation as Action : The Risk of Inquiry", ''Inquiry : Critical Thinking Across the Disciplines'' 15(1), pp. 40–52. [http://www.chss.montclair.edu/inquiry/fall95/awbrey.html Online].
* Awbrey, J.L., and Awbrey, S.M. (June 1992), "Interpretation as Action : The Risk of Inquiry", ''The Eleventh International Human Science Research Conference'', Oakland University, Rochester, Michigan.
* Awbrey, S.M., and Awbrey, J.L. (May 1991), "An Architecture for Inquiry : Building Computer Platforms for Discovery", ''Proceedings of the Eighth International Conference on Technology and Education'', Toronto, Canada, pp. 874–875. [http://home.m04.itscom.net/hhomey/tmp-a.html Online].
* Awbrey, J.L., and Awbrey, S.M. (January 1991), "Exploring Research Data Interactively : Developing a Computer Architecture for Inquiry", Poster presented at the ''Annual Sigma Xi Research Forum'', University of Texas Medical Branch, Galveston, TX.
* Awbrey, J.L., and Awbrey, S.M. (August 1990), "Exploring Research Data Interactively. Theme One : A Program of Inquiry", ''Proceedings of the Sixth Annual Conference on Applications of Artificial Intelligence and CD-ROM in Education and Training'', Society for Applied Learning Technology, Washington, DC, pp. 9–15.
* [[Cornelius F. Delaney|Delaney, C.F.]] (1993), ''Science, Knowledge, and Mind: A Study in the Philosophy of C.S. Peirce'', University of Notre Dame Press, Notre Dame, IN.
* [[Cornelius F. Delaney|Delaney, C.F.]] (1993), ''Science, Knowledge, and Mind: A Study in the Philosophy of C.S. Peirce'', University of Notre Dame Press, Notre Dame, IN.
* [[John Dewey|Dewey, John]] (1910), ''How We Think'', [[D.C. Heath]], Lexington, MA, 1910. Reprinted, Prometheus Books, Buffalo, NY, 1991.
* [[John Dewey|Dewey, John]] (1910), ''How We Think'', [[D.C. Heath]], Lexington, MA, 1910. Reprinted, Prometheus Books, Buffalo, NY, 1991.
* Dewey, John (1938), ''Logic: The Theory of Inquiry'', Henry Holt and Company, New York, NY, 1938. Reprinted as pp. 1–527 in ''John Dewey, The Later Works, 1925–1953, Volume 12: 1938'', Jo Ann Boydston (ed.), Kathleen Poulos (text. ed.), [[Ernest Nagel]] (intro.), Southern Illinois University Press, Carbondale and Edwardsville, IL, 1986.
* Dewey, John (1938), ''Logic: The Theory of Inquiry'', Henry Holt and Company, New York, NY, 1938. Reprinted as pp. 1–527 in ''John Dewey, The Later Works, 1925–1953, Volume 12 : 1938'', Jo Ann Boydston (ed.), Kathleen Poulos (text. ed.), [[Ernest Nagel]] (intro.), Southern Illinois University Press, Carbondale and Edwardsville, IL, 1986.
* [[Susan Haack|Haack, Susan]] (1993), ''Evidence and Inquiry: Towards Reconstruction in Epistemology'', Blackwell Publishers, Oxford, UK.
* [[Susan Haack|Haack, Susan]] (1993), ''Evidence and Inquiry : Towards Reconstruction in Epistemology'', Blackwell Publishers, Oxford, UK.
* [[Norwood Russell Hanson|Hanson, Norwood Russell]] (1958), ''Patterns of Discovery, An Inquiry into the Conceptual Foundations of Science'', Cambridge University Press, Cambridge, UK.
* [[Norwood Russell Hanson|Hanson, Norwood Russell]] (1958), ''Patterns of Discovery, An Inquiry into the Conceptual Foundations of Science'', Cambridge University Press, Cambridge, UK.
* [[Vincent F. Hendricks|Hendricks, Vincent F.]] (2005), ''Thought 2 Talk: A Crash Course in Reflection and Expression'', Automatic Press / VIP, New York, NY. ISBN 87-991013-7-8
* [[Vincent F. Hendricks|Hendricks, Vincent F.]] (2005), ''Thought 2 Talk : A Crash Course in Reflection and Expression'', Automatic Press, New York, NY.
* [[Cheryl J. Misak|Misak, Cheryl J.]] (1991), ''Truth and the End of Inquiry, A Peircean Account of Truth'', Oxford University Press, Oxford, UK.
* [[Cheryl J. Misak|Misak, Cheryl J.]] (1991), ''Truth and the End of Inquiry, A Peircean Account of Truth'', Oxford University Press, Oxford, UK.
* [[Charles Peirce (Bibliography)|Peirce, C.S., Bibliography]].
* [[Charles Peirce (Bibliography)|Peirce, C.S., Bibliography]].
* [[Charles Sanders Peirce|Peirce, C.S.]], (1931–1935, 1958), ''Collected Papers of Charles Sanders Peirce'', vols. 1–6, [[Charles Hartshorne]] and [[Paul Weiss (philosopher)|Paul Weiss]] (eds.), vols. 7–8, [[Arthur W. Burks]] (ed.), Harvard University Press, Cambridge, MA. Cited as CP volume.paragraph.
* [[Charles Sanders Peirce|Peirce, C.S.]], (1931–1935, 1958), ''Collected Papers of Charles Sanders Peirce'', vols. 1–6, [[Charles Hartshorne]] and [[Paul Weiss (philosopher)|Paul Weiss]] (eds.), vols. 7–8, [[Arthur W. Burks]] (ed.), Harvard University Press, Cambridge, MA. Cited as CP volume.paragraph.
* [[Robert C. Stalnaker|Stalnaker, Robert C.]] (1984), ''Inquiry'', MIT Press, Cambridge, MA.
* [[Robert C. Stalnaker|Stalnaker, Robert C.]] (1984), ''Inquiry'', MIT Press, Cambridge, MA.
==See also==
==Syllabus==
===Focal nodes===
* [[Inquiry Live]]
* [[Logic Live]]
===Peer nodes===
* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry Inquiry @ InterSciWiki]
* [http://mywikibiz.com/Inquiry Inquiry @ MyWikiBiz]
* [http://ref.subwiki.org/wiki/Inquiry Inquiry @ Subject Wikis]
* [http://en.wikiversity.org/wiki/Inquiry Inquiry @ Wikiversity]
* [http://beta.wikiversity.org/wiki/Inquiry Inquiry @ Wikiversity Beta]
===Logical operators===
{{col-begin}}
{{col-break}}
* [[Exclusive disjunction]]
* [[Logical conjunction]]
* [[Logical disjunction]]
* [[Logical equality]]
{{col-break}}
* [[Logical implication]]
* [[Logical NAND]]
* [[Logical NNOR]]
* [[Logical negation|Negation]]
{{col-end}}
===Related topics===
{{col-begin}}
{{col-break}}
* [[Ampheck]]
* [[Boolean domain]]
* [[Boolean function]]
* [[Boolean-valued function]]
* [[Differential logic]]
{{col-break}}
* [[Logical graph]]
* [[Minimal negation operator]]
* [[Multigrade operator]]
* [[Parametric operator]]
* [[Peirce's law]]
{{col-break}}
* [[Propositional calculus]]
* [[Sole sufficient operator]]
* [[Truth table]]
* [[Universe of discourse]]
* [[Zeroth order logic]]
{{col-end}}
===History===
===Relational concepts===
{| cellspacing="4"
{{col-begin}}
{{col-break}}
* [[Continuous predicate]]
* [[Hypostatic abstraction]]
* [[Logic of relatives]]
* [[Logical matrix]]
{{col-break}}
* [[Relation (mathematics)|Relation]]
* [[Relation composition]]
* [[Relation construction]]
* [[Relation reduction]]
{{col-break}}
* [[Relation theory]]
* [[Relative term]]
* [[Sign relation]]
* [[Triadic relation]]
{{col-end}}
===Concepts and topics===
===Information, Inquiry===
{{col-begin}}
{{col-begin}}
{{col-break}}
{{col-break}}
* [[Curiosity]]
* [[Inquiry]]
* [[Dynamics of inquiry]]
* [[Dynamics of inquiry]]
* [[Information theory]]
{{col-break}}
* [[Semeiotic]]
* [[Logic of information]]
* [[Logic of information]]
* [[Philosophy of science]]
{{col-break}}
* [[Descriptive science]]
* [[Normative science]]
{{col-break}}
{{col-break}}
* [[Pragmatic maxim]]
* [[Pragmatic maxim]]
* [[Pragmatic information]]
* [[Truth theory]]
{{col-end}}
{{col-end}}
===Essays and projects===
===Related articles===
* [[Introduction To Inquiry Driven Systems]]
{{col-begin}}
* [[Prospects For Inquiry Driven Systems]]
{{col-break}}
* [[Inquiry Driven Systems : Inquiry Into Inquiry]]
* [http://intersci.ss.uci.edu/wiki/index.php/Semiotic_Information Semiotic Information]
* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
{{col-break}}
* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]
* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus]
* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
{{col-break}}
* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
{{col-end}}
==Document history==
==Document history==
Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
* [http://www.getwiki.net/-Inquiry Inquiry] @ [http://www.getwiki.net/ GetWiki]
* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry Inquiry], [http://intersci.ss.uci.edu/ InterSciWiki]
* [http://mywikibiz.com/Inquiry Inquiry], [http://mywikibiz.com/ MyWikiBiz]
* [http://www.wikinfo.org/index.php/Inquiry Inquiry] @ [http://wikinfo.org/index.php/Main_Page Wikinfo]
* [http://forum.wolframscience.com/showthread.php?threadid=595 Inquiry], [http://forum.wolframscience.com/ NKS Forum]
* [http://semanticweb.org/wiki/Inquiry Inquiry], [http://semanticweb.org/ SemanticWeb]
* [http://en.wikipedia.org/wiki/Inquiry Inquiry] @ [http://en.wikipedia.org/wiki/ Wikipedia]
* [http://wikinfo.org/w/index.php/Inquiry Inquiry], [http://wikinfo.org/w/ Wikinfo]
* [http://en.wikiversity.org/wiki/Inquiry Inquiry], [http://en.wikiversity.org/ Wikiversity]
* [http://beta.wikiversity.org/wiki/Inquiry Inquiry], [http://beta.wikiversity.org/ Wikiversity Beta]
* [http://en.wikipedia.org/w/index.php?title=Inquiry&oldid=71880922 Inquiry], [http://en.wikipedia.org/ Wikipedia]
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