| | | | | | | | | | | | | R U L E | | | | | | | | | | | | o Y | | / | | / | | / | | / | | / | | / C A S E | | / | | / | | / | | / | | / | | | | Y, > | Z, > | Z. > | | Y, > | Z, > | Z. > | | Z, > | Z, > | Y. > | | | | | | | o-------------------------------------------------oFigure 1. Elementary Structure and Terminology | In its original usage a statement of Fact has to do with a deed done or a record made, that is, a type of event that is openly observable and not riddled with speculation as to its very occurrence. In contrast, a statement of Case may refer to a hidden or a hypothetical cause, that is, a type of event that is not immediately observable to all concerned. Obviously, the distinction is a rough one and the question of which mode applies can depend on the points of view that different observers adopt over time. Finally, a statement of a Rule is called that because it states a regularity or a regulation that governs a whole class of situations, and not because of its syntactic form. So far in this discussion, all three types of constraint are expressed in the form of conditional propositions, but this is not a fixed requirement. In practice, these modes of statement are distinguished by the roles that they play within an argument, not by their style of expression. When the time comes to branch out from the syllogistic framework, we will find that propositional constraints can be discovered and represented in arbitrary syntactic forms.Usman and KishoreExample of inquiryExamples 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.A man is walking on a warm day. The sky was clear the last time he observed it; but presently he notes, while occupied primarily with other things, that the air is cooler. It occurs to him that it is probably going to rain; looking up, he sees a dark cloud between him and the sun, and he then quickens his steps. What, if anything, in such a situation can be called thought? Neither the act of walking nor the noting of the cold is a thought. Walking is one direction of activity; looking and noting are other modes of activity. The likelihood that it will rain is, however, something suggested. The pedestrian feels the cold; he thinks of clouds and a coming shower. (John Dewey, How We Think, pp. 6-7). Once over quicklyLet's first give Dewey's elegant example of inquiry in everyday life the quick once over, hitting just the high points of its analysis into Peirce's three kinds of reasoning.Abductive phaseIn Dewey's 'Rainy Day' or 'Sign of Rain' story, we find our peripatetic hero presented with a surprising Fact:
* Fact: C => A, In the Current situation the Air is cool.
Responding to an intellectual reflex of puzzlement about the situation, his resource of common knowledge about the world is impelled to seize on an approximate Rule:
* Rule: B => A, Just Before it rains, the Air is cool.
This Rule can be recognized as having a potential relevance to the situation because it matches the surprising Fact, C => A, in its consequential feature A.All of this suggests that the present Case may be one in which it is just about to rain:
* Case: C => B, The Current situation is just Before it rains.
The whole mental performance, however automatic and semi-conscious it may be, that leads up from a problematic Fact and a previously settled knowledge base of Rules to the plausible suggestion of a Case description, is what we are calling an abductive inference.Deductive phaseThe next phase of inquiry uses deductive inference to expand the implied consequences of the abductive hypothesis, with the aim of testing its truth. For this purpose, the inquirer needs to think of other things that would follow from the consequence of his precipitate explanation. Thus, he now reflects on the Case just assumed:
* Case: C => B, The Current situation is just Before it rains.
He looks up to scan the sky, perhaps in a random search for further information, but since the sky is a logical place to look for details of an imminent rainstorm, symbolized in our story by the letter B, we may safely suppose that our reasoner has already detached the consequence of the abduced Case, C => B, and has begun to expand on its further implications. So let us imagine that our up-looker has a more deliberate purpose in mind, and that his search for additional data is driven by the new-found, determinate Rule:
* Rule: B => D, Just Before it rains, Dark clouds appear.
Contemplating the assumed Case in combination with this new Rule leads him by an immediate deduction to predict an additional Fact:
* Fact: C => D, In the Current situation Dark clouds appear.
The reconstructed picture of reasoning assembled in this second phase of inquiry is true to the pattern of deductive inference.Inductive phaseWhatever the case, our subject observes a Dark cloud, just as he would expect on the basis of the new hypothesis. The explanation of imminent rain removes the discrepancy between observations and expectations and thereby reduces the shock of surprise that made this process of inquiry necessary.Looking more closelySeeding hypothesesFigure 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.o-----------------------------------------------------------o | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | o-----------------------------------------------------------oFigure 4. Dewey's 'Rainy Day' Inquiry | In this analysis of the first steps of Inquiry, we have a complex or a mixed form of inference that can be seen as taking place in two steps:
* The first step is an Abduction that abstracts a Case from the consideration of a Fact and a Rule.
Fact: C => A, In the Current situation the Air is cool.
Rule: B => A, Just Before it rains, the Air is cool.
Case: C => B, The Current situation is just Before it rains.
* The final step is a Deduction that admits this Case to another Rule and so arrives at a novel Fact.
Case: C => B, The Current situation is just Before it rains.
Rule: B => D, Just Before it rains, a Dark cloud will appear.
Fact: C => D, In the Current situation, a Dark cloud will appear.
Weeding hypothesesIn order to comprehend the bearing of inductive reasoning on the closing phases of inquiry there are a couple of observations that we need to make:
* First, we need to recognize that smaller inquiries are typically woven into larger inquiries, whether we view the whole pattern of inquiry as carried on by a single agent or by a complex community.
* Further, we need to consider the different ways in which the particular instances of inquiry can be related to ongoing inquiries at larger scales. Three modes of inductive interaction between the micro-inquiries and the macro-inquiries that are salient here can be described under the headings of the 'Learning', the 'Transfer', and the 'Testing' of rules.
Analogy of experienceThroughout inquiry the reasoner makes use of rules that have to be transported across intervals of experience, from the masses of experience where they are learned to the moments of experience where they are applied. Inductive reasoning is involved in the learning and the transfer of these rules, both in accumulating a knowledge base and in carrying it through the times between acquisition and application.
* Learning. The principal way that induction contributes to an ongoing inquiry is through the learning of rules, that is, by creating each of the rules that goes into the knowledge base, or ever gets used along the way.
* Transfer. The continuing way that induction contributes to an ongoing inquiry is through the exploit of analogy, a two-step combination of induction and deduction that serves to transfer rules from one context to another.
* Testing. Finally, every inquiry that makes use of a knowledge base constitutes a 'field test' of its accumulated contents. If the knowledge base fails to serve any live inquiry in a satisfactory manner, then there is a prima facie reason to reconsider and possibly to amend some of its rules.
Let's now consider how these principles of learning, transfer, and testing apply to John Dewey's 'Sign of Rain' example.LearningRules in a knowledge base, as far as their effective content goes, can be obtained by any mode of inference.For example, a rule like:
* Rule: B => A, Just Before it rains, the Air is cool,
is usually induced from a consideration of many past events, in a manner that can be rationally reconstructed as follows:
* Case: C => B, In Certain events, it is just Before it rains,
* Fact: C => A, In Certain events, the Air is cool,
--------------------------------------------------------------------------------------
:* Rule: B => A, Just Before it rains, the Air is cool.
However, the very same proposition could also be abduced as an explanation of a singular occurrence or deduced as a conclusion of a presumptive theory.TransferWhat is it that gives a distinctively inductive character to the acquisition of a knowledge base? It is evidently the 'analogy of experience' that underlies its useful application. Whenever we find ourselves prefacing an argument with the phrase 'If past experience is any guide …' then we can be sure that this principle has come into play. We are invoking an analogy between past experience, considered as a totality, and present experience, considered as a point of application. What we mean in practice is this: 'If past experience is a fair sample of possible experience, then the knowledge gained in it applies to present experience'. This is the mechanism that allows a knowledge base to be carried across gulfs of experience that are indifferent to the effective contents of its rules.Here are the details of how this notion of transfer works out in the case of the 'Sign of Rain' example:Let K(pres) be a portion of the reasoner's knowledge base that is logically equivalent to the conjunction of two rules, as follows:
* K(pres) = (B => A) and (B => D).
K(pres) is the present knowledge base, expressed in the form of a logical constraint on the present universe of discourse.It is convenient to have the option of expressing all logical statements in terms of their logical models, that is, in terms of the primitive circumstances or the elements of experience over which they hold true.
* Let E(past) be the chosen set of experiences, or the circumstances that we have in mind when we refer to 'past experience'.
* Let E(poss) be the collective set of experiences, or the projective total of possible circumstances.
* Let E(pres) be the present experience, or the circumstances that are present to the reasoner at the current moment.
If we think of the knowledge base K(pres) as referring to the 'regime of experience' over which it is valid, then all of these sets of models can be compared by the simple relations of set inclusion or logical implication.Figure 5 schematizes this way of viewing the 'analogy of experience'.o-----------------------------------------------------------o | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | o-----------------------------------------------------------oFigure 5. Analogy of Experience | In these terms, the 'analogy of experience' proceeds by inducing a Rule about the validity of a current knowledge base and then deducing a Fact, its applicability to a current experience, as in the following sequence:Inductive Phase:
* Given Case: E(past) => E(poss), Chosen events fairly sample Collective events.
* Given Fact: E(past) => K(pres), Chosen events support the Knowledge regime.
-------------------------------------------------------------------------------------------------------------------------
:* Induce Rule: E(poss) => K(pres), Collective events support the Knowledge regime.
Deductive Phase:
* Given Case: E(pres) => E(poss), Current events fairly sample Collective events.
* Given Rule: E(poss) => K(pres), Collective events support the Knowledge regime.
----------------------------------------------------------------------------------------------------------------------------
:* Deduce Fact: E(pres) => K(pres), Current events support the Knowledge regime.
TestingIf the observer looks up and does not see dark clouds, or if he runs for shelter but it does not rain, then there is fresh occasion to question the utility or the validity of his knowledge base. But we must leave our foulweather friend for now and defer the logical analysis of this testing phase to another occasion.Citations
Bibliography
- 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.
- Awbrey, Jon, and Awbrey, Susan (1995), "Interpretation as Action : The Risk of Inquiry", Inquiry : Critical Thinking Across the Disciplines 15, 40–52. Eprint.
- 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.
- 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.
- Haack, Susan (1993), Evidence and Inquiry: Towards Reconstruction in Epistemology, Blackwell Publishers, Oxford, UK.
- Hanson, Norwood Russell (1958), Patterns of Discovery, An Inquiry into the Conceptual Foundations of Science, Cambridge University Press, Cambridge, UK.
- 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
- Misak, Cheryl J. (1991), Truth and the End of Inquiry, A Peircean Account of Truth, Oxford University Press, Oxford, UK.
- Peirce, C.S., (1931–1935, 1958), Collected Papers of Charles Sanders Peirce, vols. 1–6, Charles Hartshorne and Paul Weiss (eds.), vols. 7–8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA. Cited as CP volume.paragraph.
See also{{Wiktionary}}
{{philosophy of science}}EnquêteEnquêteתחקיר ארגוניInchiestaEnquête探究DochodzenieEnkät
- content above as imported from The Pseudopedia
- "inquiry" does not exist on GetWiki
- time: 7:31pm EDT - Fri, Mar 19 2010
|
|
|
|
