Inquiry theories
Deduction
When three terms are so related to one another that the last is wholly contained in the middle and the middle is wholly contained in or excluded from the first, the extremes must admit of perfect syllogism. By 'middle term' I mean that which both is contained in another and contains another in itself, and which is the middle by its position also; and by 'extremes' (a) that which is contained in another, and (b) that in which another is contained. For if ''A'' is predicated of all ''B'', and ''B'' of all ''C'', ''A'' must necessarily be predicated of all ''C''. ... I call this kind of figure the First. (Aristotle, ''Prior Analytics'', 1.4)
Induction
Inductive reasoning consists in establishing a relation between one extreme term and the middle term by means of the other extreme; for example, if ''B'' is the middle term of ''A'' and ''C'', in proving by means of ''C'' that ''A'' applies to ''B''; for this is how we effect inductions. (Aristotle, ''Prior Analytics'', 2.23)
Abduction
The ''locus classicus'' for the study of abductive reasoning is found inWe have Reduction (απαγωγη,By way of explanation,abduction Abduction may refer to: Media Film and television * "Abduction" (''The Outer Limits''), a 2001 television episode * " Abduction" (''Death Note'') a Japanese animation television series * " Abductions" (''Totally Spies!''), a 2002 episode of an ...): :# When it is obvious that the first term applies to the middle, but that the middle applies to the last term is not obvious, yet is nevertheless more probable or not less probable than the conclusion; :# Or if there are not many intermediate terms between the last and the middle; For in all such cases the effect is to bring us nearer to knowledge.
:# For example, let ''A'' stand for "that which can be taught", ''B'' for "knowledge", and ''C'' for "morality". Then that knowledge can be taught is evident; but whether virtue is knowledge is not clear. Then if ''BC'' is not less probable or is more probable than ''AC'', we have reduction; for we are nearer to knowledge for having introduced an additional term, whereas before we had no knowledge that ''AC'' is true. :# Or again we have reduction if there are not many intermediate terms between ''B'' and ''C''; for in this case too we are brought nearer to knowledge. For example, suppose that ''D'' is "to square", ''E'' "rectilinear figure", and ''F'' "circle". Assuming that between ''E'' and ''F'' there is only one intermediate term — that the circle becomes equal to a rectilinear figure by means of lunules — we should approximate to knowledge. (Aristotle's latter variety of abductive reasoning, though it will take some explaining in the sequel, is well worth our contemplation, since it hints already at streams of inquiry that course well beyond the syllogistic source from which they spring, and into regions that Peirce will explore more broadly and deeply.Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ..., " Prior Analytics", 2.25, with minor alterations)
Inquiry in the pragmatic paradigm
In the pragmatic philosophies ofArt and science of inquiry
For our present purposes, the first feature to note in distinguishing the three principal modes of reasoning from each other is whether each of them is exact or approximate in character. In this light, deduction is the only one of the three types of reasoning that can be made exact, in essence, always deriving true conclusions from true premises, while abduction and induction are unavoidably approximate in their modes of operation, involving elements of fallible judgment in practice and inescapable error in their application. The reason for this is that deduction, in the ideal limit, can be rendered a purely internal process of the reasoning agent, while the other two modes of reasoning essentially demand a constant interaction with the outside world, a source of phenomena and problems that will no doubt continue to exceed the capacities of any finite resource, human or machine, to master. Situated in this larger reality, approximations can be judged appropriate only in relation to their context of use and can be judged fitting only with regard to a purpose in view. A parallel distinction that is often made in this connection is to call deduction a ''demonstrative'' form of inference, while abduction and induction are classed as '' non-demonstrative'' forms of reasoning. Strictly speaking, the latter two modes of reasoning are not properly called inferences at all. They are more like controlled associations of words or ideas that just happen to be successful often enough to be preserved as useful heuristic strategies in the repertoire of the agent. But non-demonstrative ways of thinking are inherently subject to error, and must be constantly checked out and corrected as needed in practice. In classical terminology, forms of judgment that require attention to the context and the purpose of the judgment are said to involve an element of "art", in a sense that is judged to distinguish them from "science", and in their renderings as expressive judgments to implicate arbiters in styles ofZeroth order inquiry
Many aspects of inquiry can be recognized and usefully studied in very basic logical settings, even simpler than the level ofExample 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.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'', 1910, pp. 6-7).
Once over quickly
Let's first give Dewey's 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 phase
In 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 phase
The 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 phase
Whatever 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 closely
Seeding hypotheses
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.o-----------------------------------------------------------o , , , A D , , o o , , \ * * / , , \ * * / , , \ * * / , , \ * * / , , \ * * / , , \ R u l e R u l e / , , \ * * / , , \ * * / , , \ * * / , , \ * B * / , , F a c t o F a c t , , \ * / , , \ * / , , \ * / , , \ * / , , \ C a s e / , , \ * / , , \ * / , , \ * / , , \ * / , , \ * / , , \*/ , , o , , C , , , , A = the Air is cool , , B = just Before it rains , , C = the Current situation , , D = a Dark cloud appears , , , , A is a major term , , B is a middle term , , C is a minor term , , D is a major term, associated with A , , , o-----------------------------------------------------------o Figure 4. Dewey's 'Rainy Day' InquiryIn 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. This is nowhere near a complete analysis of the Rainy Day inquiry, even insofar as it might be carried out within the constraints of the syllogistic framework, and it covers only the first two steps of the relevant inquiry process, but maybe it will do for a start. One other thing needs to be noticed here, the formal duality between this expansion phase of inquiry and the argument from analogy. This can be seen most clearly in the propositional lattice diagrams shown in Figures 3 and 4, where analogy exhibits a rough "A" shape and the first two steps of inquiry exhibit a rough "V" shape, respectively. Since we find ourselves repeatedly referring to this expansion phase of inquiry as a unit, let's give it a name that suggests its duality with analogy—" catalogy" will do for the moment. This usage is apt enough if one thinks of a catalogue entry for an item as a text that lists its salient features. Notice that analogy has to do with the examples of a given quality, while catalogy has to do with the qualities of a given example. Peirce noted similar forms of duality in many of his early writings, leading to the consummate treatment in his 1867 pape
Weeding hypotheses
In 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 experience
Throughout 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.=Learning
= Rules 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.=Transfer
= What 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 , , , K(pres) , , o , , /, \ , , / , \ , , / , \ , , / , \ , , / Rule \ , , / , \ , , / , \ , , / , \ , , / E(poss) \ , , Fact / o \ Fact , , / * * \ , , / * * \ , , / * * \ , , / * * \ , , / * * \ , , / * Case Case * \ , , / * * \ , , / * * \ , , /* *\ , , o<<<---------------<<<---------------<<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.
=Testing
= If 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.
See also
*Charles Sanders Peirce bibliography This Charles Sanders Peirce bibliography consolidates numerous references to the writings of Charles Sanders Peirce, including letters, manuscripts, publications, and . For an extensive chronological list of Peirce's works (titled in English), se ...* Community of inquiry * C. West Churchman *Curiosity Curiosity (from Latin '' cūriōsitās'', from ''cūriōsus'' "careful, diligent, curious", akin to ''cura'' "care") is a quality related to inquisitive thinking such as exploration, investigation, and learning, evident by observation in human ...* Empirical limits in science * Information entropy *Information theory Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...* Inquisitive learning *Instrumental and intrinsic value In moral philosophy, instrumental and intrinsic value are the distinction between what is a ''means to an end'' and what is as an ''end in itself''. Things are deemed to have instrumental value if they help one achieve a particular end; intrinsic ...* Logic of information *Models of scientific inquiry Models of scientific inquiry have two functions: first, to provide a descriptive account of ''how'' scientific inquiry is carried out in practice, and second, to provide an explanatory account of ''why'' scientific inquiry succeeds as well as it ap ...* Pragmatic information * Pragmatic theory of truth * Pragmaticism *Research Research is "creative and systematic work undertaken to increase the stock of knowledge". It involves the collection, organization and analysis of evidence to increase understanding of a topic, characterized by a particular attentiveness ...* Research question *Uncertainty Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable ...
Notes
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. *Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ..., " Prior Analytics",Hugh Tredennick Hugh may refer to: * Hugh (given name) Noblemen and clergy French * Hugh the Great (died 956), Duke of the Franks * Hugh Magnus of France (1007–1025), co-King of France under his father, Robert II * Hugh, Duke of Alsace (died 895), modern-da ...(trans.), pp. 181–531 in ''Aristotle, Volume 1'', Loeb Classical Library, 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.
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. * Maxwell, Nicholas (2007
From Knowledge to Wisdom
Pentire Press, London. * Maxwell, Nicholas (2017)
In Praise of Natural Philosophy: A Revolution for Thought and Life
McGill-Queen's University Press, Montreal. * 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. * Stalnaker, Robert C. (1984), ''Inquiry'', MIT Press, Cambridge, MA.
External links
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