Abstract
In spite of his unusually broad knowledge of the history of science, Peirce did not pay attention to the most significant key idea in the history of heuristic reasoning and problem-solving, viz. the method of analysis and synthesis in Greek geometry. As described by Pappus (c. 300 AD), analysis is inverse inference from a theorem to axioms, or from a problem to its solutions, and synthesis then gives the desired direct proof or construction (Sect. 2.2). This inference resembles the regressive method of Renaissance Aristotelians, consisting of a “resolution” from facts to their causes and a “composition” from causes to effects. These methods influenced also such great figures of modern science as Galileo Galilei, Isaac Newton, and Karl Marx (Sect. 2.1). It is argued in this chapter that Peirce’s description of hypothesis, as a retroductive inference of a cause from its effect, is an instance of what Jaakko Hintikka calls the upward propositional interpretation of theoretical analysis. Further, the backward solution of a crime case by a detective is an instance of problematic analysis. This thesis is vindicated by Edgar Allan Poe’s stories of ratiocination written in the 1840s (Sect. 2.4). Another illustration of the same idea is given in Poe’s essay “Philosophy of Composition” where he describes the analytical construction of his poem The Raven (1845) (Sect. 2.5).
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Notes
- 1.
This chapter is largely (except Sect. 2.3) based on a paper presented in the conference on Model-Based Reasoning in Scientific Discovery, Pavia, December 17–19, 1998 (see Niiniluoto 1999c). The prehistory of this paper goes back to the year 1975 when I acted as one of the opponents of Unto Remes’s (1942–1975) doctoral dissertation on the geometrical method of analysis and synthesis (see Hintikka and Remes 1974) . During the disputation, I suggested that Edgar Allan Poe’s detective stories follow the method of analysis which has also a close resemblance to Peirce’s account of abductive inference. Two years later I found by accident a short article, published by my father Yrjö Niiniluoto (1900–1961) as a young man in 1925, which referred to Poe’s fascinating essay on the “philosophy of composition ”. My paper was published in Finnish in 1978, and later with some revisions in 1990. In the meantime, Thomas A. Sebeok had published in 1980 his article on Peirce and Sherlock Holmes, followed by a collection of essays on abduction and detective stories (see Eco and Sebeok 1983) . Therefore, I did not hurry to write an English version of my paper, but waited for a suitable occasion for its presentation until 1998.
- 2.
As far as I know, Peirce never treated the regressive method , but in 1898 he remarked that Aristotle “was driven to his strange distinction between what is better known to Nature and what is better known to us” (EP 2:43).
- 3.
The distinction between Aristotle’s substantial invariances and Galileo’s dynamical invariances was made by Eino Kaila in 1939 (see Kaila 2014).
- 4.
Hilpinen (2007) argues that practical reasoning , following Aristotelean practical syllogisms, is a form of abduction in Peirce’s sense.
- 5.
See Pappus (1986), 82.
- 6.
See the essay by A. Szabó in Hintikka and Remes (1974) , 118–130.
- 7.
It is ironic that the custos (chairman) of the doctoral disputation of Unto Remes (see note 1) was Oiva Ketonen , who in his 1944 doctoral thesis had improved Gentzen’s sequent calculus into a system with invertible rules: if the conclusion of a rule follows from the premises, the premises are derivable from the conclusion. This system was generalized from propositional logic to predicate logic by S. C. Kleene in 1952. In an invertible system the distinction between downward and upward analysis disappears. Ketonen never mentioned this conclusion in our discussions, but a sophisticated treatment of his system with applications to automated deduction is given by Sara Negri and Jan von Plato (2001).
- 8.
- 9.
Petri Mäenpää’s (1997) elegant formalization of this method uses, instead of predicate logic, Per Martin-Löf’s type theory to account for constructions and their results.
- 10.
McMullin (1992) also points out that Peirce’s abduction is not demonstrative in the same strong sense as resolution was often described in the regressive method .
- 11.
Minnameier (2017), 188, also proposes a model of “inverse abduction” which seeks concrete instances of abstract theories or concepts.
- 12.
For some remarks about “manipulative abduction ” as a form of practical reasoning , see Sect. 5.3.
- 13.
Rubén Sampieri Cábal has suggested that Poe’s ”prose poem” Eureka (in 1848) anticipates the ideas of Peirce’s abduction .
- 14.
- 15.
This example is discussed in Hintikka and Bachman (1991) . Hintikka relates the “logic of Sherlock Holmes” to his interrogative model of inquiry , when all inferential steps are deductive while abduction has a role in information-seeking through questioning (see Hintikka and Hintikka 1983; Hintikka 1998) . This model of inquiry is discussed in Sect. 3.5.
- 16.
Similar analytic or abductive methods of reasoning (like fingerprints and DNA sequences) are used in contemporary forensic science, familiar from the tv-series C.S.I.
- 17.
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Niiniluoto, I. (2018). Analysis and Synthesis. In: Truth-Seeking by Abduction. Synthese Library, vol 400. Springer, Cham. https://doi.org/10.1007/978-3-319-99157-3_2
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