Abstract
In this article I will take advantage of the logical and cognitive studies I have illustrated in my recent book The Abductive Structure of Scientific Creativity. An Essay on the Ecology of Cognition (2017), in which the process of building new hypotheses is clarified thanks to my eco-cognitive model (EC-Model) of abduction. Also resorting to a new interpretation of Aristotle’s seminal work on abduction, I will emphasize the crucial role played in abductive cognition by the so-called “optimization of eco-cognitive openness and situatedness”. Indeed, in the chapter B25 of Prior Analytics concerning 
(“leading away”), we can see some of the current well-known distinctive characters of abductive cognition already expressed, which are in tune with the EC-Model: Aristotle is still pointing to the fundamental inferential role in reasoning of those externalities that substantiate the process of “leading away” (
). Hence, we can gain a new positive perspective about the “constitutive” eco-cognitive character of abduction, just thanks to Aristotle himself. Situatedness is related to eco-cognitive aspects: to favor the solution of the abductive problem input and output of the formula
have to be thought as optimally positioned: indeed I also contend than a disregarded issue concerning abduction is related to the current lack of knowledge about what I call “discoverability” and “diagnosticability”. In the formula above \(\Vdash _L^X\) indicates that inputs and outputs do not stand each other in an expected relation and that the modification of the inputs \(?_I\) can provide the abductive solution. In general, in this characterization the direction is not from evidence/premises to abductive result but the forward fashion is adopted, where the inferential parameter \(\Vdash \) sets some appropriate logical relationship between an input which consists in both the abductive guess to be found and a background theory (or just some premisses), and an output—for example an evidence, a novel phenomenon to be abductively “explained” through facts, rules, or even new theories. Further, in the case of scientific settings, this optimality is made possible by a maximization of changeability of both input and output: not only inputs have to be enriched with the possible solution but, to do that, other inputs have usually to be changed and/or modified. This changeability first of all refers to a wide epistemological openness.
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Notes
- 1.
- 2.
These kinds of abduction can be called “knowledge enhancing”: Peirce implicity provides various justifications of the knowledge enhancing role of abduction, that is when abduction is not considered an inference to the best explanation in the classical sense of the expression, that is an inference necessarily characterized by an empirical evaluation phase, or inductive phase. In chapter three of [29] I have provided the example of conventions: abducing conventions favors and increases knowledge even if these hypotheses remain evidentially inert—at least in the sense that it is not possible to empirically falsify them. Consequently abduced conventions are evidentially inert but knowledge enhancing at the rational level of science.
- 3.
For example, selective abduction is active in diagnostic reasoning, where it is merely seen as an activity of “selecting” from an encyclopedia of pre-stored hypotheses; creative abduction instead refers to the building of new hypotheses. I have proposed the dichotomic distinction between selective and creative abduction in [22]. A recent and clear analysis of this dichotomy and of other classifications emphasizing different aspects of abduction I have described is given in [37].
- 4.
In this article for every English word or expression that refers to Plato and Aristotle’s texts from Meno, Phaedo, and Prior Analytics I have indicated the original Greek in parentheses. Since the translations are not uniformly satisfactory, it is best to include the original Greek.
- 5.
Apellicon was the ancient editor of Aristotle’s works. Amazingly, Peirce considers him, in other passages from his writings, “stupid” but also “blundering” and “scamp” ([20], p. 248).
- 6.
- 7.
Recently Woods has changed a bit his position: there are also the consequence-spotting arguments, for example the refutation-arguments of Sophistical Refutations, the refuted party cannot add to his beliefs the conclusion of the refutation since it contradicts the thesis he’s been defending. Consequence-having occurs in logical space, consequence-spotting occurs in psychological space, and consequence-drawing occurs in the inferential subspace of psychological space ([54], p. 14). Woods also contends that the syllogistic is the logic of consequence-having only for syllogisms-as-such; for syllogisms-in-use, consequence-having remains a background condition, but the specific targets of the arguments are not themselves satisfaction of the consequence-having relation.
- 8.
It is interesting to address the reader to a recent research in the field of logic, which approaches abduction without disregarding its pragmatic/dialectical dimension, thanks to the adoption of a dialogical logic. This current logical illustration of the dialectic involved in abduction is able to model argumentative interactions leading to conjectures. In this case the authors can conclude: “Thus, the consequence-having is dialectified and the having-drawing distinction is somewhat broken” [3].
- 9.
Aristotle insists that all syllogisms are valid (by definition) [52], there is no such thing as an invalid syllogism. We know the syllogistic tradition began to relax this requirement quite early on.
- 10.
We have to anticipate (see below Sect. 1.3.2) that, having given the geometrical description of the argument “from hypothesis” Plato/Socrates, in the Meno, had already clearly considered the statement “Is virtue teachable?” a genuine hypothesis: “In the same way with regard to our question about virtue, since we do not know either what it is or what kind of thing it may be, we had best make use of a hypothesis in considering whether it can be taught or not” ([44], 87b).
- 11.
Let me reiterate that Aristotle insists that all syllogisms are valid; there is no such thing as an invalid syllogism. The syllogistic tradition began to relax this requirement: here I will use the term syllogism in this modern not strictly Aristotelian sense.
- 12.
I agree with Pietarinen recent limpid analysis that attributes to Peirce the seminal refinement of the ancient concept of abduction in terms of the precise moods and modalities involved in conjecture-making [42]: “The mood of abductive conclusions is not only interrogative or imperative but rather a complex mixture of them and closer to what linguistics call co-hortative or jussive moods; those that capture both the important idea of ‘pursuit-worthiness’ of abduced conclusions as well as the ‘rational hopes’ of our guesses to turn out in the way our minds or machines predict. Investigands are invitations to proceed investigating conjectures further. But those investigations have to start off at the level of pre-beliefs. It is in the nature of the logic of abduction that some reasons are found why its conclusions are worthy of further investment. Abductive conclusions cannot be neutral indicative or epistemic statements; they carry normative and pragmatic force. [...] we see Peirce taking abductive conclusions drawn in an interrogative mood, considered as a formalization of the Socratic questioning method”. I think these considerations and this conclusion about Socratic method further support my referral to the important role of Plato’s dialectics in the background of Aristotle’s considerations about abduction as “leading away”, I am presenting in this article.
- 13.
- 14.
Cf. for example [18].
- 15.
Porism is usually translated as lemma or corollary. I am referring here to another meaning that goes deeper into the philosophy of ancient Greek mathematics. In this case porisms are active in solving problems in which it is necessary to adopt new suitable constructions. The most famous collection of porisms of ancient times was the book The Porisms of Euclid. This work is lost: the trace survived thanks to the Collection of Pappus. Playfair noted that, thanks to porisms, the analysis of all possible particular cases of a proposition would establish that: (1) under some conditions a problem becomes impossible; (2) under some other conditions, indeterminate or related to an infinite number of solutions the problem can be solved. Classical works on porisms are [45, 48]. The concept is controversial and still subjected to studies and interpretations provided by researchers in ancient philosophy: a rich reference to the literature available is given in ([19], pp. 39–40).
- 16.
I have provided an analysis of heuristics in the light of abductive cognition in [25]. Heuristics, in so far they can be algorithmically rendered, are still rules-based, even if these rules are weaker from the normative point of view, when compared with the logical rules, and typically closer to what actual human reasoners do.
- 17.
In ([24], chapters two and three), I have illustrated how abductive cognition is also characteristically related to various examples of diagrammatic reasoning (based on porisms, we can say), for example in the case of the discovery of the first non-Euclidean geometries.
- 18.
Karasmanis usefully notes that the term “good” is not given in the analogous Aristotelian example I have illustrated in the previous subsection. Aristotle only says that an intermediate term is introduced ([19], p. 37).
- 19.
This proposition corresponds to that arche (
) which was so called, in the case of the geometrical analysis, by Hippocrates of Chios [cf. ([23], chapter four)].
- 20.
In sum, to render more acceptable and justifiable that virtue is teachable it has been necessary to analyze its nature: “what is virtue”; it has been necessary the method of hypothesis to examine the features of an obscure subject.
- 21.
Cherniss ([7], p. 140).
- 22.
The following is another translation that adopts the term principle instead of hypothesis (for
), but that expresses the same argument: “And when you had to give an explanation of the principle, you would give it in the same way by assuming some other principle which seemed to you the best of the higher ones, and so on until you reached one which was adequate ” ([43],101d–101e). - 23.
We have already seen that this expression means “taking something in addition”; see above in Sect. 1 the English translation of chapter B25 that contains this expression.
- 24.
This first example given by Aristotle and derived from Plato is also unfavorably commented by Peirce, and I think the negative verdict does not concern its formal congruity with the idea of abduction expressed in chapter B25, but instead the philosophical content and quality: “But when we come to the examples, the ordinary interpretation reduces the latter, at least, to nonsense. The first becomes, Comprehension can be taught, Virtue is comprehension; .\(\cdot \). Virtue can be taught. In the first place, this is a petitio principii, or very near to one since there is no way of proving that virtue is comprehension, except by its being taught. In the next place, few in Aristotle’s time had used this absurd argument; it had scarcely been seriously doubted, what all experience shows, that virtue can be taught. A very few ethical writers of modern times have denied it; but it had hardly been denied then, except as a temporary shift in debate. A philosopher who, like Socrates, maintained that it was better to do wrong, knowing it, could not doubt that righteousness could be taught” ([39], 7.251).
- 25.
Cf. above, footnote 15 at p. 88.
- 26.
It is interesting to note that the term topoi (in Latin loci) migrates to Aristotle’s rhetoric and later rhetoricians’ studies, probably parasitic of its origin in geometrical analysis [11].
- 27.
A strict relationship between geometry and dialectics stills echoes in Proclus: “[...] mathematics reaches some of its results with analysis, others by synthesis, expounds some matters by division, others by definition, and some of its discoveries binds fast by demonstration, adapting these methods to its subjects and employing each of them for gaining insight into mediating ideas. Thus its analyses are under the control of dialectic, and its definitions, divisions, and demonstrations are of the same family and unfold in conformity with the way of mathematical understanding. It is reasonable, then, to say that dialectic is the capstone of the mathematical sciences” ([46], 43, p. 35).
- 28.
Manders’ definition describes the co-exact properties “as those conditions unaffected by some range of every continuous variation of the diagram” and the exact ones as “those which, for at least some continuous variation of the diagram, obtain only in isolated cases” [32]. “Diagrams of a single triangle, for instance, vary with respect to their exact properties. That is, the lengths of the sides, the size of the angles, the area enclosed, vary. Yet with respect to their co-exact properties the diagrams are all the same. Each consists of three bounded linear regions, which together define an area” ([34], p. 264).
- 29.
An interesting reconstruction is given in [10].
- 30.
See again the considerations about the classic problem of squaring the circle with the help of the lunes given at p. 86.
- 31.
This Hintikka’s article “What was Aristotle doing in his early logic, anyway? A reply to Woods and Hansen”, belongs to the published intellectual fight between Hintikka and Woods and it is an answer to Woods and Hansen’s “Hintikka on Aristotle’s Fallacies” [55].
- 32.
Woods further observes that the great achievement of Prior Analytics is metalogical. It provides an almost perfect (and easily repairable) proof of the semi-decidability of validity for arguments framed under syllogistic constraints. The proof rules for this are both syllogistic and “common”, and there is nothing remotely dialectical about the procedure in the Hintikkean sense.
- 33.
This means that abduction is not necessarily ignorance-preserving (reached hypotheses would always be “presumptive” and to be accepted they always need empirical confirmation), as contended by Gabbay and Woods (see [51]). Abduction can creatively build new knowledge by itself (that as an inference not necessarily characterized by an empirical evaluation phase, or inductive phase), as various examples coming from the area of history of science and other fields of human cognition clearly show. I better supported my claim about the knowledge enhancing character of abduction in the recent [27, 28]. On this issue see also above footnote 2. Woods has recently enriched, modified, and moderated his views of ignorance-preservation, see [53].
- 34.
Cf. the previous section of this article.
- 35.
More details concerning the role of locked and unlocked strategies are illustrated in the recent [30].
- 36.
I plan to devote part of my future research to study these aspects of abductive cognition.
- 37.
- 38.
More details are illustrated in ([28], section three).
) which was so called, in the case of the geometrical analysis, by Hippocrates of Chios [cf. ([
), but that expresses the same argument: “And when you had to give an explanation of the principle, you would give it in the same way by assuming some other principle which seemed to you the best of the higher ones, and so on until you reached one which was adequate ” ([References
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now: Naturalizing the logic of abduction. J. Appl. Logic 13, 285–315 (2015b)Acknowledgements
Parts of this article are excerpted from chapters five and six of the book The Abductive Structure of Scientific Creativity. An Essay on the Ecology of Cognition, Springer, Cham, 2017. For the instructive criticisms and precedent discussions and correspondence that helped me to develop my analysis of abductive cognition I am indebted and grateful to John Woods, Atocha Aliseda, Woosuk Park, Luís Moniz Pereira, Paul Thagard, Ping Li, Athanassios Raftopoulos, Michael Hoffmann, Ahti-Veikko Pietarinen, Gerhard Schurz, Walter Carnielli, Akinori Abe, Yukio Ohsawa, Cameron Shelley, Shahid Rahman, Cristina Barés Gómez, Matthieu Fontaine, Gerhard Minnameier, Pat Langley, Oliver Ray, John Josephson, Ferdinand D. Rivera and to my collaborators Selene Arfini and Riccardo Dossena.
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Magnani, L. (2021). Abduction as “Leading Away”. In: Shook, J.R., Paavola, S. (eds) Abduction in Cognition and Action. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-030-61773-8_4
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