Abstract
The analysis of abductive processes illustrated in the previous chapters, in terms of the effort to naturalize the logic of its special consequence relation, leads us to the emphasis on the importance of the following main aspects: “optimization of eco-cognitive situatedness”, “maximization of changeability” of both input and output of the general form of an inferential abductive problem, and high “information-sensitiveness”.
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Notes
- 1.
Cf. Sect. 3.3, Chap. 3, this book.
- 2.
I have illustrated non-explanatory and instrumental abduction in (Magnani 2009, Chap. 2), also providing some case studies.
- 3.
On the fact that considering logical reasoning a discursive process is an “optical illusion” cf. Sect. 7.2.3.1: for example Hintikka maintains that deduction is a form of “experimental model construction”.
- 4.
Cf. Sect. 1.3, Chap. 1, this book.
- 5.
An evolved mind is unlikely to have a natural home for complicated concepts like the ones logic introduced, as such concepts do not exist in a definite way in the natural (not artificially manipulated) world: so whereas evolved minds could construct reasoning frameworks and perform some simple reasoning inferences in a more or less tacit way by exploiting modules shaped by natural selection, how could one think exploiting explicit complicated logical concepts without having picked them up outside, after having produced them?
- 6.
We have to remember that one limitation of ALP (Abductive Logic Programming) is that it requires a set of “abducibles” in advance, and these are limited to facts (literals). From this perspective, this framework is not better than any other inferential-based one.
- 7.
CL, computational logic, refers to the computational approach to logic that has proved to be fruitful for creating non-trivial applications in computing, artificial intelligence (AI), and law.
- 8.
In (Magnani 2009, Chap. 1, Sect. 4) I have provided an illustration of the tradition of logic programming related to the exploitation of the belief revision framework: I described the application to selective abduction also in the field of artificial intelligence (AI) and the role of coherence and foundations approach, reason and truth maintenance systems, model-based diagnosis, etc. Abductive belief revision in science is illustrated in the recent (Schurz 2011).
- 9.
As previously indicated, it is important to distinguish between selective abduction (that merely selects from an encyclopedia of pre-stored hypotheses), and creative abduction (abduction that generates new hypotheses).
- 10.
Cf. also (Fischer 2001).
- 11.
- 12.
From this mathematical perspective artifacts, in so far as they are expressed through icons, visual and other non-linguistic configurations, are “memory stores” in themselves (Leyton 2006).
- 13.
A recent survey about the importance of models in abductive cognition is illustrated in (Figueroa 2012).
- 14.
Clarifications of exact processes and semantic requirements of manipulative inferences and distributed cognition are given in (Shimojima 2002).
- 15.
Often made possible thanks to conceptual creative abductions.
- 16.
Woods provides other examples of institutional agents, such as Nato, M15 or an university. In this perspective individual organic agents possess “fewer” cognitive assets than institutional agents (Woods 2013, Chap. 8).
- 17.
- 18.
A recent book by Caterina and Gangle (2016), addresses the problems involved in formalizing abductive cognition by implementing the concept and method of iconicity, modeling this theoretical framework mathematically through category theory and topoi. Peirce’s concept of iconic signs is treated in depth, and it is shown how Peirce’s diagrammatic logical notation of existential graphs makes use of iconicity and how important features of this iconicity are representable within category theory.
- 19.
It is worth to be noted that semantic tableaux method provides further insight on the problem of theory evaluation, intrinsic in abductive reasoning. Semantic tableaux can deal with “causal” aspects of abductive reasoning that cannot easily be considered with the only help of the logic programming tradition—cf. Aliseda (2006, Chaps. 6 and 7).
- 20.
In this perspective, the employment of logical rules in deduction calls for a strategic reasoning: this kind of reasoning is not co-extensive with heuristic reasoning in general, which seems more psychological, but this fact does not attenuate the “logical” nature of these strategies in deductive proofs. Moreover, even if heuristic reasoning seems, at a first sight, more psychological than logical, we do not have to forget that heuristic templates of reasoning can be rendered explicit and objectified in a kind of classificatory system (see for example the well-known works by Gigerenzer and his colleagues (Gigerenzer and Selten 2002; Gigerenzer and Brighton 2009; Gigerenzer et al. 2016)).
- 21.
A rich analysis of the role of individual diagrams in deduction and in problem solving processes (that is in abductive cognition) is given by Shin (2012). The interesting interplay between contentual axiomatics (dealing with the locality of diagrams) and formal axiomatics in Hilbert’s research is deeply analyzed by Smadya (2012). Indeed, Hilbert held that diagrams are to be thought of as “drawn formulas”, and formulas as “written diagrams”, suggesting that the former encapsulate propositional information which can be extracted and translated into formulas.
- 22.
Cf. above, Chap.1, Sect. 1.3, this book.
- 23.
Cf. also Sect. 7.1.4.
- 24.
Also the notion “of proof-nets” (a geometry of proofs), such as graphical representations of proof in Girard’s linear logic (Girard 1987) can be related to this perspective resorting both to Hilbert and Gentzen . (Grialou and Okada 2005) also provide neurological evidence of the involvement of both language and visual/diagrammatic processing systems in logical reasoning. On the role of errors, due to the context, in spontaneously performed logical reasoning in humans and on their rudimentary deductive competence see the classical (Evans 2002).
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Magnani, L. (2017). Science Maximizes Abducibility. In: The Abductive Structure of Scientific Creativity. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-319-59256-5_7
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