Understanding Abduction

Abstract

The status of abduction is still controversial. When dealing with abductive reasoning misinterpretations and equivocations are common. What did Peirce mean when he considered abduction both a kind of inference and a kind of instinct or when he considered perception a kind of abduction? Does abduction involve only the generation of hypotheses or their evaluation too? Are the criteria for the best explanation in abductive reasoning epistemic, or pragmatic, or both? Does abduction preserve ignorance or extend truth or both? To study some of these conundrums and to better understand the concept of abduction, which Hintikka [20] classified the “fundamental problem of contemporary epistemology”, I think that an interdisciplinary effort is needed, at the same time fecundated by a wide philosophical analysis. To this aim I will take advantage of some reflections upon Peirce’s philosophy of abduction that I consider central to highlight the complexity of the concept, too often seen in the partial perspective of limited (even if tremendously epistemologically useful) formal and computational models. I will ponder over some seminal Peircean philosophical considerations concerning the entanglement of abduction, perception, inference, and instinct, which I consider are still important to current cognitive research. Peircean analysis helps us to better grasp how model-based, sentential and manipulative aspects of abduction—I have introduced in my book Abductive Cognition [38]—have to be seen as intertwined, and indispensable for building an acceptable integrated model of abduction. Even if speculative, Peircean philosophical results on abduction certainly anticipate various tenets of recent cognitive research, as I will remark.

Unless man has a natural bent in accordance with nature’s, he has no chance of understanding nature at all.

Charles Sanders Peirce, A Neglected Argument for the Reality of God, 1908.

Appendix: GW and AKM Schemas of Abduction

I have already said that the GW-model³⁵ does a good job in modeling the ignorance-preserving character of abduction and—I am convinced—in designing the correct intellectual framework we should adopt especially when dealing with the problem of abduction as an inference to the best hypothesis/explanation. Following Gabbay and Woods’ contention, it is clear that “[...] abduction is a procedure in which something that lacks epistemic virtue is accepted because it has virtue of another kind” [17, p. 62].

For example: “Let $S$ be the standard that you are not able to meet (e.g., that of mathematical proof). It is possible that there is a lesser epistemic standard $S^{\prime }$ (e.g., having reason to believe) that you do meet” [77, Chap. 10]. Focusing attention on this cognitive aspect of abduction, and adopting a logical framework centered on practical agents, Gabbay and Woods [17] contend that abduction (basically seen as a scant-resource strategy, which proceeds in absence of knowledge) presents an ignorance-preserving (or, better, an ignorance mitigating) character. Of course “[...] it is not at all necessary, or frequent, that the abducer be wholly in the dark, that his ignorance be total. It needs not be the case, and typically isn’t, that the abducer’s choice of a hypothesis is a blind guess, or that nothing positive can be said of it beyond the role it plays in the subjunctive attainment of the abducer’s original target (although sometimes this is precisely so)” (cit.). In this perspective, abductive reasoning is a response to an ignorance-problem: one has an ignorance-problem when one has a cognitive target that cannot be attained on the basis of what one currently knows. Ignorance problems trigger one or other of three responses. In the first case, one overcomes one’s ignorance by attaining some additional knowledge (subduance). In the second instance, one yields to one’s ignorance (at least for the time being) (surrender). In the third instance, one abduces [77, Chap. 10] and so has some positive basis for new action even if in the presence of the constitutive ignorance.

From this perspective the general form of an abductive inference can be symbolically rendered as follows. Let $\alpha$ be a proposition with respect to which you have an ignorance problem. Putting $T$ for the agent’s epistemic target with respect to the proposition $\alpha$ at any given time, $K$ for his knowledge-base at that time, $K^*$ for an immediate accessible successor-base of $K$ that lies within the agent’s means to produce in a timely way,³⁶ $R$ as the attainment relation for $T$, $\rightsquigarrow$ as the subjunctive conditional relation, $H$ as the agent’s hypothesis, $K(H)$ as the revision of $K$ upon the addition of $H$, $C(H)$ denotes the conjecture of $H$ and $H^c$ its activation. The general structure of abduction can be illustrated as follows (GW-schema):

1. $T!\alpha$	[setting of $T$ as an epistemic target with respect to a proposition $\alpha$]
2. $\lnot (R(K,T)$	[fact]
3. $\lnot (R(K^*,T)$	[fact]
4. $H \not \in K$	[fact]
5. $H \not \in K^*$	[fact]
6. $\lnot R(H,T)$	[fact]
7. $\lnot R(K(H),T)$	[fact]
8. If $H$ $\rightsquigarrow$ $R(K(H),T$)	[fact]
9. $H$ meets further conditions $S_1, ....S_n$	[fact]
10. Therefore, $C(H)$	[sub-conclusion, 1–9]
11. Therefore, $H^c$	[conclusion, 1–10]

It is easy to see that the distinctive epistemic feature of abduction is captured by the schema. It is a given that $H$ is not in the agent’s knowledge-set. Nor is it in its immediate successor. Since $H$ is not in $K$, then the revision of $K$ by $H$ is not a knowledge-successor set to $K$. Even so, $H \rightsquigarrow (K(H),T$). So we have an ignorance-preservation, as required (cf. [77, Chap. 10]).

[Note: Basically, line 9. indicates that $H$ has no more plausible or relevant rival constituting a greater degree of subjunctive attainment. Characterizing the $S_i$ is the most difficult problem for abductive cognition, given the fact that in general there are many possible candidate hypotheses. It involves for instance the consistency and minimality constraints.³⁷ These constraints correspond to the lines 4 and 5 of the standard AKM schema of abduction,³⁸ which is illustrated as follows:

1. $E$

2. $K \not \looparrowright E$

3. $H \not \looparrowright E$

4. $K(H)$ is consistent

5. $K(H)$ is minimal

6. $K(H) \looparrowright E$

7. Therefore, $H.$

[17, pp. 48–49].

where of course the conclusion operator $\looparrowright$ cannot be classically interpreted].³⁹

Finally, in the GW-schema $C(H)$ is read “It is justified (or reasonable) to conjecture that $H$” and $H^c$ is its activation, as the basis for planned “actions”.

In sum, in the GW-schema $T$ cannot be attained on the basis of $K$. Neither can it be attained on the basis of any successor $K^*$ of $K$ that the agent knows then and there how to construct. $H$ is not in $K$: $H$ is a hypothesis that when reconciled to $K$ produces an updated $K(H)$. $H$ is such that if it were true, then $K(H)$ would attain $T$. The problem is that $H$ is only hypothesized, so that the truth is not assured. Accordingly Gabbay and Woods contend that $K(H)$ presumptively attains $T$. That is, having hypothesized that $H$, the agent just “presumes” that his target is now attained. Given the fact that presumptive attainment is not attainment, the agent’s abduction must be considered as preserving the ignorance that already gave rise to her (or its, in the case for example of a machine) initial ignorance-problem. Accordingly, abduction does not have to be considered the “solution” of an ignorance problem, but rather a response to it, in which the agent reaches presumptive attainment rather than actual attainment. $C(H)$ expresses the conclusion that it follows from the facts of the schema that $H$ is a worthy object of conjecture. It is important to note that in order to solve a problem it is not necessary that an agent actually conjectures a hypothesis, but it is necessary that she states that the hypothesis is worthy of conjecture.

Finally, considering $H$ justified to conjecture is not equivalent to considering it justified to accept/activate it and eventually to send $H$ to experimental trial. $H^c$ denotes the decision to release $H$ for further premissory work in the domain of enquiry in which the original ignorance-problem arose, that is the activation of $H$ as a positive cognitive basis for action. Woods usefully observes:

There are lots of cases in which abduction stops at line 10, that is, with the conjecture of the hypothesis in question but not its activation. When this happens, the reasoning that generates the conjecture does not constitute a positive basis for new action, that is, for acting on that hypothesis. Call these abductions partial as opposed to full. Peirce has drawn our attention to an important subclass of partial abductions. These are cases in which the conjecture of $H$ is followed by a decision to submit it to experimental test. Now, to be sure, doing this is an action. It is an action involving $H$ but it is not a case of acting on it. In a full abduction, $H$ is activated by being released for inferential work in the domain of enquiry within which the ignorance-problem arose in the first place. In the Peircean cases, what counts is that $H$ is withheld from such work. Of course, if $H$ goes on to test favourably, it may then be released for subsequent inferential engagement [75].

We have to remember that this process of evaluation and so of activation of the hypothesis, is not abductive, but inductive, as Peirce contended. Woods adds: “Now it is quite true that epistemologists of a certain risk-averse bent might be drawn to the admonition that partial abduction is as good as abduction ever gets and that complete abduction, inference-activation and all, is a mistake that leaves any action prompted by it without an adequate rational grounding. This is not an unserious objection, but I have no time to give it its due here. Suffice it to say that there are real-life contexts of reasoning in which such conservatism is given short shrift, in fact is ignored altogether. One of these contexts is the criminal trial at common law” [75].

In the framework of the GW-schema it cannot be said that testability is intrinsic to abduction, such as it is instead maintained in the case of some passages of Peirce’s writings.⁴⁰ This activity of testing, I repeat, which in turn involves degrees of risk proportioned to the strength of the conjecture, is strictly cognitive/epistemic and inductive in itself, for example an experimental test, and it is an intermediate step to release the abduced hypothesis for inferential work in the domain of enquiry within which the ignorance-problem arose in the first place.

Through abduction the basic ignorance—that does not have to be considered total “ignorance”—is neither solved nor left intact: it is an ignorance-preserving accommodation of the problem at hand, which “mitigates” the initial cognitive “irritation” (Peirce says “the irritation of doubt”).⁴¹ As I have already stressed, in a defeasible way, further action can be triggered either to find further abductions or to “solve” the ignorance problem, possibly leading to what the “received view” has called the inference to the best explanation (IBE).

It is clear that in the framework of the GW-schema the inference to the best explanation— if considered as a truth conferring achievement justified by the empirical approval—cannot be a case of abduction, because abductive inference is constitutively ignorance-preserving. In this perspective the inference to the best explanation involves the generalizing and evaluating role of induction. Of course it can be said that the requests of originary thinking are related to the depth of the abducer’s ignorance.

In [41] I have extensively analyzed and criticized the ignorance-preserving character of abduction, taking advantage of my eco-cognitive model (EC-model) of abduction and of three examples taken from the areas of both philosophy and epistemology. Indeed, through abduction, knowledge can be enhanced, even 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 an inductive phase, as Peirce called it. Hence, abduction is not always ignorance-preserving, but knowledge enhancing.

Finally, let us reiterate a passage taken from Woods’ quotation above: “There are lots of cases in which abduction stops at line 10, that is, with the conjecture of the hypothesis in question but not its activation. When this happens, the reasoning that generates the conjecture does not constitute a positive basis for new action, that is, for acting on that hypothesis”. We do not have to forget that, as I have illustrated in this paper, various ways of positively enhancing knowledge are occurring also in the case of evidentially inert abductions (perception, instinct, scientific models [41], etc.), and very often a human abductive guess is activated and becomes a basis for action even if it has provided absolutely unreliable—if seen in the light of positive rational criteria of acceptation—knowledge. This is the case for example of the role of abductive guesses in the so-called fallacious and other kinds of reasoning, where the simple struggle that is occurring at the level of the so-called coalition enforcement is at stake.⁴²