Forthcoming in the Proceedings of the 6th Congress of the IASS-AIS, International Association for Semiotic Studies in Guadalajara, Mexico, July, 13-18, 1997
Michael Hoffmann
Charles S. Peirce defines his famous concept of "abduction" as follows: "Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea" (Peirce, 1903:CP 5.171). My point in this paper is the question how abduction can be grasped as a form of logical inference. In order to answer this question it is important to make clear at first what may be meant by the term "logic".
I would like to distinguish four rather different descriptions of the term "logic". Today, it seems to be common that there is only one solid definition of logic, the first in my list below, but it is important to keep in mind that there have been others. Peirce, who had studied the history of philosophy thoroughly, seems to have been influenced by all.
There are of course many problems in these rough definitions, and there are other possible differentiations and definitions, but that is not my point here. I only want to show that the term "logic" has a wide range of applications in philosophy. So the question whether there is a "logic" of abduction implies the further question: What kind of logic must be assumed as including abductive reasoning, the process of generating a hypothesis?
The merits of Peirce as a founding father of modern deductive logic are well known (Putnam, 1982, Quine, 1995, Dipert, 1995, Houser, Roberts, and Van Evra, 1997). But especially his later concept of abduction requires a broader understanding of "logic" which is not easy to reconstruct. For Peirce, abduction is essential for an understanding of scientific discoveries. He was convinced that science in all its parts is based on "logical" reasoning, and that "the science of the Laws of Development of Science ... must be an offshoot of logic and must rest on a sound general theory of logic" (Peirce, 1902:L75C,492). A concept of logic which includes the possibility of describing the "Laws of Development of Science", which includes also what Popper called a "Logic of Discovery", must be a very broad one.
The best way for understanding abductive inference might be a comparison with deduction and induction with respect to their different roles in the processes of scientific discovery:
" ... there are but three elementary kinds of reasoning. The first, which I call abduction ... consists in examining a mass of facts and in allowing these facts to suggest a theory. In this way we gain new ideas; but there is no force in the reasoning. The second kind of reasoning is deduction, or necessary reasoning. It is applicable only to an ideal state of things, or to a state of things in so far as it may conform to an ideal. It merely gives a new aspect to the premisses. ... The third way of reasoning is induction, or experimental research. Its procedure is this. Abduction having suggested a theory, we employ deduction to deduce from that ideal theory a promiscuous variety of consequences to the effect that if we perform certain acts, we shall find ourselves confronted with certain experiences. We then proceed to try these experiments, and if the predictions of the theory are verified, we have a proportionate confidence that the experiments that remain to be tried will confirm the theory. I say that these three are the only elementary modes of reasoning there are" (Peirce, 1905, c.:CP 8.209).
In describing this interplay of abduction, deduction, and induction, Peirce formulates a clear differentiation of these "three elementary kinds of reasoning". The criterion of this differentiation is not the question of "rules" but the function of these inferential forms in the scientific process. It is very important to note that with respect to its function we get a perhaps uncommon view of induction: For Peirce, induction is not the inference from particular to general in the classical sense (although sometimes he defines induction in the classical way). Peirce’s induction starts from given generals, from abductively inferred hypotheses, and from deductively inferred implications of those hypotheses. The specific difference between induction and abduction is here that abduction is part of the discovery process while induction is part of the process of testing discoveries. By induction a given general will only be confirmed or falsified by future experiments.
The validity of an argument for Peirce depends on two criteria, its security and its productiveness. The three kinds of reasoning fulfill these criteria in a different manner (cf. Peirce, 1913b:CP 8.384, 8.387f.). Abductive reasoning is not determined by a "rule of inference" in the sense of deduction or analytical reasoning. There exists, however, a specific form of abductive inference:
| (1) | The surprising fact, F, is observed; | |
|
(2) |
But if H were true, F would be a matter of course. | |
| (3) | Hence, | There is reason to suspect that H is true (CP 5.189). |
The essential question is of course: How is it possible to create or to find the hypothesis H? At first glance, Peirce’s answer to this question seems to be rather unsatisfactory. He identifies abduction with guessing, guessing being seen on the one hand as an "instinctive power" and as a process which operates "on the basis of other information ... under our control" on the other (Kapitan, 1992:8). The meaning of such formulations is rather vague. But, I think, it is possible to find a fruitful interpretation which also throws some light on what the logical character of abduction might be.
In principle, we can distinguish two ways of obtaining a hypothesis: Firstly, we could say, according to Eco’s definition of "creative abduction", that the explanatory hypothesis "has to be invented ex novo" (Eco, 1984:42f.). But it is hard to see how such a "creation" out of nothing might be possible. From nothing, nothing comes. There is, however, another possibility of obtaining a hypothesis: Instead of assuming that no hypothesis is given, we may imagine that an infinite collection of possible hypotheses exists. Both ways of obtaining hypotheses are equivalent insofar as it is irrelevant, regarding the search for a hypothesis, whether there is no given hypothesis or whether there is an infinite set of possible hypotheses.
If we formulate the problem of obtaining a hypothesis as the problem of determining one hypothesis out of an infinite set of possible ones, as I would suggest, the Peircean identification of abductive reasoning with "guessing" as an "instinctive power" can be interpreted within a reasoning which I shall now elaborate in ten steps, beginning with some general considerations concerning Peirce’s epistemology.
(1) The central feature of Peirce’s epistemology is that all cognition – from perception to logical and mathematical reasoning – is mediated by "signs" or "elements of generality".
(2) Sign-mediated cognition implies that every set of data given as the starting point of an abductive inference is never given "purely", but always determined by modes of perception, by perspectives, background theories, etc. Every cognition is embedded within a set of contexts. I use the term "context" in Gregory Bateson’s sense. Bateson gives the example of the co-evolution of horse and savanna: The evolution of the horses is determined by the savanna in which they graze as well as the evolution of the savanna is determined by the horses (Bateson, 1972:155). Thus there exists one context of mutual dependence between both. In order to define the meaning of "context" more precisely, I would say that a "context" is a relation of mutual dependence of the habits of several entities. Context is not "environment" as a set of certain things "outside", but a specific relation between habits of interacting entities. In contrast to the term context I define "situation" as a temporally and spatially determined set of entities regardless of possible relations between them. While a situation is a concrete and particular "event", a context is general in the same way as habits as forms of acting and perceiving are general.
With respect to our epistemological considerations, we may distinguish between the following contexts: contexts of natural capacities of living entities insofar as they evolve in and with respect to certain natural environments (for example our sensual perception according to the theory of :chap. 8); contexts ofpractical know-how within a certain practice;contexts of technical instruments insofar as they are developed with respect to certain properties of our world (for example the very different forms of microscopes as described by :chap. XI); socialcontexts between the habits of individuals; contexts ofbeliefswhich are developed in mutual dependence with certain experiences or other beliefs, etc. Contexts are general and play the role of rules or laws which determine the possibility of perception and reasoning.
(3) In contrast to Platonic "ideas", it is important to note: first, that contexts are not "eternal" but part of a process of evolution and, second, that these general elements are not disjoined from the "facts" or particular "states of affairs" which they determine. For Peirce, there exists a mutual determination between the general and the particular and a "co-evolution" of both.
(4) If according to point (2) every cognition is mediated by some general elements, then the same must be assumed for so-called "surprising facts", at least in so far as they are perceivable. Their surprising character exists only with respect to certain expectations under certain circumstances (cf. :CP 2.776; :CP 6.469). Insofar as they are perceived, the surprising facts are facts of mediated perception, while in their genuine surprising character they are immediately experienced as "brute facts" or pure "secondness", as Peirce says. In order to transform the psychological notion of "surprise" into a more general form, one could say that a "surprising fact" is a fact which is not covered by certain expectations generated by certain contexts of belief, although the fact is such that it ought in some way to be part of the intended applications of those contexts of belief.
(5) Assuming that a surprising fact should be an intended application of a certain set of contexts, but is not really covered by these, and assuming, according to (1), (2), and (3), that every cognition is mediated by contexts, the surprising fact ought to prompt us to doubt the adequacy of our set of contexts. My thesis is that coping with a surprising situation in abductive reasoning becomes possible by "rearranging" our contexts. But how?
(6) Given that for Peirce "abductive inference shades into perceptual judgment without any sharp line of demarcation between them" (Peirce, 1903:CP 5.181), we can also say that every abduction in the face of "surprising facts" is nothing more than a search for a mode of perception of these facts (cf. Peirce:1908:CP 6.469). But how to get a new point of view, a new perspective on surprising facts and: can there be a logic of such a "creative intuition"?
(7) A central condition for taking
new perspectives is activity. It is a simple fact of perception theory that
for a child it is hardly possible to learn to see if the head cannot be turned
and the whole body moved. Peirce emphasizes this element of activity in particular
in respect to discoveries in mathematics: Proofs and deductive reasoning are
essential characteristics of mathematics, but if we want to prove that the sum
of angles in a triangle is exactly 180°, we need a form of reasoning which Peirce
called "diagrammatic": When we draw a diagram of a triangle and try some experiments
with this diagram, we easily see that by drawing the parallel to the triangle’s
base through its apex we shall suddenly obtain the possibility of a proof by
seeing that all the triangle’s angles occur below this straight line, so that
their sum must be 180° (cf. Peirce, 1888, c.:CP 1.383). The essence of diagrammatic
thinking is to create new representations out of a given one. The point is that
one representation in a continuum of possible representations "compels
us" to perceive new relations or a new organizing structure of a set of data.
But how can we find a promising point of view, if there is no direct path from
a set of data to an explanatory hypothesis for such data (cf. Peirce, 1901:MS
692, 23,25)?
(8) For Peirce, the necessity of
"instincts" results from his belief that it is impossible to explain the rate
of scientific progress and its success by chance alone: "there are myriads of
false hypotheses to account for any given phenomenon, against one sole true
one" (Peirce, 1905b:CP 5.431).
(9) Rescher wants to substitute this "somewhat mysterious capacity of insight or instinct" by a "historically developed methodology for guiding the search for efficiently data-accommodating hypotheses" (Rescher, 1995:323). But there are two problems which might lead us back eventually to Peirce’s concept of instinct: First, if we ask how search-guiding methodology can be developed and legitimized, we fall into the circle that a search-guiding methodology in itself can only be found by a search which must be guided by a methodology of higher level, etc. ad infinitum. Thus it is necessary to discuss the problem of infinite regress. Second, isolating a search-guiding "historically developed methodology" neglects that such a context, too, is in itself determined by the acts of those who use this method. As we have seen in (3): the context cannot be separated from the particulars whose interacting habits constitute a certain context. What is missing in Rescher’s suggestion is the problematical relation between the historical development of methodology and the activities of scientists who constitute this methodology by their own particular work.
(10) How do these considerations lead back to Peirce’s conception of instinct? And first of all: What does the term "instinct" mean for him? Reading his late-life Essay toward improving our Reasoning in Security & Uberty (Peirce, 1913a:EP 2, 464 ff.), I see four principal characteristics of "instincts": First, we cannot leave the context of our own instincts, just as we cannot leave, according to Kuhn, the context of scientific paradigms in a phase of "normal science". Secondly, and this point can also be covered in accordance with Kuhn, "the instincts of the more intelligent mammals, birds and insects sometimes undergo modification under new experience"; and that must be true especially for "instincts of mankind", which "should prove more mutable by far" than those of animals (ibid. 467 f.). My reference to Kuhn’s Structure of Scientific Revolutions (Kuhn, 1962, 1970)was to emphasize that when one considers science from a functional standpoint, there may be no difference between Peirce’s "instincts" and Kuhn’s methodological "paradigms": Both determine our activity and perception immediately, and both are changeable.
But there seems to be a difference
with respect to the other characteristics of Peirce’s instincts: Third, instincts
are "a way of acting". Thus no separation is possible between the general character
of an instinct and its manifestation in particular actions. Forth, and even
more importantly, Peirce defines a certain aim or telos of his instinctive
"reasoning-power": An instinctive action "conduces to the probable perpetuation"
of a race (Peirce, 1913a:EP 2, 464 f.). Thus Peirce’s abductive talent must
be seen within the world in which it takes place. While Rescher does
not legitimize his "historically developed methodology" further, Peirce’s account
of instinct seems to be legitimized by its success and adequacy in a certain
world. Thus we are confronted with a contextual conception of epistemology
and science in the sense developed in point (2): The basis of cognition is a
relation of mutual dependence between the habits of a cognitive actor and the
habits of the world in which he acts. This context also is the condition
of the possibility of abduction (cf. Peirce, 1905a:S&S 187).
Peirce’s concept of "instinct", I would say, emphasizes what I would call a contextual view of cognition. Thus the reference to instincts does not highlight some inborn capacities, as Chomsky’s interpretation of Peirce’s abduction tries to make plausible (cf. Wirth, 1993), but it rather highlights in a more general sense the adequacy of certain habits of action within certain situations. Instincts as well as my "contexts" are determining but changeable programs of activity within a certain world; their function is defined by their relatedness to this world.
To focus our ten points on the question
of the logical character of abductive inference, I will conclude as follows:
Beginning with a negative statement we can say that for Peirce an essential
point for the logical character of abduction seems to be the obvious fact that
our abductive reasoning cannot be explained by chance alone (cf. Rescher, 1995):
"Consider the multitude of theories
that might have been suggested. A physicist comes across some new phenomenon
in his laboratory. How does he know but the conjunctions of the planets have
something to do with it or that it is not perhaps because the dowager empress
of China has at that same time a year ago chanced to pronounce some word of
mystical power or some invisible jinnee may be present. Think of what trillions
of trillions of hypotheses might be made of which one only is true; and yet
after two or three or at the very most a dozen guesses, the physicist hits pretty
nearly on the correct hypothesis. By chance he would not have been likely to
do so in the whole time that has elapsed since the earth was solidified" (Peirce,
1903:CP 5.172).
It is evident that many hypotheses are impossible in the physicist’s situation. But what does that mean? This means, I would say, that there is a specific relation between the situation of abductive reasoning and the process of guessing and finding a promising hypothesis. The range of hypotheses accepted as possible in a specific situation is limited by a complex interplay of several contexts which are given in that situation.
If for Peirce the logical character of abduction depends on its not being an arbitrary process of hypothesis selection, it becomes clear that the constraining character of contexts is essential for the logic of abduction. An abductive inference is "logical", we could tentatively formulate a first positive approach, if and only if the chosen set of possible hypotheses is determined by a certain set of contexts which are assumed as relevant in a given historical situation.
The problem of the vague formulation "assumed as relevant in a given historical situation" seems to be insoluble: We have to accept that there are contexts which are obviously impossible in specific historical situations, as indicated in Peirce’s example above, and others which seems to be more or less arbitrary. Thus Peirce proposes in a manuscript the example of Carl Georg Christian von Staudt’s (1798 - 1867) discovery that the "Ten points theorem" – at its time a famous problem of geometry – is provable when the two-dimensional representation of this problem is seen as a perspective representation (Peirce, 1907:MS 318, CSP 50ff.=ISP 42ff.). Von Staudt’s work about projective geometry and especially his experiences with perspectives and the relations between two- and three-dimensional representations were exactly that context which enabled him to change the habit of seeing the problem. Geometers without these experiences had no chance of finding this solution.
This example is very instructive for understanding the possibility of gaining new perspectives, new modes of perception, and new hypotheses: Von Staudt’s context – his cognitive ability to conceive two-dimensional figures as representations of three-dimensional figures – was originally developed in his work about projective geometry. But the general form of this context, the generality of mutual dependence of certain cognitive habits and certain properties of projective figures, allows the application on others than the originally intended applications. Thus abduction can be explained as the application of given habits on new situations. In this way the "creation of new modes of perception" is possible.
The specific contextual background
of the situation determined the range of possible hypothesis in a specific way.
Hence, we can say that the logic of abduction is a kind of "contextualized logic".
But what does that mean? The situation in itself, the relevant contexts and
their specific order, is a result of a process which can be reconstructed in
the same way as a series of abductive inferences, which in themselves are determined
by certain hierarchical orders of contexts, etc. ad infinitum. In this
manner, the problem of abduction is connected with the problem of evolution.