previous knowledge. But the whole idea of inference to the best explanation

is that the choice is determined by the facts that are to be explained”that the

outcome is the best explanation of these particular data.

Some defenders of the idea of inference to the best explanation have even

tried to subsume enumerative induction under such a procedure (e.g., Harman

1968). This was in effect Peirce™s early perspective on abduction, but it was not

Peirce™s mature view. On the one hand, induction for Peirce is essentially a

procedure of testing and con¬rming hypotheses arrived at by abduction. On

the other hand abduction was for Peirce the only way of introducing new

hypotheses into inquiry. (See Comprehension Thesis) Yet nobody has in his

Socratic Epistemology

44

wildest dreams suggested that all out new general knowledge is ¬rst arrived at

by enumerative induction.

There are still other ways of seeing the limitations of the idea of “inference

to the best explanation.” One of them is probabilistic. From a probabilistic

point of view, this idea amounts to using only the likelihood in the search of

new hypotheses. Even though this might have satis¬ed Sir Ronald Fisher, it

means leaving other kinds of relevant information unused. (For a defense of

the importance of likelihoods, see Edwards 1992.)

Before venturing my own solution to the problem of abduction, I will ¬rst

call attention to a dimension of this problem that has not yet come up. This

dimension is present in Peirce, albeit not fully articulated. One context in which

it can be seen is Peirce™s notion of inference. It has already been seen that it is

not quite what we are used to. As Peirce himself puts it,

I call all such inference by the peculiar name, abduction, because its legitimacy

depends upon altogether different principles from those of other kinds of inference.

“Hume on Miracles,” CP 6.524-525, 1901.

What are those “altogether different principles?” Peirce™s views on inference

have been summarized as follows (Kapitan, 1997, p. 479):

(1) Inference is a conscious, voluntary act over which the reasoner exercises

control (5.109, 2.144).

(2) The aim of inference is to discover (acquire, attain) new knowledge

from a consideration that which is already known (MS 628: 4).

(3) One who infers a conclusion C from a premise P accepts C as a result of

both accepting P and approving a general method of reasoning according

to which if any P-like proposition is true, so is the correlated C-like

proposition (7.536, 2.444, 5.130, 2.773, 4.53“55, 7.459, L232:56).

(4) An inference can be either valid or invalid depending on whether it

follows a method of reasoning it professes to and that method is con-

ductive to satisfying the aim of reasoning”namely, the acquisition of

truth (2.153, 2.780, 7.444, MS 692: 5).

The most interesting aspect of Peirce™s notion of inference is (4). Usually

the validity and the other merits of an inference are judged in terms of the

relation of the premise or premises to the conclusion”for instance, whether

the truth of the premises guarantees the truth of the conclusion or perhaps

whether it makes the conclusion probable to a certain degree. The term “rule of

inference” is usually restricted to cover only such inferences as can be justi¬ed

in terms of the premise-conclusion relation either because the step from the

premises to the conclusion is truth-preserving or because the premises make

the conclusion probable to a certain degree. Peirce is making a much more

important break with this traditional idea than he himself seems to realize.

He is going beyond rules of inference that depend on the premise-conclusion

relation alone and is considering also rules or principles of inference “of an

Abduction”Inference, Conjecture, or Answer? 45

altogether different kind.” These rules or principles are justi¬ed by the fact that

they exemplify a method that is conducive to the acquisition of new knowledge.

Hence there are two different kinds of rules (principles) that can justify

an inference. Peirce does not seem to distinguish these two kinds of rules

or principles from each other systematically. It would have been most helpful,

however, if he had done so. I have called the former kind of rules de¬nitory rules

and assimilated them to the rules that de¬ne a strategic game like chess”or

deduction or scienti¬c inquiry, for that matter. Such de¬nitory rules are merely

permissive. They tell us what moves one may make in given circumstances, but

they do not tell anything about which moves are good, bad, or indifferent. Such

advice is codi¬ed in what I have called strategic rules (or principles). From the

general theory of games, we know that such rules cannot be formulated in

move-by-move terms”for instance, in terms of the relationship of premises

to a conclusion”but only in terms of complete strategies. (A game theorist

would express this point by saying that in general, utilities can absolutely

speaking be associated only with entire strategies, not with particular moves.)

Now we can see that Peirce™s vantage point contained at one and the same

time a brilliant insight and a serious limitation. The insight was into the impor-

tance of strategic rules. For what Peirce™s statement quoted earlier amounts

to is that the validity of an abductive inference is to be judged by strategic

principles rather than by de¬nitory (move-by-move) rules. This is what makes

an abductive inference depend for its legitimacy “upon altogether different

principles from those of other kinds of inference.” What these “different prin-

ciples” were in Peirce™s mind can be gathered from his various statements. One

typical expression of the difference is Peirce™s distinction between the validity

and the strength of an argument.

. . . it is only in Deduction that there is no difference between a valid argument and a

strong one. (“Pragmatism as the Logic of Abduction,” p. 17)

Thus an argument can be logical but weak. Such statements leave little doubt

that the kind of validity Peirce had in mind was essentially strategic.

There was nevertheless a limitation that handicapped Peirce™s thinking in

his failure to appreciate fully the difference between de¬nitory and strategic

rules. Whenever he tries to explain the kind of validity that does not go with

strength, he becomes hesitant and resorts to examples. He never gives a gen-

eral characterization of the difference between what I have called de¬nitory

and strategic rules. These two kinds of rules do not deal with different kinds

of inference. They are different kinds of rules governing the same kinds of

inferential steps. Peirce recognizes the difference between the ways in which

de¬nitory and strategic rules are legitimized or validated. De¬nitory rules of

inquiry are validated insofar as they confer truth or high probability on the

conclusion of each particular application of theirs. In contrast, strategic rules

of inquiry are justi¬ed by their propensity to lead the inquirer to new truths

when consistently pursued as a general policy. It is worth emphasizing that this

Socratic Epistemology

46

propensity to lead to new knowledge must not be assimilated to an inference

rule™s ability to confer truth or high probability on its conclusion in each parti-

cular case. The former propensity can, for instance, be manifested when a rule

application opens up new future possibilities of knowledge acquisition even

when it does not itself provide the inquirer with any new truths or even new

hypotheses. Peirce seems to have realized fairly clearly what a strategic justi¬-

cation of a rule application consists in. Indeed, he seems to see the justi¬cation

not only of abductive but also inductive steps as strategic.

Induction is reasoning which professes to pursue such a method that, being persistent

in, each special application of it . . . must at least inde¬nitely approximate to the truth

about the subject in hand, in the long run. [Emphasis added.] Abduction is reasoning,

which professes to be such, that in the case there is any ascertainable truth concerning

the matter in hand, the general method of this reasoning though not necessarily each

special application of it must eventually [emphasis added] approximate the truth.

(Eisele, ed., The New Elements of Mathematics, vol. 4, p. 37)

What Peirce does not realize is that one and the same step of reasoning,

including deductive reasoning, can normally be considered both as an appli-

cation of a de¬nitory rule and as an application of a strategic rule”in fact,

several alternative strategic rules that differ in their consequences for other

particular cases. It is admittedly the case that deduction differs from abduction

in the kind of justi¬cation of particular steps. As Peirce puts it:

Deduction is reasoning which proposes to pursue such a method that if the premises

are true the conclusion will in every case be true. (loc. cit.)

But this does not obliterate the fact that we can in deduction, too, distinguish

de¬nitory and strategic rules from each other. Furthermore, if abduction is to

obey formal laws like any other inference, as Peirce believes, it must likewise be

subject to de¬nitory (formal) rules. In brief, what Peirce does not realize is that

there is a de¬nitory versus strategic distinction that cuts across his trichotomy,

deduction-abduction-induction.

The same shortcoming can also be described by saying that even though

Peirce recognized the vital importance of strategic rules in inquiry, he did

not possess the general concept of strategy in the abstract sense which was

¬rst spelled out clearly by von Neumann (1928; see also von Neumann and

Morgenstern, 1944). He had to try to make other concepts do the job of the

notion of strategy. How he did that requires a separate investigation. I believe

that such an investigation might yield interesting insights into Peirce™s ways

of thinking and into the concepts he employed. For instance, it seems to me

that the concept of habit was one of the notions he used to serve some of the

same purposes as the notion of strategy introduced by later thinkers. This

would, among other things, help to understand why Peirce™s concept of