Seminario del Grupo de Estudios Peirceanos
Universidad de Navarra, 27 de septiembre

Is Qualitative Induction a Kind of Induction?

Giovanni Tuzet

1. Peirce’s Scientific Method

After 1900, Peirce elaborates his conception of scientific method as constituted by three inferential steps1.


The underlying metaphysical issue concerning induction: the Uniformity of Nature, or the reality of the Laws of Nature.

Although the universe need have no peculiar constitution to render ampliative inference valid, yet it is worth while to inquire whether or not it has such a constitution; for if it has, that circumstance must have its effect upon all our inferences (CP 2.750). (Cf. e.g. CP 1.92).

The methodological importance of induction: it is a self-correcting, or error-correcting, inference and procedure4.

2. Three Kinds of Induction

In a paper of c. 1905, Peirce distinguishes three kinds of induction: Crude Induction, Quantitative Induction, and Qualitative Induction5

Now, Peirce says that the first is the weakest kind of induction and the second the strongest, while the third mediates between them and is, in a sense, "of more general utility than either of the others" (CP 2.759). The conclusions provided by Qualitative Induction are not as secure as those provided by Quantitative Induction, but may be more useful for the testing of the starting hypothesis. The difference lays in the evidential value of the premises. All the instances considered in Quantitative Induction have the same evidential value, while, according to Peirce, the different parts of the “stream of experience” of Qualitative Induction have different evidential values "to be estimated according to our sense of the impressions they make upon us” (CP 2.759). So, one might say that Qualitative Induction provides richer conclusions from richer premises.

To illustrate the dynamics of Qualitative Induction, Peirce uses the example of an investigator who starts from a hypothesis and tries to test it elaborating some conditional predictions out of it. So, to assess the hypothesis, the investigator must judge of the combined value of the evidence, and such an estimation is the proper business of Qualitative Induction.

In a paper of 1908, both the second and third kind of induction are called Gradual Induction – "which makes a new estimate of the proportion of truth in the hypothesis with every new instance" (CP 6.473). Gradual Induction is contrasted with Crude Induction, the weakest of inductions, which proceeds by enumeration and whose logical conclusion is a universal proposition "liable to be demolished in a moment", that is falsified by a single counter-instance7. Gradual Induction qua genus comprehends the two species we already considered: "Gradual Induction is either Qualitative or Quantitative and the latter either depends on measurements, or on statistics, or on countings" (CP 6.473).

3. Is Qualitative Induction a Kind of Induction?

One may ask whether Qualitative Induction is really a kind of induction or rather something else. Assuming Peirce’s scientific methodology as constituted by three inferential steps (Abduction, Deduction, and Induction), the final inductive step is certainly concerned with hypothesis testing, but the features of the so-called Qualitative Induction might generate the suspect that it is nothing but a (more complex) kind of abduction, or a complex inferential process analogue to what in contemporary literature is called ‘Inference to the Best Explanation’, or something basically different from inference and rather similar to evaluation or discretionary appreciation. So, is Qualitative Induction a genuine kind of induction?

A further problem: Does (Qualitative) Induction to the discovery of singular facts?

Pro: the historical examples provided by Peirce himself (see e.g. CP 2.625, 2.714).

Contra: scientific method aims at discovering the laws of nature.

Two examples from the legal filed and legal evidentiary inferences.

(A) The case of the three dead wives.

(B) Image that at the scene of a crime we collect some evidence suggesting that Anastasia killed Basil. We might, on the basis of the hypothesis that Anastasia killed Basil, formulate various predictions in order to confirm or disconfirm the hypothesis. For instance, predictions on what might be found in Anastasia's house if it were true that she killed Basil. Suppose then that some of those predictions are confirmed and some are not. Of course their evidential value is not the same. How to determine it in a non subjective and discretionary way? Moreover, would such a determination be a form of induction?

Once the predictions are tested, the investigator has "to judge of the combined value of the evidence, and to decide whether the hypothesis should be regarded as proved, or as well on the way toward being proved, or as unworthy of further attention, or whether it ought to receive a definite modification in the light of the new experiments and be inductively rexamined ab ovo, or whether finally, that while not true it probably presents some analogy to the truth, and that the results of the induction may help to suggest a better hypothesis" (CP 2.759).

4. Some Answers to the Question

(1) Yes, Qualitative Induction is a form of Induction.

(2) No, Qualitative Induction is just a form of (disguised) Abduction.

(3) No, Qualitative Induction is rather Inference to the Best Explanation.

(4) No, Qualitative Induction is neither an Induction nor a form of inference, but rather a form of evaluation.

Answer (4) implies a highly questionable separation between evaluation and inference.

Answer (3) is certainly more plausible but risks to make the whole issue less clear, since the notion of ‘Inference to the Best Explanation’ is far from being clearly defined8.

In my opinion, Inference to the best explanation is distinct from both abduction (hypothesis generation or suggestion) and induction (hypothesis testing or evaluation)9.

Inference to the best explanation as abduction plus deduction plus induction? In this sense, is Inference to the best explanation nothing more nor less than scientific method? But, again, what about singular facts and events?

Answer (2) rules out the basic difference between induction and abduction, a difference that seems to hold with respect to Qualitative Induction as well: induction without abduction is blind; abduction without induction is empty.

For instance, any historical fact, as that Napoleon Bonaparte once lived, is a hypothesis; we believe the fact, because its effects - I mean current tradition, the historics, the monuments, etc. -are observed. But no mere generalization of observed facts could ever teach us that Napoleon lived (CP 2.714; 1883).
Retroduction and Induction face opposite ways. [] The order of the march of suggestion in retroduction is from experience to hypothesis. [] On the contrary, the only sound procedure for induction, whose business consists in testing a hypothesis already recommended by the retroductive procedure, is to receive its suggestion from the hypothesis first, to take up the predictions of experience which it conditionally makes, and then try the experiment and see whether it turns out as it was virtually predicted in the hypothesis that it would" (CP 2.755; 1905 c.).

However, notice that some contemporary authors claim that confirmation, if it is not enumerative, is abductive10.

Answer (1) must explain in what sense the estimation of the evidential values "according to our sense of the impressions they make upon us" (CP 2.759) – which in fact, as a criterion, is quite vague – is still an inductive inference and not a form of merely subjective evaluation or discretionary appreciation or something else.



# 1 "The first order of induction, which I will call Rudimentary Induction, or the Pooh-pooh argument, proceeds from the premises that the reasoned has no evidence of the existence of any fact of a given description and concludes that there never was, is not, and never will be any such thing. The justification of this is that it goes by such light as we have. and that truth is bound eventually to come to light; and therefore if this mode of reasoning temporarily leads us away from the truth, yet steadily pursued, it will lead to the truth at last. This is certainly very weak justification; and were it possible to dispense with this method of reasoning, I would certainly not recommend it. But the strong point of it is that it is indispensable. It goes upon the roughest kind of information, upon merely negative information; but that is the only information we can have concerning the great majority of subjects" (CP 7.111).

# 2 "The second order of induction consists in the argument from the fulfillment of predictions. After a hypothesis has been suggested to us by the agreement between its consequences and observed fact, there are two different lines that our further studies of it may pursue. In the first place, we may look through the known facts and scrutinize them carefully to see how far they agree with the hypothesis and how far they call for modifications of it. That is a very proper and needful inquiry. But it is Abduction, not Induction, and proves nothing but the ingenuity with which the hypothesis has been adapted to the facts of the case" (CP 7.114).

# 3 "The other line which our studies of the relation of the hypothesis to experience may pursue, consists in directing our attention, not primarily to the facts, but primarily to the hypothesis, and in studying out what effect that hypothesis, if embraced, must have in modifying our expectations in regard to future experience. Thereupon we make experiments, or quasi-experiments, in order to find out how far these new conditional expectations are going to be fulfilled. […] The strength of any argument of the Second Order depends upon how much the confirmation of the prediction runs counter to what our expectation would have been without the hypothesis. It is entirely a question of how much; and yet there is no measurable quantity. For when such measure is possible the argument assumes quite another complexion, and becomes an induction of the Third Order" (CP 7.115).

# 4 "The third order of induction, which may be called Statistical Induction, differs entirely from the other two in that it assigns a definite value to a quantity. It draws a sample of a class, finds a numerical expression for a predesignate character of that sample and extends this evaluation, under proper qualification, to the entire class, by the aid of the doctrine of chances" (CP 7.120).

c. 1905

# 5 "It is well to distinguish three different varieties of induction. The first and weakest kind of inductive reasoning is that which goes on the presumption that future experience as to the matter in hand will not be utterly at variance with all past experience. Example: ‘No instance of a genuine power of clairvoyance has ever been established: So I presume there is no such thing’. I promise to call such reasoning crude induction. Bacon seems to refer to this when he speaks of 'inductio quae procedit per enumerationem simplicem'. But I hardly think he meant to say that that phrase exactly describes it. It certainly does not; since in most cases no enumeration is attempted; and the enumeration, even if given, would not be the reasoner’s chief reliance, which is rather the absence of instances to the contrary" (CP 2.756).

# 6 "From the weakest kind of induction let us pass at once to the strongest. This investigates the interrogative suggestion of retroduction, 'What is the "real probability" that an individual member of a certain experiential class, say the S's, will have a certain character, say that of being P?' This it does by first collecting, on scientific principles, a ‘fair sample’ of the S’s, taking due account, in doing so, of the intention of using its proportion of members that possess the predesignate character of being P. This sample will contain none of those S’s on which the retroduction was founded. The induction then presumes that the value of the proportion, among the S's of the sample, of those that are P, probably approximates, within a certain limit of approximation, to the value of the real probability in question. I propose to term such reasoning Quantitative Induction" (CP 2.758).

# 7 "The remaining kind of induction, which I shall call Qualitative Induction, is of more general utility than either of the others, while it is intermediate between them, alike in respect to security and to the scientific value of its conclusions. In both these respects it is well separated from each of the other kinds. It consists of those inductions which are neither founded upon experience in one mass, as Crude Induction is, nor upon a collection of numerable instances of equal evidential values, but upon a stream of experience in which the relative evidential values of different parts of it have to be estimated according to our sense of the impressions they make upon us.

Qualitative Induction consists in the investigator’s first deducing from the retroductive hypothesis as great an evidential weight of genuine conditional predictions as he can conveniently undertake to make and to bring to the test, the condition under which he asserts them being that of the retroductive hypothesis having such degree and kind of truth as to assure their truth. In calling them ‘predictions’, I do not mean that they need relate to future events but that they must antecede the investigator’s knowledge of their truth, or at least that they must virtually antecede it" (CP 2.759).

# 8 "Having made his initial predictions the investigator proceeds to ascertain their truth or falsity; and then, having taken account of such subsidiary arguments as there may be, goes on to judge of the combined value of the evidence, and to decide whether the hypothesis should be regarded as proved, or as well on the way toward being proved, or as unworthy of further attention, or whether it ought to receive a definite modification in the light of the new experiments and be inductively reëxamined ab ovo, or whether finally, that while not true it probably presents some analogy to the truth, and that the results of the induction may help to suggest a better hypothesis" (CP 2.759).


# 9 "The Probabions, or direct Inductive Argumentations, are of two kinds. The first is that which Bacon ill described as 'inductio illa quae procedit per enumerationem simplicem'. So at least he has been understood. For an enumeration of instances is not essential to the argument that, for example, there are no such beings as fairies, or no such events as miracles. The point is that there is no well-established instance of such a thing. I call this Crude Induction. It is the only Induction which concludes a logically Universal Proposition. It is the weakest of arguments, being liable to be demolished in a moment, as happened toward the end of the eighteenth century to the opinion of the scientific world that no stones fall from the sky. The other kind is Gradual Induction, which makes a new estimate of the proportion of truth in the hypothesis with every new instance; and given any degree of error there will sometime be an estimate (or would be, if the probation were persisted in) which will be absolutely the last to be infected with so much falsity. Gradual Induction is either Qualitative or Quantitative and the latter either depends on measurements, or on statistics, or on countings" (CP 6.473).



1. See e.g. CP 7.162-255 (1901), CP 5.14-212 (1903), CP 6.472 (1908). On Peirce and scientific method, cf. e.g. Fann 1970, Davis 1972, Moore 1993, O’Neill 1998, Tuzet 2006.

2. See Reichenbach 1938 and 1949, Goodman 1954, Hempel 1965, Quine 1969 (Chap. 5), Salmon 1991. From a Peircean point of view, cf. Harris and Hoover 1980, McMullin 1992, Levi 1997.

3. For Peirce’s early account of induction, see e.g. W1: 393 ff. (1866), CP 5.275 (1868), W4: 408-450 (1883). On the validity conditions of the sampling procedure (i.e. random sampling and predesignation of the character), see e.g. CP 1.95, 2.737, 2.790. Cf. Jessup 1974.

4. See e.g. CP 5.575, 5.579 (1898); RLT: 165, 170. Cf. Lenz 1964 and Mayo 2005.

5. Cf. the 1903 similar classification of Rudimentary Induction, Fulfillment of Predictions, Statistical Induction (CP 7.110-130), where the first is what he subsequently calls Crude Induction while the second is Qualitative Induction and the third is Quantitative Induction.

6. Cf. CP 2.269, 2.780 (1902); CP 8.233 (c. 1910). See also NEM 3: 189 ff.

7. Moreover, according to CP 7.111, the weakest kind of induction goes upon merely negative information.

8. See in particular Harman 1965, Thagard 1978 and 1988 (Chap. 8), Day and Kincaid 1994, Barnes 1995.

9. "Abduction only generates hypotheses, whereas inference to the best explanation evaluates them" (Thagard 1988: 143).

10. Smokler 1968 claimed that there are at least two different (and conflicting) conceptions of confirmation: the enumerative and the abductive. On confirmation and its paradoxes, see in particular Nicod 1924 and Hempel 1965 (part I). See also CP 2.729, n. 1. On Hempel's notion of qualitative confirmation, cf. Smokler 1968: 304-305. On the issue cf. Niiniluoto 1999.

On abduction and induction in the contemporary debate, cf. Flack and Kakas 2000, Gabbay and Kruse 2000. The account given in particular by Flach and Kakas, namely the idea of considering abduction as hypothesis generation and induction as hypothesis evaluation, is acceptable in principle but does not distinguish the different kinds of inductions distinguished by Peirce.


Una de las ventajas de los textos en formato electrónico respecto de los textos impresos es que pueden corregirse con gran facilidad mediante la colaboración activa de los lectores que adviertan errataso errores. En este sentido agradeceríamos que se enviaran todas las sugerencias y correcciones a

Fecha del documento: 3 de octubre 2007
Ultima actualización: 31 de agosto 2009

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