Bibliography

A Neglected Argument for the Reality of God (G)

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. [—]

Crude induction is the only kind of induction that is capable of inferring the truth of what, in logic, is termed a universal proposition. For what is called “complete induction” is not inductive reasoning, but is logistic deduction. We might further say, if we chose, that every crude induction concludes a universal proposition; but this would be merely the expression of a way of regarding matters. For any proposition concerning the general run of future experience may be regarded as universal, even if it be “A pair of dice will, every now and then, turn up doublets.” The undipped heel of crude induction is that if its conclusion be understood as indefinite, it will be of little use, while if it be taken definitely, it is liable at any moment to be utterly shattered by a single experience; for a series of experiences, if the whole constitutes but a single one of the instances to which an inductive conclusion refers, is to be regarded as a single experience.

…belief is essentially satisfactory; and the state of Cartesian doubt is mere pretence or self-deception. For real doubt is most distressing, and nobody can pass from the naturally satisfied state of belief to a state of distressing doubt, unless some still stronger belief forces him to doubt. We cannot pass from satisfaction to dissatisfaction from sheer dissatisfaction with satisfaction.

[An icon is] a sign which represents its object by virtue of being like it, whether qualitatively or by the analogy of its parts, such as a diagram. [—] The denotation of Icons is essentially indefinite.

[Indices are] signs which represent their objects by virtue of being connected with them in fact, although this fact be but the actual occurrence of a thought. [—] The denotation of an index is essentially singular.

The true guarantee of the validity of induction is that it is a method of reaching conclusions which, if it be persisted in long enough, will assuredly correct any error concerning future experience into which it may temporarily lead us. This it will do not by virtue of any deductive necessity (since it never uses all the facts of experience, even of the past), but because it is manifestly adequate, with the aid of retroduction and of deductions from retroductive suggestions, to discovering any regularity there may be among experiences, while utter irregularity is not surpassed in regularity by any other relation of parts to whole, and is thus readily discovered by induction to exist where it does exist, and the amount of departure therefrom to be mathematically determinable from observation where it is imperfect.

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. [—]

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. [—]

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 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.

[The strongest kind of induction] 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.

Retroduction and Induction face opposite ways. The function of retroduction is not unlike those fortuitous variations in reproduction which played so important a rôle in Darwin’s original theory. In point of fact, according to him every step in the long history of the development of the moner into the man was first taken in that arbitrary and lawless mode. Whatever truth or error there may be in that, it is quite indubitable, as it appears to me, that every step in the development of primitive notions into modern science was in the first instance mere guess-work, or at least mere conjecture. But the stimulus to guessing, the hint of the conjecture, was derived from experience. The order of the march of suggestion in retroduction is from experience to hypothesis.

… Another question to be noted for later consideration is whether this first step in inquiry can conclude, if it can be called “concluding,” otherwise than in the interrogative mood, if grammarians will acknowledge such a mood. Certain it is that if a series of experience does no more than suggest an idea interrogatively, the mere occurrence of the suggestion, warrants us in regarding the movement of thought as having the essential character of this first stage of inquiry. I call this mode of inference, or, if you please, this step toward inference, in which an explanatory hypothesis is first suggested, by the name of retroduction, since it regresses from a consequent to a hypothetical antecedent. But while this explains why I have selected the vocable ‘retroduction’ to express my meaning, I claim the right, as inventor of the term, to make its definition to be, the passage of thought from experiencing something, E, to predicating a concept of the mind’s creating; the subject of the predication being a specified class to which E belongs, or an indefinite part of such class.

The second stage of inquiry consists in deducing the consequences of the retroductive hypothesis. The word “retroductive,” however, is surplusage; for every hypothesis, however arbitrary, is suggested by something observed, whether externally or internally and such suggestion is, from a purely logical point of view, retroduction.

…the doctrine of scholastic realism neither is that all concepts are real (which would be the ne plus ultra of absurdity) nor that any concept is perfectly real; but that some concepts are real in some measure.

[Symbols are] signs which represent their objects simply because they will be so understood, or arbitrary signs. [—] The denotation of a symbol is always definitely general, that is it stands for any object its interpreter may choose provided it be of a certain description, and not merely for some unspecified object of that description which its utterer may have in mind.