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DWI. Note 1

Having once again run into what is now a familiar block
in my understanding of Peirce's development and thought,
here, with respect to the nature and place of inductive
inference, probable reasoning, and statistics generally
in the theory and praxis of inquiry, I shall drop this
anchor for the ravelling up of hopeful once and future
clues to the soultion of the problem.

Jon Awbrey

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DWI. Note 2

| The purpose of Deduction, that of collecting consequents of the hypothesis,
| having been sufficiently carried out, the inquiry enters upon its Third Stage,
| that of ascertaining how far those consequents accord with Experience, and of
| judging accordingly whether the hypothesis is sensibly correct, or requires some
| inessential modification, or must be entirely rejected. Its characteristic way
| of reasoning is Induction. This stage has three parts. For it must begin with
| Classification, which is an Inductive Non-argumentational kind of Argument, by
| which general Ideas are attached to objects of Experience; or rather by which
| the latter are subordinated to the former. Following this will come the testing-
| argumentations, the Probations; and the whole inquiry will be wound up with the
| Sentential part of the Third Stage, which, by Inductive reasonings, appraises the
| different Probations singly, then their combinations, then makes self-appraisal of
| these very appraisals themselves, and passes final judgment on the whole result.
|
| C.S. Peirce, NAFTROG, CP 6.472.
|
| C.S. Peirce, 'Collected Papers', CP 6.452-493,
| Harvard University Press, Cambridge, MA, 1960.
|
| C.S. Peirce,
|"A Neglected Argument for the Reality of God",
| Hibbert Journal, Volume 7, pp. 90-112, 1908.
|
| Wiener, Philip P. (ed.),
|'Charles S. Peirce: Selected Writings',
| Dover, New York, NY, pp. 358-379, 1966.

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DWI. Note 3

| The Probations, or direct Inductive Argumentations, are
| of two kinds. The first is that which Bacon ill described
| as "inductio illa quae procedit per enumerationem simplicem"
| [that induction which proceeds by simple enumeration]. 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 later either depends
| on measurements, or on statistics, or on countings.
|
| C.S. Peirce, NAFTROG, CP 6.473.
|
| C.S. Peirce, 'Collected Papers', CP 6.452-493,
| Harvard University Press, Cambridge, MA, 1960.
|
| C.S. Peirce,
|"A Neglected Argument for the Reality of God",
| Hibbert Journal, Volume 7, pp. 90-112, 1908.
|
| Wiener, Philip P. (ed.),
|'Charles S. Peirce: Selected Writings',
| Dover, New York, NY, pp. 358-379, 1966.

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DWI. Note 4

| The Varieties and Validity of Induction
|
| Crude, Quantitative, and Qualitative Induction
|
| Retroduction and Induction face opposite ways.
| The function of retroduction is not unlike those
| fortuitous variations in reproduction which played so
| important a role 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. A great many people who
| may be admirably trained in divinity, or in the humanities,
| or in law and equity, but who are certainly not well trained
| in scientific reasoning, imagine that Induction should follow
| the same course. My Lord Chancellor Bacon was one of them.
| 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 suggestions 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. Throughout
| an investigation it is well to bear prominently in mind just what
| it is that we are trying to accomplish in the particular stage of
| the work at which we have arrived. Now when we get to the inductive
| stage what we are about is finding out how much like the truth our
| hypothesis is, that is, what proportion of its anticipations will
| be verified.
|
| C.S. Peirce, VAVOI, CP 2.755.
|
| C.S. Peirce, "The Varieties and Validity of Induction",
| From MS. "G", c. 1905, reprinted in 'Collected Papers',
| CP 2.755-772, Harvard University Press, Cambridge, MA, 1960.

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DWI. Note 5

| Crude, Quantitative, and Qualitative Induction (cont.)
|
| 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.
|
| C.S. Peirce, VAVOI, CP 2.756.
|
| C.S. Peirce, "The Varieties and Validity of Induction",
| From MS. "G", c. 1905, reprinted in 'Collected Papers',
| CP 2.755-772, Harvard University Press, Cambridge, MA, 1960.

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DWI. Note 6

| Crude, Quantitative, and Qualitative Induction (cont.)
|
| When I say that it goes on that presumption, I merely
| mean to describe the presumption of the reasoning as
| being that the particular uniformity as to a certain
| matter that has attached to past experience will be
| maintained in the future. I shall explain below how
| there is a certain justification in this, though a very
| slender one. I do not mean to say, as some logicians do,
| that the force of the induction is just the same as that
| of a syllogism whose major premiss should be, "Future
| experience will not violate the uniformity of past
| experience". For such a syllogism being a fallacy
| of the particularly atrocious kind called "logical
| fallacy", would have no justification whatsoever.
| For a sound syllogism must have a major premiss of
| definite meaning: otherwise it may be thrown into
| the form of a fallacy of undistributed middle. Now
| the induction in question, though weak, is by no means
| without justification.
|
| C.S. Peirce, VAVOI, Footnote 1 to CP 2.756.
|
| C.S. Peirce, "The Varieties and Validity of Induction",
| From MS. "G", c. 1905, reprinted in 'Collected Papers',
| CP 2.755-772, Harvard University Press, Cambridge, MA, 1960.

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DWI. Note 7

| Crude, Quantitative, and Qualitative Induction (cont.)
|
| 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.
|
| C.S. Peirce, VAVOI, CP 2.757.
|
| C.S. Peirce, "The Varieties and Validity of Induction",
| From MS. "G", c. 1905, reprinted in 'Collected Papers',
| CP 2.755-772, Harvard University Press, Cambridge, MA, 1960.

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DWI. Note 8

| Crude, Quantitative, and Qualitative Induction (cont.)
|
| 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'.
|
| C.S. Peirce, VAVOI, CP 2.758.
|
| C.S. Peirce, "The Varieties and Validity of Induction",
| From MS. "G", c. 1905, reprinted in 'Collected Papers',
| CP 2.755-772, Harvard University Press, Cambridge, MA, 1960.

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DWI. Note 9

| Crude, Quantitative, and Qualitative Induction (cont.)
|
| 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.
|
| C.S. Peirce, VAVOI, CP 2.759.
|
| C.S. Peirce, "The Varieties and Validity of Induction",
| From MS. "G", c. 1905, reprinted in 'Collected Papers',
| CP 2.755-772, Harvard University Press, Cambridge, MA, 1960.

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DWI. Note 10

| Crude, Quantitative, and Qualitative Induction (concl.)
|
| 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 re-examined '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.
|
| C.S. Peirce, VAVOI, CP 2.759.
|
| C.S. Peirce, "The Varieties and Validity of Induction",
| From MS. "G", c. 1905, reprinted in 'Collected Papers',
| CP 2.755-772, Harvard University Press, Cambridge, MA, 1960.

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DWI. Note 11

Let's see if we can get a succinct description,
or a summary image, that gets at the essential
differences and similarities among the three
types of induction that Peirce noted for us.

In my discussions with Gary Richmond on the Peirce List,
the following statement of inductive principles evinced
a certain saliency:

| Now when we get to the inductive stage
| what we are about is finding out how much
| like the truth our hypothesis is, that is,
| what proportion of its anticipations will
| be verified.
|
| C.S. Peirce, VAVOI, CP 2.755

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