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MWB -- Difficulties With Induction
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DWI. Note 1
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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 solution of the problem.
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DWI. Note 2
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| 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
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| 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
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| 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
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| 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
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| 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
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| 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
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| 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
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| 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
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| 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
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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
In a sense, this says that the good of an "abductive hypothesis" (AH)
is in being a copy, icon, image, likeness, proxy, representative, or
simulacre of the truth, a likely story, as Plato or Socrates quipped.
o-------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` P_1 ` P_2 ` ` ` ` P_3 ` P_4 ` ` ` ` ` |
| ` ` ` ` ` `o` ` `o` ` ` ` ` `o` ` `o` ` ` ` ` ` |
| ` ` ` ` ` ` \*` ` \ ` ` ` ` / ` `*/|` ` ` ` ` ` |
| ` ` ` ` ` ` `\`*` `\` ` ` `/` `*`/`|` ` ` ` ` ` |
| ` ` ` ` ` ` ` \ `*` \ ` ` / `*` / `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` `\` `* \` `/`*` `/` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` \ ` `*\ /*` ` / ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `.` ` `Q` ` `.` ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|`*` `|` ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|` `*`|` ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|` ` `|` ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|` ` `|`*` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|` ` `|` `*`|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `.` ` `|` ` `.` ` `M` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` \ ` `|` ` / ` `*` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` `\` `|` `/` `*` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` \ `|` / `*`Case ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` `\`|`/`*` `S=>M ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` \|/*` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` `o` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` `S` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-------------------------------------------------o
Figure 11. Abduction to the Case S => M
Seeing things in this light, it occurs to me that
induction may be a way of grading or quantifying
the degree of fidelity, likeness, or resemblance
of the abductive icon.
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DWI. Note 12
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DWI. Work Area
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DWI. Discussion Note 1
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GR = Gary Richmond
JA = Jon Awbrey
Re: DWI 4. http://stderr.org/pipermail/inquiry/2004-November/001851.html
In: DWI. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1845
GR: You quoted Peirce as saying:
CSP: The order of the march of suggestion in retroduction
is from experience to hypothesis. A great many people
who may be admirably trained . . . in the humanities,
or in law . . ., but who are certainly not well trained
in scientific reasoning, imagine that Induction should
follow the same course.
GR: The "Neglected Argument" too, as you've made clear, will
certainly make this point: the error in thinking that
good scientific method follows from experience. Rather:
CSP: 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.
GR: This, is of course, pragmaticism: future directed.
The abduction -- the hypothesis -- was formed
retroductively from experience, from the past.
Yes, there is a footnote very nearly to this effect
that I was just getting ready to add to the account.
GR: But the induction, the experiment, tends towards the
future -- how much truth will there be in the abduction?
Or as Peirce puts it:
CSP: 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.
Yes, this is the 'New List' connection between "abductive hypotheses" (AH's)
and copies, icons, images, likenesses, proxies, representatives, simulacra.
o-------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` P_1 ` P_2 ` ` ` ` P_3 ` P_4 ` ` ` ` ` |
| ` ` ` ` ` `o` ` `o` ` ` ` ` `o` ` `o` ` ` ` ` ` |
| ` ` ` ` ` ` \*` ` \ ` ` ` ` / ` `*/|` ` ` ` ` ` |
| ` ` ` ` ` ` `\`*` `\` ` ` `/` `*`/`|` ` ` ` ` ` |
| ` ` ` ` ` ` ` \ `*` \ ` ` / `*` / `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` `\` `* \` `/`*` `/` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` \ ` `*\ /*` ` / ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `.` ` `Q` ` `.` ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|`*` `|` ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|` `*`|` ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|` ` `|` ` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|` ` `|`*` `|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `|` ` `|` ` `|` `*`|` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `.` ` `|` ` `.` ` `M` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` \ ` `|` ` / ` `*` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` `\` `|` `/` `*` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` \ `|` / `*`Case ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` `\`|`/`*` `S=>M ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` \|/*` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` `o` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` `S` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-------------------------------------------------o
Figure. Abduction of the Case S => M
Seeing things in this light, it occurs to me that
induction may be a way of grading or quantifying
the degree of fidelity, likeness, or resemblance
of the abductive icon.
Thanks for the clairvoyant observation!
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DWI. Discussion Note 2
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
GR = Gary Richmond
JA = Jon Awbrey
Re: DWI-DIS 1. http://stderr.org/pipermail/inquiry/2004-November/001855.html
In: DWI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1855
GR: You wrote that:
JA: ... induction may be a way of grading or quantifying
the degree of fidelity, likeness, or resemblance of
the abductive icon.
GR: Here I think you are approaching the truth of the matter.
With respect to your futuristic premarks, note
the nuanced (somewhere twixt shady and subtle)
sense of "prediction" at CP 2.759, copied here:
Cf: DWI 9. http://stderr.org/pipermail/inquiry/2004-November/001861.html
In: DWI. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1845
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DWI. Discussion Note 3
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
GR = Gary Richmond
JA = Jon Awbrey
Re: DWI-DIS 2. http://stderr.org/pipermail/inquiry/2004-November/001862.html
In: DWI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1855
GR: This seems an important -- though admittedly subtle -- point.
You noted, in commenting on my approval of your notion that
while hypothesis formation is entirely backward looking,
retroductive, as Peirce sometimes terms it (yet,
paradoxically constituting the only creative
moment in inquiry), that induction is
future oriented --
GR: This [view of induction] is of course, pragmaticism: future directed.
The abduction -- the hypothesis -- was formed retroductively from
experience, from the past.
GR: Your comment:
JA: With respect to your futuristic premarks, note
the nuanced (somewhere twixt shady and subtle)
sense of "prediction" at CP 2.759, copied here:
| 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.
GR: What seems especially important in CP 2.579,
at least to my way of thinking, is this:
CSP: In calling [Qualitative Inductions] "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 rest of the paragraph, that I omitted,
explains what he means by the "virtually".
GR: Yet the "truth will out" if the prediction is such that the experiment
shows it to be so. Thus, Peirce's theory of inquiry holds that while
the creative moment of hypothesis formation is yet entirely retroductive,
that at least in this quintessential form of induction, Qualitative
Induction, the future will be anticipated, if only "virtually".
There is a very important general issue that I need to mark here --->!
It is extremely crucial not to confound logical order (=>) with either
causal or temporal order. And I say this in spite of Peirce's all too
cute witticism about physical dynamics proceeding quasi-barbaraic, for
the "as if" can be a very tangled hedge indeed!
In light of this caution, we need to associate "prediction"
with "predication" and not with "prophesy". In addition, I
personally got the sense that Peirce employed "retroduction"
in this context in order to rhyme with "reproduction", all
the better to make the point that abduction in inquiry is
akin to mutation in evolution.
More about this later, but I have to run to a previous engagement ...
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DWI. Discussion Note 4
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
GR = Gary Richmond
JA = Jon Awbrey
Re: DWI-DIS 3. http://stderr.org/pipermail/inquiry/2004-November/001864.html
In: DWI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1855
GR: I'd written:
GR: Yet the "truth will out" if the prediction is such that the experiment
shows it to be so. Thus, Peirce's theory of inquiry holds that while
the creative moment of hypothesis formation is yet entirely retroductive,
that at least in this quintessential form of induction, Qualitative
Induction, the future will be anticipated, if only "virtually".
GR: And you commented:
JA: There is a very important general issue that I need to mark here --->!
It is extremely crucial not to confound logical order (=>) with either
causal or temporal order.
GR: I agree that it is exceedingly important not to confuse logical with causal
or temporal order, or for that matter any of the directions, or vectors as
I refer to them when considering them in relation to the categories. See:
http://members.door.net/arisbe/menu/library/aboutcsp/richmond/trikonicb.ppt
for a PowerPoint presentation I worked up
with Ben Udell on the theme, described here:
http://members.door.net/arisbe/menu/library/aboutcsp/richmond/trikonicdescribed.htm
I liked the storm and flash of the presentation,
but I hope you understand that "vector" is one
of the holy words where I hail from, so I'll
have to think a little more carefully about
that usage before I can tell if it fits.
GR: There are many hints throughout Peirce's work of the importance
of not conflating one with any of the others, but I have found
"The Logic of Mathematics" (Chapter 4 in the first volume of
the CP) especially instructive in distinguishing Hegelian
dialectical order, here called the order of evolution
(firstness, 1ns, followed by secondness, 2ns, followed
by thirdness, 3ns) from the order of involution, which
moves in the opposite direction (3ns, then 2ns, then
1ns).
2 much 2 fast, maybe my end-of-the-day brain will be able to catch up ...
GR: Temporal evolution in nature (or inquiry for that matter) famously
follows yet another order in Peirce with sporting, then habit-forming,
resulting in structural change (1ns -->3ns -->2ns).
GR: So you are quite right I believe in insisting upon such distinctions.
Still, this is thorny territory, and there is some overlapping and
interpenetration of these especially as one moves beyond formal
logic into, for example, the analysis of natural phenomena, etc.
You suggest as much in writing:
JA: And I say this in spite of Peirce's all too cute witticism about
physical dynamics proceeding quasi-barbaraic, for the "as if"
can be a very tangled hedge indeed!
GR: Well, despite the "tangled hedge, "I do think you
may be overstating the case a bit when you write:
JA: In light of this caution, we need to associate "prediction"
with "predication" and not with "prophesy".
No, I think that's a fair caution. The point is simply that
we test hypotheses about past events every bit as much as we
test hypotheses about present and future events -- consider
the Big Bang theory, just for starters.
GR: For example, in an extended discussion of induction,
in considering a moment of Kepler's work (see CP 2.96),
predication and prediction (the latter possibly confirmed
in future experimentation) are related in interesting ways
(which also exemplify Peirce's use of "virtual" which you
quite correctly suggested ought not be conflated with
contemporary associations). Peirce concludes 2.96
thus (note the definition of "virtual prediction"
at the bottom of this passage on Induction as
Transuasive Argument.
| A Transuasive Argument, or Induction, is an Argument which
| sets out from a hypothesis, resulting from a previous Abduction,
| and from virtual predictions, drawn by Deduction, of the results
| of possible experiments, and having performed the experiments,
| concludes that the hypothesis is true in the measure in which
| those predictions are verified, this conclusion, however, being
| held subject to probable modification to suit future experiments.
| Since the significance of the facts stated in the premisses depends
| upon their predictive character, which they could not have had if the
| conclusion had not been hypothetically entertained, they satisfy the
| definition of a Symbol of the fact stated in the conclusion. This
| argument is Transuasive, also, in respect to its alone affording
| us a reasonable assurance of an ampliation of our positive knowledge.
| By the term "virtual prediction", I mean an experiential consequence
| deduced from the hypothesis, and selected from among possible consequences
| independently of whether it is known, or believed, to be true, or not;
| so that at the time it is selected as a test of the hypothesis, we are
| either ignorant of whether it will support or refute the hypothesis, or,
| at least, do not select a test which we should not have selected if we
| had been so ignorant.
|
| C.S. Peirce, 'Collected Papers', CP 2.96
GR: So I think we are more or less in agreement up to this point.
However, I cannot go with you in your personal take on the
etymology of "retroduction". You wrote:
JA: I personally got the sense that Peirce employed "retroduction"
in this context in order to rhyme with "reproduction", all
the better to make the point that abduction in inquiry was
akin to mutation in evolution.
GR: Actually, I think your final point here concerning abduction in inquiry
being akin to mutation in evolution is most intriguing so that I hope
you'll say more about that soon. But as to the word "retroduction"
itself, where do you find Peirce even hinting at its being introduced
to rhyme with "reproduction"?
Well, I didn't call it an "etymology", even a folk or personal one,
but the resonance did have a certain ring to it in this one setting.
And the retro- in retroduction must refer primarily to logical order,
going from logical consequents (facts) to logical antecedents (cases).
Speaking of bells, it's time for dinner!
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DWI. Discussion Note 5
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GR = Gary Richmond
JA = Jon Awbrey
Re: DWI-DIS 3. http://stderr.org/pipermail/inquiry/2004-November/001864.html
In: DWI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1855
GR: Even in this passage (which supports your Darwinian interpretation of
retroduction) we read that "Retroduction and Induction face opposite ways",
retroduction to past experience, induction to the hypothesis possibly being
supported by future experimentation.
| 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.
|
| C.S. Peirce, 'Collected Papers', CP 2.755
GR: and shortly after in the same passage:
| 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.
|
| C.S. Peirce, 'Collected Papers', CP 2.755
The thing that we 'hope' moves forward is our state of knowledge,
and we act as if we had reason to think that inquiry does that,
but our "state of information" (SOI) can be about things past,
present, and prospective. Moreover, to say that "the order of
the march of suggestion in retroduction is from experience to
hypothesis" can be read to say that retroduction moves 'from'
past experience 'toward' the tentative hypothesis, and thus
faces forward in time. So I think that any attempt to align
logical order with temporal order is a dimension-reducing
move, and likely to be an overly reductive conflation.
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DWI. Discussion Note 6
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
GR = Gary Richmond
JA = Jon Awbrey
Re: DWI-DIS 5. http://stderr.org/pipermail/inquiry/2004-November/001899.html
In: DWI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1855
GR: You wrote:
JA: So I think that any attempt to align logical order with temporal order is
a dimension-reducing move, and likely to be an overly reductive conflation.
GR: Who are you arguing with? It was Peirce who said:
CSP: "Retroduction and Induction face opposite ways"
GR: I've already said that I don't support "an overly reductive conflation."
GR: What's your point?
To say that they face opposite ways is not
to say that they face opposite ways in time,
although it sometimes happens to be that way,
it's still not to say which faces which way,
that's all I'm trying to say at this time.
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DWI. Discussion Note 7
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
GR = Gary Richmond
JA = Jon Awbrey
Re: DWI-DIS 6. http://stderr.org/pipermail/inquiry/2004-November/001901.html
In: DWI-DIS. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1855
JA: To say that they face opposite ways is not
to say that they face opposite ways in time,
although it sometimes happens to be that way,
it's still not to say which faces which way,
that's all I'm trying to say at this time.
GR: "it's still not to say which faces which way" --
but I thought that that was your original point --
Peirce's point -- that abduction faces towards
experience.
CSP: The order of the march of suggestion in retroduction
is from experience to hypothesis. A great many people
who may be admirably trained . . . in the humanities,
or in law . . ., but who are certainly not well trained
in scientific reasoning, imagine that Induction should
follow the same course.
CSP: 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.
GR: Your comment that "it's still not to say which faces which way"
seems to me sophistic in the light of your previous comments
and Peirce quotations.
GR, quoting PL du N:
| Personally, I believe that, even if actual scientific discoveries
| bring us rapidly face to face with great philosophical problems,
| we shall not solve these problems by syntactical or logistical
| methods. Some of these efforts, which fascinate us by their
| ingenuity, are at bottom surprisingly conceited and childish.
|
| Pierre Lecomte du Nouy
As a general rule, one faces in the direction one is marching ---
And you can quote me on that ...
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DWI. Discussion Note 8
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DWI. Difficulties With Induction
Inquiry List
00. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1845
01. http://stderr.org/pipermail/inquiry/2004-November/001845.html
02. http://stderr.org/pipermail/inquiry/2004-November/001848.html
03. http://stderr.org/pipermail/inquiry/2004-November/001849.html
04. http://stderr.org/pipermail/inquiry/2004-November/001851.html
05. http://stderr.org/pipermail/inquiry/2004-November/001854.html
06. http://stderr.org/pipermail/inquiry/2004-November/001857.html
07. http://stderr.org/pipermail/inquiry/2004-November/001859.html
08. http://stderr.org/pipermail/inquiry/2004-November/001860.html
09. http://stderr.org/pipermail/inquiry/2004-November/001861.html
10. http://stderr.org/pipermail/inquiry/2004-November/001863.html
11. http://stderr.org/pipermail/inquiry/2004-November/001910.html
12.
NKS Forum
00. http://forum.wolframscience.com/showthread.php?threadid=604
01. http://forum.wolframscience.com/showthread.php?postid=1975#post1975
02. http://forum.wolframscience.com/showthread.php?postid=1976#post1976
03. http://forum.wolframscience.com/showthread.php?postid=1977#post1977
04. http://forum.wolframscience.com/showthread.php?postid=1978#post1978
05. http://forum.wolframscience.com/showthread.php?postid=1979#post1979
06. http://forum.wolframscience.com/showthread.php?postid=1980#post1980
07. http://forum.wolframscience.com/showthread.php?postid=1981#post1981
08. http://forum.wolframscience.com/showthread.php?postid=1983#post1983
09. http://forum.wolframscience.com/showthread.php?postid=1984#post1984
10. http://forum.wolframscience.com/showthread.php?postid=1987#post1987
11. http://forum.wolframscience.com/showthread.php?postid=1992#post1992
12.
DWI. Difficulties With Induction -- Discussion
00. http://stderr.org/pipermail/inquiry/2004-November/thread.html#1855
01. http://stderr.org/pipermail/inquiry/2004-November/001855.html
02. http://stderr.org/pipermail/inquiry/2004-November/001862.html
03. http://stderr.org/pipermail/inquiry/2004-November/001864.html
04. http://stderr.org/pipermail/inquiry/2004-November/001898.html
05. http://stderr.org/pipermail/inquiry/2004-November/001899.html
06. http://stderr.org/pipermail/inquiry/2004-November/001901.html
07. http://stderr.org/pipermail/inquiry/2004-November/001906.html
08.
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