ONT Inquiry Into Information
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I continue with my consideration of Peirce's theory of information.
For convenience of reference and review, I repeat here the earlier
material on his notion of determination, which is key to unlocking
everything from the definition of a sign relation to his teachings
about the integral relationships among inference, information, and
inquiry itself.
¤~~~~~~~~~¤~~~~~~~~~¤~REVIEW~¤~~~~~~~~~¤~~~~~~~~~¤
Determination, Information, Logic As Semiotic
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Note 1
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| Now that I have proved sufficiently that everything
| comes to pass according to determinate reasons, there
| cannot be any more difficulty over these principles
| of God's foreknowledge. Although these determinations
| do not compel, they cannot but be certain, and they
| foreshadow what shall happen.
|
| It is true that God sees all at once the whole sequence
| of this universe, when he chooses it, and that thus he
| has no need of the connexion of effects and causes in
| order to foresee these effects. But since his wisdom
| causes him to choose a sequence in perfect connexion,
| he cannot but see one part of the sequence in the other.
|
| It is one of the rules of my system of general harmony,
| 'that the present is big with the future', and that he
| who sees all sees in that which is that which shall be.
|
| What is more, I have proved conclusively that God sees in
| each portion of the universe the whole universe, owing to
| the perfect connexion of things. He is infinitely more
| discerning than Pythagoras, who judged the height of
| Hercules by the size of his footprint. There must
| therefore be no doubt that effects follow their
| causes determinately, in spite of contingency
| and even of freedom, which nevertheless exist
| together with certainty or determination.
|
| Gottfried Wilhelm (Freiherr von) Leibniz,
|'Theodicy: Essays on the Goodness of God,
| the Freedom of Man, and the Origin of Evil',
| Edited with an Introduction by Austin Farrer,
| Translated by E.M. Huggard from C.J. Gerhardt's
| Edition of the 'Collected Philosophical Works',
| 1875-1890. Routledge 1951. Open Court 1985.
| Paragraph 360, page 341.
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Note 2
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| Earlier this century in 'The Open Universe: An Argument for Indeterminism',
| Karl Popper wrote, "Common sense inclines, on the one hand, to assert that
| every event is caused by some preceding events, so that every event can be
| explained or predicted. ... On the other hand, ... common sense attributes
| to mature and sane human persons ... the ability to choose freely between
| alternative possibilities of acting." This "dilemma of determinism", as
| William James called it, is closely related to the meaning of time. Is the
| future given, or is it under perpetual construction? A profound dilemma for
| all of mankind, as time is the fundamental dimension of our existence.
|
| Ilya Prigogine (In Collaboration with Isabelle Stengers),
|'The End of Certainty: Time, Chaos, and the New Laws of Nature',
| The Free Press, New York, NY, 1997, p. 1. Originally published as:
|'La Fin des Certitudes', Éditions Odile Jacob, 1996.
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Note 3
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| Of triadic Being the multitude of forms
| is so terrific that I have usually shrunk
| from the task of enumerating them; and for
| the present purpose such an enumeration would
| be worse than superfluous: it would be a great
| inconvenience. In another paper, I intend to
| give the formal definition of a sign, which I
| have worked out by arduous and long labour.
| I will omit the explanation of it here.
| Suffice it to say that a sign endeavors
| to represent, in part at least, an Object,
| which is therefore in a sense the cause, or
| determinant, of the sign even if the sign
| represents its object falsely. But to say
| that it represents its Object implies that
| it affects a mind, and so affects it as,
| in some respect, to determine in that mind
| something that is mediately due to the Object.
| That determination of which the immediate cause,
| or determinant, is the Sign, and of which the
| mediate cause is the Object may be termed the
| 'Interpretant' ...
|
| Charles Sanders Peirce, CP 6.347
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Note 4
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| That whatever action is brute, unintelligent, and unconcerned
| with the result of it is purely dyadic is either demonstrable
| or is too evident to be demonstrable. But in case that dyadic
| action is merely a member of a triadic action, then so far from
| its furnishing the least shade of presumption that all the action
| in the physical universe is dyadic, on the contrary, the entire and
| triadic action justifies a guess that there may be other and more marked
| examples in the universe of the triadic pattern. No sooner is the guess
| made than instances swarm upon us amply verifying it, and refuting the
| agnostic position; while others present new problems for our study.
| With the refutation of agnosticism, the agnostic is shown to be
| a superficial neophyte in philosophy, entitled at most to
| an occasional audience on special points, yet infinitely
| more respectable than those who seek to bolster up what
| is really true by sophistical arguments -- the traitors
| to truth that they are ...
|
| Charles Sanders Peirce, CP 6.332
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Note 5
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| Accurate writers have apparently made a distinction
| between the 'definite' and the 'determinate'. A subject
| is 'determinate' in respect to any character which inheres
| in it or is (universally and affirmatively) predicated of
| it, as well as in respect to the negative of such character,
| these being the very same respect. In all other respects it
| is 'indeterminate'. The 'definite' shall be defined presently.
|
| A sign (under which designation I place every kind of thought,
| and not alone external signs), that is in any respect objectively
| indeterminate (i.e., whose object is undetermined by the sign itself)
| is objectively 'general' in so far as it extends to the interpreter
| the privilege of carrying its determination further. 'Example':
| "Man is mortal." To the question, What man? the reply is that the
| proposition explicitly leaves it to you to apply its assertion to
| what man or men you will.
|
| A sign that is objectively indeterminate in any respect
| is objectively 'vague' in so far as it reserves further
| determination to be made in some other conceivable sign,
| or at least does not appoint the interpreter as its deputy
| in this office. 'Example': "A man whom I could mention seems
| to be a little conceited." The 'suggestion' here is that the
| man in view is the person addressed; but the utterer does not
| authorize such an interpretation or 'any' other application of
| what she says. She can still say, if she likes, that she does
| 'not' mean the person addressed. Every utterance naturally
| leaves the right of further exposition in the utterer; and
| therefore, in so far as a sign is indeterminate, it is vague,
| unless it is expressly or by a well-understood convention
| rendered general.
|
| Charles Sanders Peirce, 'Collected Papers', CP 5.447
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Note 6
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| Perhaps a more scientific pair of definitions would be
| that anything is 'general' in so far as the principle of
| the excluded middle does not apply to it and is 'vague'
| in so far as the principle of contradiction does not
| apply to it.
|
| Thus, although it is true that "Any proposition
| you please, 'once you have determined its identity',
| is either true or false"; yet 'so long as it remains
| indeterminate and so without identity', it need neither
| be true that any proposition you please is true, nor that
| any proposition you please is false.
|
| So likewise, while it is false that "A proposition 'whose
| identity I have determined' is both true and false", yet
| until it is determinate, it may be true that a proposition
| is true and that a proposition is false.
|
| Charles Sanders Peirce, 'Collected Papers', CP 5.448
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Note 7
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| These remarks require supplementation. Determination, in general, is not
| defined at all; and the attempt at defining the determination of a subject
| with respect to a character only covers (or seems only to cover) explicit
| propositional determination. The incidental remark [5.447] to the effect
| that words whose meaning should be determinate would leave "no latitude of
| interpretation" is more satisfactory, since the context makes it plain that
| there must be no such latitude either for the interpreter or for the utterer.
| The explicitness of the words would leave the utterer no room for explanation
| of his meaning. This definition has the advantage of being applicable to a
| command, to a purpose, to a medieval substantial form; in short to anything
| capable of indeterminacy. (That everything indeterminate is of the nature
| of a sign can be proved inductively by imagining and analyzing instances of
| the surdest description. Thus, the indetermination of an event which should
| happen by pure chance without cause, 'sua sponte', as the Romans mythologically
| said, 'spontanément' in French (as if what was done of one's own motion were sure
| to be irrational), does not belong to the event -- say, an explosion -- 'per se',
| or as an explosion. Neither is it by virtue of any real relation: it is by
| virtue of a relation of reason. Now what is true by virtue of a relation of
| reason is representative, that is, is of the nature of a sign. A similar
| consideration applies to the indiscriminate shots and blows of a Kentucky
| free fight.) Even a future event can only be determinate in so far as it
| is a consequent. Now the concept of a consequent is a logical concept.
| It is derived from the concept of the conclusion of an argument. But an
| argument is a sign of the truth of its conclusion; its conclusion is the
| rational 'interpretation' of the sign. This is in the spirit of the Kantian
| doctrine that metaphysical concepts are logical concepts applied somewhat
| differently from their logical application. The difference, however, is
| not really as great as Kant represents it to be, and as he was obliged to
| represent it to be, owing to his mistaking the logical and metaphysical
| correspondents in almost every case.
|
| Charles Sanders Peirce, 'Collected Papers', CP 5.448, note 1
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Note 8
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| Another advantage of this definition is that it saves us
| from the blunder of thinking that a sign is indeterminate
| simply because there is much to which it makes no reference;
| that, for example, to say, "C.S. Peirce wrote this article",
| is indeterminate because it does not say what the color of
| the ink used was, who made the ink, how old the father of
| the ink-maker when his son was born, nor what the aspect
| of the planets was when that father was born. By making
| the definition turn upon the interpretation, all that is
| cut off.
|
| Charles Sanders Peirce, 'Collected Papers', CP 5.448, note 1
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Note 9
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| At the same time, it is tolerably evident that the definition,
| as it stands, is not sufficiently explicit, and further, that
| at the present stage of our inquiry cannot be made altogether
| satisfactory. For what is the interpretation alluded to?
| To answer that convincingly would be either to establish
| or to refute the doctrine of pragmaticism.
|
| Still some explanations may be made. Every sign has a single object,
| though this single object may be a single set or a single continuum
| of objects. No general description can identify an object. But the
| common sense of the interpreter of the sign will assure him that the
| object must be one of a limited collection of objects. [Long example].
|
| [And so] the latitude of interpretation which constitutes the
| indeterminacy of a sign must be understood as a latitude which
| might affect the achievement of a purpose. For two signs whose
| meanings are for all possible purposes equivalent are absolutely
| equivalent. This, to be sure, is rank pragmaticism; for a purpose
| is an affection of action.
|
| Charles Sanders Peirce, 'Collected Papers', CP 5.448, note 1
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Note 10
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| The October remarks [i.e. those in the above paper] made the
| proper distinction between the two kinds of indeterminacy, viz.:
| indefiniteness and generality, of which the former consists in
| the sign's not sufficiently expressing itself to allow of an
| indubitable determinate interpretation, while the [latter]
| turns over to the interpreter the right to complete the
| determination as he please.
|
| It seems a strange thing, when one comes to ponder over it, that a sign
| should leave its interpreter to supply a part of its meaning; but the
| explanation of the phenomenon lies in the fact that the entire universe --
| not merely the universe of existents, but all that wider universe,
| embracing the universe of existents as a part, the universe which
| we are all accustomed to refer to as "the truth" -- that all this
| universe is perfused with signs, if it is not composed exclusively
| of signs. Let us note this in passing as having a bearing upon the
| question of pragmaticism.
|
| The October remarks, with a view to brevity, omitted to mention that
| both indefiniteness and generality might primarily affect either the
| logical breadth or the logical depth of the sign to which it belongs.
| It now becomes pertinent to notice this. When we speak of the depth,
| or signification, of a sign we are resorting to hypostatic abstraction,
| that process whereby we regard a thought as a thing, make an interpretant
| sign the object of a sign. It has been a butt of ridicule since Molière's
| dying week, and the depth of a writer on philosophy can conveniently be
| sounded by his disposition to make fun of the basis of voluntary inhibition,
| which is the chief characteristic of mankind. For cautious thinkers will
| not be in haste to deride a kind of thinking that is evidently founded
| upon observation -- namely, upon observation of a sign. At any rate,
| whenever we speak of a predicate we are representing a thought as
| a thing, as a 'substantia', since the concepts of 'substance' and
| 'subject' are one, its concomitants only being different in the two
| cases. It is needful to remark this in the present connexion, because,
| were it not for hypostatic abstraction, there could be no generality of
| a predicate, since a sign which should make its interpreter its deputy to
| determine its signification at his pleasure would not signify anything,
| unless 'nothing' be its significate.
|
| Charles Sanders Peirce, 'Collected Papers', CP 5.448, note 1
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Note 11
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| Concepts, or terms, are, in logic, conceived to have
| 'subjective parts', being the narrower terms into which
| they are divisible, and 'definitive parts', which are the
| higher terms of which their definitions or descriptions are
| composed: these relationships constitute "quantity".
|
| This double way of regarding a class-term as a whole of parts
| is remarked by Aristotle in several places (e.g., 'Metaphysics',
| D. xxv. 1023 b22). It was familiar to logicians of every age.
| ... and it really seems to have been Kant who made these ideas
| pervade logic and who first expressly called them quantities.
| But the idea was old. Archbishop Thomson, W.D. Wilson, and
| C.S. Peirce endeavor to make out a third quantity of terms.
| The last calls his third quantity "information", and defines
| it as the "sum of synthetical propositions in which the symbol
| is subject or predicate", antecedent or consequent. The word
| "symbol" is here employed because this logician regards the
| quantities as belonging to propositions and to arguments,
| as well as to terms.
|
| A distinction of 'extensive' and 'comprehensive distinctness' is
| due to Scotus ('Opus Oxon.', I. ii. 3): namely, the usual effect
| upon a term of an increase of information will be either to increase
| its breadth without without diminishing its depth, or to increase its
| depth without diminishing its breadth. But the effect may be to show
| that the subjects to which the term was already known to be applicable
| include the entire breadth of another another term which had not been
| known to be so included. In that case, the first term has gained in
| 'extensive distinctness'. Or the effect may be to teach that the
| marks already known to be predicable of the term include the
| entire depth of another term not previously known to be so
| included, thus increasing the 'comprehensive distinctness'
| of the former term.
|
| The passage of thought from a broader to a narrower concept
| without change of information, and consequently with increase
| of depth, is called 'descent'; the reverse passage, 'ascent'.
|
| For various purposes, we often imagine our information to be less than
| it is. When this has the effect of diminishing the breadth of a term
| without increasing its depth, the change is called 'restriction';
| just as when, by an increase of real information, a term gains
| breadth without losing depth, it is said to gain extension.
| This is, for example, a common effect of 'induction'.
| In such case, the effect is called generalization.
|
| A decrease of supposed information may have the effect
| of diminishing the depth of a term without increasing its
| information. This is often called 'abstraction'; but it is
| far better to call it 'prescission'; for the word 'abstraction'
| is wanted as the designation of an even far more important procedure,
| whereby a transitive element of thought is made substantive, as in the
| grammatical change of an adjective into an abstract noun. This may be
| called the principal engine of mathematical thought.
|
| When an increase of real information has the effect of increasing the
| depth of a term without diminishing the breadth, the proper word for the
| process is 'amplification'. In ordinary language, we are inaccurately said
| to 'specify', instead of to 'amplify', when we add to information in this way.
| The logical operation of forming a hypothesis often has this effect, which may,
| in such case, be called 'supposition'. Almost any increase of depth may be called
| 'determination'.
|
| Charles Sanders Peirce, 'Collected Papers', CP 2.364
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Note 12
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| Determine.
|
| The 'termination' is an ending, and a 'term' is
| a period (that comes to an end). 'Terminal' was
| first (and still may be) an adjective; The Latin
| noun 'terminus' has come directly into English:
| Latin 'terminare, terminat-', to end; 'terminus',
| boundary. From the limit itself, as in 'term' of
| office or imprisonment, 'term' grew to mean the
| limiting conditions (the 'terms' of an agreement);
| hence, the 'defining' (Latin 'finis', end; compare
| 'finance') of the idea, as in a 'term' of reproach;
| 'terminology'. To 'determine' is to set down limits
| or bounds to something, as when you 'determine' to
| perform a task, or as 'determinism' pictures limits
| set to man's freedom. 'Predetermined' follows this
| sense; but 'extermination' comes later. Otherwise,
| existence would be 'interminable'.
|
| Joseph T. Shipley, 'Dictionary of Word Origins',
| Rowman & Allanheld, Totowa, NJ, 1967, 1985.
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Note 13
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| To determine means to make a circumstance different from what
| it might have been otherwise. For example, a drop of rain
| falling on a stone determines it to be wet, provided the
| stone may have been dry before. But if the fact of
| a whole shower half an hour previous is given,
| then one drop does not determine the stone to
| be wet; for it would be wet, at any rate.
|
| CSP, CE 1, pages 245-246.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
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Note 14
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| Taking it for granted, then, that the inner and outer worlds are
| superposed throughout, without possibility of separation, let us
| now proceed to another point. There is a third world, besides the
| inner and the outer; and all three are coëxtensive and contain every
| experience. Suppose that we have an experience. That experience has
| three determinations -- three different references to a substratum or
| substrata, lying behind it and determining it. In the first place,
| it is a determination of an object external to ourselves -- we feel
| that it is so because it is extended in space. Thereby it is in the
| external world. In the second place, it is a determination of our own
| soul, it is 'our' experience; we feel that it is so because it lasts in
| time. Were it a flash of sensation, there for less than an instant, and
| then utterly gone from memory, we should not have time to think it ours.
| But while it lasts, and we reflect upon it, it enters into the internal
| world. We have now considered that experience as a determination of the
| modifying object and of the modified soul; now, I say, it may be and is
| naturally regarded as also a determination of an idea of the Universal
| mind; a preëxistent, archetypal Idea. Arithmetic, the law of number,
| 'was' before anything to be numbered or any mind to number had been
| created. It 'was' though it did not 'exist'. It was not 'a fact'
| nor a thought, but it was an unuttered word. 'En arche en o logos'.
| We feel an experience to be a determination of such an archetypal
| Logos, by virtue of its // 'depth of tone' / logical intension //,
| and thereby it is in the 'logical world'.
|
| Note the great difference between this view and Hegel's.
| Hegel says, logic is the science of the pure idea. I should
| describe it as the science of the laws of experience in virtue
| of its being a determination of the idea, or in other words as
| the formal science of the logical world.
|
| In this point of view, efforts to ascertain precisely how the
| intellect works in thinking, -- that is to say investigation
| of internal characterictics -- is no more to the purpose which
| logical writers as such, however vaguely have in view, than
| would be the investigation of external characteristics.
|
| CSP, CE 1, pages 168-169.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
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Note 15
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| But not to follow this subject too far, we have
| now established three species of representations:
| 'copies', 'signs', and 'symbols'; of the last of
| which only logic treats. A second approximation to
| a definition of it then will be, the science of symbols
| in general and as such. But this definition is still
| too broad; this might, indeed, form the definition of
| a certain science which would be a branch of Semiotic
| or the general science of representations which might
| be called Symbolistic, and of this logic would be
| a species. But logic only considers symbols
| from a particular point of view.
|
| A symbol in general and as such has three relations.
| The first is its relation to the pure Idea or Logos
| and this (from the analogy of the grammatical terms
| for the pronouns I, It, Thou) I call its relation
| of the first person, since it is its relation to
| its own essence. The second is its relation to
| the Consciousness as being thinkable, or to any
| language as being translatable, which I call its
| relation to the second person, since it refers to
| its power of appealing to a mind. The third is its
| relation to its object, which I call its relation to
| the third person or It. Every symbol is subject to
| three distinct systems of formal law as conditions
| of its taking up these three relations. If it
| violates either one of these three codes, the
| condition of its having either of the three
| relations, it ceases to be a symbol and makes
| 'nonsense'. Nonsense is that which has a certain
| resemblance to a symbol without being a symbol. But
| since it simulates the symbolic character it is usually
| only one of the three codes which it violates; at any rate,
| flagrantly. Hence there should be at least three different kinds
| of nonsense. And accordingly we remark that that we call nonsense
| meaningless, absurd, or quibbling, in different cases. If a symbol
| violates the conditions of its being a determination of the pure
| Idea or logos, it may be so nearly a determination thereof as
| to be perfectly intelligible. If for instance instead
| of 'I am' one should say 'I is'.
| 'I is' is in itself meaningless,
| it violates the conditions of its
| relation to the form it is meant
| to embody. Thus we see that the
| conditions of the relation of the
| first person are the laws of grammar.
|
| I will now take another example. I know my opinion is false, still I hold it.
| This is grammatical, but the difficulty is that it violates the conditions
| of its having an object. Observe that this is precisely the difficulty.
| It not only cannot be a determination of this or that object, but it
| cannot be a determination of any object, whatever. This is the
| whole difficulty. I say that, I receive contradictories into
| one opinion or symbolical representation; now this implies
| that it is a symbol of nothing. Here is another example:
| This very proposition is false. This is a proposition to
| which the law of excluded middle namely that every symbol
| must be false or true, does not apply. For if it is false it
| is thereby true. And if not false it is thereby not true. Now
| why does not this law apply to this proposition. Simply because it
| does itself state that it has no object. It talks of itself and only
| of itself and has no external relation whatever. These examples show
| that logical laws only hold good, as conditions of a symbol's having
| an object. The fact that it has often been called the science of
| truth confirms this view.
|
| I define logic therefore as the science of the conditions
| which enable symbols in general to refer to objects.
|
| At the same time 'symbolistic' in general gives a trivium consisting of
| Universal Grammar, Logic, and Universal Rhetoric, using this last term to
| signify the science of the formal conditions of intelligibility of symbols.
|
| CSP, CE 1, pages 174-175.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
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Note 16
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| The consideration of this imperfect datum leads us to make
| a fundamental observation; namely, that the problem how we
| can make an induction is one and the same with the problem how
| we can make any general statement, with reason; for there is
| no way left in which such a statement can originate except from
| induction or pure fiction. Hereby, we strike down at once all
| attempts at solving the problem as involve the supposition of
| a major premiss as a datum. Such explanations merely show
| that we can arrive at one general statement by deduction
| from another, while they leave the real question,
| untouched. The peculiar merit of Aristotle's
| theory is that after the objectionable portion
| of it is swept away and after it has thereby been
| left utterly powerless to account for any certainty
| or even probability in the inference from induction,
| we still retain these 'forms' which show what the
| 'actual process' is.
|
| And what is this process? We have in the apodictic conclusion,
| some most extraordinary observation, as for example that a great
| number of animals -- namely neat and deer, feed only upon vegetables.
| This proposition, be it remarked, need not have had any generality; if
| the animals observed instead of being all 'neat' had been so very various
| that we knew not what to say of them except that they were 'herbivora' and
| 'cloven-footed', the effect would have been to render the argument simply
| irresistable. In addition to this datum, we have another; namely that
| these same animals are all cloven-footed. Now it would not be so very
| strange that all cloven-footed animals should be herbivora; animals
| of a particular structure very likely may use a particular food.
| But if this be indeed so, then all the marvel of the conclusion
| is explained away. So in order to avoid a marvel which must in
| some form be accepted, we are led to believe what is easy to
| believe though it is entirely uncertain.
|
| CSP, CE 1, page 179.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
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Note 17
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| There is a large class of reasonings which are neither deductive nor inductive.
| I mean the inference of a cause from its effect or reasoning to a physical hypothesis.
| I call this reasoning 'à posteriori'. If I reason that certain conduct is wise because
| it has a character which belongs 'only' to wise things, I reason 'à priori'. If I think
| it is wise because it once turned out to be wise, that is if I infer that it is wise on
| this occasion because it was wise on that occasion, I reason inductively. But if
| I think it is wise because a wise man does it, I then make the pure hypothesis
| that he does it because he is wise, and I reason 'à posteriori'. The form
| this reasoning assumes, is that of an inference of a minor premiss in
| any of the figures. The following is an example.
|
| Light gives certain fringes. | Ether waves give certain fringes.
| Ether waves gives these fringes. | Light is ether waves.
| .: Light is ether waves. | .: Light gives these fringes.
|
| CSP, CE 1, page 180.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
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Note 18
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| We come now to the question, what is the 'rationale' of these three kinds
| of reasoning. And first let us understand precisely what we intend by this.
| It is clear then that it is none of our business to inquire in what manner we
| think when we reason, for we have already seen that logic is wholly separate
| from psychology. What we seek is an explicit statement of the logical ground
| of these different kinds of inference. This logical ground will have two parts,
| 1st the ground of possibility and 2nd the ground of proceedure. The ground of
| possibility is the special property of symbols upon which every inference of
| a certain kind rests. The ground of proceedure is the property of symbols
| which makes a certain inference possible from certain premisses. The
| ground of possibility must be both discovered and demonstrated, fully.
| The ground of proceedure must be exhibited in outline, but it is not
| requisite to fill up all the details of this subject, especially
| as that would lead us too far into the technicalities of logic.
|
| As the three kinds of reasoning are entirely distinct, each must have
| a different ground of possibility; and the principle of each kind must
| be proved by that same kind of inference for it would be absurd to attempt
| to rest it on a weaker kind of inference and to rest it on one as strong as
| itself would be simply to reduce it to that other kind of reasoning. Moreover,
| these principles must be logical principles because we do not seek any other
| ground now, than a logical ground. As logical principles, they will not
| relate to the symbol in itself or in its relation to equivalent symbols
| but wholly in its relation to what it symbolizes. In other words
| it will relate to the symbolization of objects.
|
| CSP, CE 1, page 183.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
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Note 19
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| Now all symbolization is of three objects, at once; the first is a possible thing,
| the second is a possible form, the third is a possible symbol. It will be objected
| that the two latter are not properly objects. We have hitherto regarded the symbol
| as 'standing for' the thing, as a concrete determination of its form, and addressing
| a symbol; and it is true that it is only by referring to a possible thing that a
| symbol has an objective relation, it is only by bearing in it a form that it has
| any subjective relation, and it is only by equaling another symbol that it has any
| tuistical relation. But this objective relation once given to a symbol is at once
| applicable to all to which it necessarily refers; and this is shown by the fact
| of our regarding every symbol as 'connotative' as well as 'denotative', and by our
| regarding one word as standing for another whenever we endeavor to clear up a little
| obscurity of meaning. And the reason that this is so is that the possible symbol and
| the possible form to which a symbol is related each relate also to that thing which
| is its immediate object. Things, forms, and symbols, therefore, are symbolized in
| every symbolization. And this being so, it is natural to suppose that our three
| principles of inference which we know already refer to some three objects of
| symbolization, refer to these.
|
| That such really is the case admits of proof. For the principle of inference 'à priori'
| must be established 'à priori'; that is by reasoning analytically from determinant to
| determinate, in other words from definition. But this can only be applied to an object
| whose characteristics depend upon its definition. Now of most things the definition
| depends upon the character, the definition of a symbol alone determines its character.
| Hence the principle of inference 'à priori' must relate to symbols. The principle of
| inference 'à posteriori' must be established 'à posteriori', that is by reasoning from
| determinate to determinant. This is only applicable to that which is determined by what
| it determines; in other words, to that which is only subject to the truth and falsehood
| which affects its determinant and which in itself is mere 'zero'. But this is only true
| of pure forms. Hence the principle of inference 'à posteriori' must relate to pure form.
| The principle of inductive inference must be established inductively; that is by reasoning
| from parts to whole. This is only applicable to that whose whole is given in the sum of the
| parts; and this is only the case with things. Hence the principle of inductive inference
| must relate to things.
|
| CSP, CE 1, pages 183-184.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
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Logic As Semiotic
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Note 1
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| Logic, in its general sense, is, as I believe I have shown, only another name for
|'semiotic' ([Greek: semeiotike]), the quasi-necessary, or formal, doctrine of signs.
| By describing the doctrine as "quasi-necessary", or formal, I mean that we observe the
| characters of such signs as we know, and from such an observation, by a process which
| I will not object to naming Abstraction, we are led to statements, eminently fallible,
| and therefore in one sense by no means necessary, as to what 'must be' the characters
| of all signs used by a "scientific" intelligence, that is to say, by an intelligence
| capable of learning by experience. As to that process of abstraction, it is itself
| a sort of observation. The faculty which I call abstractive observation is one which
| ordinary people perfectly recognize, but for which the theories of philosophers sometimes
| hardly leave room. It is a familiar experience to every human being to wish for something
| quite beyond his present means, and to follow that wish by the question, "Should I wish for
| that thing just the same, if I had ample means to gratify it?" To answer that question, he
| searches his heart, and in doing so makes what I term an abstractive observation. He makes
| in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what
| modifications the hypothetical state of things would require to be made in that picture, and
| then examines it, that is, 'observes' what he has imagined, to see whether the same ardent
| desire is there to be discerned. By such a process, which is at bottom very much like
| mathematical reasoning, we can reach conclusions as to what 'would be' true of signs
| in all cases, so long as the intelligence using them was scientific. (CP 2.227).
|
| Charles Sanders Peirce, 'Collected Papers', CP 2.227,
| Editors' Note: From an unidentified fragment, c. 1897.
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Note 2
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| Logic is an analysis of forms not a study of the mind.
| It tells 'why' an inference follows not 'how' it arises
| in the mind. It is the business therefore of the logician
| to break up complicated inferences from numerous premisses
| into the simplest possible parts and not to leave them
| as they are.
|
| CSP, CE 1, page 217.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
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Determination
http://suo.ieee.org/ontology/msg02377.html
http://suo.ieee.org/ontology/msg02378.html
http://suo.ieee.org/ontology/msg02379.html
http://suo.ieee.org/ontology/msg02380.html
http://suo.ieee.org/ontology/msg02384.html
http://suo.ieee.org/ontology/msg02387.html
http://suo.ieee.org/ontology/msg02388.html
http://suo.ieee.org/ontology/msg02389.html
http://suo.ieee.org/ontology/msg02390.html
http://suo.ieee.org/ontology/msg02391.html
http://suo.ieee.org/ontology/msg02395.html
http://suo.ieee.org/ontology/msg02407.html
http://suo.ieee.org/ontology/msg02550.html
http://suo.ieee.org/ontology/msg02552.html
http://suo.ieee.org/ontology/msg02556.html
http://suo.ieee.org/ontology/msg02594.html
http://suo.ieee.org/ontology/msg02651.html
http://suo.ieee.org/ontology/msg02673.html
http://suo.ieee.org/ontology/msg02706.html
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Inference, Information, Inquiry
http://suo.ieee.org/ontology/msg03006.html
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Logic As Semiotic
http://suo.ieee.org/ontology/msg03070.html
http://suo.ieee.org/ontology/msg03171.html
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