Project : Peircean Pragmata

Anamnesis

Recent readings on the Web have brought to mind a congeries of perennial themes out of Peirce. I am prompted to collect what old notes of mine I can glean off the Internet, and — The Horror! The Horror! — maybe even plumb the verdimmerung depths of that old box of papyrus under the desk …

Peirce's Law : Tertia Datur And Non

Shawn Standefer @ Words and Other Things
- Classical Howard–Curry

Peirce's Law and the Pragmatic Maxim

Jacob Longshore conjectures a link between Peirce's Law and the Pragmatic Maxim.

Jacob Longshore @ Wordverter

Jon Awbrey freely associates to Post N°3.

Pieces of the Puzzle

For the Time Being, a Sleightly Random Recap of Notes …

Pragmatic Maxim as Closure Principle

Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object. (C.S. Peirce, CP 5.438).

Consider the following attempts at interpretation:

Your concept of \(x\!\) is your concept of the practical effects of \(x.\!\)

Not exactly. It seems a bit more like:

Your concept of \(x\!\) is your concept of your-conceived-practical-effects of \(x.\!\)

Converting to a third person point of view:

\[j\!\]'s concept of \(x\!\) is \(j\!\)'s concept of \(j\!\)'s-conceived-practical-effects of \(x.\!\)

An ordinary closure principle looks like this:

\[C(x) = C(C(x))\!\]

It is tempting to try and read the pragmatic maxim as if it had the following form, where \(C\!\) and \(E\!\) are supposed to be a 1-adic functions for "concept of" and "effects of", respectively.

1-adic functional case:

\[C(x) = C(E(x))\!\]

But it is really more like:

2-adic functional case:

\[C(y, x) = C(y, E(y, x))\!\]

where:

\[y\!\] = you.

\[C(y, x)\!\] = the concept that you have of \(x.\!\)

\[E(y, x)\!\] = the effects that you know of \(x.\!\)

      x           C(y, x)
      o------------>o 
     /|\            ^  
    / | \           =
   /  |  \          =
  /   |   \         =
e_1  e_2  e_3       =
  \   |   /         =
   \  |  /          =
    \ | /           =
     \|/            =
      o------------>o
    E(y, x)       C(y, E(y, x))

The concept that you have of \(x\!\) is the concept that you have of the effects that you know of \(x.\!\)

It is also very likely that the functional interpretations will not do the trick, and that 3-adic relations will need to be used instead.

Source. Jon Awbrey (08 Aug 2002), "Inquiry Driven Systems : Note 23", Ontology List, Peirce List.

Determination

Logic As Semiotic

Inquiry Into Information

Collection Of Source Materials (COSM)

Determination

Excerpt 1. Leibniz

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.

Excerpt 2. Prigogine

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 (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.

Excerpt 3. Peirce (CP 6.347)

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.

C.S. Peirce, Collected Papers, CP 6.347

Excerpt 4. Peirce (CP 6.332)

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.

C.S. Peirce, Collected Papers, CP 6.332

Excerpt 5. Peirce (CP 5.447)

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.

C.S. Peirce, Collected Papers, CP 5.447

Excerpt 6. Peirce (CP 5.448)

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.

C.S. Peirce, Collected Papers, CP 5.448

Excerpt 7. Peirce (CP 5.448, n. 1)

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.

C.S. Peirce, Collected Papers, CP 5.448, n. 1

Excerpt 8. Peirce (CP 5.448, n. 1)

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.

C.S. Peirce, Collected Papers;, CP 5.448, n. 1

Excerpt 9. Peirce (CP 5.448, n. 1)

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.

C.S. Peirce, Collected Papers, CP 5.448, n. 1

Excerpt 10. Peirce (CP 5.448, n. 1)

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.

C.S. Peirce, Collected Papers, CP 5.448, n. 1

Excerpt 11. Peirce (CP 2.364)

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.

C.S. Peirce, Collected Papers, CP 2.364

Excerpt 12. Shipley

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 and Allanheld, Totowa, NJ, 1967, 1985.

Excerpt 13. Peirce (CE 1, 245–246)

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.

C.S. Peirce, Chronological Edition, CE 1, 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.

Excerpt 14. Peirce (CE 1, 168–169)

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. Ἐν ἀρχῇ ἦν ὁ λόγος. 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.

C.S. Peirce, Chronological Edition, CE 1, 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.

Excerpt 15. Peirce (CE 1, 174–175)

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.

C.S. Peirce, Chronological Edition, CE 1, 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.

Excerpt 16. Peirce (CE 1, 179)

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.

C.S. Peirce, Chronological Edition, CE 1, 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.

Excerpt 17. Peirce (CE 1, 180)

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.

C.S. Peirce, Chronological Edition, CE 1, 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.

Excerpt 18. Peirce (CE 1, 183)

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.

C.S. Peirce, Chronological Edition, CE 1, 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.

Excerpt 19. Peirce (CE 1, 183–184)

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.

C.S. Peirce, Chronological Edition, CE 1, 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.

Excerpt 20. Peirce (CE 1, 246–247)

Is there any knowledge à priori? All our thought begins with experience, the mind furnishes no material for thought whatever. This is acknowledged by all the philosophers with whom we need concern ourselves at all. The mind only works over the materials furnished by sense; no dream is so strange but that all its elementary parts are reminiscences of appearance, the collocation of these alone are we capable of originating. In one sense, therefore, everything may be said to be inferred from experience; everything that we know, or think or guess or make up may be said to be inferred by some process valid or fallacious from the impressions of sense. But though everything in this loose sense is inferred from experience, yet everything does not require experience to be as it is in order to afford data for the inference. Give me the relations of any geometrical intuition you please and you give me the data for proving all the propositions of geometry. In other words, everything is not determined by experience. And this admits of proof. For suppose there may be universal and necessary judgements; as for example the moon must be made of green cheese. But there is no element of necessity in an impression of sense for necessity implies that things would be the same as they are were certain accidental circumstances different from what they are. I may here note that it is very common to misstate this point, as though the necessity here intended were a necessity of thinking. But it is not meant to say that what we feel compelled to think we are absolutely compelled to think, as this would imply; but that if we think a fact must be we cannot have observed that it must be. The principle is thus reduced to an analytical one. In the same way universality implies that the event would be the same were the things within certain limits different from what they are. Hence universal and necessary elements of experience are not determined from without. But are they, therefore, determined from within? Are they determined at all? Does not this very conception of determination imply causality and thus beg the whole question of causality at the very outset? Not at all. The determination here meant is not real determination but logical determination. A cognition à priori is one which any experience contains reason for and therefore which no experience determines but which contains elements such as the mind introduces in working up the materials of sense, or rather as they are not new materials, they are the working up.

C.S. Peirce, Chronological Edition, CE 1, 246–247

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.

Excerpt 21. Peirce (CE 1, 245–246)

The terms à priori and à posteriori in their ancient sense denote respectively reasoning from an antecedent to a consequent and from a consequent to an antecedent. Thus suppose we know that every incompetent general will meet with defeat. Then if we reason that because a given general is incompetent that he must meet with a defeat, we reason à priori; but if we reason that because a general is defeated he was a bad one, we reason à posteriori.

Kant however uses these terms in another and derived sense. He did not entirely originate their modern use, for his contemporaries were already beginning to apply them in the same way, but he fixed their meaning in the new application and made them household words in subsequent philosophy.

If one judges that a house falls down on the testimony of his eyesight then it is clear that he reasons à posteriori because he infers the fact from an effect of it on his eyes. If he judges that a house falls because he knows that the props have been removed he reasons à priori; yet not purely à priori for his premisses were obtained from experience. But if he infers it from axioms innate in the constitution of the mind, he may be said to reason purely 'à priori'. All this had been said previously to Kant. I will now state how he modified the meaning of the terms while preserving this application of them. What is known from experience must be known à posteriori, because the thought is determined from without. 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. Now, it is said that the results of experience are inferred à posteriori, for this reason that they are determined from without the mind by something not previously present to it; being so determined their determinants or // causes / reasons // are not present to the mind and of course could not be reasoned from. Hence, a thought determined from without by something not in consciousness even implicitly is inferred à posteriori.

Kant, accordingly, uses the term à posteriori as meaning what is determined from without. The term à priori he uses to mean determined from within or involved implicitly in the whole of what is present to consciousness (or in a conception which is the logical condition of what is in consciousness). The twist given to the words is so slight that their application remains almost exactly the same. If there is any change it is this. A primary belief is à priori according to Kant; for it is determined from within. But it is not inferred at all and therefore neither of the terms is applicable in their ancient sense. And yet as an explicit judgment it is inferred and inferred à priori.

C.S. Peirce, Chronological Edition, CE 1, 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.

Excerpt 22. Peirce (CE 1, 256)

Though I talk of forms as something independent of the mind, I only mean that the mind so conceives them and that that conception is valid. I thus say that all the qualities we know are determinations of the pure idea. But that we have any further knowledge of the idea or that this is to know it in itself I entirely deny.

C.S. Peirce, Chronological Edition, CE 1, 256

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.

Logic As Semiotic

Excerpt 1. Peirce (CP 2.227)

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.

C.S. Peirce, Collected Papers, CP 2.227. (Eds. Note. "From an unidentified fragment, c. 1897")

Excerpt 2. Peirce (CE 1, 217)

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.

C.S. Peirce, Chronological Edition, CE 1, 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.

Excerpt 3. Peirce (CE 1, 169–170)

Some reasons having now been given for adopting the unpsychological conception of the science, let us now seek to make this conception sufficiently distinct to serve for a definition of logic. For this purpose we must bring our logos from the abstract to the concrete, from the absolute to the dependent. There is no science of absolutes. The metaphysical logos is no more to us than the metaphysical soul or the metaphysical matter. To the absolute Idea or Logos, the dependent or relative word corresponds. The word horse, is thought of as being a word though it be unwritten, unsaid, and unthought. It is true, it must be considered as having been thought; but it need not have been thought by the same mind which regards it as being a word. I can think of a word in Feejee, though I can attach no definite articulation to it, and do not guess what it would be like. Such a word, abstract but not absolute, is no more than the genus of all symbols having the same meaning. We can also think of the higher genus which contains words of all meanings. A first approximation to a definition, then, will be that logic is the science of representations in general, whether mental or material. This definition coincides with Locke's. It is however too wide for logic does not treat of all kinds of representations. The resemblance of a portrait to its object, for example, is not logical truth. It is necessary, therefore, to divide the genus representation according to the different ways in which it may accord with its object.

The first and simplest kind of truth is the resemblance of a copy. It may be roughly stated to consist in a sameness of predicates. Leibniz would say that carried to its highest point, it would destroy itself by becoming identity. Whether that is true or not, all known resemblance has a limit. Hence, resemblance is always partial truth. On the other hand, no two things are so different as to resemble each other in no particular. Such a case is supposed in the proverb that Dreams go by contraries, — an absurd notion, since concretes have no contraries. A false copy is one which claims to resemble an object which it does not resemble. But this never fully occurs, for two reasons; in the first place, the falsehood does not lie in the copy itself but in the claim which is made for it, in the superscription for instance; in the second place, as there must be some resemblance between the copy and its object, this falsehood cannot be entire. Hence, there is no absolute truth or falsehood of copies. Now logical representations have absolute truth and falsehood as we know à posteriori from the law of excluded middle. Hence, logic does not treat of copies.

The second kind of truth, is the denotation of a sign, according to a previous convention. A child's name, for example, by a convention made at baptism, denotes that person. Signs may be plural but they cannot have genuine generality because each of the objects to which they refer must have been fixed upon by convention. It is true that we may agree that a certain sign shall denote a certain individual conception, an individual act of an individual mind, and that conception may stand for all conceptions resembling it; but in this case, the generality belongs to the conception and not to the sign. Signs, therefore, in this narrow sense are not treated of in logic, because logic deals only with general terms.

The third kind of truth or accordance of a representation with its object, is that which inheres in the very nature of the representation whether that nature be original or acquired. Such a representation I name a symbol.

C.S. Peirce, Chronological Edition, CE 1, 169–170

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.

Excerpt 4. Peirce (CE 1, 173)

How often do we think of the thing in algebra? When we use the symbol of multiplication we do not even think out the conception of multiplication, we think merely of the laws of that symbol, which coincide with the laws of the conception, and what is more to the purpose, coincide with the laws of multiplication in the object. Now, I ask, how is it that anything can be done with a symbol, without reflecting upon the conception, much less imagining the object that belongs to it? It is simply because the symbol has acquired a nature, which may be described thus, that when it is brought before the mind certain principles of its use — whether reflected on or not — by association immediately regulate the action of the mind; and these may be regarded as laws of the symbol itself which it cannot as a symbol transgress.

C.S. Peirce, Chronological Edition, CE 1, 173

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.

Excerpt 5. Peirce (CE 1, 184–185)

Finally, these principles as principles applying not to this or that symbol, form, thing, but to all equally, must be universal. And as grounds of possibility they must state what is possible. Now what is the universal principle of the possible symbolization of symbols? It is that all symbols are symbolizable. And the other principles must predicate the same thing of forms and things.

These, then, are the three principles of inference. Our next business is to demonstrate their truth. But before doing so, let me repeat that these principles do not serve to prove that the kinds of inference are valid, since their own proof, on the contrary, must rest on the assumption of that validity. Their use is only to show what the condition of that validity is. Hence, the only proof of the truth of these principles is this; to show, that if these principles be admitted as sufficient, and if the validity of the several kinds of inference be also admitted, that then the truth of these principles follows by the respective kinds of inference which each establishes.

C.S. Peirce, Chronological Edition, CE 1, 184–185

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.

Excerpt 6. Peirce (CE 1, 185–186)

To prove then, first, that all symbols are symbolizable. Every syllogism consists of three propositions with two terms each, a subject and a predicate, and three terms in all each term being used twice. It is obvious that one term must occur both as subject and predicate. Now a predicate is a symbol of its subject. Hence in all reasoning à priori a symbol must be symbolized. But as reasoning à priori is possible about a statement without reference to its predicate, all symbols must be symbolizable.

2nd To prove that all forms are symbolizable. Since this proposition relates to pure form it is sufficient to show that its consequences are true. Now the consequence will be that if a symbol of any object be given, but if this symbol does not adequately represent any form then another symbol more formal may always be substituted for it, or in other words as soon as we know what form it ought to symbolize the symbol may be so changed as to symbolize that form. But this process is a description of inference à posteriori. Thus in the example relating to light; the symbol of "giving such and such phenomena" which is altogether inadequate to express a form is replaced by "ether-waves" which is much more formal. The consequence then of the universal symbolization of forms is the inference à posteriori, and there is no truth or falsehood in the principle except what appears in the consequence. Hence, the consequence being valid, the principle may be accepted.

3rd To prove that all things may be symbolized. If we have a proposition, the subject of which is not properly a symbol of the thing it signifies; then in case everything may be symbolized, it is possible to replace this subject by another which is true of it and which does symbolize the subject. But this process is inductive inference. Thus having observed of a great variety of animals that they all eat herbs, if I substitute for this subject which is not a true symbol, the symbol "cloven-footed animals" which is true of these animals, I make an induction. Accordingly I must acknowledge that this principle leads to induction; and as it is a principle of objects, what is true of its subalterns is true of it; and since induction is always possible and valid, this principle is true.

C.S. Peirce, Chronological Edition, CE 1, 185–186

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.

Excerpt 7. Peirce (CE 1, 186)

Having discovered and demonstrated the grounds of the possibility of the three inferences, let us take a preliminary glance at the manner in which additions to these principles may make them grounds of proceedure.

The principle of inference à priori has been apodictically demonstrated; the principle of inductive inference has been shown upon sufficient evidence to be true; the principle of inference à posteriori has been shown to be one which nothing can contradict. These three degrees of modality in the principles of the three inferences show the amount of certainty which each is capable of affording. Inference à priori is as we all know the only apodictic proceedure; yet no one thinks of questioning a good induction; while inference à posteriori is proverbially uncertain. Hypotheses non fingo, said Newton; striving to place his theory on a firm inductive basis. Yet provisionally we must make hypotheses; we start with them; the baby when he lies turning his fingers before his eyes is testing a hypothesis he has already formed, as to the connection of touch and sight. Apodictic reasoning can only be applied to the manipulation of our knowledge; it never can extend it. So that it is an induction which eventually settles every question of science; and nine-tenths of the inferences we draw in any hour not of study are of this kind.

C.S. Peirce, Chronological Edition, CE 1, 186

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.

Excerpt 8. Peirce (CE 1, 256–257)

The first distinction we found it necessary to draw — the first set of conceptions we have to signalize — forms a triad:

Thing Representation Form.

Kant you remember distinguishes in all mental representations the matter and the form. The distinction here is slightly different. In the first place, I do not use the word Representation as a translation of the German Vorstellung which is the general term for any product of the cognitive power. Representation, indeed, is not a perfect translation of that term, because it seems necessarily to imply a mediate reference to its object, which Vorstellung does not. I however would limit the term neither to that which is mediate nor to that which is mental, but would use it in its broad, usual, and etymological sense for anything which is supposed to stand for another and which might express that other to a mind which truly could understand it. Thus our whole world — that which we can comprehend — is a world of representations.

No one can deny that there are representations, for every thought is one. But with things and forms scepticism, though still unfounded, is at first possible. The thing is that for which a representation might stand prescinded from all that would constitute a relation with any representation. The form is the respect in which a representation might stand for a thing, prescinded from both thing and representation. We thus see that things and forms stand very differently with us from representations. Not in being prescinded elements, for representations also are prescinded from other representations. But because we know representations absolutely, while we only know forms and things through representations. Thus scepticism is possible concerning them. But for the very reason that they are known only relatively and therefore do not belong to our world, the hypothesis of things and forms introduces nothing false. For truth and falsity only apply to an object as far as it can be known. If indeed we could know things and forms in themselves, then perhaps our representations of them might contradict this knowledge. But since all that we know of them we know through representations, if our representations be consistent they have all the truth that the case admits of.

C.S. Peirce, Chronological Edition, CE 1, 256–257

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.

Excerpt 9. Peirce (CE 1, 257–258)

We found representations to be of three kinds:

Signs Copies Symbols.

By a copy, I mean a representation whose agreement with its object depends merely upon a sameness of predicates.

By a sign, I mean a representation whose reference to its object is fixed by convention.

By a symbol, I mean one which upon being presented to the mind — without any resemblance to its object and without any reference to a previous convention — calls up a concept. I consider concepts, themselves, as a species of symbols.

A symbol is subject to three conditions. First it must represent an object, or informed and representable thing. Second it must be a manifestation of a logos, or represented and realizable form. Third it must be translatable into another language or system of symbols.

The science of the general laws of relations of symbols to logoi is general grammar. The science of the general laws of their relations to objects is logic. And the science of the general laws of their relations to other systems of symbols is general rhetoric.

C.S. Peirce, Chronological Edition, CE 1, 257–258

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.

Excerpt 10. Peirce (CE 1, 267–268)

When have then three different kinds of inference.

Deduction or inference à priori,

Induction or inference à particularis, and

Hypothesis or inference à posteriori.

It is necessary now to examine this classification critically.

And first let me specify what I claim for my invention. I do not claim that it is a natural classification, in the sense of being right while all others are wrong. I do not know that such a thing as a natural classification is possible in the nature of the case. The science which most resembles logic is mathematics. Now among mathematical forms there does not seem to be any natural classification. It is true that in the solutions of quadratic equations, there are generally two solutions from the positive and negative values of the root with an impossible gulf between them. But this classing is owing to the forms being restricted by the conditions of the problem; and I believe that all natural classes arise from some problem — something which was to be accomplished and which could be accomplished only in certain ways. Required to make a musical instrument; you must set either a plate or a string in vibration. Required to make an animal; it must be either a vertebrate, an articulate, a mollusk, or a radiate. However this may be, in Geometry we find ourselves free to make several different classifications of curves, either of which shall be equally good. In fact, in order to make any classification of them whatever we must introduce the purely arbitrary element of a system of coördinates or something of the kind which constitutes the point of view from which we regard the curves and which determines their classification completely. Now it may be said that one system of coördinates is more natural than another; and it is obvious that the conditions of binocular vision limit us in our use of our eyes to the use of particular coördinates. But this fact that one such system is more natural to us has clearly nothing to do with pure mathematics but is merely introducing a problem; given two eyes, required to form geometrical judgements, how can we do it? In the same way, I conceive that the syllogism is nothing but the system of coördinates or method of analysis which we adopt in logic. There is no reason why arguments should not be analyzed just as correctly in some other way. It is a great mistake to suppose that arguments as they are thought are often syllogisms, but even if this were the case it would have no bearing upon pure logic as a formal science. It is the principal business of the logician to analyze arguments into their elements just as it is part of the business of the geometer to analyze curves; but the one is no more bound to follow the natural process of the intellect in his analysis, than the other is bound to follow the natural process of perception.

C.S. Peirce, Chronological Edition, CE 1, 267–268

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.

Inquiry Into Information

Note 1. Comment

I continue with my consideration of Peirce's theory of information. For convenience of reference and review, I repeat above 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.

Note 2. Peirce (CE 1, 187)

In order to understand how these principles of à posteriori and inductive inference can be put into practice, we must consider by itself the substitution of one symbol for another. Symbols are alterable and comparable in three ways.

In the first place they may denote more or fewer possible differing things; in this regard they are said to have extension.

In the second place, they may imply more or less as to the quality of these things; in this respect they are said to have intension.

In the third place they may involve more or less real knowledge; in this respect they have information and distinctness.

Logical writers generally speak only of extension and intension and Kant has laid down the law that these quantities are inverse in respect of each other.

C.S. Peirce, Chronological Edition, CE 1, 187

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.

Note 3. Peirce (CE 1, 187–188)

I am going to run through the series of concrete illustrations that Peirce lays out to explain his take on the conceptions of extension, intension, and information. It is a mite long, but helps better than anything else I know to bring what Peirce is talking about down to earth. For ease of comprehension I will divide this extended paragraph into more moderate-sized chunks.

For example, take cat; now increase the extension of that greatly — cat or rabbit or dog; now apply to this extended class the additional intension feline; — feline cat or feline rabbit or feline dog is equal to cat again. This law holds good as long as the information remains constant, but when this is changed the relation is changed. Thus cats are before we know about them separable into blue cats and cats not blue of which classes cats is the most extensive and least intensive. But afterwards we find out that one of those classes cannot exist; so that cats increases its intension to equal cats not blue while cats not blue increases its extension to equal cats.

Again, to give a better case, rational animal is divisible into mortal rational animal and immortal rational animal; but upon information we find that no rational animal is immortal and this fact is symbolized in the word man. Man, therefore, has at once the extension of rational animal with the intension of mortal rational animal, and far more beside, because it involves more information than either of the previous symbols. Man is more distinct than rational animal, and more formal than mortal rational animal.

Now of two statements both of which are true, it is obvious that that contains the most truth which contains the most information. If two predicates of the same intension, therefore, are true of the same subject, the most formal one contains the most truth.

Thus, it is better to say Socrates is a man, than to say Socrates is an animal who is rational mortal risible biped &c. because the former contains all the last and in addition it forms the synthesis of the whole under a definite form.

On the other hand if the same predicate is applicable to two equivalent subjects, that one is to be preferred which is the most distinct; thus it conveys more truth to say All men are born of women, than All rational animals are born of women, because the former has at once as much extension as the latter, and a much closer reference to the things spoken of.

C.S. Peirce, Chronological Edition, CE 1, 187–188

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.

Note 4. Peirce (CE 1, 188–189)

Let us now take the two statements, S is P, Σ is P; let us suppose that Σ is much more distinct than S and that it is also more extensive. But we know that S is P. Now if Σ were not more extensive than S, Σ is P would contain more truth than S is P; being more extensive it may contain more truth and it may also introduce a falsehood. Which of these probabilities is the greatest? Σ by being more extensive becomes less intensive; it is the intension which introduces truth and the extension which introduces falsehood. If therefore Σ increases the intension of S more than its extension, Σ is to be preferred to S; otherwise not. Now this is the case of induction. Which contains most truth, neat and deer are herbivora, or cloven-footed animals are herbivora?

In the two statements, S is P, S is Π, let Π be at once more formal and more intensive than P; and suppose we only know that S is P. In this case the increase of formality gives a chance of additional truth and the increase of intension a chance of error. If the extension of Π is more increased than than its intension, then S is Π is likely to contain more truth than S is P and vice versa. This is the case of à posteriori reasoning. We have for instance to choose between:

Light gives fringes of such and such a description

and Light is ether-waves.

C.S. Peirce, Chronological Edition, CE 1, 188–189

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.

Note 5. Peirce (CE 1, 276)

Thus the process of information disturbs the relations of extension and comprehension for a moment and the class which results from the equivalence of two others has a greater intension than one and a greater extension than the other. Hence, we may conveniently alter the formula for the relations of extension and comprehension; thus, instead of saying that one is the reciprocal of the other, or:

comprehension × extension = constant,

we may say:

comprehension × extension = information.

We see then that all symbols besides their denotative and connotative objects have another; their informative object. The denotative object is the total of possible things denoted. The connotative object is the total of symbols translated or implied. The informative object is the total of forms manifested and is measured by the amount of intension the term has, over and above what is necessary for limiting its extension. For example, the denotative object of man is such collections of matter the word knows while it knows them, i.e., while they are organized. The connotative object of man is the total form which the word expresses. The informative object of man is the total fact which it embodies; or the value of the conception which is its equivalent symbol.

C.S. Peirce, Chronological Edition, CE 1, 276

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.

Note 6. Peirce (CE 1, 278–279)

The difference between connotation, denotation, and information supplies the basis for another division of terms and propositions; a division which is related to the one we have just considered in precisely the same way as the division of syllogism into 3 figures is related to the division into Deduction, Induction, and Hypothesis.

Every symbol which has connotation and denotation has also information. For by the denotative character of a symbol, I understand application to objects implied in the symbol itself. The existence therefore of objects of a certain kind is implied in every connotative denotative symbol; and this is information.

Now there are certain imperfect or false symbols produced by the combination of true symbols which have lost either their denotation or their connotation. When symbols are combined together in extension as for example in the compound term "cats and dogs", their sum possesses denotation but no connotation or at least no connotation which determines their denotation. Hence, such terms, which I prefer to call enumerative terms, have no information and it remains unknown whether there be any real kind corresponding to cats and dogs taken together. On the other hand when symbols are combined together in comprehension as for example in the compound "tailed men" the product possesses connotation but no denotation, it not being therein implied that there may be any tailed men. Such conjunctive terms have therefore no information. Thirdly there are names purporting to be of real kinds as men; and these are perfect symbols.

Enumerative terms are not truly symbols but only signs; and Conjunctive terms are copies; but these copies and signs must be considered in symbolistic because they are composed of symbols.

When an enumerative term forms the subject of a grammatical proposition, as when we say "cats and dogs have tails", there is no logical unity in the proposition at all. Logically, therefore, it is two propositions and not one. The same is the case when a conjunctive proposition forms the predicate of a sentence; for to say that "hens are feathered bipeds" is simply to predicate two unconnected marks of them.

When an enumerative term as such is the predicate of a proposition, that proposition cannot be a denotative one, for a denotative proposition is one which merely analyzes the denotation of its predicate, but the denotation of an enumerative term is analyzed in the term itself; hence if an enumerative term as such were the predicate of a proposition that proposition would be equivalent in meaning to its own predicate. On the other hand, if a conjunctive term as such is the subject of a proposition, that proposition cannot be connotative, for the connotation of a conjunctive term is already analyzed in the term itself, and a connotative proposition does no more than analyze the connotation of its subject. Thus we have

Conjunctive Simple Enumerative

propositions so related to

Denotative Informative Connotative

propositions that what is on the left hand of one line cannot be on the right hand of the other.

C.S. Peirce, Chronological Edition, CE 1, 278–279

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.

Note 7. Peirce (CE 1, 279–280)

We are now in a condition to discuss the question of the grounds of scientific inference. This problem naturally divides itself into parts:

1st To state and prove the principles upon which the possibility in general of each kind of inference depends,

2nd To state and prove the rules for making inferences in particular cases.

The first point I shall discuss in the remainder of this lecture; the second I shall scarcely be able to touch upon in these lectures.

Inference in general obviously supposes symbolization; and all symbolization is inference. For every symbol as we have seen contains information. And in the last lecture we saw that all kinds of information involve inference. Inference, then, is symbolization. They are the same notions. Now we have already analyzed the notion of a symbol, and we have found that it depends upon the possibility of representations acquiring a nature, that is to say an immediate representative power. This principle is therefore the ground of inference in general.

C.S. Peirce, Chronological Edition, CE 1, 279–280

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.

Note 8. Peirce (CE 1, 280)

But there are three distinct kinds of inference; inconvertible and different in their conception. There must, therefore, be three different principles to serve for their grounds. These three principles must also be indemonstrable; that is to say, each of them so far as it can be proved must be proved by means of that kind of inference of which it is the ground. For if the principle of either kind of inference were proved by another kind of inference, the former kind of inference would be reduced to the latter; and since the different kinds of inference are in all respects different this cannot be. You will say that it is no proof of these principles at all to support them by that which they themselves support. But I take it for granted at the outset, as I said at the beginning of my first lecture, that induction and hypothesis have their own validity. The question before us is why they are valid. The principles, therefore, of which we are in search, are not to be used to prove that the three kinds of inference are valid, but only to show how they come to be valid, and the proof of them consists in showing that they determine the validity of the three kinds of inference.

C.S. Peirce, Chronological Edition, CE 1, 280

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.

Note 9. Peirce (CE 1, 280–281)

But these three principles must have this in common that they refer to symbolization for they are principles of inference which is symbolization. As grounds of the possibility of inference they must refer to the possibility of symbolization or symbolizability. And as logical principles they must relate to the reference of symbols to objects; for logic has been defined as the science of the general conditions of the relations of symbols to objects. But as three different principles they must state three different relations of symbols to objects. Now we already found that a symbol has three different relations to objects; namely, connotation, denotation, and information, which are its relations to the object considered as a thing, a form, and an equivalent representation. Hence, it is obvious that these three principles must relate to the symbolizability of things, of forms, and of symbols.

C.S. Peirce, Chronological Edition, CE 1, 280–281

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.

Note 10. Peirce (CE 1, 281–282)

Our next business is to find out which is which. For this purpose we must consider that each principle is to be proved by the kind of inference which it supports.

The ground of deductive inference then must be established deductively; that is by reasoning from determinant to determinate, or in other words by reasoning from definition. But this kind of reasoning can only be applied to an object whose character depends upon its definition. Now of most objects it is the definition which depends upon the character; and so the definition must therefore itself rest on induction or hypothesis. But the principle of deduction must rest on nothing but deduction, and therefore it must relate to something whose character depends upon its definition. Now the only objects of which this is true are symbols; they indeed are created by their definition; while neither forms nor things are. Hence, the principle of deduction must relate to the symbolizability of symbols.

The principle of hypothetic inference must be established hypothetically, that is by reasoning from determinate to determinant. Now it is clear that this kind of reasoning is applicable only to that which is determined by what it determines; or that which is only subject to truth and falsehood so far as its determinate is, and is thus of itself pure zero. Now this is the case with nothing whatever except the pure forms; they indeed are what they are only in so far as they determine some symbol or object. Hence the principle of hypothetic inference must relate to the symbolizability of forms.

The principle of inductive inference must be established inductively, that is by reasoning from parts to whole. This kind of reasoning can apply only to those objects whose parts collectively are their whole. Now of symbols this is not true. If I write man here and dog here that does not constitute the symbol of man and dog, for symbols have to be reduced to the unity of symbolization which Kant calls the unity of apperception and unless this be indicated by some special mark they do not constitute a whole. In the same way forms have to determine the same matter before they are added; if the curtains are green and the wainscot yellow that does not make a yellow-green. But with things it is altogether different; wrench the blade and handle of a knife apart and the form of the knife has disappeared but they are the same thing — the same matter — that they were before. Hence, the principle of induction must relate to the symbolizability of things.

All these principles must as principles be universal. Hence they are as follows: —

All things, forms, symbols are symbolizable.

C.S. Peirce, Chronological Edition, CE 1, 281–282

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.

Locations Cited

DET. Determination

Ontology List — May-Aug 2001

http://suo.ieee.org/ontology/thrd63.html#02377

Arisbe List — May-Aug 2001

Inquiry List — Dec 2004

http://stderr.org/pipermail/inquiry/2004-December/thread.html#2197

LAS. Logic As Semiotic

INF. Inquiry Into Information

Ontology List — Aug 2001

http://suo.ieee.org/ontology/thrd47.html#03172

Arisbe List — Aug 2001

http://stderr.org/pipermail/arisbe/2001-August/thread.html#935

Inquiry List — Dec 2004

http://stderr.org/pipermail/inquiry/2004-December/thread.html#2229

Resources

Peirce, C.S. (13 Nov 1867), "Upon Logical Comprehension and Extension".

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See Talk:Jon Awbrey/Projects/Peircean Pragmata for discussions/comments regarding this article.
See Jon Awbrey/Projects/Peircean Pragmata/Aficionados for those who have listed Jon Awbrey/Projects/Peircean Pragmata as an interest.
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	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.

	Light gives fringes of such and such a description
and	Light is ether-waves.

1st	To state and prove the principles upon which the possibility in general of each kind of inference depends,
2nd	To state and prove the rules for making inferences in particular cases.

Project : Peircean Pragmata

Anamnesis

Peirce's Law : Tertia Datur And Non

Peirce's Law and the Pragmatic Maxim

Pieces of the Puzzle

Pragmatic Maxim as Closure Principle

Determination

Logic As Semiotic

Inquiry Into Information

Collection Of Source Materials (COSM)

Determination

Excerpt 1. Leibniz

Excerpt 2. Prigogine

Excerpt 3. Peirce (CP 6.347)

Excerpt 4. Peirce (CP 6.332)

Excerpt 5. Peirce (CP 5.447)

Excerpt 6. Peirce (CP 5.448)

Excerpt 7. Peirce (CP 5.448, n. 1)

Excerpt 8. Peirce (CP 5.448, n. 1)

Excerpt 9. Peirce (CP 5.448, n. 1)

Excerpt 10. Peirce (CP 5.448, n. 1)

Excerpt 11. Peirce (CP 2.364)

Excerpt 12. Shipley

Excerpt 13. Peirce (CE 1, 245–246)

Excerpt 14. Peirce (CE 1, 168–169)

Excerpt 15. Peirce (CE 1, 174–175)

Excerpt 16. Peirce (CE 1, 179)

Excerpt 17. Peirce (CE 1, 180)

Excerpt 18. Peirce (CE 1, 183)

Excerpt 19. Peirce (CE 1, 183–184)

Excerpt 20. Peirce (CE 1, 246–247)

Excerpt 21. Peirce (CE 1, 245–246)

Excerpt 22. Peirce (CE 1, 256)

Logic As Semiotic

Excerpt 1. Peirce (CP 2.227)

Excerpt 2. Peirce (CE 1, 217)

Excerpt 3. Peirce (CE 1, 169–170)

Excerpt 4. Peirce (CE 1, 173)

Excerpt 5. Peirce (CE 1, 184–185)

Excerpt 6. Peirce (CE 1, 185–186)

Excerpt 7. Peirce (CE 1, 186)

Excerpt 8. Peirce (CE 1, 256–257)

Excerpt 9. Peirce (CE 1, 257–258)

Excerpt 10. Peirce (CE 1, 267–268)

Inquiry Into Information

Note 1. Comment

Note 2. Peirce (CE 1, 187)

Note 3. Peirce (CE 1, 187–188)

Note 4. Peirce (CE 1, 188–189)

Note 5. Peirce (CE 1, 276)

Note 6. Peirce (CE 1, 278–279)

Note 7. Peirce (CE 1, 279–280)

Note 8. Peirce (CE 1, 280)

Note 9. Peirce (CE 1, 280–281)

Note 10. Peirce (CE 1, 281–282)

Locations Cited

DET. Determination

Ontology List — May-Aug 2001

Arisbe List — May-Aug 2001

Inquiry List — Dec 2004

LAS. Logic As Semiotic

Ontology List — Aug 2001

Arisbe List — Aug 2001

Inquiry List — Dec 2004

INF. Inquiry Into Information

Ontology List — Aug 2001

Arisbe List — Aug 2001

Inquiry List — Dec 2004

Resources

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