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| <p>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.</p> | | <p>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.</p> |
| </blockquote> | | </blockquote> |
| + | |
| + | ===LAS. Logic As Semiotic=== |
| + | |
| + | ====LAS. Note 1==== |
| + | |
| + | <pre> |
| + | | 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. |
| + | | |
| + | | Charles Sanders Peirce, 'Collected Papers', CP 2.227. |
| + | | Eds. Note. "From an unidentified fragment, c. 1897". |
| + | </pre> |
| + | |
| + | ====LAS. Note 2==== |
| + | |
| + | <pre> |
| + | | 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, p. 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. |
| + | </pre> |
| + | |
| + | ====LAS. Note 3==== |
| + | |
| + | <pre> |
| + | | 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, pp. 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. |
| + | </pre> |
| + | |
| + | ====LAS. Note 4==== |
| + | |
| + | <pre> |
| + | | 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, p. 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. |
| + | </pre> |
| + | |
| + | ====LAS. Note 5==== |
| + | |
| + | <pre> |
| + | | 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, pp. 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. |
| + | </pre> |
| + | |
| + | ====LAS. Note 6==== |
| + | |
| + | <pre> |
| + | | 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, pp. 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. |
| + | </pre> |
| + | |
| + | ====LAS. Note 7==== |
| + | |
| + | <pre> |
| + | | 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, p. 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. |
| + | </pre> |
| + | |
| + | ====LAS. Note 8==== |
| + | |
| + | <pre> |
| + | | 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, pp. 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. |
| + | </pre> |
| + | |
| + | ====LAS. Note 9==== |
| + | |
| + | <pre> |
| + | | 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, pp. 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. |
| + | </pre> |
| + | |
| + | ====LAS. Note 10==== |
| + | |
| + | <pre> |
| + | | 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, pp. 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. |
| + | </pre> |
| | | |
| ===Inquiry Into Information=== | | ===Inquiry Into Information=== |
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Line 1,129: |
| | | | | |
| | Joe Ransdell | | | Joe Ransdell |
− | </pre>
| |
− |
| |
− | ===LAS. Logic As Semiotic===
| |
− |
| |
− | ====LAS. Note 1====
| |
− |
| |
− | <pre>
| |
− | | 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.
| |
− | |
| |
− | | Charles Sanders Peirce, 'Collected Papers', CP 2.227.
| |
− | | Eds. Note. "From an unidentified fragment, c. 1897".
| |
− | </pre>
| |
− |
| |
− | ====LAS. Note 2====
| |
− |
| |
− | <pre>
| |
− | | 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, p. 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.
| |
− | </pre>
| |
− |
| |
− | ====LAS. Note 3====
| |
− |
| |
− | <pre>
| |
− | | 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, pp. 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.
| |
− | </pre>
| |
− |
| |
− | ====LAS. Note 4====
| |
− |
| |
− | <pre>
| |
− | | 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, p. 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.
| |
− | </pre>
| |
− |
| |
− | ====LAS. Note 5====
| |
− |
| |
− | <pre>
| |
− | | 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, pp. 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.
| |
− | </pre>
| |
− |
| |
− | ====LAS. Note 6====
| |
− |
| |
− | <pre>
| |
− | | 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, pp. 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.
| |
− | </pre>
| |
− |
| |
− | ====LAS. Note 7====
| |
− |
| |
− | <pre>
| |
− | | 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, p. 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.
| |
− | </pre>
| |
− |
| |
− | ====LAS. Note 8====
| |
− |
| |
− | <pre>
| |
− | | 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, pp. 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.
| |
− | </pre>
| |
− |
| |
− | ====LAS. Note 9====
| |
− |
| |
− | <pre>
| |
− | | 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, pp. 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.
| |
− | </pre>
| |
− |
| |
− | ====LAS. Note 10====
| |
− |
| |
− | <pre>
| |
− | | 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, pp. 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.
| |
| </pre> | | </pre> |
| | | |