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===LAS. Logic As Semiotic===
===Logic As Semiotic===
====Excerpt 1. Peirce (CP 2.227)====
<blockquote>
<p>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.</p>
<p>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.</p>
<p>C.S. Peirce, ''Collected Papers'', CP 2.227. (Eds. Note. "From an unidentified fragment, ''c.'' 1897")</p>
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====Excerpt 2. Peirce (CE 1, 217)====
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<p>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.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 217</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>
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====Excerpt 3. Peirce (CE 1, 169–170)====
<blockquote>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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''.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 169–170</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>
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====Excerpt 4. Peirce (CE 1, 173)====
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<p>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.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 173</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>
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====Excerpt 5. Peirce (CE 1, 184–185)====
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<p>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.</p>
<p>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.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 184–185</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>
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====Excerpt 6. Peirce (CE 1, 185–186)====
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<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 185–186</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>
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====Excerpt 7. Peirce (CE 1, 186)====
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<p>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.</p>
<p>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.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 186</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>
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====Excerpt 8. Peirce (CE 1, 256–257)====
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<p>The first distinction we found it necessary to draw — the first set of conceptions we have to signalize — forms a triad:</p>
<center>
<p>Thing Representation Form.</p>
</center>
<p>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.</p>
<p>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.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 256–257</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>
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====Excerpt 9. Peirce (CE 1, 257–258)====
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<p>We found representations to be of three kinds:</p>
<pre>
<center>
<p>Signs Copies Symbols.</p>
</center>
</pre>
<p>By a ''copy'', I mean a representation whose agreement with its object depends merely upon a sameness of predicates.</p>
<pre>
<p>By a ''sign'', I mean a representation whose reference to its object is fixed by convention.</p>
</pre>
<p>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.</p>
<pre>
<p>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.</p>
</pre>
<p>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.</p>
<pre>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 257–258</p>
</pre>
<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>
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====Excerpt 10. Peirce (CE 1, 267–268)====
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<p>When have then three different kinds of inference.</p>
<pre>
:<p>Deduction or inference ''à priori'',</p>
</pre>
:<p>Induction or inference ''à particularis'', and</p>
<pre>
:<p>Hypothesis or inference ''à posteriori''.</p>
</pre>
<p>It is necessary now to examine this classification critically.</p>
<pre>
<p>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.</p>
</pre>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 267–268</p>
<pre>
<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>
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</pre>
===Inquiry Into Information===
===Inquiry Into Information===
====Note 2. Peirce (CE 1, 187)====
====Note 2. Peirce (CE 1, 187)====
<pre>
<blockquote>
<p>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.</p>
</pre>
<p>In the first place they may denote more or fewer possible differing things; in this regard they are said to have ''extension''.</p>
<pre>
<p>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''.</p>
<p>In the third place they may involve more or less real knowledge; in this respect they have ''information'' and ''distinctness''.</p>
</pre>
<p>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.</p>
<pre>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 187</p>
</pre>
<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>
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====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.
<pre>
<blockquote>
<p>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''.</p>
</pre>
<p>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''.</p>
<pre>
<p>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.</p>
</pre>
<p>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''.</p>
<pre>
<p>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.</p>
</pre>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 187–188</p>
<pre>
<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>
</pre>
====Note 10.====
====Note 4. Peirce (CE 1, 188–189)====
<pre>
<blockquote>
<p>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?</p>
<p>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:</p>
:{| cellpadding="4"
| || Light gives fringes of such and such a description
|-
| and || Light is ether-waves.
|}
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 188–189</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>
====Note 5. Peirce (CE 1, 276)====
<blockquote>
<p>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:</p>
<center>
<p>comprehension × extension = constant,</p>
</center>
<p>we may say:</p>
<center>
|
<p>comprehension × extension = information.</p>
| The principle of inductive inference must be established inductively,
</center>
| that is by reasoning from parts to whole. This kind of reasoning can
| apply only to those objects whose parts collectively are their whole.
<p>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.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 276</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>
====Note 6. Peirce (CE 1, 278–279)====
<blockquote>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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</p>
<center>
<p>Conjunctive Simple Enumerative</p>
</pre>
</center>
<p>propositions so related to</p>
<center>
<p>Denotative Informative Connotative</p>
</center>
<p>propositions that what is on the left hand of one line cannot be on the right hand of the other.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 278–279</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>
====Note 7. Peirce (CE 1, 279–280)====
<blockquote>
<p>We are now in a condition to discuss the question of the grounds of scientific inference. This problem naturally divides itself into parts:</p>
:{| cellpadding="4"
| valign="top" | 1st
| To state and prove the principles upon which the possibility in general of each kind of inference depends,
|-
| valign="top" | 2nd
| To state and prove the rules for making inferences in particular cases.
|}
<p>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.</p>
<p>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.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 279–280</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>
====Note 8. Peirce (CE 1, 280)====
<blockquote>
<p>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.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 280</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>
====Note 9. Peirce (CE 1, 280–281)====
<blockquote>
<p>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.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 280–281</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>
====Note 10. Peirce (CE 1, 281–282)====
<blockquote>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>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.</p>
<p>All these principles must as principles be universal. Hence they are as follows: —</p>
<p>All things, forms, symbols are symbolizable.</p>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 281–282</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>
==Locations Cited==
==Locations Cited==
# http://suo.ieee.org/ontology/msg03200.html
# http://suo.ieee.org/ontology/msg03200.html
# http://suo.ieee.org/ontology/msg03203.html
# http://suo.ieee.org/ontology/msg03203.html
====Arisbe List — Aug 2001====
====Arisbe List — Aug 2001====
# http://stderr.org/pipermail/inquiry/2004-December/002238.html
# http://stderr.org/pipermail/inquiry/2004-December/002238.html
# http://stderr.org/pipermail/inquiry/2004-December/002239.html
# http://stderr.org/pipermail/inquiry/2004-December/002239.html
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[[Category:Charles Sanders Peirce]]