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<p>If a definition is to be understood as introducing the definitum, so that it means “Let so and so — the definitum — mean so and so — the definition”, then it is a proposition in the imperative mood, and consequently, not a proposition; for a proposition is equivalent to a sentence in the indicative mood.</p>
<p>If a definition is to be understood as introducing the definitum, so that it means “Let so and so — the definitum — mean so and so — the definition”, then it is a proposition in the imperative mood, and consequently, not a proposition; for a proposition is equivalent to a sentence in the indicative mood.</p>
<p>The definition is thus only a proposition if the definitum be already known to the interpreter. But in that case it clearly conveys information as to the character of this definitum, which is a matter of fact.</p>
<p>The definition is thus only a proposition if the definitum be already known to the interpreter. But in that case it clearly conveys information as to the character of this definitum, which is a matter of fact.</p>
<p align="right">C.S. Peirce, “Syllabus” (''c.'' 1902).<br>
<p align="right">C.S. Peirce, “Syllabus” (c. 1902)<br>
''Collected Papers'' (CP 2.309–331).</p>
''Collected Papers'' (CP 2.309–331)</p>
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<p>But take an “analytical”, ''i.e.'', an explicative proposition; and to begin with, take the formula “A is A”. If this be intended to state anything about real things, it is quite unintelligible. It must be understood to mean something about symbols; no doubt, that the substantive verb “is“ expresses one of those relations that everything bears to itself, like “loves whatever may be loved by”. So understood, it conveys information about a symbol. A symbol is not an individual, it is true. But any information about a symbol is information about every replica of it; and a replica is strictly an individual. What information, then, does the proposition “A is A” furnish concerning this replica?</p>
<p>But take an “analytical”, ''i.e.'', an explicative proposition; and to begin with, take the formula “A is A”. If this be intended to state anything about real things, it is quite unintelligible. It must be understood to mean something about symbols; no doubt, that the substantive verb “is“ expresses one of those relations that everything bears to itself, like “loves whatever may be loved by”. So understood, it conveys information about a symbol. A symbol is not an individual, it is true. But any information about a symbol is information about every replica of it; and a replica is strictly an individual. What information, then, does the proposition “A is A” furnish concerning this replica?</p>
<p align="right">C.S. Peirce, “Syllabus” (''c.'' 1902).<br>
<p>The information is that if the replica be modified so as to bring the same name before it and after it, then the result will be a replica of a proposition which will never be in conflict with any fact. To say that something ''never'' will be is not to state any real fact, and until some experience occurs — whether outward experience, or experience of fancies — which might be an occasion for a conflict with the proposition in question, it does not, to our knowledge, represent any actual Secondness. But as soon as such an occasion does arise, the proposition relates to the single replica that then occurs and to the single expeerience, and describes the relation between them. Similar remarks apply to every explicative proposition.</p>
''Collected Papers'' (CP 2.309–331).</p>
<p align="right">C.S. Peirce, “Syllabus” (c. 1902)<br>
''Collected Papers'' (CP 2.309–331)</p>
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<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>Logic, in its general sense, is, as I believe I have shown, only another name for ''semiotic'' (σημειωτική), 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>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 align="right">C.S. Peirce, ''Collected Papers'', CP 2.227<br>
<p align="right">C.S. Peirce, ''Collected Papers'', CP 2.227<br>
(“From an unidentified fragment, ''c.'' 1897”)
(“From an unidentified fragment, ''c.'' 1897”)</p>
</p>
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====Excerpt 2. Peirce (CE 1, 217)====
====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>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 align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 217</p>
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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>
====Excerpt 3. Peirce (CE 1, 169–170)====
====Excerpt 3. Peirce (CE 1, 169–170)====
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<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>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 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>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 align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 169–170</p>
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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>
====Excerpt 4. Peirce (CE 1, 173)====
====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>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 align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 173</p>
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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>
====Excerpt 5. Peirce (CE 1, 184–185)====
====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>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>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 align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 184–185</p>
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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>
====Excerpt 6. Peirce (CE 1, 185–186)====
====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>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>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>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 align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 185–186</p>
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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>
====Excerpt 7. Peirce (CE 1, 186)====
====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>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>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 align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 186</p>
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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>
====Excerpt 8. Peirce (CE 1, 256–257)====
====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>
<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 align="center">Thing Representation Form.</p>
<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>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>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 align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 256–257</p>
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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>
====Excerpt 9. Peirce (CE 1, 257–258)====
====Excerpt 9. Peirce (CE 1, 257–258)====
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<p>We found representations to be of three kinds:</p>
<p>We found representations to be of three kinds:</p>
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<p align="center">Signs Copies Symbols.</p>
<p>By a ''copy'', I mean a representation whose agreement with its object depends merely upon a sameness of predicates.</p>
<p>By a ''copy'', I mean a representation whose agreement with its object depends merely upon a sameness of predicates.</p>
<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>
<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>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 257–258</p>
<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 257–258</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>
<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>
====Excerpt 10. Peirce (CE 1, 267–268)====
====Excerpt 10. Peirce (CE 1, 267–268)====
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<p>When have then three different kinds of inference.</p>
<p>When have then three different kinds of inference.</p>
:<p>Deduction or inference ''à priori'',</p>
:: <p>Deduction or inference ''à priori'',</p>
:<p>Induction or inference ''à particularis'', and</p>
:: <p>Induction or inference ''à particularis'', and</p>
:<p>Hypothesis or inference ''à posteriori''.</p>
:: <p>Hypothesis or inference ''à posteriori''.</p>
<p>It is necessary now to examine this classification critically.</p>
<p>It is necessary now to examine this classification critically.</p>
<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>
<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>
<p>C.S. Peirce, ''Chronological Edition'', CE 1, 267–268</p>
<p align="right">C.S. Peirce, ''Chronological Edition'', CE 1, 267–268</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>
<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>
===Inquiry Into Information===
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[[Category:Charles Sanders Peirce]]
[[Category:Charles Sanders Peirce]]