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Directory:Jon Awbrey/EXCERPTS (view source)
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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>
====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>
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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>
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[[Category:Charles Sanders Peirce]]
[[Category:Charles Sanders Peirce]]