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Directory:Jon Awbrey/Papers/Information = Comprehension × Extension (view source)
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<p>We are all, then, sufficiently familiar with the fact that many words have much implication; but I think we need to reflect upon the circumstance that every word implies some proposition or, what is the same thing, every word, concept, symbol has an equivalent term — or one which has become identified with it, — in short, has an ''interpretant''.</p>
<p>We are all, then, sufficiently familiar with the fact that many words have much implication; but I think we need to reflect upon the circumstance that every word implies some proposition or, what is the same thing, every word, concept, symbol has an equivalent term — or one which has become identified with it, — in short, has an ''interpretant''.</p>
<p>Consider, what a word or symbol is; it is a sort of representation. Now a representation is something which stands for something. I will not undertake to analyze, this evening, this conception of ''standing for'' something — but, it is sufficiently plain that it involves the standing ''to'' something ''for'' something. A thing cannot stand for something without standing ''to'' something ''for'' that something. Now, what is this that a word stands ''to''? Is it a person? We usually say that the word ''homme'' stands to a Frenchman for ''man''. It would be a little more precise to say that it stands ''to'' the Frenchman's mind — to his memory. It is still more accurate to say that it addresses a particular remembrance or image in that memory. And what ''image'', what remembrance? Plainly, the one which is the mental equivalent of the word ''homme'' — in short, its interpretant. Whatever a word addresses then or ''stands to'', is its interpretant or identified symbol. Conversely, every interpretant is addressed by the word; for were it not so, did it not as it were overhear what the words says, how could it interpret what it says.</p>
<p>Consider, what a word or symbol is; it is a sort of representation. Now a representation is something which stands for something. I will not undertake to analyze, this evening, this conception of ''standing for'' something — but, it is sufficiently plain that it involves the standing ''to'' something ''for'' something. A thing cannot stand for something without standing ''to'' something ''for'' that something. Now, what is this that a word stands ''to''? Is it a person? We usually say that the word ''homme'' stands to a Frenchman for ''man''. It would be a little more precise to say that it stands ''to'' the Frenchman's mind — to his memory. It is still more accurate to say that it addresses a particular remembrance or image in that memory. And what ''image'', what remembrance? Plainly, the one which is the mental equivalent of the word ''homme'' — in short, its interpretant. Whatever a word addresses then or ''stands to'', is its interpretant or identified symbol. Conversely, every interpretant is addressed by the word; for were it not so, did it not as it were overhear what the words says, how could it interpret what it says.</p>
<p>There are doubtless some who cannot understand this metaphorical argument. I wish to show that the relation of a word to that which it addresses is the same as its relation to its equivalent or identified terms. For that purpose, I first show that whatever a word addresses is an equivalent term, — its mental equivalent. I next show that, since the intelligent reception of a term is the being addressed by that term, and since the explication of a term's implication is the intelligent reception of that term, that the interpretant or equivalent of a term which as we have already seen explicates the implication of a term is addressed by the term.</p>
<p>There are doubtless some who cannot understand this metaphorical argument. I wish to show that the relation of a word to that which it addresses is the same as its relation to its equivalent or identified terms. For that purpose, I first show that whatever a word addresses is an equivalent term, — its mental equivalent. I next show that, since the intelligent reception of a term is the being addressed by that term, and since the explication of a term's implication is the intelligent reception of that term, that the interpretant or equivalent of a term which as we have already seen explicates the implication of a term is addressed by the term.</p>
<p>The interpretant of a term, then, and that which it stands to are identical. Hence, since it is of the very essence of a symbol that it should stand ''to'' something, every symbol — every word and every ''conception'' — must have an interpretant — or what is the same thing, must have information or implication.</p>
<p>The interpretant of a term, then, and that which it stands to are identical. Hence, since it is of the very essence of a symbol that it should stand ''to'' something, every symbol — every word and every ''conception'' — must have an interpretant — or what is the same thing, must have information or implication.</p>
<p>Let us now return to the information. The information of a term is the measure of its superfluous comprehension. That is to say that the proper office of the comprehension is to determine the extension of the term. For instance, you and I are men because we possess those attributes — having two legs, being rational, &c. — which make up the comprehension of ''man''. Every addition to the comprehension of a term lessens its extension up to a certain point, after that further additions increase the information instead. (Peirce 1866, Lowell Lecture 7, CE 1, 466–467).</p>
<p>Let us now return to the information. The information of a term is the measure of its superfluous comprehension. That is to say that the proper office of the comprehension is to determine the extension of the term. For instance, you and I are men because we possess those attributes — having two legs, being rational, &c. — which make up the comprehension of ''man''. Every addition to the comprehension of a term lessens its extension up to a certain point, after that further additions increase the information instead.</p>
<p>(Peirce 1866, Lowell Lecture 7, CE 1, 466–467).</p>
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