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<p>We must therefore modify the law of the inverse proportionality of extension and comprehension and instead of writing:</p>

<p>We must therefore modify the law of the inverse proportionality of extension and comprehension and instead of writing:</p>

 

<center>Extension × Comprehension = Constant,</center>

| align="center" | <p><math>\operatorname{Extension} \times \operatorname{Comprehension} = \operatorname{Constant},</math></p>

 

<p>which crudely expresses the fact that the greater the extension the less the comprehension, we must write:</p>

<p>which crudely expresses the fact that the greater the extension the less the comprehension, we must write:</p>

<center>Extension × Comprehension = Information,</center>

<p>Now, ladies and gentlemen, as it is true that every increase of our knowledge is an increase in the information of a term &mdash; that is, is an addition to the number of terms equivalent to that term &mdash; so it is also true that the first step in the knowledge of a thing, the first framing of a term, is also the origin of the information of that term because it gives the first term equivalent to that term.  I here announce the great and fundamental secret of the logic of science.  There is no term, properly so called, which is entirely destitute of information, of equivalent terms.  The moment an expression acquires sufficient comprehension to determine its extension, it already has more than enough to do so.</p>

 

<p>which means that when the information is increased there is an increase of either extension or comprehension without any diminution of the other of these quantities.</p>

<p>Now, ladies and gentlemen, as it is true that every increase of our knowledge is an increase in the information of a term — that is, is an addition to the number of terms equivalent to that term — so it is also true that the first step in the knowledge of a thing, the first framing of a term, is also the origin of the information of that term because it gives the first term equivalent to that term.  I here announce the great and fundamental secret of the logic of science.  There is no term, properly so called, which is entirely destitute of information, of equivalent terms.  The moment an expression acquires sufficient comprehension to determine its extension, it already has more than enough to do so.  (Peirce 1866, Lowell Lecture 7, CE 1, 465).</p>

<p>(Peirce 1866, Lowell Lecture 7, CE 1, 465).</p>

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