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<p>It is important to distinguish between the two functions of a word:  1st to denote something — to stand for something, and 2nd to mean something — or as Mr. Mill phrases it — to ''connote'' something.</p>

<p>It is important to distinguish between the two functions of a word:  1st to denote something &mdash; to stand for something, and 2nd to mean something &mdash; or as Mr. Mill phrases it &mdash; to ''connote'' something.</p>

<p>What it denotes is called its ''Sphere''.  What it connotes is called its ''Content''.  Thus the ''sphere'' of the word ''man'' is for me every man I know;  and for each of you it is every man you know.  The ''content'' of ''man'' is all that we know of all men, as being two-legged, having souls, having language, &c., &c.  It is plain that both the ''sphere'' and the ''content'' admit of more and less.  &hellip;</p>

<p>What it denotes is called its ''Sphere''.  What it connotes is called its ''Content''.  Thus the ''sphere'' of the word ''man'' is for me every man I know;  and for each of you it is every man you know.  The ''content'' of ''man'' is all that we know of all men, as being two-legged, having souls, having language, &c., &c.  It is plain that both the ''sphere'' and the ''content'' admit of more and less.  &hellip;</p>

<p>We have then:</p>

<p>We have then:</p>

 

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<p>The principle of explicatory or deductive reasoning then is that:</p>

| <p>The principle of explicatory or deductive reasoning then is that:</p>

<p>Now this maxim would not be true if the Extension and Comprehension were directly proportional to one another;  this is to say if the Greater the one the greater the other.  For in that case, though the whole Content would belong to the whole Sphere;  yet only a particular part of it would belong to a part of that Sphere and not every part to every part.  On the other hand if the Comprehension and Extension were not in some way proportional to one another, that is if terms of different spheres could have the same content or terms of the same content different spheres;  then there would be no such fact as a content's ''belonging'' to a sphere and hence again the maxim would fail.  For the maxim to be true, then, it is absolutely necessary that the comprehension and extension should be inversely proportional to one another.  That is that the greater the sphere, the less the content.</p>

<p>Every part of a word's Content belongs to every part of its Sphere,</p>

<p>Now this evidently true.  If we take the term ''man'' and increase its ''comprehension'' by the addition of ''black'', we have ''black man'' and this has less ''extension'' than ''man''.  So if we take ''black man'' and add ''non-black man'' to its sphere, we have ''man'' again, and so have decreased the comprehension.  So that whenever the extension is increased the comprehension is diminished and ''vice versa''.</p>

 

 

<p>Whatever is contained ''in'' a word belongs to whatever is contained under it.</p>

 

<p>Now this maxim would not be true if the Extension and Comprehension were directly proportional to one another;  this is to say if the Greater the one the greater the other.  For in that case, though the whole Content would belong to the whole Sphere;  yet only a particular part of it would belong to a part of that Sphere and not every part to every part.  On the other hand if the Comprehension and Extension were not in some way proportional to one another, that is if terms of different spheres could have the same content or terms of the same content different spheres;  then there would be no such fact as a content's ''belonging'' to a sphere and hence again the maxim would fail.  For the maxim to be true, then, it is absolutely necessary that the comprehension and extension should be inversely proportional to one another.  That is that the greater the sphere, the less the content.</p>

<p>Now this evidently true.  If we take the term ''man'' and increase its ''comprehension'' by the addition of ''black'', we have ''black man'' and this has less ''extension'' than ''man''.  So if we take ''black man'' and add ''non-black man'' to its sphere, we have ''man'' again, and so have decreased the comprehension.  So that whenever the extension is increased the comprehension is diminished and ''vice versa''.  (Peirce 1866, "Lowell Lecture 7", CE 1, 459–460).</p>

<p>(Peirce 1866, Lowell Lecture 7, CE 1, 459&ndash;460).</p>

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