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<p>The moment, then, that we pass from nothing and the vacuity of being to any content or sphere, we come at once to a composite content and sphere.  In fact, extension and comprehension — like space and time — are quantities which are not composed of ultimate elements;  but every part however small is divisible.</p>

<p>The moment, then, that we pass from nothing and the vacuity of being to any content or sphere, we come at once to a composite content and sphere.  In fact, extension and comprehension &mdash; like space and time &mdash; are quantities which are not composed of ultimate elements;  but every part however small is divisible.</p>

<p>The consequence of this fact is that when we wish to enumerate the sphere of a term — a process termed ''division'' — or when we wish to run over the content of a term — a process called ''definition'' — since we cannot take the elements of our enumeration singly but must take them in groups, there is danger that we shall take some element twice over, or that we shall omit some.  Hence the extension and comprehension which we know will be somewhat indeterminate.  But we must distinguish two kinds of these quantities.  If we were to subtilize we might make other distinctions but I shall be content with two.  They are the extension and comprehension relatively to our actual knowledge, and what these would be were our knowledge perfect.</p>

<p>The consequence of this fact is that when we wish to enumerate the sphere of a term &mdash; a process termed ''division'' &mdash; or when we wish to run over the content of a term &mdash; a process called ''definition'' &mdash; since we cannot take the elements of our enumeration singly but must take them in groups, there is danger that we shall take some element twice over, or that we shall omit some.  Hence the extension and comprehension which we know will be somewhat indeterminate.  But we must distinguish two kinds of these quantities.  If we were to subtilize we might make other distinctions but I shall be content with two.  They are the extension and comprehension relatively to our actual knowledge, and what these would be were our knowledge perfect.</p>

<p>Logicians have hitherto left the doctrine of extension and comprehension in a very imperfect state owing to the blinding influence of a psychological treatment of the matter.  They have, therefore, not made this distinction and have reduced the comprehension of a term to what it would be if we had no knowledge of fact at all.  I mention this because if you should come across the matter I am now discussing in any book, you would find the matter left in quite a different state. (Peirce 1866, "Lowell Lecture 7", CE 1, 462).</p>

<p>Logicians have hitherto left the doctrine of extension and comprehension in a very imperfect state owing to the blinding influence of a psychological treatment of the matter.  They have, therefore, not made this distinction and have reduced the comprehension of a term to what it would be if we had no knowledge of fact at all.  I mention this because if you should come across the matter I am now discussing in any book, you would find the matter left in quite a different state.</p>

 

<p>(Peirce 1866, Lowell Lecture 7, CE 1, 462).</p>

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