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<p>To explain this, we must remember that the process of induction is a process of adding to our knowledge; it differs therein from deduction — which merely explicates what we know — and is on this very account called scientific inference. Now deduction rests as we have seen upon the inverse proportionality of the extension and comprehension of every term; and this principle makes it impossible apparently to proceed in the direction of ascent to universals. But a little reflection will show that when our knowledge receives an addition this principle does not hold.</p>
<p>To explain this, we must remember that the process of induction is a process of adding to our knowledge; it differs therein from deduction — which merely explicates what we know — and is on this very account called scientific inference. Now deduction rests as we have seen upon the inverse proportionality of the extension and comprehension of every term; and this principle makes it impossible apparently to proceed in the direction of ascent to universals. But a little reflection will show that when our knowledge receives an addition this principle does not hold.</p>
<p>Thus suppose a blind man to be told that no red things are blue. He has previously known only that red is a color; and that certain things ''A'', ''B'', and ''C'' are red.</p>
<p>Thus suppose a blind man to be told that no red things are blue. He has previously known only that red is a color; and that certain things ''A'', ''B'', and ''C'' are red.</p>
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| The comprehension of red then has been for him || || ''color''.
| The comprehension of red then has been for him || || ''color''.
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| Its extension has been || || ''A'', ''B'', ''C''.
| Its extension has been || || ''A'', ''B'', ''C''.
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<p>But when he learns that no red thing is blue, ''non-blue'' is added to the comprehension of red, without the least diminution of its extension.</p>
<p>But when he learns that no red thing is blue, ''non-blue'' is added to the comprehension of red, without the least diminution of its extension.</p>
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<p>For example we have here a number of circles dotted and undotted, crossed and uncrossed:</p>
<p>For example we have here a number of circles dotted and undotted, crossed and uncrossed:</p>
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<pre>
<pre>
(·X·) (···) (·X·) (···) ( X ) ( ) ( X ) ( )
(·X·) (···) (·X·) (···) ( X ) ( ) ( X ) ( )
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</pre>
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<p>Here it is evident that the greater the extension the less the comprehension:</p>
<p>Here it is evident that the greater the extension the less the comprehension:</p>
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<pre>
<pre>
o-------------------o-------------------o
o-------------------o-------------------o
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<p>Now suppose we make these two terms ''dotted circle'' and ''crossed and dotted circle'' equivalent. This we can do by crossing our uncrossed dotted circles. In that way, we increase the comprehension of ''dotted circle'' and at the same time increase the extension of ''crossed and dotted circle'' since we now make it denote ''all dotted circles''.</p>
<p>Now suppose we make these two terms ''dotted circle'' and ''crossed and dotted circle'' equivalent. This we can do by crossing our uncrossed dotted circles. In that way, we increase the comprehension of ''dotted circle'' and at the same time increase the extension of ''crossed and dotted circle'' since we now make it denote ''all dotted circles''.</p>
