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<p>In the case of hypothesis we have given some remarkable state of things:</p>

<p>In the case of hypothesis we have given some remarkable state of things:</p>

 

: <p>X is P,</p>

| align="center" | <math>X ~\operatorname{is}~ P</math>

 

<p>where X is an object of denotation;  we explain this by supposing that:</p>

 

<p>where <math>X\!</math> is an object of denotation;  we explain this by supposing that:</p>

: <p>X is Q,</p>

 

| align="center" | <math>X ~\operatorname{is}~ \Pi</math>

<p>and Q always contains more information than P.  If Q, therefore, has no more comprehension than P, it is better to say "X is Q" than "X is P".</p>

<p>and <math>\Pi\!</math> always contains more information than <math>P.\!</math> If <math>\Pi,\!</math> therefore, has no more comprehension than <math>P,\!</math> it is better to say <math>X ~\operatorname{is}~ \Pi</math> than <math>X ~\operatorname{is}~ P.</math></p>

<p>It is ''clearer'' to say that Every man is mortal than to say that Every man is either a good mortal or a bad mortal.</p>

<p>It is ''clearer'' to say that Every man is mortal than to say that Every man is either a good mortal or a bad mortal.</p>

<p>But in the case of hypothesis, Q always comprehends more than P.  To decide then between the two;  we have to consider whether Q has more denotation than P for if it has, the information of P is increased more in Q than its comprehension is and ''vice versa'';  and we must be decided which to take by our motives.</p>

<p>But in the case of hypothesis, <math>\Pi\!</math> always comprehends more than <math>P.\!</math> To decide then between the two;  we have to consider whether <math>\Pi\!</math> has more denotation than <math>P\!</math> for if it has, the information of <math>P\!</math> is increased more in <math>\Pi\!</math> than its comprehension is and ''vice versa'';  and we must be decided which to take by our motives.</p>

<p>This is the case of a preference between hypotheses.  But in the first proceedure from facts, P is a mere conjunctive term, destitute of any denotation before this proposition.  Hence in this case the information is increased absolutely, the connotation only relatively, and the hypothesis is absolutely needed and must be taken as a ''pis aller'' unless opposed by some other argument and until a better one presents itself.</p>

<p>This is the case of a preference between hypotheses.  But in the first proceedure from facts, <math>P\!</math> is a mere conjunctive term, destitute of any denotation before this proposition.  Hence in this case the information is increased absolutely, the connotation only relatively, and the hypothesis is absolutely needed and must be taken as a ''pis aller'' unless opposed by some other argument and until a better one presents itself.</p>

<p>Polarization for instance is a series of phenomena which it is impossible to name or define without the use of a hypothesis.</p>

<p>Polarization for instance is a series of phenomena which it is impossible to name or define without the use of a hypothesis.</p>

<p>(Peirce 1865, "Harvard Lecture 10.  Grounds of Induction", CE 1, 285–286).</p>

<p>(Peirce 1865, Harvard Lecture 10 : Grounds of Induction, CE 1, 285&ndash;286).</p>

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===Selection 35===

===Selection 35===