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</blockquote>

</blockquote>

====Excerpt 11====

====Excerpt 11.  Peirce (CP 2.364)====

<pre>

<blockquote>

| Concepts, or terms, are, in logic, conceived to have

<p>Concepts, or terms, are, in logic, conceived to have ''subjective parts'', being the narrower terms into which they are divisible, and ''definitive parts'', which are the higher terms of which their definitions or descriptions are composed:  these relationships constitute "quantity".</p>

| 'subjective parts', being the narrower terms into which

 

| they are divisible, and 'definitive parts', which are the

<p>This double way of regarding a class-term as a whole of parts is remarked by Aristotle in several places (e.g., ''Metaphysics'', D. xxv. 1023 b22).  It was familiar to logicians of every age. &hellip; and it really seems to have been Kant who made these ideas pervade logic and who first expressly called them quantities. But the idea was old.</p>

| higher terms of which their definitions or descriptions are

 

| composed:  these relationships constitute "quantity".

<p>Archbishop Thomson, W.D. Wilson, and C.S. Peirce endeavor to make out a third quantity of terms. The last calls his third quantity "information", and defines it as the "sum of synthetical propositions in which the symbol is subject or predicate", antecedent or consequent.  The word "symbol" is here employed because this logician regards the quantities as belonging to propositions and to arguments, as well as to terms.</p>

 

| This double way of regarding a class-term as a whole of parts

<p>A distinction of ''extensive'' and ''comprehensive distinctness'' is due to Scotus (''Opus Oxon.'', I. ii. 3):  namely, the usual effect upon a term of an increase of information will be either to increase its breadth without without diminishing its depth, or to increase its depth without diminishing its breadth.  But the effect may be to show that the subjects to which the term was already known to be applicable include the entire breadth of another another term which had not been known to be so included.  In that case, the first term has gained in ''extensive distinctness''.  Or the effect may be to teach that the marks already known to be predicable of the term include the entire depth of another term not previously known to be so included, thus increasing the ''comprehensive distinctness'' of the former term.</p>

| is remarked by Aristotle in several places (e.g., 'Metaphysics',

 

| D. xxv. 1023 b22).  It was familiar to logicians of every age.

<p>The passage of thought from a broader to a narrower concept without change of information, and consequently with increase of depth, is called ''descent'';  the reverse passage, ''ascent''.</p>

| ... and it really seems to have been Kant who made these ideas

 

| pervade logic and who first expressly called them quantities.

<p>For various purposes, we often imagine our information to be less than it is.  When this has the effect of diminishing the breadth of a term without increasing its depth, the change is called ''restriction''; just as when, by an increase of real information, a term gains breadth without losing depth, it is said to gain extension. This is, for example, a common effect of ''induction''. In such case, the effect is called generalization.</p>

| But the idea was old. Archbishop Thomson, W.D. Wilson, and

 

| C.S. Peirce endeavor to make out a third quantity of terms.

<p>A decrease of supposed information may have the effect of diminishing the depth of a term without increasing its information.  This is often called ''abstraction'';  but it is far better to call it ''prescission'';  for the word ''abstraction'' is wanted as the designation of an even far more important procedure, whereby a transitive element of thought is made substantive, as in the grammatical change of an adjective into an abstract noun.  This may be called the principal engine of mathematical thought.</p>

| The last calls his third quantity "information", and defines

 

| it as the "sum of synthetical propositions in which the symbol

<p>When an increase of real information has the effect of increasing the depth of a term without diminishing the breadth, the proper word for the process is ''amplification''.  In ordinary language, we are inaccurately said to ''specify'', instead of to ''amplify'', when we add to information in this way. The logical operation of forming a hypothesis often has this effect, which may, in such case, be called ''supposition''.  Almost any increase of depth may be called ''determination''.</p>

| is subject or predicate", antecedent or consequent.  The word

 

| "symbol" is here employed because this logician regards the

<p>C.S. Peirce, ''Collected Papers'', CP 2.364</p>

| quantities as belonging to propositions and to arguments,

</blockquote>

| as well as to terms.

| A distinction of 'extensive' and 'comprehensive distinctness' is

| due to Scotus ('Opus Oxon.', I. ii. 3):  namely, the usual effect

| upon a term of an increase of information will be either to increase

| its breadth without without diminishing its depth, or to increase its

| depth without diminishing its breadth.  But the effect may be to show

| that the subjects to which the term was already known to be applicable

| include the entire breadth of another another term which had not been

| known to be so included.  In that case, the first term has gained in

| 'extensive distinctness'.  Or the effect may be to teach that the

| marks already known to be predicable of the term include the

| entire depth of another term not previously known to be so

| included, thus increasing the 'comprehensive distinctness'

| of the former term.

| The passage of thought from a broader to a narrower concept

| without change of information, and consequently with increase

| of depth, is called 'descent';  the reverse passage, 'ascent'.

| For various purposes, we often imagine our information to be less than

| it is.  When this has the effect of diminishing the breadth of a term

| without increasing its depth, the change is called 'restriction';

| just as when, by an increase of real information, a term gains

| breadth without losing depth, it is said to gain extension.

| This is, for example, a common effect of 'induction'.

| In such case, the effect is called generalization.

| A decrease of supposed information may have the effect

| of diminishing the depth of a term without increasing its

| information.  This is often called 'abstraction';  but it is

| far better to call it 'prescission';  for the word 'abstraction'

| is wanted as the designation of an even far more important procedure,

| whereby a transitive element of thought is made substantive, as in the

| grammatical change of an adjective into an abstract noun.  This may be

| called the principal engine of mathematical thought.

| When an increase of real information has the effect of increasing the

| depth of a term without diminishing the breadth, the proper word for the

| process is 'amplification'.  In ordinary language, we are inaccurately said

| to 'specify', instead of to 'amplify', when we add to information in this way.

| The logical operation of forming a hypothesis often has this effect, which may,

| in such case, be called 'supposition'.  Almost any increase of depth may be called

| 'determination'.

| C.S. Peirce, 'Collected Papers', CP 2.364

</pre>

====Excerpt 12====

====Excerpt 12====