SUO: Re: Determination
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
| 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".
|
| 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.
| ... 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. 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.
|
| 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 passgae 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'.
|
| Charles Sanders Peirce, 'Collected Papers', CP 2.364
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤