Peirce's Terms: Comparative Tables

I'll improve this as time goes by.

Real, Figment, Mental, External. Based on CP 6.327-8. Read the passage here.


Question of significance.
Mental. External.
Question
of
Denotation.
Real. Can vary by what people think (since it is a thought), but not by what people think about it. Doesn't vary by what people think or by what people think about it.
For instance everyday objects, and colors which would normally be perceived under certain circumstances. Colors are relative to sight but still external.
Figment. Can vary by what people think (since it is a thought), and by what people think about it. There's nothing that both (A) doesn't vary (as a thought varies) by what people think and (B) can vary by what people think about it. There are no figments but of thought.

Vague, Determinate, General.

Based on Peirce, C. S. (1905), "Issues of Pragmaticism", The Monist, vol. XV, no. 4, pp. 481-499, The Open Court Publishing Co., Chicago, IL, October 1905, for the Hegeler Institute. Reprinted (CP 5.438-463), (SW 203-226). Internet Archive The Monist 15.

The SUBJECT (or object) is determinate or indeterminate. A subject is determinate in respect of being subject of a universal (and this covers the singular as well) proposition, and indeterminate in all other respects.

"A subject is determinate in respect to any character which inheres in it or is (universally and affirmatively) predicated of it, as well as in respect to the negative of such character, these being the very same respect. In all other respects it is indeterminate"

The SIGN is objectively either vague or determinate or general. For instance it is objectively indeterminate if its object is undetermined by it. (Note: Peirce, from 1906 onward, in regard to sign and object, uses the word "determination" for the determination of the sign by the object, not vice versa).


The sign is objectively either vague, determinate, or general.
Vague Vague Indeterminate Not general
Determinate Not vague, i.e.:
definite or, with a slightly
different mode of application,
precise
Determinate
General Indeterminate General
Vague   =   indefinite or imprecise   =   indeterminate but not general.
Determinate   =   neither vague nor general, i.e., definite/precise but not general.
General   =   indeterminate but not vague, i.e., indeterminate but definite/precise.

But see the quote further below, where Peirce discusses intermediacies between the general and the vague.

In quantity, a sign such as a proposition is as the distribution of its first subject.
Quantity (my examples) Dialogue aspect
Inapplicabilities of logical principles
Particular, i.e., vague (indefinite or imprecise). "Some man is mortal." The sign (or speaker) reserves the exclusive right to further determination of subject. "A certain man who I could name is conceited." * Principle of contradiction doesn't apply. Unidentified proposition need not be either true or false. "Some proposition is true" does not contradict "Some proposition is false." **
Singular, i.e. determinate. "Socrates is mortal." Determination is complete.
Universal, i.e., general. "Every man is mortal." The interpreter gets to further determine subjects for the sign. Principle of excluded middle doesn't apply. Neither "Any proposition is true" nor "Any proposition is false" needs to be true.** Another example might consist of "Man is arrogant" and "Man is not arrogant." 

* My comment: The subject pronomial here seems more quîdem than aliquî — more "a certain" than "some" — more an unknown or "veiled" constant than a variable. However, I recall seeing, some years ago, old pages (via Google Books) showing quîdem as an example of the (Aristotelian) particular affirmative ("some... [is ....]"); so Peirce has some precedent in this.
** My comment: Peirce seems to have a conception of proposition as much like a predicate (notwithstanding the idea of a proposition as a zero-place predicate). Nowadays we'd call false both "Any proposition is true" and "Any proposition is false".

Peirce:
The purely formal conception that the three affections of terms, determination, generality, and vagueness, form a group dividing a category of what Kant calls "functions of judgment" will be passed by as unimportant by those who have yet to learn how important a part purely formal conceptions may play in philosophy. Without stopping to discuss this, it may be pointed out that the "quantity" of propositions in logic, that is, the distribution of the first subject, is either singular (that is, determinate, which renders it substantially negligible in formal logic), or universal (that is, general), or particular (as the mediaeval logicians say, that is, vague or indefinite). It is a curious fact that in the logic of relations it is the first and last quantifiers of a proposition that are of chief importance. To affirm of anything that it is a horse is to yield to it every essential character of a horse; to deny of anything that it is a horse is vaguely to refuse to it some one or more of those essential characters of the horse. There are, however, predicates that are unanalyzable in a given state of intelligence and experience. These are, therefore, determinately affirmed or denied. Thus, this same group of concepts reappears. Affirmation and denial are in themselves unaffected by these concepts, but it is to be remarked that there are cases in which we can have an apparently definite idea of a border line between affirmation and negation. Thus, a point of a surface may be in a region of that surface, or out of it, or on its boundary. This gives us an indirect and vague conception of an intermediary between affirmation and denial in general, and consequently of an intermediate, or nascent state, between determination and indetermination. There must be a similar intermediacy between generality and vagueness. Indeed, in an article in the seventh volume of The Monist there lies just beneath the surface of what is explicitly said, the idea of an endless series of such intermediacies. We shall find below some application for these reflections.
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