Correspondingly:
(4b) An idea is obscure and confused if and only if it is either too inclusive or too restrictive (i.e., if either it represents as essential what are accidental properties of its object or represents as accidental what are essential properties or its obj
ect).
(6b) An idea is distinct if and only if its intension provides adequate criteria for judging a given object to fall under/outside the idea.
Correspondingly:
(6c) An idea is obscure if and only if its extension has fuzzy boundaries (e.g., your idea of gold is obscure if you can't tell it from pyrite).
(6d) An idea is confused if and only if its intension lacks adequate criteria for judging a given object to fall under/outside the idea (your idea of gold is confused if you don't know by what criteria to distinguish gold from anything and everything that
is not gold) .
(7b) For example: if the concepts equiangularity and equilaterality are understood clearly and distinctly, the judgment "all equilateral triangles are equiangular" is a necessary truth.
(IIa) Your idea of the legal structure of a marriage (the contract);
(IIIa) Your idea of the nature of your own mind;
(IVa) Your idea of the motion of billiard balls;
1. The rationalists in general, and Descartes in particular, deploy attributions of clarity and distinctness to ideas for a variety of different if overlapping purposes: (a) to individuate objects; (b) to explain error; (c) to describe cognition; (d) to e
stablish standards of evidence; and (e) to generalize the logical status of axioms in deductive systems. Owing more to the overlap than to the multiplicity of these purposes, what a given rationalist philosopher says s/he means by the terms "clear" and "
distinct" is often at odds with how s/he actually uses the terms. Following Wittgenstein, we are probably well advised--when hunting for meaning in such cases--to follow trails of usage rather than to explicate definitions.
2. In the Regulae, Descartes discusses clear and distinct ideas as results of a "mental
operation" he terms intuition. He says: "By intuition I understand, not the fluctuating testimony of the senses, nor the misleading judgment that proceeds from the bl
undering constructions of imagination, but the conception which an unclouded and attentive mind gives us so readily and distinctly that we are wholly freed from doubt about that which we understand" (Rule III, ¶5). He's using the notion of intuition to a
ccount for the introduction of axioms to a deductive system, so he means by clear and distinct ideas: the propositions with which any deductive system must begin, given that it cannot bootstrap the proof of all propositions contained in the system. Less
than a mathematical formalist, Descartes supposes axioms to be "self-evident truths," and we can take him to regard the notion of self-evidence as the primary notion here: ideas are not self-evident because they are clear and distinct, but clear and disti
nct because they are self-evident (i.e., clarity and distinctness are the properties all self-evident truths have).
3. In the Principles, Descartes explicitly defines and distinguishes clear and
distinct
ideas as follows: "I call 'clear' that perception which is present and manifest to an attentive mind: just as we say that we clearly see those things which are present
to our intent eye and act upon it sufficiently strongly and manifestly. On the other hand, I call 'distinct', that perception which, while clear, is so separated and delineated from all others that it contains absolutely nothing except what is clear" (I
,45). Here he's using the distinction in order to outline, articulate, and defend his theory of error ("if we give assent only to those things which we clearly and distinctly perceive, we will never accept anything false as being true. . . .we always jud
ge badly when we assent to things which are not clearly perceived" (I,43 & 44)).
4. In the Meditations, the notion of clear and distinct ideas plays an additional
role
(besides providing an account of error): to provide standards of evidence which permit the application of rationalist epistemology/method to metaphysics. Descartes, Le
ibniz, and Spinoza all use some version of the premise that "all clear and distinct ideas are true" as an integral part of their respective versions of the ontological argument. Descartes' usage suggests that we read "all clear and distinct ideas are tru
e" as excluding propositions from the set of ideas, so that he means "all clear and distinct ideas have objects to which they conform." Reading Descartes' meaning in this manner avoids the embarrassing interpretive consequence of having to say that incre
asing the clarity of an idea increases its truth (this would be embarrassing for Descartes because he understands truth as an all-or-nothing proposition); we can say instead that the more clear and distinct an idea is then the more its referent conforms t
o the idea. On this reading, we can tidy up Descartes' formulae a bit and derive for him the definition:
(4a) An idea is clear and distinct if and only if all and only properties essential to the object of that idea (its referent or ideatum) are represented in the idea.
5. Spinoza has a more active notion of ideas in general (they are for the most part coextensive with judgments, and are therefore not so much things the mind has as things the mind does); he rejects the cartesian tendency (as in 4a above) to think of idea
s as maps or pictures of objects. Spinoza would have us ideate clearly and distinctly rather than acquire a collection of clear and distinct ideas; accordingly, clarity and distinctness are, for him, the virtues of good reasoning: the terms index deducti
ve rigor rather than true belief.
6. Leibniz, however, follows Descartes more closely. In the Discourse, he asserts
that:
". . . we sometimes know something clearly, without being in any doubt whether a poem or picture is done well or badly, simply because it has a certain something, I
know not what, that satisfies or offends us. But when I can explain the marks which I have, the knowledge is distinct. And such is the knowledge of the assayer, who discerns the true from the false by means of certain tests or marks which make up the de
finition of gold" (24). We can tidy up these formulae as follows:
(6a) An idea is clear if and only if its extension has precise boundaries.
7. For both Descartes and Leibniz ideas must be conjoined into propositions in order for them to perform evidential work in a deductive system; to say that "we proceed without risk of error only so long as our ideas are clear and distinct," means somethin
g like the following:
(7a) If you know precisely which objects are included under an idea, I-1, which are not, and why; and so too for a second idea, I-2, then, if analyses of I-1 and I-2 show that either (i) nothing can be included under I-1 without being included under I-2 o
r (ii) nothing can be included under I-2 without being included under I-1 or (iii) that I-1 and I-2 are coextensive, then the corresponding judgments about the objects to which I-1 and I-2 refer are necessarily true.
8. Cartesian Exercises: in each of the following pairs, consider whether one idea (a) or (b) is more clear and distinct than the other, and if so, which objects would you expect most to conform to your idea:
(Ia) Your idea of a triangle;
(Ib) Your idea of the shape of a map of the United States.
(IIb) Your idea of the emotional structure of a marriage (the relationship).
(IIIb) Your idea of the nature of your own body.
(IVb) Your idea of the motion of electrons.