How to Make "How to Make Our Ideas Clear" Clear

"How to Make Our Ideas Clear" (HTM) is the second article in a six-article series, "The Logic of Science", published in The Popular Science Monthly between 1877 and 1878. In HTM, Peirce labels and exalts what he terms "the third grade of clearness of apprehension" (3GC). Peirce's canonical expression of 3GC is his famous pragmatic maxim (PM):¹

PM: "Consider what effects, which might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object."

We should conceive of and describe things in terms of what effects we will observe when we test them.²

Before examining the three grades, a terminological clarification is helpful. Although Peirce presents PM as a "rule for attaining the third grade of clearness of apprehension", it is more intuitively understood as a type of conception. Note that conceptions (small 'c') differ from Concepts. Concepts function as universals and are therefore shared, unifying particulars across a logical dimension, whereas conceptions are mental particulars, always someone's conception of something. Both can be formulated in definitions. We may also hold tacit conceptions that we cannot yet adequately define, though Socratic questioning can draw them into workable definitions. Peirce declares for pragmatic conceptions and pragmatic definitions.

Peirce's first two "grades of clearness" follow Descartes and Leibniz's discussion of "clear and distinct ideas". First-grade clearness (1GC) is ordinary intuitive certitude: unreflective engagement with the world when nothing unexpected occurs. It's not certitude in the sense of infallibility, but in the sense that one believes something to be true and acts on it successfully. This corresponds to the certainty Peirce addresses in section IV of "Fixation of Belief":

The most that can be maintained is, that we seek for a belief that we shall think to be true. But we think each one of our beliefs to be true, and, indeed, it is mere tautology to say so.

We ordinarily think all our beliefs are true.³ We hold many such beliefs that are unverified, unexamined, and not treated tentatively. This ordinary certainty is 1GC.

Second-grade clearness (2GC) is typified by classical essential definitions in abstract terms, such as defining 'bachelor' as 'an unmarried man'. These definitions typically employ the copula 'is' and abstract categories ('unmarried' and 'man'). This is also called an Aristotelian definition: genus and differentia—the general class and the distinguishing feature that picks out the particular subset of cases—often represented by Venn diagrams. When we can create a Venn diagram showing the abstract overlap of component conceptions, and when those components possess 1GC, we have 2GC—what Descartes called clear and distinct. Leibniz updated this to say we have 1GC when we can give a 2GC definition of those components.

Peirce's point in HTM is that the "clear and distinct ideas" (1GC and 2GC) of Descartes and Leibniz are inadequate and long outdated. While these grades of clearness have long structured philosophical accounts of clarity, Peirce argues that they fail to capture a "higher perspicuity of thought" that has been at work in inquiry but has not yet been explicitly identified as a distinct grade. Peirce's critique of Descartes and Leibniz's treatment of 1GC and 2GC is very brief, but it is intended to motivate the need for this higher grade of clearness.

Of Descartes' conception of 1GC, Peirce says that "the distinction between an idea seeming clear and really being so, never occurred to him", so we can have "clear apprehensions of ideas which in truth are very hazy". For Leibniz, "no better remedy occurred to him than to require an abstract definition of every important term". In other words, Descartes overlooked that clear ideas could actually be obscure, so Leibniz added a further criterion: we must have a 2GC abstract definition of every important term—even 1GC must "sustain the test of dialectical examination". However, Leibniz "missed the most essential point of the Cartesian philosophy, which is, that to accept propositions which seem perfectly evident to us is a thing which, whether it be logical or illogical, we cannot help doing". Descartes recognized that this clarifying method must bottom out somewhere, but failed to distinguish ideas that seem clear from those that truly are. Leibniz attempted to solve this, but introduced a method that doesn't bottom out.

Peirce's verdict: "Nothing new can ever be learned by analyzing definitions" and "the machinery of the mind can only transform knowledge, but never originate it, unless it be fed with facts of observation". The Cartesian–Leibnizian framework methodologically neglects observation in favor of a priori reasoning and abstract definition. This neglect reflects traditional philosophy's rationalist bias toward universal, necessary, and certain knowledge, and away from the contingent, particular, and probabilistic character of empirical observation.⁴ Without observation, we cannot learn anything new, yet we are learning constantly and systematically in science. 1GC and 2GC are therefore inadequate to account for scientific progress.

The foregoing discussion of 1GC and 2GC occupies only the first of HTM's four parts. HTM is primarily a feature article on his third and highest grade of clearness of apprehension (3GC). Peirce doesn't claim to have discovered 3GC; rather, he holds that it has long been operative in human inquiry.⁵ His implicit claim, however, is that philosophers have overlooked this grade, and that he is the first to identify it as a distinct type. Peirce would likely say that 3GC pragmatic conceptions are distinctively conducive to the progress of science and, ultimately, to truth. We should therefore pursue pragmatic conceptions/definitions to the exclusion of other forms.

The pragmatic maxim (PM) is the canonical statement of 3GC, but it is not the most intuitive or accessible point of entry for grasping 3GC and its contrast with 2GC. The most effective way to grasp 3GC is through example. Consider this exchange:

The 3GC/pragmatic meaning of any conception consists in what experimental results will actually happen under testing conditions. Timeless essences and what would, could, or might happen are not testable—we should concern ourselves only with is, and will be.⁶