Q1: What is the pragmatic definition of hardness?
FP3 (the first paragraph of section III of Charles Sanders Peirce’s “How To Make Our Ideas Clear”) is a 23-sentence paragraph that is nominally devoted to the application of PM (the pragmatic maxim) to the physical conception of hardness. Peirce answers Q1 (title above) in the second sentence of FP3. Call this pragmatic definition of hardness, PDH:
PDH: “[when something] will not be scratched by many other substances”.
In the remaining 21-sentences of FP3, CSP does not discuss how he arrived at this definition or offer any support for its adequacy; CSP treats PDH as a straightforward and uncontroversial application of PM to hardness (and I am not challenging this). This means that the remaining 21 sentences are not devoted to answering Q1, yet answering Q1 seems to be the task for FP3. Peirce discusses Q2-4 in the rest of the paragraph, and Q2 and Q3 are relevant to his definition of hardness, but they assume the adequacy of the definition and serve to point out the boundaries of the definition. In this section I will just discuss Q1 and PDH.
PDH is a kind of definition of hardness. The standard form of an essential definition, as you find in a dictionary, is a subject-predicate sentence using the present tense, e.g. hard things are not scratched by many other substances. A vixen is a female fox. PDH says that hard things “will not” be scratched by much. ‘Will not’ is the simple future tense. The simple future tense distinctly refers to future events. Peirce doesn’t explicitly draw attention to the prospective dimension to pragmatic definition, but I aim to explicate in this guide and I think this prospective dimension is evident in HTM.
Although it is beyond the scope of FP3, another example that brings out the prospective aspect to Q1 is Peirce’s example of the potentially brilliant stone buried in a cave at the bottom of the ocean in section IV of HTM. This cave stone has never actually gleamed for an eye or even a sensor, and Peirce asks: is it “brilliant”? Peirce is judging the meaningfulness of saying that the stone is brilliant. There have been no effects up till now and Peirce says “it probably makes no difference, remembering always that that stone may be fished up to-morrow” (ital. CSP). The implication is that the question/hypothesis (The cave stone is brilliant, or not) is meaningful in proportion to the likelihood that it will gleam for an eye some day in the future. Using PDH as a model, I think it is safe to say that a prospective pragmatic definition of ‘brilliance’ is: it will gleam for an eye/sensor.
The following may be a bit of a reach but I think the Peirce who wrote HTM, the Peirce of this prospective conception of pragmatic definition would say that a “past possibility” is an oxymoron. I think Peirce would say what’s done is done and the past is actual fact. Future possibilities become current actualities and this actuality is preserved into the past. Thus I think Peirce would say it is absurd to talk about possible pasts. The possible prospective pragmatic payload is that it “may be fished up to-morrow”, and thus it would gleam for those who fished it up.