On the first logical interlude of the first paragraph of section III of C.S. Peirce's "How To Make Our Ideas Clear"
Charles Sanders Peirce begins the first paragraph of section III (FP3) of “How To Make Our Ideas Clear” (HTM) by presenting his pragmatic definition of hardness (PDH) as the answer to Q1 (what is the pragmatic definition of hardness?). To follow PDH, one might expect Peirce to consider some particular straightforward cases of hard things and what PDH has to say about them. For example, what does it mean to say ‘the Hope diamond is hard’. CSP does not do this. Instead, in the next 21 sentences of FP3, Peirce is up to something else.
Before presenting Q2, Peirce offers this short 2-sentence logical interlude:
L1: “The whole conception of this quality, as of every other, lies in its conceived effects. There is absolutely no difference between a hard thing and a soft thing so long as they are not brought to the test.“
The first sentence is a condensed statement of PM (the pragmatic maxim from the previous paragraph of HTM). The second sentence requires special attention, so let’s call the second sentence D (because it is the 4th sentence of FP3):
D: “There is absolutely no difference between a hard thing and a soft thing so long as they are not brought to the test.”
Following the first sentence of L1, call it C, I read D as a corollary of PDH. And by corollary, I mean it follows with logical necessity for Peirce. In other words, Peirce isn’t sneaking in anything in D that isn’t entailed by C. From C to D is an inference without further assumption.
D can be read a few different ways. In one sense, D is internally inconsistent. According to PM and PDH, hardness is the effects of hardness. If there are no effects, then there is no hardness. But here Peirce is talking about a hard thing and a soft thing. If it is a hard thing, then it has effects, but Peirce stipulates that these things have no effects. The only to say something is hard without effects is via an a priori judgment, which takes you deeper into metaphysics. But if we can say one is hard and the other is soft a priori, then there is a difference. So, in this sense, either Peirce is introducing a priori judgements here or he is uncharacteristically sloppy. Perhaps Peirce would say this isn’t a problem in the realm of logic.
One might also ask: is Peirce talking about two things or one-and-the-same thing? Peirce could be saying that there is no difference in scratchability between two numerically distinct untested things. Peirce could also be saying there is no difference between attributing different degrees of scratchability (at different times) to one and the same untested thing? But to say there are one or two things also requires effects, so it doesn’t matter whether he is talking about two or one thing.
More likely, Peirce is just uncharacteristically sloppy in D. Considering that D seems to invoke a mysterious a priori judgment about these things and that we shouldn’t be able to even say there are two things or one thing, I think it is more accurate to restate D: there is absolutely no difference so long as there is no test. PM uses the word ‘effects’, D uses ‘tests’. Therefore, I think Peirce would also say: if there are no effects, there is no difference. If there are no effects, then we can’t even say there are two things, one thing, or anything.
Speaking factually, it is inconsistent to speak of an ‘untested hard thing’. The “realm of logic” allows for considerations/thoughts that are just “arrangements” and correspond to no facts. Peirce is saying that although it makes no sense realistically speaking, in the logical realm we can say things like: there is no difference in terms of hardness between a never-tested diamond and a never-tested cotton ball. Forget that we could only know it was a diamond if there were some effects. The logical realm is boundless.