The following is a stroll through the interconnections between a locus of concepts: vagueness, clarity, possibility, questions, and belief. The result is an offering that vagueness belongs to possibility while clarity is closer to an opposition from possibility, which goes against some thinkers on the topic of possibility, including Descartes.
“I must confess that it makes very little difference whether we say that a stone on the bottom of the ocean, in complete darkness, is brilliant or not—that is to say, that it probably makes no difference, remembering always that that stone may be fished up to-morrow. But that there are gems at the bottom of the sea, flowers in the untraveled desert, etc., are propositions which, like that about a diamond being hard when it is not pressed, concern much more the arrangement of our language than they do the meaning of our ideas.” (C.S. Peirce ed. Houser and Kloesel 1992, p 140)
First, contrast with Kuhn:
“As the problems change, so, often does the standard that distinguishes a real scientific solution from a mere metaphysical speculation, word game, or mathematical play. The normal-scientific tradition that emerges from a scientific revolution is not only incompatible but often actually incommensurable with that which has gone before.”(Kuhn 1962, p. 103)
The “meaning of our ideas” can be shifted fundamentally, so that what was a mere mathematical play (such as in https://questionsarepower.org/2014/08/) suddenly is taken seriously. What is a joke and what is serious changes, the grave becomes light, uplifting wonderment gives way to cold sadness, and with it our world shifts.
Peirce’s quote is interesting because it brings up the relationship between possibility and realism. Diodorus defined the possible, in perhaps the first definition of its kind: “a proposition is possible if and only if it either is true or will be true.” (Mates 1953, p. 6) Under that assumption, the realist question “If a tree falls in the forest where no-one hears it, does it make a sound?” is relevant; but here we must modify the question to be more difficult. Ask: “If a tree falls into the ocean and is washed to the ocean’s bottom, is it burnable?” The two questions are more related than they may seem. In the second question we have to ponder the meaning of possibility. Are things possible even if they neither are nor will be? In the first question we are asking if something is when its being can only be inferred, not experienced. We associate sound with the falling of a tree to the point of inference, that is how we can make the realist claim that such things happen without our experiencing it. But inference depends on our definition of the possible. For Diodorus, beginning with his restriction on the possible (we may, for arguments sake, suppose that the tree at the bottom of the ocean is neither burnable nor will be burnable) took his own definition of inference from it.
“a conditional proposition is true if and only if it neither is nor was possible for the antecedent to be true and the consequent false.” (Mates 1953, p. 6) Such a definition is more strict than the material implication, so strict that it rejects the realism of a tree falling in the forest and making a sound. With this definition, both “If a tree falls in the forest, then it makes a sound” and “If this tree falls into the ocean, then it is burnable” are false, because it is possible for a tree to fall and not make a sound (maybe a small tree fell a small distance on many feet of snow?), and when I say possible I must use Diodorus’s definition, and say that “at some point either now or in the future, a tree will fall in a snowstorm and make no sound.” This means that realism is entangled in a consideration of possible futures. To say that, at the very least, being able to imagine and execute our next step in our stroll is a least part of this entanglement of realism and possibility.
Also there is the problem of genera. For realism does not exactly refer to actual objects, but to the general principle that things occur “out there” without anyone experiencing them. Stoics seemed to think that genera, such as “a (any) tree” were neither true nor false, since “…the generic Man is neither Greek, (for then all men would have been of the species Greek) nor barbarian (for the same reason).” (Mates 1953, p 35) This puts realism outside the consideration of logical truth and falsehood.
Pierce, on the other hand, uses his idea of possibility to assert his idea of truth and realism. “Our idea of anything is our idea of its sensible effects…”p132 Peirce asserts realism, but says that “the meaning of our ideas” is sensible effects. However, possibility enters again:
“Who would have said, a few years ago, that we could ever know of what substances stars are made whos light may have been longer in reaching us than the human race has existed?…And if it[scientific investigation] were to go on for a million, or a billion, or any number of years you please, how is it possible to say that there is any question which might not ultimately be solved?” (C.S. Peirce ed. Houser and Kloesel 1992, p140)
So that “Reals,” as he calls them, guide our inquiries toward them in such a way that any question is answerable, and questions that are not answerable—such as Zeno’s questions or the Liar, are merely the product of language arrangements. They are not “living doubts” that drive a real investigation towards something real.
Circling back again to Kuhn, what was a mere language game can become a serious crisis for someone: “…the new paradigm, or a sufficient hint to permit later articulation, emerges all at once, sometimes in the middle of the night, in the mind of a man deeply immersed in crisis. What the nature of that final stage is must here remain inscrutable and may be permanently so.” (Kuhn 1962, p 90)
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