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)

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

“House-builder, you’re seen!
You will not build a house again.
All your rafters broken,
the ridge pole destroyed,
gone to the Unformed, the mind
has come to the end of craving.”

-Siddhārtha Gautama (the founder of Buddhism), upon his reaching enlightenment (Dhammapada)

It was speculated by Thanissaro Bikkhu that the house meant selfhood or perhaps entity-hood in the commentary of the Dhammapada.

I would propose a model for logic that is a house. Some logical structures are immense. The light that passes through a window would be Truth, the laws that light follows as it interacts with the building would be the laws of logic, the specific form of this particular building would be the logical statements, determining the way truth(light) moves through the logical structure. The trouble is completing the logical elements- what is falsehood? Obviously it is darkness, but the building would have to have no qualities except its form- no colors, no features, just featureless glass mirrors, otherwise truth would fade as it interacts with opaque surfaces- making truth and falsehood mingle. If the walls are perfect mirrors that propagate the light perfectly, a false space would have to be totally cut off from the light. Hypotheticals would be doors, sometimes open, sometimes shut. The only danger of falling into darkness would be entering through a door and closing it, completely cutting yourself off.

The theory that comes to mind is Anaximander’s, who thought the sun was just a hole in the cosmos, where light could enter from outside the Universe. And why is this ideal of logic impossible in the real world? There are no perfect mirrors, matter has color that absorbs light, making it an intermediate between truth and falsehood. When logic from true principles is applied to real things, interacting with matter, the truth will fade into darkness as the logical statements progress, regardless of how perfectly the laws of logic are followed. If the world of logic were to be perfect, the truth could not originate from our world, or else light that is reflected back out the window of our house would fall, logically, onto ambiguous matter. Thus, passing out the window must lead to a world that looked mostly the same as the building of mirrors.

With the modern conception that words can provide totally transparent access to an object, matter would be the only medium between truth and falsehood, but words simply aren’t transparent. They grow out of metaphors, (as argued in the essay linked in my first post) the word “be” grew out of a Proto-Indo European root which also meant grow- so that someone who is aware of the ancestry of words would have resurrected the feeling of metaphor in the word “be”, coloring the word, giving it a connection that is warranted because “be” would not be what it is now without a fathering metaphor: “being is growing”.

And the design or form of this fun-house of mirrors? Would it carry nameable concepts with it, concepts one would come to know or feel by living there? It would if it had any architectural design. How is this different from allowing a word, or a sign for an idea or feeling, into our logic?

The house of logic cannot allow matter, words, or form, except in a part of the house that is totally dark and without doors- they can be allowed into the part sectioned off as unconditionally false. Otherwise we are allowing degrees of truth, qualifications of truth, and a co-mingling of truth and falsehood.

The focus of this blog (expressed in the previous post) has changed to looking for systems of truth that gradually and naturally falsify themselves. What if we allowed matter in our house, and accepted gradations of truth? How could Aristotelian logic be modified so that each “step” in a logical progression reduced the amount of truth it propagated? The goal would initially be a logic that is calculable, so while we could take our lessons on how the logical system would be set up from how light interacts with matter, the resulting system would not be realistic initially. Following the logical system leads you out of the logical system, however, since the logical laws are not perfect propagators of truth. The logic I am formulating here, while not realistic, leads into a real world.