“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 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. (And by “truth” here I mostly mean the clarity and warrant that travels with what we can rightly assert—what survives transmission. Edit based in Pierre’s feedback: I will develop this idea of a clarity that degrades from true proposals partially true conclusions, to more partial conclusions, etc. The next essay will apply this loss in a truth property as a loss in the meaning of a number, or the numerousness of a number, as they progress indefinitely toward infinity. Then I will apply this idea to probability theory, which are revisions of my line of thought from 2015)

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 the light 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 dim 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 aware of the ancestry of words would resurrect 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. (For example: if a statement has “brightness” $b$b, perhaps each inferential step discounts it by a factor $k\le 1$k≤1, so that long chains necessarily dim.) 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.