Wittgenstein: “Thought is Surrounded by a Halo”

The Quadrature is the “halo” described here by Ludwig Wittgenstein:

“Thought is surrounded by a halo. Its essence, logic, presents an order, in fact the a priori order of the world: that is, the order of possibilities. which must be common to both world and thought. But this order, it seems, must be utterly simple. It is prior to all experience, must run through all experience; no empirical cloudiness or uncertainty can be allowed two affect it—it must rather be of the purest crystal. But this crystal does not appear as an abstraction; but as something concrete, indeed, as the most concrete, as it were the hardest thing there is.” — (Ludwig Wittgenstein, “Philosophical Investigations,” 1953)

As pointed to be S. Cullinane ( http://www.log24.com/ ) , Wittgenstein’s idea is similar to a statement by Lukasiewicz:

“Whenever I am occupied even with the tiniest logistical problem, e.g. trying to find the shortest axiom of the implicational calculus, I have the impression that I am confronted with a mighty construction, of indescribable complexity and immeasurable rigidity. This construction has the effect on me of a concrete tangible object, fashioned form the hardest of materials, a hundred times stronger than concrete and steel. I cannot change anything it it; by intense labour I merely find in it even new details, and attain unshakable and eternal truths. Where and what is this ideal construction””? A Catholic philosopher would say: it is in God it is God’s thought.” — (Quoted by P.T. Geach in “A Wittgenstein Workbook,” 1970)