II would like to participate in the deliberations on Diagrams connect. I mentioned some problems of logic. Now I became aware of a passage from Aurobindo:
"Logic, by its very nature, is intolerant even of apparent contradiction; its method is verbal, ideative; it accepts words and thoughts as rigid and iron facts instead of what they really are, imperfect symbols and separate sidelights on truth." (Aurobindo Isha Upansiad p. 570)
For a while, I was taken with the logic of possible worlds. David Lewis is a philosopher we discussed in the advanced seminar. In 1986 he published On the Plurality of Worlds. The basic idea is a radical answer to a major problem of logic in epistemology. If true propositions refer to facts in the world, what do false propositions refer to? Davis Lewis's answer, somewhat abbreviated, is that there are actually no false propositions. Sentences can only be false relative to a world. A sentence such as "There is a tree outside my window" is true if there is a tree outside my window. If another person says this sentence in a place where there are no trees, the sentence is false. So it depends on the context. Very few sentences are universally true. These include, for example, mathematical propositions.
Counterfactual sentences
When sentences are used in the 'right' context, i.e. when they refer to facts, they are true. They mean what is the case. It is, of course, a little more complicated. Alfred Tarski came up with a nice puzzle in 1936: the Indefinability sets.
"Informally, the theorem says that the concept of truth in a language cannot be defined with the means of expression of the language itself. The proof is based on the so-called Tarski propositions, self-referential propositions of the form: I am an element of M for a set M. If one chooses the set of all false propositions of a system for M, the construction of a Tarski proposition leads to a contradiction: a true proposition that is unprovable in the system. From this it can be concluded that the set of all true propositions of a system is not definable within this system." (Wikipedia)
The problem is not trivial. What do propositions mean that cannot be proved? We now have to deal with two kinds of problems. First, the question of what sentences mean in the wrong context, and then the question of what sentences mean that are unprovable. David Lewis says that these and similar problems are very easy to solve. There is an infinite number of worlds. All propositions are true, just not necessarily in our world. If a sentence is not true here, then there is a world in which the sentence is true, it's just not my world. I have no relationship with this world, we do not share the same space or time, there are no causal links or other mechanisms of action that connect these worlds. But they must exist because they are sayable. Everything that is sayable is therefore true, i.e. it is the case, i.e. it is real - in one of an infinite number of possible worlds. But are these again countably infinitely many worlds or uncountably infinitely many worlds (i.e. infinitely many worlds in the class of natural numbers, or more, i.e. in the class of rational numbers, or even irrational numbers)? The puzzles continue...
Ein sich selbst transzendierender Materialismus
This fascinates me because David Lewis is serious about it. The logic here goes beyond itself, so to speak. That's great. It seemed like a proof of God to me. Physics has similar ideas about the multiverse, dark matter, the theory of everything or whatever else is growing in the colorful garden of those searching for the grand unified theory. The cosmos is much more complex than we can perceive or think. We really don't know the vast majority of it. Edwin A. Abbott actually made a very funny point with his classic from 1884 "Flatland: A Romance of Many Dimensions" pointed this out.
The universes are probably much crazier than we can dream of. And I am always impressed by the fact that the Vedas already knew this:
"He who knows That as both in one, the Birth and the dissolution of Birth, by the dissolution crosses beyond death and by the Birth enjoys Immortality." (Isha Upanishad, 14. Translated by Aurobino )
