I would like to pick up the reflections on diagrams. I mentioned some problems of logic there. Now a passage in Aurobindo has been brought to my attention:
“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 Upanishad 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, On the Plurality of Worlds was published. The basic idea is a radical answer to a major problem of logic in epistemology. If true sentences refer to facts in the world, what do false sentences refer to? David Lewis answers, somewhat briefly put, that there are actually no false sentences. Sentences can be false only relative to a world. A sentence such as “There is a tree outside my window” is true precisely when 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 context. Very few sentences are universally true. They include, for example, sentences of mathematics.
Counterfactual Sentences
If sentences are used in the ‘right’ context, if they refer to facts, then they are true. They mean what is the case. Of course it is a little more complicated. In 1936 Alfred Tarski found a lovely puzzle here: the undefinability theorems.
“Informally, the theorem states that the concept of truth in a language cannot be defined using the expressive resources of that language itself. The proof proceeds through so-called Tarski sentences, self-referential sentences of the form: I am an element of M for a set M. If M is chosen as the set of all false sentences of a system, constructing a Tarski sentence leads to a contradiction: A true sentence that is unprovable in the system. From this it can be concluded that the set of all true sentences of a system is not definable within that system.” (Wikipedia)
The problem is not trivial. What do sentences that cannot be proved mean? So we are already dealing with two kinds of problems. First the question of what sentences in the wrong context mean, and then the question of what sentences that cannot be proved mean. David Lewis says that these and similar problems are very easy to solve. There is an infinite number of worlds. All sentences are true, just not necessarily in our world. If a sentence is not true here, there is a world in which it is true; it is simply not my world. I have no relationship with this world, we do not share space or time, there are no causal connections or other mechanisms of action connecting these worlds. But they must exist because they can be spoken of. Everything that can be said is therefore true, that is, it is the case, that is, it is real—in one of infinitely many possible worlds. But are these, in turn, countably infinitely many worlds or uncountably infinitely many worlds (that is, infinitely many worlds in the class of natural numbers, or more, that is, in the class of rational numbers, or even irrational numbers)? The puzzles continue…
A Materialism That Transcends Itself
This fascinates me because David Lewis means it seriously. Logic here, in a sense, leads beyond itself. That is magnificent. It seemed to me like a proof of God’s existence. Physics has similar ideas about the multiverse, Dark Matter, Theory of everything, or whatever else grows in the colorful garden of those searching for the grand unifyed theory. The cosmos is much more complex than we can perceive or think it. By far the greater part we do not know. Edwin A. Abbott actually pointed this out very amusingly with his 1884 classic “Flatland: A Romance of Many Dimensions“.
The universes are probably much crazier than we could dream. And I am impressed again and again 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 )
