Meaningless is Meaningful
Today I had a long and philosophical discussion with one of my friends. He started the conversation with a baited question: “Have you ever met a Solipsist?”. How could I avoid that one? Of course the conversation delved into the nature of the solipsistic belief system, and because I do not subscribe to that system I did my best to refute it.
- The Solipsistic Hypothesis is non-falsifiable.
- Non-falsifiable postulates about the world in which they are uttered are wrong (inadmissible within that world).
- Therefore Solipsism is hokum.
We had no quarrel about the first point, but the second one required justification. After first asserting that it was an axiom (an obvious cop-out) I had to think critically to invent some proof of the statement. Because it’s formulation is recursive (it is an utterable sentence in this world) I had to take my steps somewhat carefully.
My conversation partner wished to cast out the postulate, but I had to prevent such an occurrence. It occurred to me that, although I wanted the the statement to be axiomatic (and I thought it was straightforwardly obvious), it must be provable, because it can be uttered in our world. In fact, it must be provable for all worlds, including the solipsistic ones. At this point I reasoned that a proof must exist. And because the statement is recursive, the obvious thing to try was proof-by-contradiction.
Suppose the we want to invalidate the sentence, lets assume the opposite and project ourselves into the world described. We now have a statement: “non-falsifiable postulates about this world can be right”, which describes our world. This sentence means that I can find some other sentence S which is non-falsifiable and makes reference to this world. But, because S speaks about the world and is non-falsifiable, it falls under the category ‘meaningless’; for neither logical outcome from evaluating S would change our knowledge about the world. Furthermore, there is no imaginable sense of the word ‘describes’ that would allow me to apply meaningless sentences (such as S) to the world.
Let’s verify the initial postulate “non-falsifiable sentences about the world in which they are uttered are wrong”. Because this postulate exists in our world, and we already assume our world follows logical laws (otherwise we’re doomed), it must be true in our world. If it is true and not an axiom, it must have a proof. The above argument is a proof. Behold! The postulate is sound, and doesn’t blow up in logical paradox.
The most interesting thing about postulate 2 though, is that it’s true in all possible worlds in which it can be uttered. (This reminds me of Godel’s theorems, and I’m quite sure I wouldn’t have discovered the reasoning given, without that prior exposure.) Because the Solipistic Hypothesis is a possible world, postulate 2 must occur within that world. Therefore all Solipsists are operating under a logical system which has an internal contradiction. (Back to Godel. It should therefore be possible for the Solipsist to exploit that ‘feature’ and create proof that their model is a correct and accurate description, since a logically inconsistent body of knowledge can be used to prove whatever the hell you want.) Because their system is internally contradictory, their world cannot exist (and certainly can’t be our world, which is logically consistent).