I’ve been thinking about that old saw, the debate between rationalists and empiricists. Where does knowledge come from? Everyone is more or less agreed that it comes from sensory experience. The debate is between those who think it also can come from somewhere else – rational reflection, pure intuition a la Kant, or some Platonic faculty. The empiricists think that knowledge is only ever created by sensory contact with the world. A priori reasoning can only ever be ’empty’ – the mere manipulation of ways of saying the same thing. Rationalists can agree that there is such a practice as merely deriving the analytic or syntactic consequences of existing knowledge. But they also claim something more: that genuinely new knowledge can be generated a priori.
What can the subject of this new knowledge possibly be? The logical empiricists ruled out the possibility of new (or we could say, synthetic) a priori knowledge using a linguistic argument. The meaning of any proposition is given by picturing some state of affairs, or by being formally isomorphic with each of some set of pictures of affairs (this is the Tractatus in a nutshell). But I don’t see any compelling reason to believe that this is a correct picture of language in general. It’s certainly a good picture of some of what we do with language. Maps come to mind as an example where this picture-theory of language is most literally true: the relations between the elements mirrors the relations between elements of the world, displaying them.
But there are precious few people willing to claim that picturing states of affairs is all language is good for. And maybe, the rationalist would like to suggest, one of the things that language can do is picture the space of possibility. Kant thought he could describe the space of possible experiences with the categories. Steven Wolfram thinks we should do experimental computer science, making inductive generalizations over the space of possible programs.
But I’m having trouble drawing a clear a priori/a posteriori line. If a simulation is inspired by empirical data, are the results we get from it empirical? The purely syntactic consequences of observations statements are surely themselves empirical results. As truth is preserved, so are empirical foundations. But there seems to me a large swath of ambiguous cases, where the empirical world informs our reasoning indirectly. What do we say about them?