What a description can say: by JOHN BURNHEIM

There are so many pitfalls here. Mathematics enables us to construct moving pictures of almost any possible state of affairs. But no picture can say that there is a real state of affairs corresponding to it in the real world. Much less can it say the picture explains or predicts some future state of affairs. It is equally meaningful whatever relationship it has to reality. There is no place for explanations within it of how we can assess it as true or false or having some other relation to anything else .

Explanation depends on counterfactual conditionals: if this had not happened that would not have happened, and mathematical logics cannot even depict what counterfactuals purport to say. So Wittgenstein in the Tractatus asserted that causality is a superstition, in the knowledge that if he was right, it was impossible to say that and many other things he wanted to say. He concluded that science (physics) contained all that could be known, and that it was utterly irrelevant to anything that mattered to us.

This conclusion was congenial to him because he was dominated, like so many others, by Spengler’s Decline of the West, and more generally by Back to Nature thinking, like Heidegger. He never shook off this conviction, continuing to think that scientism was a pandemic disease. It is, of course if we take the content of the pictures science constructs as all there is to science. But science is primarily a search for explanations, especially causal relations, knowledge of which is expressed in counterfactuals. Mathematical constructions are of great use in getting the components of those counterfactuals precise, but as tools in the process of enquiry and discovery, not as information about the composition of what the picture depicts. It is absurd to conclude from the fact that a portrait that gives a good picture of a person consists of pigments on canvas that the person depicted must consist of then too. But that is exactly what philosophers and most of us tend to do. Pictures resemble what they depict only in very limited respects.

The remedy lies in the sophisticated pragmatism of the later Wittgenstein, which cannot be reduced to a formula, but needs to be a practice of detecting and remedying the various ways in which we are misled by language and our quest for generality and simplicity.

I first realised that the operating logic of our brains is not mathematical when I realised my three year old daughter was regularly using counterfactuals, as did her peers, long before thy had learned to count.

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