A previous instalment showed how Descartes established the activity of modern philosophy… as a daring imaginative exploration of the possibilities of future knowledge.

But closer to home there is a very potent development which should be taken into account in re-thinking philosophy.

It is that Ludwig Wittgenstein’s principal mantra <<Don’t look for the meaning, look for the use!>> was essentially the reason why Wittgenstein’s analysis of meaning lost its lustre around the 1960s.  It was pointed out that during Wittgenstein’s lifetime the “uses” (“applications”) of mathematics were tiny compared with a huge archive of non-useful (“Academic Pure”) maths.

It was a body-blow to Wittgenstein’s analysis at the time, but now, as time has passed, it has gradually become a powerful support.

After the emergence of solid-state computers, a new vista of putative uses of maths began to be explored… they used automated (computerised) maths which was undoubtedly “useful” —actually commercially profitable. It has now (66 years later) dramatically turned the tables.  Computerised “useful” maths has now become a much larger archive of maths results than “pure” maths.

So now the table has turned, and the new situation should have re-energised Wittgenstein’s vision. He has turned out to be right after all.

Unfortunately the main corpus of Wittgensteinian philosophers is a body of theorists who prefer the pessimistic side of his thinking. So no one seems to have taken-in this putative revival of Wittgensteinism.

Plato was responsible for defining mathematics in a way which suited a smallish circle of amateur mathematicians for thousands of years, because they were looking for neatness, elegance and unexpectedness in myopic  maths research.  It was a hobby. They were not really bothered at all about others who used it to do jobs in the real world.

Charles Peirce brilliantly saw that maths was the “science of hypotheses” in the 1880s, but the professional establishment didn’t want to know.

So the “usefulness” of maths has —it is now clear— been the bit which fundamentally swayed the main body of lay observers all through history.

There are three over-hanging public U-turns which are badly needed and sadly overdue here:

(1) Maths is a priceless way to model proposed developments (like the Pyramids of Giza) and it does this by building a very secure confidence that the project can be done.

(2)  Wittgenstein’s analysis of meaning was correct.

(3) The school subject can be revolutionised by treating the meaning of the activity as an illumination of interesting proposals. It was tried for 10 years in the 1970s (Mathematics Applicable)  and the result was tangible. The jaded students who did the course soon recovered their interest in maths. (The key move is to use many examples of projects which appeal to youngsters.) It was a development which was snuffed-out by Mrs Thatcher when she decreed that “all experimental maths schemes are OUT”.

CHRISTOPHER ORMELL around 1^st June 2026