This blog switches from the grand philosophic issues derived from anti-mathematics, to a specific problematic feature of Wittgenstein’s conception of the nature of philosophy.  A paper in the current issue of the  journal Philosophy took the line that Wittgenstein’s concept of philosophy was essentially therapeutic.

Various commentators have taken this line, arguing that Wittgenstein swung into this ‘therapeutic’ mode partly as a result of his admiration for his Viennese compatriot, Freud.

Whether this way of classifying and conceptualising Wittgenstein’s achievement in philosophy does it full justice is another question. The obvious argument against it is the fact that there is no recognised category of linguistic-philosophic discomforted patients in need of such ‘therapy’.

At the time when Wittgenstein’s philosophic contributions made the greatest difference (the 1930s) there were many thoughtful people with deep misgivings about the social, moral and militaristic dangers of rampant irrationality, hedonism and fascism in post WW1 war-torn Europe. To suppose that any ‘therapeutic’ effect deriving from Wittgenstein’s linguistic analysis would assuage these raw worries is not convincing.

To say that linguistic analysis offers ‘therapy’ also suggests that the discomfort it attacks is essentially in the eye of the beholder. But the problems Wittgenstein actually tackled were much more serious than this. He was clearly deeply aware of the conceptual confusion which had been imported into mathematics by Russell’s simplistic arguments, such as treating all sets as mathematic objects, blackening ordinary language as being ‘naïve’, suggesting an axiom of infinity —claiming to know something which quite obviously could never be known.

Wittgenstein took the step, which was seriously unfashionable at the time. of spending years trying to get clear about the meaning of ordinary language. He persistently “worried” the problem like a dog with a bone. He clearly saw the meaning of words at the end in a new, down-to-earth, naturalistic fashion. The result was a sea-change in our attitude to the meaning of words. He finally managed to disengage linguistics from its millennia-old fixation on Plato’s mathematics-worshiping dogma.

Yes, he famously said that he was helping the fly get out of the fly-bottle. But the ‘fly-bottle’ was not just a personal syndrome which could be thrown off by ‘therapy’. It was an ancient fixation which was, in effect, totally dominating and suffocating progress in mathematics and science (and later in IT).

Yes, he agreed with Frank Ramsey that mere philosophy could not explain the universe. That was, they thought, a job for scientists. They seemed to be unaware of the extent to which the scientists were still enthralled with Platonic mathematics. And they were right that merely verbal philosophy could not throw much light onto the architecture of the universe. There were two arenas: ordinary language and extra-ordinary language. The latter included religion and science.

They were right in their rejection of Platonic fudges in maths, such as restrictive set theory and transfinite metaphysics. But Wittgenstein’s failure to pin-down the main “use” of mathematics (which Charles Peirce had correctly pronounced forty years earlier) meant that his account of meaning was vulnerable and incomplete.  To find a modelling mode which would do justice to the unexpectedness of reality would require a totally unexpected new abstract discipline, anti-mathematics. In the 1930s this was an ask much too far.

Later, philosophers of education claiming to be broadly Wittgensteinian supposed in the 1960s that their linguistic analysis could never justify 1^st order moral claims. This meant that their only contribution to solving the devilishly dangerous predicaments of simplistic education was to highlight verbal truisms. It eventually cost their approach its credibility. In the 1990s the P E R group took philosophy for education forward, by appealing to 1^st order democratic values, based on the axiom of the democratic accountability of education.

So Wittgenstein was the ground-breaking philosopher of the 20^th century and his philosophy was much more than mere linguistic therapy. However he left the problem of meaning in mathematics unsolved, thus providing his detractors with a worrying hostage. It has since been solved, using Peirce’s insight that <<mathematics is the science of hypothesis>>. This effectively consolidates Wittgenstein’s analysis of the meaning of  language, and removes him from being treated as a mere ‘therapist’.

CHRISTOPHER ORMELL 1^st March 2024