How do we start philosophy —which can look like a word-game played by ‘philosophers’ who are either narrowly trapped in scholastic tramlines, or else are roaming about in all kinds of woolly, portentious, idiosyncratic ways?

In the previous instalment of this blog we looked at the massive progress in philosophy made by one remarkable individual, Rene Descartes, four centuries ago.  For him philosophy was not a private word-game. Rather he built his philosophy on a secure foundation of new mathematical insights, stemming from his great discovery, coordinate geometry.

In this instalment we look at how, in the 20^th century,  philosophy finally began to throw off the shackles implied by a fixation onto self-serving in-house mathematics. This was the achievement of Ludwig Wittgenstein, who started off as a Viennese philosopher, but later became a British citizen. G. E. Moore described him as the philosophical equivalent of Einstein.

Years ago there was a writer called Cyril Joad who was a permanent member of a BBC Radio programme ‘The Brains Trust’.  Joad was the programme’s resident philosopher.  He could be understood by ordinary people, which was not something which could always be said of more famous, academic, figures like Freddie Ayer or Alfred Whitehead.  Joad’s catchphrase was <<It all depends on what you mean by X (a word)>>.  It was a capital, straightforward way to start thinking philosophically, because all philosophical questions pivot on the elusive meaning of abstract words. Indeed philosophical questions typically consist of two apparently self-evident abstract claims which are patently in direct contradiction. (For example, a typical philosophical problem is how a mental act can have physical consequences.) So Joad’s first move would be to say <<It all depends on what you mean by ‘a mental act’>>.

The only problem with this effective, down-to-earth approach was that ‘meaning’ itself was philosophically problematic.  This was potentially stultifying, but the problem had long since been “solved”, after a fashion, by adopting Plato’s concept of meaning. Plato had assumed (1) that the meaning of a word is an object (item) which it names, (2) and because this can be ambiguous, it is always necessary to refer back to the ideal form of the item in question.

This Platonic approach to meaning had been around since the golden age of Greece. Plato’s success had been to answer the previously baffling question: <<what did common geometric terms like ‘a circle’, ‘a point’ ‘parallel lines’… really mean?>>

It is difficult today, forty years into the post modern era —and after some unnerving “truth decay” which  has been widely spread by trendy pessimistic gurus— to convey the sheer austere unrivalled authority Plato enjoyed within the educated class in the early 20^th century.

A common line at the time was <<All Western Philosophy is simply a series of footnotes on Plato>>.

Plato probably had this unequalled hold on educated people, because he had, it appeared, lucidly envalued the nature of mathematical truth: this stemmed, he thought, from the role of ideal forms.  From the mid-19^th century onwards mathematics had been regarded by virtually everybody as the supreme pinnacle of human knowledge. It was identified by its own superstars as <<the timeless  language used by God to create the universe!>> or in rational circles <<The Queen of the Sciences>>  or among numerate lawyers and politicians <<the Heartland of Truth>>.

At that time to claim that a statement was true was roughly to say <<If this statement could be transformed into its best, final (mathematical) form, it would be seen to be self-evidently, necessarily, timelessly correct.>>.  There was an unconscious implication here that some eternal (Godlike) standard had been met.

Wittgenstein began as a Platonist. He famously declared in his first book (the Tractatus Logico-Philosophicus(1921))   <<The world is everything that is the case!>>. He was implying that a vast definitive totality of precise, well-formed truths existed somehow timelessly. (Was this supposed to be in an abstract, metaphysical Platonic Realm?).

Of course there was no such thing —which is a way of saying that you would never get a consensus of ‘The Learned’ to agree on which items should be on the list. (The very idea was especially ludicrous in the shell-shocked, fluid context of the early 1920s when previously important states like Austro-Hungary were disappearing.)

Fortunately Wittgenstein was still young, and he was deeply bothered by these biting,  scathing comments. They set him thinking, and he started to consider how Plato had gone so badly wrong.  Ludwig was the pioneer who brought a critical, educated, trained mind for the first time to the task of looking very hard at how ordinary language actually worked.  The background notion that mathematics was so glorious that it set the necessary standard for all “lesser” kinds of meaning was ludicrous too.

Bertrand Russell had discovered a devastating paradox in set theory in 1901. It consisted of two unexceptionable logical arguments which flatly contradicted each other. The best, formal, logic was destroying its own credibility. By the 1920s there had still not been the slightest hint of a rational explanation of this shocking fact.  The situation was so bad that Russell himself, Ernst Zermelo and Abraham Fraenkel were prepared to stoop to authorising blatant fudges to deal with the problem.   (They were trick assumptions which, if adopted, made it impossible to state the paradox.)

So mathematics’ star had dipped, and it was this, really, which allowed Wittgenstein the time and space to zoom-in and try to understand the natural mechanisms of meaning as they arose in ordinary language. If mathematics had still been on its pre-1901 pedestal, he would have found himself attacked on all sides, and it would have been almost impossible for him to get anyone to take his conclusions seriously.

The in-house conceit, which had previously been widely circulated —that mathematics was an area of “eternal meaning far superior to ordinary, vague, muddled everyday language”— had become difficult to defend, because formal logic was destroying itself, and the mathematicians were descending to black arts (fudges) to try to shore-up their subject’s basic credibility.

Was ordinary language really irremediably vague and muddled?

No, certainly not, because every member of the mathematics establishment originally acquired their comprehension of this austere subject, via their own comprehension of this much-maligned ‘ordinary language’. (Every new definition in elementary mathematics has to be introduced in ways which students could understand in ordinary language.)

There is, of course, quite a lot of vague, muddled “ordinary language” about.

In large urban populations —as a result of mass literacy and mass dissemination of information— there is, of course, a great deal of sloppy language use. This does not mean that ordinary language cannot be practised with care and close attention to the telling use of words. We are not talking here about otiose legalese, or tiresome grammatical pedantry. What is at issue is the existence of a kind of very clear, expressive, plain ordinary language: the kind of thing which hits the nail on the head, and which is understood unambiguously by almost everybody. Such language does exist. Such language users are to be found.

Wittgenstein did more than anyone else to put this kind of ‘common understanding’ back on the map, as the heartland of philosophy. He showed that conversation was a kind of ‘language game’, that the meaning of many general terms stems, not from any single precise ideal, but from a loose set of family resemblances. He summed-up his universal conclusion with the injunction <<Don’t look for the meaning, look for the use!>>.

This Wittgensteinian message is often described as ‘the meaning=use theory of language’. It is much more cogent, though, than it may appear to be, when it is attacked by people trying to defend their attachment to portentious, mystic nonsense.

‘The meaning of a word’ can be fixed by looking at the use of that word when employed by those who best practise the ‘clear, expressive, plain’ standards mentioned above.   This ‘use’ is a usage, a kind of sociological fact, because it is the way it is used by the best language users. (‘Use’ here certainly does not mean simply ‘utility’ or ‘cash value’.)

The object of many court cases is to determine what the special use of a particular word is, and what it implies, for example, whether the circumstances in which something was said counted as being ‘in public’.  The main question surrounding the ‘use’ of a word often reduces to the intention of the user, and of course whether the usage of that word carries such intentions.

Wittgenstein suffered much abuse during his lifetime from the attack dogs of the mathematic establishment. But he did manage to achieve a massive step forward in philosophy. He brought philosophy down from Mount Olympus and into the ordinary arena of talk among those with sensitivity to our common language. Henceforward it would progress only insofar as philosophers were able to identify ways of speaking which quietly embodied unusual clarity and uncanny mental ease.

His method of linguistic analysis was later perfected by John Austin, who introduced linguistic thought experiment, as the principal tool needed to establish the exact difference in the meaning of similar words and phrases, like ‘precise’ v. ‘exact’, ‘started’ v. ‘began’, ‘was caused by’ v. ‘was the reason for’.

Unfortunately, though, Wittgenstein died (relatively) young,  and he left fairly large areas of linguistic analysis unexplored.

The most obvious vacuum was, ironically, mathematics itself. Here almost nobody thought that the meaning of a theorem in pure mathematics was its use.  This had a perverse effect on his legacy, because it meant that among mathematicians and mathematical scientists, Wittgenstein’s vision was almost universally rejected… while those who saw the unique value of Wittgenstein’s insights were almost all critics, humanists, classicists, historians, etc.

Fortunately Imre Lakatos came along in the early 1960s with a thoroughly naturalistic account of research in pure mathematics. Soon after, in 1969, John Lucas gave a ground-breaking, lucid account of the meaning of ‘truth’: one which broke away from the quasi-religious treatment favoured by the mathematics hierarchy. Lucas said with a striking obviousness previously overlooked, that to say that a statement was ‘true’ was to say that it could be trusted.  This brought truth, alongside mathematics, down from Mount Olympus.  In the early 1970s the present author contributed a re-evaluation of mathematics as ‘The Science of Possibility’.  His landmark paper (1972) was largely overlooked by the mathematic hierarchy, but it did spark interest from perceptive readers around the globe. It soon turned out that almost the same thing had been said by Charles Peirce in the 1890s! The support generated enabled this ‘Peircean’ approach to become the central motif of the UK school project Mathematics Applicable which was developing a new kind of teaching in maths based on this insight. Mathematics, it now became clear, was a human activity which, strongly allied with imagination, had been prosecuted from the earliest times as a way to provide synoptic insight into… proposed plans, projects, new theories, innovations, etc.

This had been overlooked by the mathematical gurus for more than two millennia. For all this time they had been treating any “use” of mathematics as local, minor, grubby, insignificant and uninteresting. In recent times, though, their position has become rather strained. They have clearly got it wrong, because almost every industry today is driven by mathematical modelling.  The neo-Peircean view explains why.  So this, in a sense, successfully completes the scheme of research started by Wittgenstein, and counters the attacks of the anti-Wittgensteinians who are still to be found in the maths establishment.

Today the naturalistic re-evaluation of truth and mathematics is gaining momentum once again, after the setbacks of the second half of the 20^th century. In next month’s blog we shall look at the philosophical implications of this historic shift.

CHRISTOPHER ORMELL   November 2020