The word “sophistry” means lies and deception, the kind of thing that more and more is associated with the pronouncements of politicians. I was prompted to think about this when the word came up in yesterday’s *Guardian* crossword, set by Vlad, where it was the answer to the following clue:

Choice woman’s finally made to leave? Hear it’s fallacious (9)

How did it come about that a word with its origin in the Greek for wisdom came to have this meaning?

The sophists were teachers of rhetoric in ancient Athens. Specifically, they taught their students how to argue convincingly in the law courts. As such, they could be honoured as our predecessors in the teaching profession.

In fact, there is an even closer link. Apostolos Doxiadis, in a long article entitled “A streetcar named proof”, in the book *Circles Disturbed: The Interplay of Mathematics and Narrative* he edited with Barry Mazur, argues that the notion of proof in Euclid is a natural progression from the forensic rhetoric used in the law courts. In the courts, you would argue that if all the alternatives to X (your version of events) are all extremely unlikely, then X is very probably what happened. Euclid uses the stronger version that, if the alternatives to X are logically contradictory, then X is proved. So in some sense the sophists were on the streetcar or tram that carried us to mathematical proof.

So how did they get their bad name?

It seems that Socrates was largely responsible. The sophists’ great sin, in his eyes, is that (like modern teachers) they were paid for teaching; he gave his wisdom away for free in the marketplace (whether his listeners wanted it or not). In fact, he had independent means, and didn’t need payment for teaching. Socrates stands in a pivotal place in the European philosophical tradition; his successors Plato (in whose writings is contained all we know about Socrates’ teaching) and Aristotle set philosophy on its influential path. So Socrates’ views about the Sophists have been accepted largely unchallenged for millennia.

In fact Plato and (especially) Aristotle expressed views on mathematics which were influential but not without problems. Aristotle’s views on infinity (that it was legitimate to talk about potential, but not actual, infinity) and his system of logic kept European thought in a straitjacket which was not escaped without a great struggle.

Indeed, a long report in yesterday’s *Guardian* suggests that perhaps we have need of a sophist in Britain today. Savage cuts in legal aid resulting from the Tories’ austerity policy have meant that, especially in the family courts, thousands of people cannot afford legal representation and have to represent themselves, leading to numerous miscarriages such as denial of access to their children. Perhaps a television sophist could explain to them how to behave in this situation …

In a further coincidence, here is another of Vlad’s clues yesterday, where he (perhaps unwittingly) made it much easier than it needed to be:

Close to broke in most of country – no alternative to Tory policy? (9)

When I read this, I immediately thought “Tory policy: that means austerity”. On proceeding to justify this from the makeup, I realised that the definition is just “policy”; “Tory” is just there so that when “or” (alternative) is removed from it we get the last two letters of the answer. (The rest is obtained by putting “e” (close to broke) into “austri” (most of country)). But the *Guardian* report on legal aid makes clear that the cuts have happened since 2010, and so are certainly Tory policy.

I think it’s just a case of history being written by the victors. A useful reference and a more balanced view can be found in Kerferd, G.B.,

The Sophistic Movement, Cambridge University Press, Cambridge, UK, 1981.Those who are keen on puzzling etymologies may be equally amused by Sextus Empiricus’s “Against the Mathematicians”. Well, it does include the geometers and the arithmeticians, but also the rhetoricians and the musicians… all that nasty folk of mathematicians!