by Peter Salmon
On 2 October 2020, the French president Emmanuel Macron gave a two-hour speech entitled ‘The Fight Against Separatism – The Republic in Action’ at Les Mureaux, a north-western suburb of Paris. In it, Macron described Islam as ‘a religion that is in crisis all over the world today’ due to ‘an extreme hardening of positions’. While acknowledging that France was partly responsible for the ‘ghettoisation’ of large numbers of Muslim residents (‘initially with the best intentions in the world’), and that it had failed to confront its colonial past including the Algerian war, Macron insisted that radical Islam was organising a counter-society that was ‘initially separatist, but whose ultimate goal is to take over completely.’
Against this, Macron proposed a ‘republican reawakening’, including legislation that would defend the values of laïcité, enshrined in Article 1 of the French Constitution, which separates Church and state, and mandates France’s neutrality on religion – ‘Secularism,’ stated Macron, ‘is the neutrality of the state.’ One is invited to join this neutrality – an individual’s adherence to ‘the Republic’s universal principles’ gives one claim to citizenship of France. ‘We are not,’ he said, ‘a society of individuals. We’re a nation of citizens. That changes everything.’ … (continue at Aeon)
Massimo Pigliucci 
Badiou, according to this article, argues that “Set theory, however, gives us total infinity – ‘the set of all cardinal numbers’, ‘the set of odd numbers’, ‘the set of fractions’ (that these are different-size infinities was recognised by the late-19th-century mathematician Georg Cantor).” The author clearly regards this as an acceptable approach. Unfortunately, it’s utter nonsense.
Anyone with any understanding of what Cantor actually proved would realise that his achievement consisted in defining the size of an infinity in such a way that ‘the set of all cardinal numbers’, ‘the set of odd numbers’, ‘the set of fractions’ all have *exactly the same size*, thus exorcising a paradox dating back, I believe, to Galileo, while the set of all real numbers has a larger size, and an important part of modern mathematics grapples with the problem of the relative sizes of different kinds of infinity, with the set of all cardinal numbers (and by extension all numbers that can be specified in a finite number of symbols) being the smallest infinite set.
Which leaves me, as a layman, with a real problem: if the article I am reading contains such elementary errors regarding its subject matter, how can I trust what it tells me? And if I can’t trust it, then, since I am obviously not going to read for myself the dozens of philosophers cited, how can I learn from it?
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Paul, you put the finger on a big problem here. The reason I suggested this article is because, I think, is a good summary of the postmodernist approach. One major problem with that approach — which the article does NOT explore — is precisely that often these people don’t know what they are talking about when it comes to technical fields.
You pick on Badiou for good reasons. I could bring up the largely nonsensical Lacanian psychoanalysis or, even better, Bruno Latour’s famous and comic misunderstanding of general relativity.
Add to this the rather obfuscatory nature of much (though not all) postmodern writing and the conclusion (at least, my conclusion) is that there is a kernel of interesting stuff here, surrounded by a lot of bullshit.
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Hence my sense of frustration. I fully agree that my cultural and methodological biases, and my naive belief that I am objectively studying external reality, require criticism. Articles like the present one do me service by reminding me of this, and then discredit themselves by parading their technical ignorance, leaving me not much better off than I was before.
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