Here are some links to find out even more:
Our guest for this episode: Dr Clare Moriarty!
For some introductory things to learn more about Berkeley's views:
We talk a bit about what it's like to on a temporary employment contract in univerisities (I think I say that I've held 2 or 3 'permanent' appointments, but I meant to say 'temporary'!), and there's widespread growing concern about the way that universities have decided to keep people on 'precarious' contracts.
We also talk a bit about some of the challenges that go with working on a topic of research that straddles several different disciplines (history, philosophy, mathematics). Jo Wolff mentions the latter in his column for the Guardian here, including a shout-out to Berkeley's ideas about tar water!
At one point in our talk we touch briefly on some examples of reviews of philosophical books (by other philosophers) which are pointedly blunt (to the point of being amusing). Here are some links:
In this episode I try (in the first couple of minutes) to summarise what I understand Berkeley's 'idealism' to involve, and then I try to explan why it might mean that a Berkeleian idealist has some resistance to some bits of mathematics. I don't think I did a great job of summarising it, but here's what I said, if it helps to read it:
Berkeley’s famous for maintaining a position that we call ‘idealism’, which says that the only things that exist are minds and mental events – that’s all there is, minds and mental events. So, for example, physical things like coconuts or trampolines or jellyfish exist only in so far as they’re being perceived by a mind. It’s as though there aren’t really any coconuts or trampolines independently of us, instead they’re just sort of composed out of bundles of our ideas. But while this is the normal story that we tell about what Berkeley thinks about everyday objects in the external world, I really didn’t know much about Berkeley’s philosophy of mathematics before talking with Clare.
I suppose one way to think about it is this: that if like Berekely you think that for something to exist it has to be perceived by a mind, then there’ll be some things that mathematicians talk about which Berkelian idealists are going to balk at. For example, mathematical work in calculus deals with infinitesimals, and one of the things that we know about infinitesimals is that they’re really hard for us humans to think about, or to imagine or conceive of. And if Berkelely’s right, and that for something to exist it has to be perceived by a mind, then since we can’t perceive infitinitesimals (even in our imaginations), I guess he’s going to want to say that they don’t exist.
And the upshot would mean that Berkeley would have to say that the whole of calculus is concerned with something that doesn’t really exist. And as it happens, that’s precisely what he did say: in his book The Analyst Berkeley refers to Isaac Newton’s infinitesimal calculus as dealing with the ‘ghosts of departed quantities’.
The challenge that Berkeley created for himself by being an idealist is that he then needed to be able to give mathematics, and the newly invented calculus (which was proving to be really successful!), a more secure foundation in the kinds of qualities that our minds can perceive.
And as Clare mentions in the episode, one person who tried to carry out this Berkelian project is Oliver Byrne (1810–1880), and Irish mathematician who wrote a work called The Trinal Calculus which says on its title page:
"The object of the Trinal Calculus, like that of Geometry, is the investigation of the propositions of the assignable extensions, and there is no need to consider quantities, either infinitely great or indefinitely small".
Byrne also made a 'coloured Euclid', a version of the first six books of Euclid's Elements "in which Coloured Diagrams and Symbols are used instead of letters for the greater ease of learners". While it sounds like the colours are there to assist people to understand the mathematics, it's clear that Byrne's ultimate goal is to show that a huge amount of mathematics can be successfully carried out without appealing to any entities (like infinitesimals) that cannot be perceived by a mind.
Shortly after we recorded this episode, Clare was working in TCD's archive of historic books, and sent me some snapshots of their copy of Byrne's Trinal Calculus (in the back of which he had included his annotated copy of Berkeley's Analyst – a gift to posterity). Here they are:
and here the text says "the differential and integral calculus, under different forms and titles, have been based on visionary notions and false logic; these defects, which Bishop Berkeley and other writers clearly exposed, are fully remedied by The Trinal Calculus"
and here's an example of one of Byrne's delighful illustrations:
