Episode 82: Robert May discusses Frege and the problem of identity
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What is the problem of identity that Frege addresses?
Hey, Matt Segman here from Elucidations. Before we get going today, I just thought I'd ask if you're a fan of the show, to maybe go to our iTunes page and leave a rating and or review, and that way more people can discover it. Alright, thanks.
Hello, welcome to Elucidations, a philosophy podcast recorded at the University of Chicago. I'm Matt Teichman, and with us once again is Robert May, Distinguished Professor of Philosophy and Linguistics at the University of California, Davis. And he's here to talk about Frege and the problem of identity. Robert May, welcome back. Thank you, Matt. It's a pleasure to be back. So the problem of identity is a big one in twentieth century philosophy, and it goes back to the work of the philosopher Gottlob Frege, who we've talked about before a little bit on the podcast. Maybe we could just start by setting the problem up. So what is the problem exactly?
Well that's that's an interesting question, Matt. One very general way of putting it in way which you often hear it put in sort of your first class in uh philosophy of language often, is what's the difference between A equal A and A equal B. Now that's a very general way and there's all sorts of things that people say about this. My interest is in the way it presented itself in the work of Frege and to Frege in his time. It's a very interesting problem. We today often think of this as kind of a problem that sort of occurs to Frege and is discussed by him, but yet it was actually a very general problem at the time Frege was writing. It was well known and it was well known in the context of the type of project that Frege was concerned with.
If we look, what we see is that there's kind of two ways that people looked at it at the time. There was a way in which it was presented to Frege, and there's a way in which Frege presented it back, if you will. The way it was presented to Frege, it became a problem in the context of what was truly Frege's life's work, his mathematical project, which we know is logicism. So, in a very general way, logicism is a problem that goes really back to the ancients. And you can trace it through all sorts of areas of philosophy leading to the late 19th century. And it's the idea that if we really understood how people actually understood thinking in some very deep way, the following become manifest that fundamental aspects of mathematics
mathematics are just reflections of reasoning. But Frege's great breakthrough was that he took the idea that mathematics and our understanding about logic had advanced to the point where with certain new logical insights about logic, this project, logicism, could be accomplished for the most fundamental area of mathematics, arithmetic. So what Frege's project of logicism is, it's the reduction of arithmetic to logic. But Frege's great insights, or part of Frege's great insights, arise because to make this reduction required deep insights, which are core to our thinking of logic today, and which originate from Frege and his first book written in 1879, Begriffschrift. So the first thing is that the importance of the puzzle and the way it is it comes to be and thought about in Frege's work is one is trying to understand this logis project.
Now, central to the logicist project is if it's going to be a reduction of arithmetic to logic, it must be the case that there are no residue of irreducible mathematical terms. All of them have to somehow be analyzed as logical notions. And Frege does this, and partly the way he does it is in his very famous logical definition of the natural numbers. But the key notion for our concern today is with the notion of identity. So if we look at a simple arithmetic sum, 2 plus 3 equals 5, the concern is what do we mean by that double bar that we write down? If it's to be a notion which is a mathematical mathematical notion, a notion of arithmetic or mathematical equality, then of course and that was not reducible to some logical notion, then of course it would be the case that Loch's project would simply collapse, because it would fail to be what Frager took it to be, which was a reductionist project.
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Chapters
8 chapters
1
What is the problem of identity that Frege addresses?
0:00–7:12
2
How does Frege’s logicism aim to reduce arithmetic to logic?
7:12–11:58
3
Why does the equation 2 + 3 = 5 raise a puzzle about identity?
11:58–16:27
4
What is Leibniz’s problem and how does it challenge Frege’s view?
16:27–21:31
5
How does Frege distinguish sense and reference in identity statements?
21:31–26:26
6
Why do statements like 2 + 3 = 5 have greater cognitive value than 5 = 5?
26:26–31:49
7
How do proper‑name examples (e.g., Mark Twain vs. Samuel Clemens) illustrate Frege’s theory of sense?
31:49–36:34
8
Why is the problem of identity considered a central issue across analytic philosophy?
36:34–40:54
Speakers
1 identifiedMore from Elucidations
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