Socrates’ Examined Life

I think this emphasis on precise definitions is actually not that helpful.

Humans don't really learn from abstract definitions so much as from seeing a bunch of examples of what is and what is not something. We ran into the same issue with ML and trying to do image recognition. Turned out that trying to define precisely what a "car" and using that to recognize a car is much less helpful than training with a lot of examples of what is and what is not a car.

Although not precisely like an ML neural net, our brains are enough like one that that this is likely to be similar as well.

I think that the guy the Socrates is examining is actually doing a better job of having someone learn what courage is by giving examples than Socrates is by trying to state a precise definition for it.

As an aside, you see the same thing with "monads". There are a ton of articles trying to define a monad. However, a much better example is to take the student through the problem and then through a lot of patterns and show them the various patterns of monads.

If you've never read Plato before, I'd suggest not to start with the Republic — it is diving into the deep end of Plato. I'm saying this as someone who has recently completed Republic[1], and thoroughly enjoyed it (and fumed at it in some places).

Instead, get familiar with some of the earlier, and famous, Socratic dialogues: Euthyphro, Apology (this is referring to a "formal defense", i.e. apologia; not regret), Crito, et al — they're shorter, give you a great flavour of Socrates, and will prepare you for the Republic. An excellent English translation here is the Five Dialogues[2], a fine selection by Hackett Publishing. I'm happy that I started with this.

[1] There are many English translations; I'll strongly recommend the "Reeve Edition". This translation recasts the entire dialogue as direct speech, this makes it easy to keep track of the speakers. Ensure it is this Reeve-only edition (because Reeve also revised an earlier translation by Grube): https://www.hackettpublishing.com/republic

[2] https://www.hackettpublishing.com/five-dialogues

The definition comes later. When people learn math concepts, the definition is in fact often of surprisingly little value. They need to see examples, make examples, play around with instances and applications of the “thing”, to gain intuition and finally come back to the definition.

The abstract definition is also often (usually? always?) something that the person who came up with it also only came up with after finding the abstraction of otherwise concrete things they were working with.

Try understanding Fourier transforms, or worse, Laplace, from their definition alone. Unless you have an idea of what’s happening already, it’s extremely hard. Work with the concept for a while, and the definition appears laughably simple!

Once you did that, look up the definition of a Hilbert transform. What is that?! But in practice, it’s just “multiply all complex frequencies by j” or, much more intuitively: “rotate all phasors by 90°… i.e. put them on their side”. Unlike with the previous example, you might happily work with this one and use it a lot, and still be mystified by its definition.

And, yes, I only finally understood and later fully embraced Monads by “just using them” for a while. Now the concept is clear and they are everywhere. Use them even more, and you run into situations where Monads are not enough in practice. And now you’ve made the first step towards Arrows!

The best I can say for it is that it shows the way people think they have definitions of things, but they don't. Push on pretty much any nontrivial definition and it will fail. That observation, at least, is kind of interesting, in that it shows the limits of the way we think about stuff.

But we do think about stuff, and both bio and silicon neural nets do a pretty good, messy job of it. If Socrates had pushed harder on that, he might have gotten some real work done about the nature of thought. Instead, he always just struck me as being kind of a jerk, rather than contributing anything.