The following appear to be theses which hold for elementary propositions:
- They are a class of mutually independent propositions.
- They are essentially positive.
- They are such that for each of them there are not two ways of being true or false, but only true.
- They are such that there is in them no distinction between an internal and an external negation.
- They are concatenations of names, which are absolutely simple signs.
G.E.M. Anscombe An Introduction to Wittgenstein’s Tractatus
G.E.M. Anscombe’s commentary on Wittgenstein’s book is itself too dense to be the tutorial I was hoping for, but it still does a good job making a clear statement of some what Wittgenstein is getting at and even explaining some of the squiggly bits. (Literally squiggly–Wittgenstein has an unfortunate affection for the letter ξ, which I came to refer to as “Sigh” when it kept showing up as the variable of path integration in complex analysis because unless you’re actually Greek good luck making it look like anything but a chicken scratch.) In addition to being an accomplished philosopher in her own right, Anscombe was Wittgenstein’s student and his leading English language translator, and so exhibits exactly the right degree of respectful bemusement for the Great Man.
The list above comes from a chapter that seeks to ferret out what Wittgenstein means by “elementary proposition”, and what’s striking about it is that it says as much about what elementary propositions aren’t than what they are. Even with these ancillary readings I find that I keep saying, “Examples please!” Anscombe does offer up “Socrates is wise” as an example, but only in contrast to “Every man loves some girl”, and that is just in order to make some points about quantifiers and compositionality. You can’t use this old chestnut to infer nine other ones. I haven’t found anyone to come out and say it in so many words, but don’t think it’s possible to come up with examples of elementary propositions. That’s part of what they are. The question that remains is why. I can’t tell, but my guess is that they’re too elementary. It’s like if you’re a physicist who insists that everything is made of atoms, so someone waggles their house keys in front of your face and says, “Okay, smart guy, show me the atoms in this!”
For computer programmers, a better analogy might be this: elementary propositions are bits. Looking over the list above, at least the first four apply quite nicely to bits in computer memory. Each can be only true or false. These possible values have no further internal structure beyond the fact that the one is not the other, and a given bit in memory can be set or reset independent of any other bits. Also (skipping ahead in the Tractatus), it’s the pattern of these bits that matters, the way they form isomorphisms to structures of text, audio, or images. (Like the old joke you tell at the start of a software project, “Well we’ve got all the ones and zeros. Now all we have to do is put them in the right order.”) And finally, each individual bit is too simple to bear any significance on its own. If you say to a person, “A computer program is ultimately just a bunch of ones and zeros” and they respond, “Give me some examples” all you can say back is, “Oh, you know–one. Zero. One, one. Zero. One…”
I’m not sure if this is merely an analogy, or if you could repurpose the Tractatus to be a theory of software instead of the world as a whole, but the latter might be a good fit.