Interesting article. I can relate to his dictionary investigations when I was confronted with being taught about "circular definitions". I couldn't get around (no pun intended) the fact that all definitions were circular.
This is what has led me to developing ibGib, which as I stated here elsewhere (https://news.ycombinator.com/item?id=13632500) that ibGib is heavily influenced by Goedel in that it uses a SHA-256 hash of an immutable datum to effectively be the Goedelian number of that datum. So there are four fields: ib, gib, data, rel8ns. The gib is the hash of the other three fields, which allows for integrity of the data, as well as allowing it to be content addressable since the ib^gib is the address. So it's a monotonically increasing data store that focuses on the process of defining.
So instead of "proofs" that imply an ontological/objective "truth", ibGib focuses on "the meta proof" that is the prov-ing process by assigning any "proving mechanism" a number (just as it assigns anything a number). This way, you are approaching paradoxes and the like as a process of economics and evolution of proving systems. This is like the "proof" that contains the peer review process that is doing the proving.
This is what has led me to developing ibGib, which as I stated here elsewhere (https://news.ycombinator.com/item?id=13632500) that ibGib is heavily influenced by Goedel in that it uses a SHA-256 hash of an immutable datum to effectively be the Goedelian number of that datum. So there are four fields: ib, gib, data, rel8ns. The gib is the hash of the other three fields, which allows for integrity of the data, as well as allowing it to be content addressable since the ib^gib is the address. So it's a monotonically increasing data store that focuses on the process of defining.
So instead of "proofs" that imply an ontological/objective "truth", ibGib focuses on "the meta proof" that is the prov-ing process by assigning any "proving mechanism" a number (just as it assigns anything a number). This way, you are approaching paradoxes and the like as a process of economics and evolution of proving systems. This is like the "proof" that contains the peer review process that is doing the proving.