MONDAY, JUNE 20, 2022
Afternoon delights: We're prepared to admit that we succumbed—that we did so over the weekend.
We had that 12-year-old kid in mind. We decided to take another shot at Our Most Intriguing Question:
Who the heck was Kurt Gödel? Also, did he actually prove or show anything? Did his work really make sense?
Who the heck was Gödel? We perused Professor Goldstein's book about his theorems again, but we also wandered afield. We checked to see what the leading authority said.
Here's the start of what we found:
Kurt Friedrich Gödel (1906 – 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an immense effect upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, Alfred North Whitehead, and David Hilbert were using logic and set theory to investigate the foundations of mathematics, building on earlier work by the likes of Richard Dedekind, Georg Cantor and Frege.
That's the start of the leading authority's presentation on Gödel. The point we were struck by is this:
According to the leading authority, Gödel is considered to be one of the three "most significant logicians in history."
That said, you've heard of only one of the three. The other two? Not so much!
Very few people have ever heard of Frege. As far as that goes, very few people—though possibly a tiny few more—have heard of Gödel himself.
Many people have heard of Aristotle, but no one has heard of these other two. Our question would therefore be this:
What do you think that means? What does it mean when no one has heard of two of the three "most significant logicians" in the history of the western world? When no one has heard of the two "most significant logicians" of the past several thousand years!
What the heck do you think that means? Tomorrow afternoon, we'll continue along from there.
The gods have told us that we need to start posting the work which will eventually be found by that unnamed 12-year-old kid. According to The Voices, he or she will eventually find our work and will go on to save civilization, much as the Irish once did.
For that reason, these afternoon postings will continue. And yes, we still want to be convinced that Gödel's theorems—he was one of the top three of all time—actually do make sense!
Do Gödel's theorems really make sense? Yes, we're actually asking.
We don't think it's clear what the answer will be. As we noted some time back, the gods have selected Kevin Drum to be the ultimate judge.
No fair asking around in Paris! The gods are quite firm about that.
Somewhat fuller disclosure: According to The Sources, this 12-year-old kid will have the skills which equip him to save the world.
Somerby isn't qualified to discuss this topic. His questions demonstrate that. If he didn't like or understand philosophy, he should have majored in something else.ReplyDelete
Tsk. Alas, we have been chosen by the gods, but may we suggest that you, dear Bob, may want to do something about those voices?ReplyDelete
Isn’t Bob’s vision the plot from Dune?Delete
My feeling is that this question has two answers:ReplyDelete
1. Fewer people than philosophers would like are into philosophy. This is true of many of people's interests.
2. Philosophy has developed into its own study, and therefore has acquired an academic jargon. While this can give the scholars their own tools to work with and expand on their theories, it means the newest theories will likely be unreadable to the general pubic. Some highlight this as a general problem of expert vs nonexpert educators.
I'm a firm believer that all things should be explainable in layman terms. When these two agree I think you can take it to the bank:Delete
If you can't explain it simply, you don't understand it well enough. - Albert Einstein
If you can’t explain something in simple terms, you don’t understand it. - Richard Feynman
Of course some geniuses don't have the empathy or other skills necessary to do this, so the quotes are a bit misleading in that regard.
Maybe physics is that easy to explain, but other fields are not.Delete
This post is truly inane. Everybody with even a passing knowledge of these issues has heard of Godel, and practially everybody has heard of Frege. More important, Godel's theorems have been proven (by Godel, strangely enough), and have had nearly a century for mathematicians to uncover any issues with the proof. Also, the Dunning-Kruger effect is real.ReplyDelete
I'm kind of baffled that you would doubt that Godel's theorems make sense.ReplyDelete
They've been around a long time, accepted by all mathematicians. What's the case that they don't make sense?
And of course Aristotle is known for far more than his work on logic.