💥Cantoring away from being Russelled

Twenty-five years ago, as I was getting my masters in mathematics, I was surprised to find an unsolved puzzle about infinity at the heart of modern mathematics. Some of my first thoughts were published in philosophy journals, so I went on to do a masters in philosophy. I got it with distinction, and by thinking laterally as well as logically I found the solution and decided to write it up as a book for a general reader with no background in philosophy, logic or mathematics. Five years later, it is down to 25,000 words.

In the book (which was 28,000 words in July, and which I will re-post when I get it below 10,000 words), various logical puzzles are described and solved because the only perfectly logical solution to one of those puzzles—the puzzle about infinity—is only a logical possibility if there is a logical kind of God. In short, my book amounts to a perfectly logical proof that there is such a God.

      A hundred years ago, the mathematical puzzle was proving to be so puzzling that mathematicians translated the whole of mathematics into a new "language" (akin to a programming language) in order to lose it in that translation. And that sea-change to academic mathematics trickled down to school mathematics in the form of the new math. Which you may have heard of, because it was quite controversial fifty years ago. The mathematicians’ responses were logical enough, but this puzzle is essentially a logical puzzle. And philosophers like Bertrand Russell responded to it by modernizing logic.

      For a hundred years, scientific philosophers have been treating logical thinking as though it was a kind of computing, as something that might be done better on a computer. By explaining these logical puzzles properly, my book will revitalize philosophy. My book may also help to defuse America’s "culture war" by making logic more interesting to religious people while simultaneously showing that atheism is not really very scientific. Indeed, it is not very progressive: how could people growing up in a world with profound problems possibly acquire enough wisdom to change their world for the better? On a more mundane note, scientific research will progress in directions that are more realistic as a result of my book, so my book could herald the next scientific revolution. And of course, a lot of people will simply find it helpful to know that there is a reasonable sort of God.

☀️A Dark Vulcan

Vulcan was "discovered" by Lescarbault in 1859, in the sense that he saw something that he took to be the planet hypothesized by Le Verrier earlier that year. Le Verrier was already famous for his 1846 prediction of the existence and position of Uranus:

That prediction was based on observations of the planet Neptune. Neptune was not behaving as Newtonian dynamics predicted it would, not unless there was an unobserved planet like Uranus. A few days later, Uranus was discovered by Galle, who saw it roughly where Le Verrier had said it would be.

In 1859, Le Verrier hypothesized that observations of the planet Mercury might be similarly explained, by there being a planet between Mercury and the sun. And Le Verrier was sure that Lescarbault had discovered Vulcan.

Whatever Lescarbault had seen, it was not Vulcan. In the following decades, many observations of the absence of Vulcan were made. And while some astronomers claimed to have seen Vulcan, there seemed on balance to be no such planet. Now, the motion of Mercury was eventually explained in 1915, by Einstein. But my question is this:

Why was the balance of opinion before then not for the existence of a dark Vulcan?

Physicists only had to hypothesize the existence of dark matter, out of which Vulcan was made, in order to explain their observations:

If dark matter was a very heavy and very dark form of matter, ubiquitous in the universe, then most of the dark matter in the solar system would be clustered around the sun, possibly in the form of a dark Vulcan.

Physicists had good reasons not to hypothesize dark matter, of course. And they also had good reasons to deny the existence of celestial epicycles, which had, much earlier, been hypothesized to explain other astronomical observations (within a medieval culture).

But physicists do say that there is dark matter in the universe. Its existence is said to explain modern astronomical observations: the stars do not behave as Einsteinian dynamics predicts, unless there is dark matter.

In other words, those observations contradict Einsteinian dynamics, to some extent. Now, Einsteinian dynamics has also been contradicted by quantum-mechanical observations of Bell's inequality, to some extent, and by some other particle physics.

Did something happen to physics in the twentieth century?

Well, science did become more of a cultural phenomenon in the twentieth century.