Monthly Archives: December 2018

On Gödel’s Incompleteness Theorem

This is an appreciation of Gödel’s Incompleteness Theorem of 1931. I am provoked by a depreciation of the theorem.

In the “Gödel for Dummies” version of the Theorem, there are mathematical sentences that are both true and unprovable. This requires two points of clarification. Continue reading

Antitheses

The Antitheses are the six parallel teachings, delivered by Jesus of Nazareth in the Sermon on the Mount, as recounted in Chapter 5 of the Gospel According to St Matthew, starting at verse 21. I summarize:

  1. Do not kill people; do not even get angry with them.
  2. Do not commit adultery; do not even fantasize about it.
  3. In divorce, follow the established procedure; do not even divorce.
  4. Do not forswear yourself; do not even swear.
  5. Keep retribution commensurate with the crime; do not even seek retribution.
  6. Love your neighbor; love even your enemy.

For better or worse, these are part of the cultural heritage of many of us; they are at least a commentary on the cultural heritage (the Mosaic Law) of more of us.

I write now specifically, because I think the Antitheses can illustrate or illuminate some contemporary philosophical concerns, Continue reading