What is your opinion about Kronecker's resistance to Cantor's set theory?

Question

It seems that resistance to Cantor's idea of "infinities" still exists even today! Is Cantorian set theory some kind of "religious" philosophy? Note that Cantor once said that his theory is a "revelation" from God.

Answer 1

Cantor's discoveries were not a revelation from God, they were a liberation from traditional constructs about mathematics. This liberation is akin to the same type of liberation one experiences when he or she discovers philosophy. It is not a religious experience, but it is similar in nature.

Cantor may have tried to make that claim because the ideas he proposed were so revolutionary. He may have felt it would help gin up some acceptance amongst his contemporaries. Remember, of course, that back then, such a claim was not considered the realm of a crack-pot like it is now. Don't hold it against him that he made such a claim, many great thinkers "couch" their ideas in terms that are more acceptable to the "masses."

As you may be aware, Plato discussed the likely reaction we'd get from others upon discovering philosophy in his allegory of the cave. Cantor's discovery, while a lesser in the order-of-magnitude, has many similarities.

One who is philosophical would not be shocked by the reaction Cantor received. Also, as I've learned over the years, in intellectual disagreements there is usually something lurking which is apparent, but not said. In this case, the vociferous criticism Cantor received is likely do to the fact that his ideas would potentially undermine those of his critics. Also, bear in mind that those critics had spent their lives developing their ideas, and most had received accolades and acclaim.

How would you like it if you were celebrated for thinking something up...then...when you're old and done, some guy (Cantor) comes along and "blows it out of the water?"

The only thing you could do is attack...attack...attack!...As Kronecker, et al did...

Answer 2

they are both cranks who had worn out ideas.
move on already.