I wonder why he thinks there are no rational arguments in favor of Platonism. I think there have been a lot of convincing ones over the last few thousand years.
The basic gist is that the basis of Platonism is metaphysical more than logical. Mysticism is the key bedrock of the form of the Good. Plato's ideal of Ultimate Truth is self-contradictory when reconciled with Geometry. Plato's lack of subtlety with syntax causes a lot of his arguments to fall flat, such as "beauty is beautiful." The analysis of the Parmenides is beautiful, highly recommended.
https://www.preposterousuniverse.com/podcast/2021/03/08/137-...