On Gödel’s “Platonism”

Platonism in mathematics ( 1935 )

With your permission, I shall now address you on the subject of the present situation in research in the foundations of mathematics. Since there remain open questions in this field, I am not in a position to paint a definitive picture of it for you. But it must be pointed out that the situation is not so critical as one could think from listening to those who speak of a foundational crisis. Fro...

The Conceivability of Platonism†

It is widely believed that platonists face a formidable problem: that of providing an intelligible account of mathematical knowledge. The problem is that we seem unable, if the platonist is right, to have the causal relationships with the objects of mathematics without which knowledge of these objects seems unintelligible. The standard platonist response to this challenge is either to deny that...

Biolinguistics today and Platonism yesterday

This contribution expounds on ideas put forth by a group of New York City generative grammarians that language possesses certain essential features that are uncaused and adhere to an abstract ideal form. An analogy of the situation with language is made with certain natural properties of numbers. It is also noted that this situation contrasts with that of the functional structure of human color...

Platonism vs. Nominalism in Contemporary Musical Ontology

Analyzing Plato’s Arguments: Plato and Platonism

Does Plato have a philosophy? If so, what is it and how does he argue for it? Simple questions. But there are well-known obstacles standing in the way of their answer. First of all, Plato writes dialogues; and it is often unclear which character, if any, in a given dialogue speaks for Plato. Secondly, when a character in a dialogue advances a thesis, it is often unclear what the thesis is. And,...