In this work I will analyze how the works of Gödel, Penrose and Bion affect the basic ideas of realism and intuitionism in the context of the philosophy of mathematics, specifically the concept of truth that has been shown by Dummett to lay at the core of the disagreement between the two camps.
I will attempt to show that all three thinkers are beyond both schools of thought and offer glimpses into a different view which I have termed Intuitive Thinking.
I will show that Bion's concept of “O” and Penrose’s concept of "understanding" coincide with Dummet's conclusion from Gödel’s incompleteness theorem. Finely I will attempt to define the concept Intuitive Thinking and discuss the limits of defining such a concept.
