Title: Cantor's paradise and the forbidden fruit Abstract: In this talk, I discuss remarkable examples of profitable interactions between philosophy and mathematics. I am especially interested in foundational positions that are critical of today's standard "Cantorian" approaches to the concept of infinity. Critical views of infinity have their roots in foundational positions that highlight the limitation of our human condition and, for this reason, require a finitary description and treatment of mathematical entities, including infinite ones. My main concern are key aspects of the foundational reflections by mathematicians Hermann Weyl and Errett Bishop. For Weyl (1918) the sequence of the natural numbers is an ultimate foundation of mathematical thought. Bishop highlights the pivotal role of the set of integers for uncovering the computational content of mathematics. I argue that a comparison between "Cantorian" and critical views of infinity is highly fruitful. I further argue that critical views of infinity have not only produced new fundamental mathematical ideas, but also intriguing philosophical outlooks.