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What is the infinite? Can we comprehend it? Can we experience it? In this course we will explore various ways in which philosophers in the western tradition have answered questions such as these. In the first half of the semester, we will examine theoretical treatments of the infinite that inform how we understand the fabric of our world, from the ordinary objects around us to more sublime concepts of God, space, time, and mathematics. In the second half, we will turn to arguments in aesthetics and ethics that reveal an interplay between infinity and finitude occurring before our very eyes. Philosophers we will cover include Descartes, Spinoza, Locke, Kant, Hegel, Russell, Levinas, and Arendt. Throughout, we will ask such fundamental questions as, what is the starting point of philosophy? what is its methodology? what can it achieve in terms of knowledge? and in terms of practice?