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The aim of this book is to provide a realist account of the constants in physics as an alternative to the prevailing conventionalist perspective of many philosophers. To do so the author first focuses on the discussion of the most primitive categories of physical constants which underlie modern science. Subsequently, the conventionalist case is examined in depth and, while held to be coherent, is shown to provide an incomplete account of how constants and related concepts of dimensions function in science. Having repudiated the conventionalist challenge, the positive case for a realist account is then considered and is found to be comfortably accommodated by modest realist accounts such as the natural ontological attitude (NOA).