Dedicated to the memory of Leo P. Kadanoff.
This paper investigates the consequences for our understanding of physical theories as a result of the development of the renormalization group. Kadanoff’s assessment of these consequences is discussed. What he called the “extended singularity theorem” (that phase transitons only can occur in infinite systems) poses serious difficulties for philosophical interpretation of theories. Several responses are discussed. The resolution demands a philosophical rethinking of the role of mathematics in physical theorizing.
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