Corcoran reviews Boute’s 2013 paper “How to calculate proofs”.

MATHEMATICAL REVIEWS 14:444-555 (2014)
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Corcoran reviews Boute’s 2013 paper “How to calculate proofs”. There are tricky aspects to classifying occurrences of variables: is an occurrence of ‘x’ free as in ‘x + 1’, is it bound as in ‘{x: x = 1}’, or is it orthographic as in ‘extra’? The trickiness is compounded failure to employ conventions to separate use of expressions from their mention. The variable occurrence is free in the term ‘x + 1’ but it is orthographic in that term’s quotes name ‘‘{x: x = 1}’’. The term has no quotes, the term’s name has one set of quotes, and the name of the term’s name has two sets of quotes. The trickiness is further compounded by failure to explicitly distinguish a variable’s values from it substituents. The variable ranges over its values but its occurrences are replaced by occurrences of its substituents. In arithmetic the values are numbers not numerals but the substituents are numerals not numbers. See Raymond Boute tries to criticize Daniel Velleman for mistakes in this area. However, Corcoran finds mistakes in Boute’s handling of the material. The reader is invited to find mistakes in Corcoran’s handling of this tricky material. The paper and the review treat other issues as well. Acknowledgements: Raymond Boute, Joaquin Miller, Daniel Velleman, George Weaver, and others.
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