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  1. Tracking Reason: Proof, Consequence, and Truth.Jody Azzouni - 2005 - Oxford University Press USA.
    When ordinary people--mathematicians among them--take something to follow from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. One claim of the book is that, despite our apparent intuitive grasp of consequence, we do not introspect rules by which we reason, nor do we grasp the scope and range of the domain, as it were, of our reasoning. This (...)
     
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  • Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures.James R. Brown - 2001 - Erkenntnis 54 (3):404-407.
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  • The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.
    This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is given of diagram attribution: basic geometrical claims are classified as exact (equalities, proportionalities) or co-exact (containments, contiguities); exact claims may only be inferred from prior entries in the demonstration text, but co-exact claims may be asserted based on what is seen in the diagram. Diagram control by constructions is necessary (...)
     
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  • Why Do Informal Proofs Conform to Formal Norms?Jody Azzouni - 2009 - Foundations of Science 14 (1-2):9-26.
    Kant discovered a philosophical problem with mathematical proof. Despite being a priori , its methodology involves more than analytic truth. But what else is involved? This problem is widely taken to have been solved by Frege’s extension of logic beyond its restricted (and largely Aristotelian) form. Nevertheless, a successor problem remains: both traditional and contemporary (classical) mathematical proofs, although conforming to the norms of contemporary (classical) logic, never were, and still aren’t, executed by mathematicians in a way that transparently reveals (...)
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  • Philosophy of Mathematics, an Introduction to the World of Proofs and Pictures.James Robert Brown - 2003 - Bulletin of Symbolic Logic 9 (4):504-506.
     
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  • And so On... : Reasoning with Infinite Diagrams.Solomon Feferman - 2012 - Synthese 186 (1):371-386.
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