Forms of logic: Discourse, diagrams, and proof

In this dissertation, it is argued that the existence of sound diagrammatic formal systems does not suffice to legitimate the use of diagrams in mathematical proof.;The dissertation begins with the motivation and development of a "pragmatic" theory of argumentation in which proofs are taken to be artefacts used to discharge discursive responsibilities. With this framework it is shown that traditional formal logic enforces a distinctive model of everyday, informal argument. In particular, it is explained how formal derivations can be taken to be idealized exemplars of proof in virtue of the degree to which they may be used to discharge the discursive responsibilities of univocality, explicitness, and fine-grainedness.;It is then argued that traditional formal derivations are able to fulfill this role due to certain features of the linguistic representation systems they employ. Diagrammatic representation systems lack these features or possess them to a lesser degree, and hence cannot support the same idealized discursive activities supported by linguistic ones. To the extent that philosophical practice implicitly privileges the idealizations of traditional formal logic as being constitutive of proof, diagrammatic representations are thus doomed to second-class status in argumentation. This suggests that the legitimization of diagrammatic reasoning or proof would require a significant broadening of what is taken to be the proper subject-matter of logic.