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This chapter examines the role of definition in mathematics in the light of the theory of definition developed in the preceding chapters. It identifies five or six kinds of definition that occur in mathematical systems, or at least in connexion with them. These include (i) abbreviations, i.e., the introduction of a new term to mean the same as a certain complex of old terms; (ii) the analysis of concepts; (iii) the analysis of concepts into specified concepts of the system; (iv) the improvement of concepts, especially their alteration so that they can be analysed into specified concepts of the system; (v) the nominal definition of the symbols of the system, and perhaps also (vi) co-ordinating definition, if this is both a genuine form of definition and distinct from the above.

*Keywords: *
definition;
mathematics;
mathematical systems

*Chapter.*
*3183 words.*

*Subjects: *
Philosophy of Mathematics and Logic

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