...mathematical entities previously acquired, and in the shape of mathematical species ie properties supposable for mathematical entities previously acquired and satisfying the condition that if they are realized for a certain mathematical entity, they are also realized for all mathematical entities...

...shape of mathematical species, ie properties supposable for mathematical entities previously acquired, satisfying the condition that if they hold for a certain...entity, they also hold for all mathematical entities which have been defined to be 'equal' to it, definitions of equality having to satisfy the conditions...

...mathematical objects, called species. As he puts it, a mathematical species is a property (...) supposable for mathematical entities previously acquired, and...entity, they also hold for all mathematical entities which have been defined to be equal to it, relations of equality having to be symmetric, reflexive...

...ie, properties supposable for mathematical entities previously acquired, and satisfying the conditon that, if they hold for a certain mathematical entity, they also hold for all mathematical entities which have been defined to be equal to it, relations of equality having to be symmetric, reflexive...

...entities previously acquired...; secondly in the form of mathematical species, ie properties supposable for mathematical entities previously acquired, and...entity, they also hold for all mathematical entities which have been defined to be equal to it. (ibid.: 142) Mathematics, for Brouwer, is first and foremost...

...experiences of the creating subject; Secondly, in the form of mathematical species, ie, properties supposable for mathematical entities previously acquired, and...entity, they also hold for all mathematical entities which have been defined to be equal to it, equality having to be symmetric, reflexive, and transitive,...