In his article on the philosophy of mathematics Ehrenfels starts with an analysis of the presentation of number and the concepts of unity and multiplicity. He denies an empirical basis to number presentations: “The presentation of number is not extracted from external perception, but is actually inserted into it” (Ehrenfels 1891, 287). Ehrenfels takes relations of difference as the foundation for the concept of multiplicity and goes on to describe the construction of numbers through counting, by successive addition of unities (Ehrenfels 1891, 289 ff.). Like other Brentanists, he comments on the limits of our cognitive capacities and points out that we can have a presentation of higher numbers only indirectly, i.e., symbolically (Ehrenfels 1891, 292, also see 289 where he refers to Husserl 1887). Ehrenfels here chooses the Meinongian terminology, speaking of indirect or founded contents (see his notes on 292 ff.), but also follows Brentano’s approach when remarking on the power of signs to function as surrogates for presentations (Ehrenfels 1891, 296). He gives an extensive critique of Kant’s famous doctrine that “7+5=12” would be an example of a synthetic proposition a priori, with a quite idiosyncratic argumentation, stating that the a priori or a posteriori character of the sum would depend on the possibility of a direct intuition of its elements, i.e., a proper presentation. If we have to externalize the process by use of signs when the numbers exceed our cognitive capacities, then how can we claim to be able to perform such calculations a priori? Ehrenfels lists several examples that involve external aids, such as the use of logarithmic tables: looking up a number on a list is hardly an “a priori” cognitive act (Ehrenfels 1891, 329). The interesting aspect of his approach is that he takes mathematics in this way as an essentially computational science, relying on external artifacts (“physical aides”) and hence as a science which necessarily has a large a posteriori component (Ehrenfels 1891, 331). In the second half of the article, however, Ehrenfels provides a critique of J.S. Mill and empiricism in mathematics, along the same lines as Stumpf had done in his habilitation work. Like Husserl and fellow Meinong-student Konrad Zindler, he points out that in the progress of calculation with signs one often hits on “unpresentable” combinations, i.e., combinations of signs that cannot be combined into a proper presentation (Ehrenfels 1891, 342). Yet, these “impossible” combinations do then lead to correct results. (This paragraph is based in part on Ierna 2011).