  Such arguments and objections aside, Gassendi focuses his greatest efforts to deny matter's infinite divisibility on the relevance of mathematical and geometrical considerations to physical accounts of matter's ultimate or near-ultimate particles. While acknowledging the broad conceptual parellel between physical and mathematical continua in ancient discussions (O I 262b), he warns against the mistaken notion that physical magnitudes should be infinitely divisible just because mathematical magnitudes are (O I 263b). This last observation by itself fails to establish that atoms are actually divisible. Yet Gassendi views this notion as the collapse of a major argument against atomism. More generally, though, he is less swayed by any particular arguments for or against atomism than he is by the merits and value of taking atomism as a best working hypothesis, with which we may explain a wide variety of shared properties among macro-sized objects—as well as those properties that differentiate them.