PHYSICS A point is not an absolute thing distinct from substance and quality and the other quantities listed by modern writers, because if it was, it would be something other than a line But this is false Is it part of a line, or not? Not a part, because, as Aristotle tries to show, a line is not made up out of points If it is not part of a line—and a line is manifestly not part of a point—then they are two wholly distinct things, neither a part of the other (OPh 207) Ockham agrees with Aristotle about the impossibility of an actual inWnite, and uses the theorem to show that a point is not an indivisible entity really distinct from anything divisible If points were such atoms, there would be inWnitely many of them actually existing In any piece of wood you can designate any number of lines, each ending in a point If the points are real, then there will be inWnitely many actually existing entities, which is impossible and contrary to all philosophy (OPh 209–10) Fourteenth-century logicians and natural philosophers took an interest not only in the spatial continuum, but in the continua of time and motion One of Richard Kilvington’s sophismata (no 13) sets a problem about traversing a distance When Socrates traverses a distance A, should we say that he traverses it at any time he is in the process of traversing, or only when he has completed the process? There seems a problem either way If we take the second option, then Socrates is only traversing A when he has ceased to so; if we take the Wrst option, then Socrates traverses A inWnitely many times, since the motion is inWnitely divisible; yet he only traverses it once Kilvington deals with his puzzle sentence ‘Socrates will traverse distance A’ by drawing a distinction between two ways of spelling out the verb ‘will traverse’ In one way it is expounded as follows: ‘Socrates will traverse distance A’—that is, ‘Socrates will be in the process of traversing distance A’ And in this way the sophisma is true Moreover, the last conclusion—that in this way inWnitely often will Socrates traverse distance A—is granted; for inWnitely often will Socrates be in the process of traversing distance A The sophisma can be expounded in another way as follows: ‘Socrates will traverse distance A’—that is, ‘Distance A will have been traversed by Socrates’ Speaking in this way, before C [the moment of reaching the terminus] Socrates will not traverse distance A (Sophismata, 3286) The method of ‘expounding’ verbs had been popular with logicians since the time of Peter of Spain Favourite ‘exponible’ verbs were ‘begin’ (‘inci6 Introd., trans., and comm Norman Kretzmann and Barbara Ensign Kretzmann (Cambridge: Cambridge University Press, 1990) 187