a beginning . 83 In his argument , Bonaventure argues that if every element of a multitude is bounded then the multitude as a whole is also necessarily bounded . In mathematical terms , Bonaventure proposes that existence of local bounds implies the existence of a uniform bound . This relation certainly holds for finite multitudes , because in finite multitudes , the largest individual bound is always the upper bound for the multitude as a whole . However , the existence of local bounds in infinite multitudes does not guarantee the existence of a bound of the
multitude as a whole . For example , a series of numbers 1 , 2 , 3 , 4 , … , n−1
2 3 4 5 n
, … is bounded above by
1 , but the series of numbers 1 , 2 , 3 , …. is unbounded . In both series , every number is bounded individually , but only the first series is bounded as a whole .
However , admitting the existence of a day infinitely distant from the present day leads to a contradiction , as Bonaventure explains . The day immediately following the infinitely distant day , is also infinitely distant from the present , and so is the next , and the next , and hence all of the days . As a result , all days must be simultaneous and infinitely distant from the present day which is absurd . 84 However , this contradiction alone does not answer the objection since the case of an infinite succession of past days without the first day remains unanswered . Bonaventure ’ s insistence on the existence of the first day arises from his conviction that all order involves a beginning , a middle term and an end and that the middle and the end depend on the existence of the beginning . Therefore , without the first term there is no order . 85 The sequence of days is ordered , so there must be the first day , and since infinity cannot be traversed , such first day cannot be infinitely distant from the present day . √ Could you then express this in terms of ‘ traversing ’ to fit your title ?
83
Dales , Medieval Discussions , 92 .
84
Bonansea , " The Question ,” 15 .
85
Ibid , 14 Page 33 of 62