Handbook of the History of Logic: - Fordham University Faculty

Logic in the 14 th Century after Ockham 439
nians excelled not only in logic; their works on natural philosophy were probably
even more influential; they are often viewed as precursors of the ‘mathematical
turn’ in physics to take place a few centuries later (see [Sylla, 1982, 541]).
The main authors among the Mertonians of the first half of the 14 th century (for
our present purposes) are: Thomas Bradwardine, William Heytesbury, Richard
Billingham, Roger Swyneshed (not to be confounded with the famous Richard
Swyneshed, also a Mertonian and in fact known as ‘The Calculator’), and Richard
Kilvington (for a more detailed presentation of each of these authors, see [Ashworth
and Spade, 1992]).
Until not so long ago, it was though that Thomas Bradwardine’s contribution
to logic was, to say the least, meager, and that his main contributions were to
be found in the field of natural philosophy, mathematics and theology. But a
recent interest in Bradwardine’s insolubilia (including a new edition of the text
now in preparation by Stephen Read) has arisen, showing that his work on Liarlike
paradoxes was extremely innovative and sophisticated (cf. [Read, 2006b]).
Since I will not be dealing with insolubilia in this chapter (as they are the topic
of a different chapter in this volume), Bradwardine will not figure prominently in
the analyses to follow. But his historical as well as philosophical importance must
not be overlooked.
William Heytesbury was seemingly more prolific than Bradwardine. The list
of his still extant works is rather long, and includes treatises on consequence and
obligations (which are only to be found in manuscripts — cf. [Longeway, 2003,
section 2]), an influential treatise on divided and composite senses, some work on
insolubilia, among others. But he is most famous for his Regulae solvendi sophismata
(1335) 10 , a work composed of six parts, where logical, semantic and physical
sophisms are dealt with. In the first part he deals with the paradoxical propositions
known as insolubilia, and his approach to them was later to be influential,
especially in the continent (e.g. Peter of Ailly’s treatment of insolubilia). The second
part is dedicated to what we now call ‘reference in opaque contexts’; the third
and fourth parts deal with semantic puzzles (related to the supposition of relative
pronouns, in the third, and to the terms ‘begins’ and ‘ceases’ in the fourth); the
last two concern physical puzzles. Thus, since the subject-matter of the first two
parts is to be dealt with elsewhere in this volume, and since the last two parts do
not concern logic and/or semantics directly, in the analysis to follow Heytesbury
will not figure prominently. Nevertheless, it is important to notice that Heytesbury
was to become very influential in Italy in the 15 th century (while almost entirely
forgotten in England), again exemplifying the exportation of British logic to Italy
in the 14 th and 15 th centuries (see [Braakhuis, 1982]).
Richard Billingham, another influential Mertonian (apparently a few years younger
than Bradwardine and Heytesbury), was most known in his own time for one of his
works, his Speculum puerorum [Maierú, 1970; de Rijk, 1975; 1982], even though he
also wrote on all the traditional topics in 14 th century logic (obligations — also in-
10 A transcription of the text by F. Pironet, en route for a critical edition, can be found at
http://mapageweb.umontreal.ca/pironetf/Sophismata.html