Handbook of the History of Logic: - Fordham University Faculty

588 Mikko Yrjönsuuri
Bradwardine wants to say that the sentence ‘a’ is false, but the sentence ‘b’
is true. This becomes even more clear if we look at how he analyses a counter
argument, which is as follows [Bradwardine, internet, 47]:
Proof.
‘a’ and ‘b’ are equivalent
‘b’ istrue
so ‘a’ istrue
To this argument Bradwardine objects that the first premise is false. To prove
this, he works out an analysis of what ‘a’ and ‘b’ signify, and it is this analysis
that really reveals what his solution of the paradox is. Thus, let us take a close
look at the argumentation in the text.
The sentence uttered by Socrates, ‘a’, is the natural point of departure. Bradwardine
says: 12
(1) ‘a’ signifies that Socrates utters a falsehood, from which it follows
that what is uttered by Socrates is false.
Unfortunately, there are different readings of the consequence mentioned here, depending
on the reference of “from which” (ex quo). What exactly is the antecedent
of the intended consequence? Bradwardine uses the consequence to apply his second
postulate (P2), which runs as follows: 13
(P2) Every proposition signifies or means as a matter of fact or absolutely
everything which follows from it as a matter of
fact or absolutely.
Here again, the “it” (ista) is not too lucid, but the natural reading would be that
a sentence means what follows from the sentence itself. In the examined example
Bradwardine applies this principle to infer that
(2) ‘a’ signifies that what is uttered by Socrates is false.
If he means the principle (P2) in the exact form quoted above, it seems that in
(1) he should have said that the consequent at issue follows from ‘a’ itself. This
is however something that the Latin sentence does not directly mean. Either it
means that the consequent follows from ‘Socrates utters a falsehood’ or that it
follows from ‘a’ signifying that. 14
12 ”a significat quod Sortes dicit falsum, ex quo sequitur quod dictum a Sorte est falsum.”
Bradwardine, [internet, 46; translation p. 47].
13 “Quelibet propositio significat sive denotat ut nunc vel simpliciter omne quod sequitur ad
istam ut nunc vel simpliciter.” Text and translation from Bradwardine, [forthcoming, 38, 39].
Roure [1970] has ‘illam’ instead of ‘istam’.
14 To apply his second postulate correctly, Bradwardine should, it seems, have said that ‘a’ is
(rather than “signifies”) ‘Socrates utters a falsehood’. However, when medieval logicians used
letters as names of sentences they often formulated this by saying that the letter “signifies”
the intended sentence. Thus Bradwardine may be intending to say exactly that ‘a’ namesthe
sentence ‘Socrates utters a falsehood’ as an explanation why he thinks that ‘a’ implies that what
is uttered by Socrates is false.