Handbook of the History of Logic: - Fordham University Faculty

590 Mikko Yrjönsuuri
suppositum [Bradwardine, internet, 47]. This step is taken in virtue of the second
part (T1.2) of Bradwardine’s first thesis, which is as follows: 17
(T1) Every proposition whose extreme:
(T1.1) has many supposita, signifies or means affirmation or
denial for one of them, and
(T1.2) if it has only one, for that.
The idea of this thesis is to formulate for the context the theory of truth conditions
that was standard at the time, usually given in the form of supposita. Propositions
claim something about the things they refer to, which is to say that they affirm or
deny something of their supposita. Bradwardine aims at a technically satisfactory
way of saying that falsehood is affirmed in ‘a’ of‘a’ itself. Thus, the subject term
of the latter part of (2), or ‘what is uttered by Socrates’ can be substituted by ‘a’
in order to move to:
(3) ‘a’ signifies that ‘a’ is false
A reference to (P2) is again needed, and again it is applied in the form (P2)* as
allowing one to move from ‘a’: p to ‘a’: q when p → q. Substituting the pronoun
‘itself’ for ‘a’, Bradwardine achieves [Bradwardine, internet, 47]
(4) ‘a’ signifies itself to be false.
Now Bradwardine is almost there, since his second thesis applies to sentences like
this. It runs as follows 18 :
(T2) If some proposition signifies itself not to be true or itself to be
false, it signifies itself to be true and is false.
Using this thesis, Bradwardine achieves for the analyzed case the crucial result.
Thus [Bradwardine, internet, 47]:
and
(5) ‘a’ signifies itself to be true
(6) ‘a’ is false.
If we collect the argument together, it runs as follows:
Proof.
(1) ‘a’ signifies that Socrates utters a falsehood
17 ”Quelibet propositio cuius extremum multa habet supposita significant sive denotat affirmationem
vel negationem pro aliquo istorum, et si unicum, pro isto.” Text and translation
[Bradwardine, internet, 38, 39].
18 “Si aliqua propositio significet se non esse veram vel se esse falsam ipsa significant se esse
veram et est falsa.” [Bradwardine, internet, 38; 39].