Handbook of the History of Logic: - Fordham University Faculty

172 Terence Parsons
In modern logic, molecular propositions are thought of as fundamental, since
they are used to form general statements, such as
Every A is B ∀x[Ax → Bx]
Some A is B ∃x[Ax&Bx]
Since connectives are not used to analyze categorical propositions in this way in
medieval logic, hypothetical propositions usually receive very little discussion after
Abelard.
1.9 Validity and Good Consequences
I have been speaking of “valid” moods of syllogism, whereas Aristotle merely
divided potential syllogisms into syllogisms (or “deductions”) versus patterns that
aren’t syllogisms. His criterion for a pattern being a syllogism is:
a discourse in which, certain things being stated, something other than
what is stated follows of necessity from their being so. I mean by
the last phrase that it follows because of them, and by this, that no
further term is required from without in order to make the consequence
necessary. 20
It is unclear what¸ if anything, the second proposition adds to the first. 21 Much
medieval logical theory after Abelard seems based on the assumption that the
second proposition is merely explanatory, in that the criterion for a “good consequence”
is simply that the conclusion follows of necessity from the premises. This
is a modal notion of goodness of consequence. There are thus good consequences
that are not formal, because of non-formal modality, such as:
Some donkey is grey
∴ Some animal is grey
The conclusion follows of necessity since it is necessary that any donkey be an
animal. These examples were taken very seriously.
The word ‘consequence’ was used to cover two different notions. One is an
argument (where a good argument is one in which the conclusion follows necessarily
from the premises). Another is a conditional proposition (which is good iff it itself
is necessary). There is much debate in the secondary literature over whether
Aristotle used arguments or conditionals. I have nothing to say on this. It is
clear however that medieval writers tend to use either notion, usually without
bothering to distinguish them. For example, the following wordings tend to be
used interchangeably:
20 Aristotle, Prior Analytics I.1.
21 The assumption that something more is needed is crucial to Aristotle’s discussion of the
fallacies of begging the question and of non-cause as cause in his Sophistical Refutations 168b22-
26. But in most cases, such as his reduction of all categorical syllogisms to the first figure, he
ignores this consideration.