Handbook of the History of Logic: - Fordham University Faculty

318 Henrik Lagerlund
natural (or necessary), contingent, and remote (or impossible). A proposition
is in natural matter when the predicate is in the subject or it is a proprium of
the subject. The examples Peter gives are propositions like ‘A human being is
an animal’ or ‘A human being is rational’. In both these cases there is a strong
essential connection between the subject and the predicate. A proposition is in
contingent matter when the predicate can both be in and not in the subject like
in ‘A human being is white’ or ‘A human being is not white’. Obviously, if a
proposition is in remote matter then the predicate cannot be said truthfully of the
subject like in ‘A human being is a donkey’.
As we have seen earlier in this overview the doctrine of the matter of the proposition
was connected with modal propositions and modal logic, but this is not
explicitly done by any of the textbook authors. They treat modal propositions
quite independently. This particular doctrine seems more connected with truth
conditions for modal propositions than with modal propositions in themselves,
which might reflect an attempt to loosen the connection between logic and metaphysics.
They immediately go onto present equipollence rules and later embark
on a discussion of modal propositions.
Hypothetical propositions need to be dealt with before the basic rules of equipollence
can be stated, however. There are three kinds of hypothetical propositions,
namely conditional, copulative and disjunctive. A conditional proposition is made
up of categorical propositions conjoined with the words ‘If...then’. A conjunctive
proposition conjoins two categorical propositions with ‘and’, and a disjunctive
proposition does the same thing with ‘or’. It is the also common to state the
conditions under which these hypothetical propositions are true. A conditional
proposition is true, if, given the truth of the antecedent, the consequent is also
true. A copulative proposition is true if both conjuncts are true, and a disjunctive
proposition is true, if at least on of the disjuncts are true.
The part on equipollence usually begins by stating the conversion of categorical
propositions. There are three kinds of conversion, namely simple, accidental and
contra position. A simple conversion occurs when the subject and the predicate
changes place, but the quantity and the quality of the proposition are the same.
For example, the proposition ‘No human being is a stone’ converts truthfully to
‘No stone is a human being’. An accidental conversion is then when the subject
and predicate changes place, but the quantity and not the quality is changed. As
in the conversion of ‘Every human being is an animal’ to ‘Some animal is a human
being’. A contra position is when the subject and predicate change place and the
quantity and quality are the same, but the terms are changed from finite to infinite
ones. An example would be the conversion of ‘Every human being is an animal’
into ‘Every non-animal is a non-human being’.
Before turning to modal proposition some further rules of equipollence are presented.
Peter presents these:
E-rule 1: If a negation precedes a proposition (P), then it is equivalent
with P’s contradiction.
Example: ‘Not Every human being is running’ is equivalent to ‘Some