# [FOM] Medieval debate on the universal proposition

Buckner d3uckner at btinternet.com
Sat Aug 18 04:38:36 EDT 2007

```For those who are interested in the early (medieval) development of
logic, I have a new page in the Logic Museum here

http://uk.geocities.com/frege@btinternet.com/opposition/nullohomine.htm

on the question of whether the proposition 'every man is an animal' is
true, or false, when no men exist.  This was hotly debated in medieval
times.

It is of interest to us because the debate was about whether the
universal proposition should be interpreted as a conditional (if
anything is A, it is B, whether or not anything is A) or a categorical
(affirming of all existing things that are A, that each of them is B).
Under the former interpretation, the proposition can be true when there
are no A's.  In the latter case, it is not true.

It is commonly supposed that the shift from interpreting the proposition
in the latter way occurred in the nineteenth century, and is connected
with the development of modern logic (a 'paradigm shift', if you like).
But the question in dispute much earlier.  The difficulty was that
Aristotelian logic requires that a proposition is true when the
combination of terms in the proposition (e.g. 'man' with 'animal')
corresponds to some existing combination in reality (e.g. man and
animal).  Thus 'every man is an animal' ought to be false when no men
exist.  But the church authorities such as Augustine and Anselm said
that 'essential propositions' like 'three and four are seven', or 'every
man is an animal' are perpetually and eternally true even when nothing
exists to which they apply.  Problem.

Some of the participants in the dispute were even condemned of heresy.
Siger of Brabant (fl. 1260's) argued that 'every man is an animal' is
always true because men have always existed (arguing that the essence of
man is passed on from generation to generation, and that since every man
has a parent, the number of men must be infinite in past time).  This is
obviously heretical, and Siger fled into exile, and was possibly
assassinated. (He makes a brief appearance in Dante, in Paradise,
portrayed as the victim of persecution).

As late as the 17th century, we find Suarez arguing for the
'conditional' interpretation of the proposition.  This is interesting,
as Suarez had a profound influence on Leibniz.   The debate continued,
in a somewhat different form, with Kant's concept of the
analytic/synthetic distinction, and the rest is pretty much well known.

The page linked to contains a comprehensive list of primary sources.
For some of these (from the early period of the first half of the
thirteenth century) I have located the sources and translated them.
More (including translations of Ockham, Scotus, Boethius, Suarez) to
follow.

The question is also connected with Terence Parson's view of the history
of the O proposition in the SEP here

http://plato.stanford.edu/entries/square

The sources I have located suggest that the history is not is
straightforward and clear-cut as Parsons implies in the SEP article.
Logicians in the middle ages then, as now, were profoundly divided on
all sorts of questions.

```

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