Handbook of the History of Logic: - Fordham University Faculty

Treatments of the Paradoxes of Self-reference 583
If it is asked whether the predicate of this proposition refers to the proposition
itself, no answer can be given. For if the predicate describes the whole, the proposition
must be like it says, that is, a proposition not described by its predicate,
contrary to what was assumed, and if it does not, then the proposition is described
by its predicate, contrary to what was assumed. The author claims that
the mentioned clause cannot be a predicate in a proposition, and thus the considered
sentence-looking piece of language lacks a predicate and is not a proposition.
This of course solves the problem, but leaves one wondering why exactly the clause
cannot be a predicate [De Rijk, 1966, 113].
The same arbitrariness of the solution is visible in an even more serious way in
another example considered by the author. Suppose that on an otherwise empty
page, or embedded within a completely true text it reads
A proposition written on this page is false.
The author claims: “it must be said that this proposition cannot be written either
alone or with truths”. But what does this mean? Does the pen stop if one tries
to write something like this? The author seems to go back to something like
the distinction between asserting and putting forward discussed above. Literally,
he distinguishes between writing as “drawing figures” (figuras protrahere) andas
“representing figures” (figuras representare). The latter can, the author claims,
be cancelled (cassari). Thus, it appears that it is possible to draw on the page
something looking exactly like a proposition, but the ink will fail to become letters
and words [De Rijk, 1966, 113–114].
The third class of insolubles is discussed so shortly that it is impossible to see
what the author exactly means. The example is ‘something is not true about
itself’, and the idea appears to be that such examples are based on what it is to be
a proposition [De Rijk, 1966, 115]. However, in the short discussion the example
looks like it would belong together with the former example of using ‘proposition
not referred to by its predicate’ as the predicate. That example was classified as
a linguistic paradox. In the later treatises on insolubles the distinction between
insolubles arising from human acts or from linguistic structure seems to remain a
standard classification. The third category seems to disappear, though.
‘THE POSITUM IS FALSE’ AS THE POSITUM
As we noted, the author of Insolubilia Monacensia discusses the paradoxes of selfreference
in a distinctively disputational context, where the respondent evaluates
sentences put forward by the opponent. Also, he shows knowledge of the medieval
disputational technique of obligations. However, the disputational context plays
no substantial role in his ways of setting the paradox or his solutions of it. In
particular, he does not present the paradox as a technical obligation in the way
medieval obligational disputations were presented. The medieval logical genres of
obligations and insolubles thus started as distinct fields. Nevertheless, it seems