8
INTRODUCTION TO JEAN BURIDAN’S LOGIC
The universality of Mental will provide the foundation for logic to be a
full-fledged (Aristotelian) science.
Ad [2]. The adequacy of a language is a matter of its resources; a
language is expressively adequate if it has the resources to express whatever
can be expressed. But Mental is literally the language of though: we think
in Mental. If we were telepaths we would speak to one another in Men-
tal; angels, who are telepaths, do so.
13
Therefore Mental is expressively
adequate, for whatever is thought must be expressed in Mental.
This approach will have certain difficulties: it is not immediately
obvious how to handle non-declarative uses of language, performatives, and
certain indexical terms. But the general aim of the project is clear even if
not all of the details are; we shall leave them to one side.
Before we discuss [3] and [4] we need to clarify the role of translation-
rules. A translation-rule correlates expressions of ordinary language with
their perspicuous canonical representations. The best-known modern exam-
ple of a translation-rule is Russell’s rule about definite descriptions, where
a sentence such as:
The present King of France is bald
is correctly “translated” in first-order logic as:
(∃x)(Kx ∧ Bx ∧ (∀y)(Ky ∧ By → (x = y)))
For Buridan translation-rules are principles saying which elements of Mental
an inscription or utterance corresponds to. We may call this correspondence
subordination.
14
An ambiguous utterance or inscription is ambiguous be-
cause it is subordinated to more than one concept or complex on concepts in
Mental; utterances or inscriptions are synonymous because they are subordi-
nated to the same concept of complex of concepts in Mental. The utterance
or inscription ‘bank’ is ambiguous because it could signify the concept of
the side of a river, or it could signify the concept of an institution dealing
in money. The utterances ‘Tully’ and ‘Cicero’ are synonymous, because
they are subordinated to the same concept, the concept of a particular in-
dividual. Buridan takes ambiguity and synonymy to be features only of
Spoken and Written. The exact nature of the translation-rules he proposes
13
This point is made by Joan Gibson [1976].
14
“Subordination” is a technical term used by Ockham; as used here it expresses (i )
which concept(s) of Mental are immediately signified by an utterance; (ii ) which
concept(s) of Mental are immediately signified by the utterance that an inscription
immediately signifies.
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.
INTRODUCTION TO JEAN BURIDAN’S LOGIC
9
ins extremely important, for it is a key element of his nominalist approach.
We shall discuss some principles when we discuss the distinction between
absolute and appellative terms in Section 4.2. If the proper explanation of
ambiguity and of synonymy is found in the translation-rules, then clearly
Mental cannot have ambiguous or synonymous terms, for there is nothing
further to which concepts of Mental are subordinated.
Ad [3]. The terms of Mental are concepts, which have a natural
likeness to their objects. An ambiguous term in Mental, then, might be a
concept that truly applied to two distinct kinds or groups of things. We
may then have a broader concept than we originally thought, but not an
ambiguous concept. More likely, though, we have a disjunctive concept,
a concept having internal logical structure.
Thus no term in Mental is
ambiguous.
What of amphiboly, that is, ambiguous sentences, in which no single
term is ambiguous, such as “Flying planes can be dangerous”? Buridan
does not want to allow amphiboly in Mental, and equally does not want
to compromise the principle that the translation-rules correlate terms with
concepts. He avoids this problem gracefully by a general rule that the sub-
jects of Mental sentences always stand for what they signify.
15
He justifies
this rule by his realism about Mental as the “language of thought”: to have
a concept is a natural likeness; to have a concept that does not stand for
that of which it is the natural likeness would be for a person to not think
about what he is thinking about—which is impossible.
Ad [4]. The nonredundancy of Mental is a matter of its containing
no synonyms. Suppose that ‘vixen’ and ‘female fox’ are in fact synony-
mous; they then differ only by their internal make-up, which is a matter
of orthography for inscriptions and phonology for utterances. The analogy
for Mental, then, would be to have two concepts which differ only in their
“internal make-up.” What could be analogous to orthography or phonol-
ogy for concepts? Nothing at all, if we consider only simple concepts.
16
15
That is, they are always in personal and never in material supposition; these terms
will be explained in Section 6.2. For this point, see for example Summulae de di-
alectica 7.3.45, where Buridan writes, “Nevertheless, it should be known that there
is only material supposition in the significative utterance, as it seems to me, for the
reason that no term in a Mental sentence supposits materially, but always [supposits]
personally, for we do not use Mental terms conventionally as we use Spoken or Written
[terms]: no Mental expression has several significations or acceptations; the passions
of the soul are the same for all, as are those things of which they are the likenesses,
as is said in De int. 1 [16
a
3–8].” The text translated here is edited by Ebbesen in
Pinborg [1976] 155.
16
This answer needs to be made more precise, since I might acquire the concept of a
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.