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INTRODUCTION TO JEAN BURIDAN’S LOGIC
ascribe to Buridan, there are two standard philosophical reasons given for
distinguishing conditionals and rules of inference. The first is classically
expressed by Lewis Carroll in “What the Tortoise Said to Achilles,” and
takes the form of an infinite regress. Briefly, the Tortoise asserts “p” and
“If p then q” but rejects Achilles’ claim that he must perforce assert q: that
only follows, maintains the Tortoise, if he asserts “If p and if p then q, then
q.” Yet even if he accepts this principle, he continues, he need not assert q,
for that does not follow unless he also asserts “If if p and if p then q, then
q,” and so on ad infinitum. But this argument will not serve its purpose.
First, if correct, it shows that any system containing a Deduction Theorem
includes this infinite regress, though it be carefully disguised in an axiom-
schema or a schematic rule of inference. Second, the argument suggests the
seeds of its own destruction: do we not need justification for the rule of
inference, and will not this justification stand in need of justification? The
distinction does not prevent the regress.
The second argument for distinguishing conditionals from rules of
inference is based on philosophical analysis of ordinary language: it cap-
tures in a formal way the difference between assertions which do or do not
require a commitment to the truth of the first statement. One is so commit-
ted when using the inferential form, one is not so committed when using the
conditional form. Perhaps these considerations about acceptance and com-
mitment are what motivate the infinite regress given by the Tortoise—who,
after all, is dialectically arguing with Achilles, and so seeks persuasion.
The second argument is on the right track, but then there is no
overwhelming reason to distinguish the cases as being of different kinds
rather than as species of a single genus, the mediæval notion of consequence.
Hence we are not forced to distinguish them.
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Consequences are similar
to inference-rules in three principal ways: first, we have a consequence only
when it is impossible that the antecedent obtain with the consequent failing
to obtain; otherwise we do not have a consequence at all. Conditionals are
identified syntactically, though, and are no less conditional for being false in
an interpretation. Consequences thus seem more similar to inference-rules,
for there is no inference when the first formula obtains and the second does
not. Second, consequences are not specified syntactically, but are defined by
the relations obtaining between what the antecedent and consequent assert
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While the theory of consequences explores some principles about commitment, the
theory of obligationes explores in greater detail which inferential connections obtain
when the sense of a term or a sentence is altered, all else remaining the same—this
is the form known as institutio.
See Spade and Stump [1982] for a discussion of
obligationes.
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.
INTRODUCTION TO JEAN BURIDAN’S LOGIC
57
(to speak loosely). Third, consequences are called acceptable, not ‘true’ or
‘false.’
Consequences are similar to conditionals in two principal ways: first,
the sentences which appear as antecedent and consequent are used, not men-
tioned, despite the fact that technically they are not sentences (no part of
a sentence is a sentence). Second, the definition of consequence is remark-
ably similar to Lewis-Hacking’s notion of strict implication, in the modal
characteristics of the definition.
7.2 The Definition and Division of Consequences
In TC 1.3.4–12 Buridan considers the proper definition of “conse-
quence,” eventually proposing the following (see especially TC 1.3.11):
A sentence of the form “if p then q” or “p; therefore, q” or an equiv-
alent form is a consequence if and only if a sentence p
∗
equiform to
p and a sentence q
∗
equiform to q are so related that it is impossible
that both (i ) it is the case as p
∗
signifies to be, and (ii ) it is not
the case as q
∗
signifies it to be, provided that they are put forth
together, and mutatis mutandis for each class of sentences.
This definition calls for some comment. First, the constituent parts of a
sentence are not themselves sentences, which is why we must specify sen-
tences equiform to the parts of a grammatically consequential sentence,
i. e. the protasis and apodosis of the sentence; Buridan carefully calls these
the ‘first part’ or the ‘second part’ of a grammatically consequential sen-
tence.
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When we have a consequence, we may call these the antecedent
and consequent, but not otherwise. Second, the clause ‘provided they are
put forth together’ is meant to rule out cases where either part is not as-
serted (TC 1.3.8). Third, the final clause ‘mutatis mutandis for each class
of sentences’ is meant to remind us that the tense and mood of the verbs
in (i ) and (ii ) have to be taken seriously, since Buridan denies a general
formula for truth and gives criteria for each class of sentence: assertoric
or modal, past-time or present-time or future-time, affirmative or negative,
and so forth. Finally, note that the definition is semantic, because it defines
‘consequence’ in terms of the relation holding between what p
∗
and q
∗
assert
or say is the case.
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Buridan will occasionally call a grammatically consequential sentence a “consequence,”
even if it fails to satisfy his complex conditions, but this is no more than a mere
abbreviation, a harmless way of talking eliminable upon request. I shall also indulge
in this looseness when there is no danger of being misunderstood.
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Buridan is careful to argue that the supposition and appellation of terms in the pro-
tasis or apodosis is the same as their supposition in the equiform sentence p
∗
and q
∗
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.