By
Catarina Dutilh Novaes
(Cross-posted at
NewAPPS)
(I am currently finishing a paper on the definition of the syllogism according to Aristotle, Ockham, and Buridan. I post below the section where I present a dialogical interpretation of Aristotle's definition.)
Aristotle’s
definition of ‘
syllogismos’ in
Prior Analytics (APri) 24b18-22 is among one of the most
commented-upon passages of the Aristotelian corpus, by ancient as well as (Arabic
and Latin) medieval commentators. He offers very similar definitions of
syllogismos in the
Topics,
Sophistical
Refutations, and the
Rhetoric,
but the one in
APri is the one having
received most attention from commentators. In the recent
Striker (2009)
translation, it goes like this (emphasis added):
A ‘syllogismos’ is
an argument (logos) in which, (i)
certain things being posited (tethentôn), (ii) something other than what was laid down (keimenôn) (iii) results by necessity (eks anagkês sumbainei)(iv) because these things are
so. By ‘because these things are so’ I mean that it results through these, and
by ‘resulting through these’ I mean that no term is required from outside for
the necessity to come about.
It
became customary among commentators to take ‘syllogismos’ as belonging to the genus ‘logos’ (discourse, argument), and as characterized by four (sometimes
five) differentiae:
(i)
there are at least two premises which are
posited
(ii)
the conclusion is different from the premises
(iii)
the conclusion follows necessarily from the
premises
(iv)
the premises imply the conclusion by themselves;
they are jointly necessary and sufficient for the conclusion to be produced.
My
starting point is the idea that the best way to understand Aristotle’s project
in the
APri is as the formulation of
a formal theory that could be suitably applied in particular in contexts of
dialectical disputations. In other
words, dialectical (or more generally, dialogical) considerations are always in
the background in the development of the syllogistic theory (as also argued by
(Kapp 1975)). True enough, he states at the very beginning of
APri that the framework applies both to
demonstrative and to
dialectical syllogisms. But in both
cases we may think of a multi-agent, dialogical situation (e.g. demonstration in the context of teaching),
even
if there are important differences between dialectical and demonstrative
contexts. However, while the dialectical context is inherently dialogical and
multi-agent, the demonstrative context need not be.
As
Aristotle presents it in Chap. 1 of Book I, the distinction between dialectical
and demonstrative syllogisms seems to pertain exclusively to the status of the
premises: if known to be true, and more primary than the conclusion, then the
syllogism will be demonstrative; if merely ‘reputable’ (endoxa), then the syllogism is dialectical. But with respect to the
pragmatics of the two situations,
there are other relevant differences. In particular, demonstrative syllogisms
used in the context of teaching will presuppose an asymmetric relationship
between the interlocutors (teacher and pupil), whereas in a dialectical
context, although questioner and answerer have different roles to play, their
statuses are usually comparable – they are peers. Indeed, the overall goals of
a demonstration are quite different from the goals of a dialectical
disputation, even though both can rely on syllogistic as a background theory of
argumentation.
Be
that as it may, each of the clauses formulated by Aristotle and numbered above
can be given compelling dialogical, if not dialectical, explanations (on
occasion I will also refer to demonstrative contexts). Let us discuss each of
them in turn.
(i) Multiple premises. This requirement
excludes single-premise arguments as syllogistically correct. Indeed, in the
formal theory subsequently developed in APri,
the arguments considered are almost exclusively those that we now refer to as
syllogistic arguments, namely composed of two premises and one conclusion, all
of which are categorical sentences of the A, E, I, O forms. But as often noted,
this definition excludes for example the conversion rules (from AiB infer BiA
and vice-versa; from AeB infer BeA and vice-versa), creating some difficulty to
account for the nature of the validity of these rules. Moreover, consider the
following description of the general enterprise by Striker:
Aristotle intended his syllogistic to serve as a general
theory of valid deductive argument, rather than a formal system designed for a
limited class of simple propositions. (Striker 2009, 79)
If
we follow Striker (as I think we should!), the specific features of the theory
later developed in APri should not be
taken to explain the general definition at the starting point: this would
amount to putting the cart before the horse. Indeed, it is the formal theory that
is meant to offer a regimented account of the conceptual starting point, which
is the general notion of a valid deductive argument. So this specific feature
of the formal apparatus cannot be summoned to explain this aspect of the definition.
What
could then explain the requirement that there be multiple premises? As noted by
Striker (2009, 79), the verb ‘to syllogize’ originally meant something like ‘to
add up’, ‘to compute/calculate’, and so it immediately suggests the idea of
‘putting things together’, of a fusion of more than one element (a point often
made by the ancient commentators).
Plato
already used the term ‘to syllogize’ in the sense of ‘to infer’ or ‘to
conclude’, which Aristotle seems to have adopted. Indeed, from a dialectical/dialogical
perspective as illustrated in Plato’s dialogues, the multiple premises
requirement makes good sense. In a typical dialectical situation, the
questioner (e.g. Socrates) elicits a number of discourse commitments from the
answerer, and then goes on to show that they are collectively incoherent – for
example, because they entail something absurd – thus producing a refutation.
Typically, a refutation will not come about with only one discursive
commitment: it is usually the interaction
of multiple commitments that gives rise to interesting (and sometimes
embarrassing!) conclusions.
Notice
also the use of the terms ‘posited’ and ‘laid down’, which have a distinctive
dialectical flavor. They introduce the dimension of a speech-act, of an agent
actually putting forward premises to an interlocutor or audience, again
suggesting multi-agent situations. Later authors such as Boethius will make the
multi-agent dimension even more explicit, adding that the premises are not only
laid down by the producer, but also granted by the receiver.
(ii) Irreflexivity. Aristotle’s
requirement that the conclusion be different from the premises seems puzzling
at first sight, since it entails that the consequence relation underlying
syllogistic is irreflexive. This is in tension with the currently widely accepted
view that reflexivity is a core feature of deductive validity.
However,
here again, taking into account the various contexts of application of
syllogistic arguments, irreflexivity makes good sense for each of them (as
argued in
(Duncombe 2014)). Indeed, in a demonstrative context, the function of
a syllogism is to lead from the known to the unknown, and so obviously premises
and conclusion should be different. In a dialectical context, it makes no sense
to ask the opponent to grant as a premise precisely that which one seeks to
establish as a conclusion; this would amount to an instance of
petition principii. So the irreflexivity
of the syllogistic consequence relation is exactly what one would expect, given
the applications Aristotle seems to have in mind when developing the theory.
(There are issues of propositional identity that arise in connection with this requirement (e.g. are logically equivalent propositions such as AiB and BiA ‘the same’?), but we will set those aside for the present purposes.)
(iii) Necessary truth-preservation.
Aristotle distinguishes syllogistic arguments from those whose premises make
the conclusion likely but not certain, such as induction or analogy. It is in
this sense that his main target seems to be the notion of a valid deductive
argument, but from the start necessary truth-preservation will be a necessary
but not sufficient condition for deductive validity (in particular, in light of
the three other clauses).
There
is much to be said with respect to why the ‘results by necessity’ clause makes
sense in the different contexts of application of syllogistic arguments, in
particular demonstrative and dialectical contexts, but let us keep it brief for
the present purposes. In a dialectical context, an argument having this
property will force the opponent to grant the conclusion, if she has granted
the premises, so it is a strategically advantageous property for the one
proposing the argument. In a demonstrative context, Aristotle’s whole theory of
demonstration is premised on the idea of deriving rock-solid conclusions from
self-evident axioms, and thus again necessary truth-preservation becomes advantageous.
(iv) Sufficiency and necessity of the
premises. This is perhaps the most obscurely formulated of the four clauses
in the definition, and indeed Aristotle goes on to offer a gloss of what he
means, which is however still not very illuminating. In the Topics, his phrasing is more
transparent, as described by Striker:
The definition as given in the Topics is clearer in this respect: it has the clause ‘through the
things laid down’ instead of ‘because these things are so’. In this passage,
Aristotle adds the remark that this clause should also be understood to mean
that all premises needed to derive the conclusion have been explicitly stated.
(Striker 2009, 81)
This
clause has been variously interpreted by commentators. It seems to amount to
some sort of relevance requirement: it must be
precisely in virtue of the premises that the conclusion comes
about. To be sure, the premises may be false or uncertain (at least outside
demonstrative contexts), but the conclusion must be produced
through them. Some commentators, in
particular in the Arabic tradition, have interpreted this clause as a
requirement for an essential connection between premises and conclusion. But the requirement can also be interpreted logically as stating
that no premise is
redundant for the
conclusion to come about; all of them are de facto needed for the conclusion to
result of necessity. (This is indeed one of the two main formulations of the
requirement of relevance in modern relevant logics, known as ‘derivational
utility’
(Read 1988, 6.4).) This requirement is also often discussed in
connection with the fallacy of False Cause, which we will discuss briefly below.
Moreover,
as Aristotle’s gloss suggests, this clause can also be read as the requirement
that everything that is needed for
the conclusion to result of necessity has been explicitly stated; there are no
hidden premises required (“no term is required from outside”). And so, this
clause may be read as the requirement that the premises laid down are exactly those needed for the conclusion
to come about; no more, no less.
In
demonstrative contexts, this clause is very natural: for Aristotle, a
demonstration is an explication unearthing the causes of a given phenomenon, and so both redundancy and lack of
explicitness go against this desideratum. In dialectical contexts however, both
these requirements are less straightforward: the participants may have a fair
amount of endoxa in common, which
could plausibly be taken for granted without being explicitly put forward; and
redundancy may be advantageous in purely adversarial contexts, as asking for
various redundant premises may serve the strategic purpose of confusing one’s
opponent. But in the Topics,
Aristotle wants to move away from the purely adversarial dialectical disputes
(though he also gives advice on how to perform well in such cases – see also
the Sophistical Refutations) and
towards a more cooperative model – dialectic as inquiry, where two parties
together consider what would follow from given assumptions (Topics VIII.5). In such contexts, redundancy
would be out of place, and relevance comes out as a notion related to
cooperativeness.
