# 1. The Greek word

The Greek word corresponding to the English word enthymeme (adjective enthymematic) means (after Bailly, [enthymema]):

1. Thought, reflection.
2. Invention, particularly war stratagem.
3. Reasoning, counseling, warning.
4. A reason, a motive.

The general meaning of “thought, reflection” is present in all ancient rhetoric: “Any expression of thought is properly called an [enthymema]. (Cicero, Top., XIII, 55; p. 423). Quintilian also alludes the meaning “everything that is conceived in the mind”, to put it aside (IO, V, 10, 1).

# 2. An instance of an argument scheme

In rhetorical argumentation, an enthymeme is essentially an instance of a topic, an argument scheme@. An argument scheme is a general formula having an inferential (associative) form; an enthymeme is the application of such a formula to a specific case. This general definition combines with the following orientations.

(i) In relation to logic, the enthymeme is:

— A form of syllogism:

• A syllogism based on plausibility or on sign
• A truncated syllogism.

— The counterpart of the syllogism.

(iii) Functionally, the enthymeme is seen as a manifestation of cooperation with the audience.

(iv) Marginally, the enthymeme has also been defined as a concluding formula.

# 3. A special kind of syllogism

## 3.1 The enthymeme, a syllogism based on “a probability” or “a sign”

In the Prior Analytics, Aristotle defines the enthymeme as “a syllogism starting from probabilities or signs.” (P. A., II, 27)

An enthymeme is a probable reasoning such as:

Peter is tired, he must have worked hard.

The arguer can be charged with mistaking necessary and sufficient conditions, or trusted as knowing for sure that Peter did not spend the whole night celebrating, according to the context span taken into consideration by the analyst.

A natural sign is a proposition expressing a natural connection between two states of things. The connection can be probable (to be red is a sign or a symptom of fever) or necessary (as smoke to fire).

A probability is a proposition expressing either a probable natural relation or a social agreement:

A probability is a generally approved proposition: what men know to happen or not to happen, to be or not to be, for the most part thus and thus, is a probability, e.g. “the envious hate”, “the beloved show affection”. (Aristotle, PA, II, 27)

These are excellent examples of associative semantic inferences (+ envious, + hate); (+ love, + show love), S. Orientation; Topos in Semantic. Such substantial probabilities are based on common sense views of basic human tendencies. The corresponding topics underlie the current production of arguments; S. Common place.

The big strong man will prevail over the small weak one, and mothers love their children. Sometimes, however, this is not the case. A characteristic of reasoning from social probabilities is that it can be reversed, as expressed in the key Aristotelian topic n°21, “incredible things do happen” (Rhet, n°22, 1400a5; RR p. 373).

Consistency is generally a source of probabilities. Humans are rational and intentional beings; they make plans and are expected to act according to these plans, to remain true to their words and intentions. Their behavior is assumed to be probably consistent. Inconsistency is the sign of a defective personality, or of a basic mistake, S. Consistency; Ad hominem. Showing that the opponent is incoherent is a key tool for claims or narratives to be rejected. But consistency is only a probability, as noted in topic n°21, and probabilities cannot hold against hard evidence; they are default qualifications. Other topics are based on inconsistent behavior, people change their minds and criminal actions might be badly planned, S. Motives.

## 3.2 The enthymeme as a truncated syllogism

The enthymeme is also defined as a categorical syllogism where a premise is omitted:

Men are fallible, you are fallible.
You are a man, you are fallible.

Or the conclusion:

Human are fallible, after all you are a human!

The Logic of Port-Royal defines the enthymeme as:

A syllogism perfect in the mind, but imperfect in the expression, since one of the propositions is suppressed as too clear and too well known, and as being easily supplied by the mind of those to whom we speak. (Arnauld, Nicole, [1662], p. 224)

No enthymeme is conclusive, save in virtue of a proposition understood, which, consequently, has to be in the mind though it be not expressed. (Id., p. 207)

The example in the preceding paragraph can therefore be called an enthymeme for two reasons: on the one hand because it is based on probable indices and on the other hand because it is an incomplete syllogism. The definition of an enthymeme as a truncated syllogism is often not considered to be Aristotelian: “It is not of the essence of the enthymeme to be incomplete” (Tricot’s Note to Aristotle, PA, II, 27, 10, p. 323). Moreover, according to Conley, this conception of the enthymeme as a truncated syllogism is not widely used in ancient rhetoric. He finds it only in a passage by Quintilian (Conley 1984, p.174). However, the First Analytics does consider the case of the truncated syllogism, “Men do not say the latter [Pittacus is wise] because they know it” (PA, II, 27, 10). On the other hand, we read in the Rhetoric that:

If any of these propositions is a familiar fact, there is no need even to mention it; the hearer adds it himself. Thus, to show that Dorieus has been victor in a contest for which the price is a crown, it is enough to say ‘For he has been victor in the Olympic games’, without adding ‘And in the Olympic games the prize is a crown’, a fact which everybody knows. (Rhet., I, 2, 1357a15; RR, p. 113).

Under this definition, the enthymeme can be considered as a figure of speech by ellipsis, precisely a figure of thought.

# 4. The rhetorical counterpart of the syllogism

In the Aristotelian systematic, the proof is obtained by inference, whether scientific (logical), dialectical, or rhetorical. Aristotle considers that there are two kinds of scientific inferences, syllogistic deduction and induction. In rhetoric, scientific inference is replaced by “rhetorical inference” or enthymeme, the requirements of rhetorical discourse not being compatible with the exercise of scientific inference:

I call the enthymeme a rhetorical syllogism, and the example the rhetorical induction. (Rhet., I, 2, 1356b5, RR, p. 109)

The syllogism (scientific inference) and the enthymeme (rhetorical inference) are defined in a strictly parallel way:

When it is shown that certain propositions being true, a further and quite distinct proposition must also be true in consequence, whether invariably or usually, this is called syllogism in dialectic, enthymeme in rhetoric. (Rhet., I, 2, 1356b15; RR, p. 109)

But, unlike the syllogism, derived from true propositions, the enthymeme is drawn from “probabilities and signs” (Rhet., I, 2, 1357a30; RR, p. 113), see supra § 3.1.

The enthymeme is “the substance of persuasion”, “a sort of demonstration” (Rhet., I, 1, 1354a10, RR p. 95; 1355a5, RR p. 99). It deals centrally with the issue, the substance of the debate, “the fact” (Rhet, I, 1, 1354a25, RR p. 97. As such, the enthymeme is opposed to the reckless use of ethos and pathos, S. Emotion; Pathos; Ethos.

The enthymeme is also called a rhetorical syllogism, considered as an imperfect syllogism. These labels refer rhetoric to syllogistic. However, the scientific / dialectical / rhetorical parallelism, however attractive it may be, is problematic. If one accepts this opposition, one enters a very uncomfortable and empirically inadequate notional grid. On the one hand, the distinction between the three types of reasoning creates a divide between categorical scientific syllogism and probable dialectic syllogism, versus persuasive rhetorical enthymeme, the socially relevant discourse being posited as inherently unable to deal with well-grounded truth. On the other hand, argumentative rhetoric is straightjacketed in the opposition between technical@ evidence, rhetorical evidence proper, and non-technical proof, which obviously do not fit into the previous notional framework. Common judicial discourse routinely combines the two types of proof, in perfectly syllogistic forms of reasoning, S. Layout; Demonstration.

The reasons given for binding the enthymeme to syllogistic discourse are somewhat paradoxical. The enthymeme as a truncated syllogism is supposed to suit rhetoric because it would be less pedantic than the complete syllogism; this assumes that the missing premise is easy to retrieve. Another reason put forward is that one would use an enthymeme because the ordinary audience is composed of people of a mediocre intelligence, unable to follow a rigorous syllogistic chain. This second justification supposes that the missing premise is too difficult to recover: these two justifications are not immediately compatible.

# 5. Enthymeme and interpretative cooperation

From the point of view of argumentative communication, the enthymeme exploits what is implicit to achieve persuasion:

Everyone who effects persuasion through proof does in fact use either enthymeme or examples; there is no other way. (Rhet., I, 2, 1356b5, RR p. 109)

As Bitzer notes (1959, p. 408), the enthymematic form is a way of connecting speaker and audience in a process of co-construction of the meaning of discourse, “the enthymeme is satisfied if merely what is stated in it be understood”, (Quintilian, IO, V, 14, 24). Building a common speech space, implicitness produces intersubjectivity. The orator frames the audience as good listeners, and thus creates a “good intelligence” and an atmosphere of complicity. Communicative fusion thus contributes to the formation of an ethos: “you understand me; you can read my mind, I am like you, we are together”.

In Jakobson’s words, the enthymematic formulation of reasoning has a phatic function, that is to say, it keeps the communicative channel open. The effect of surprise associated with the ellipsis is supposed to wake up somnolent audiences: “Something missing!” (see supra § 3.2).

# 6. The enthymeme as a conclusive formula

The ancient rhetorical practice accorded a superior efficiency to the enthymeme founded on opposites. As the paragon, this specific enthymeme has appropriated the name of the class:

Although every expression of thought may be called enthymeme, the one which is based on contraries has, for it seems the most pointed form of argument, appropriated the common name for its sole possession. (Cicero, Top., XIII, 55; 423)
What you know is of no use; is what you do not know hindrance? (Cicero, Top., XIII, 55: 425).

The second sentence can be understood as a rhetorical question “so, what you do not know should be useful”.