Argument from OPPOSITES
We follow Freese and Rhys Roberts who use the term “(topos) from / of the opposite” in their translation of Aristotle’s Rhetoric. Ryan uses the equivalent term contrary in his discussion of the topos (Ryan 1984). Contrary is also used in logic in the pair contrary / contradictory proposition.
Since the topos plays with two pairs of opposites, the plural « topos of opposites » also seems appropriate.
In a broader sense, the terms opposition and opposite can cover a number of specific argumentative phenomena, see opposition; contradiction; contrary and contradictory.
1. Topos of opposites
Cicero recognized the enthymeme based on opposites as the archetypal enthymeme.
The topos of the opposites is the first on Aristotle’s list of rhetorical topoi:
One line of positive proof is based upon consideration of the opposite of the thing in question. Observe whether that opposite has the opposite quality. If it has not, you refute the original position. If it has, you establish it. (Rhet., II, 23; RR, p. 355)
If courage is a virtue, then cowardice is a vice.
Ryan restates the Aristotelian topos as follows
If A is the contrary of B, and C is the contrary of D,
1A — then, if C is not predicated of A, then D is not predicated of B.
1B — then if C is predicated of A, then D is predicated of B (1984, p. 97)
2. A dialectical resource
The topos of opposites is a dialectical resource, used to evaluate claims such as « A is B », “courage is a virtue.” If the proponent holds that « A is B« , then the opponent can examine the opposites of A and B.
In a dialogical format:
Confirmation – The test using the method of opposites is as follows
Question: Is courage a virtue?
Topos of the opposites:
Opposite of courage: cowardice.
Opposite of virtue: vice.
Let’s a apply the opposite of virtue to the opposite of courage:
“Cowardice is a vice.”
This proposition seems indisputable. Therefore, we can conclude that courage is indeed a virtue.
Argumentation: “Courage is (indeed) a virtue, since cowardice is certainly a vice.”
Refutation – Let’s apply the same test to the statement “Pleasant things are (intrinsically) good. »
Question: “Are pleasant things good?”
Topos of the opposite:
Opposite of pleasant: unpleasant.
Opposite of good: bad.
Derived statement: “Unpleasant things are bad.”
New question: “Are unpleasant things always bad?”
The answer is no, because cod liver oil is quite unpleasant to drink (in its natural state), yet it is good for your health.
Conclusion: unpleasant things are not always bad.
Some unpleasant things are good.
Argumentation: “Pleasant things are not intrinsically good, since unpleasant things can also be good.”
The topos of opposites can also be used to suggest practical actions:
Inhaling black coal dust made the miners sick, they will recover if they drink white milk
If the cold rain has given him a cold, a hot tea will do him good.
2.1 Linguistic and logical forms of the topos of opposites
Aristotle expresses the topos of opposites in a language that is ordinary in its construction but technical in its use of a specialized vocabulary: rhetorical terms such as topos or enthymeme, or grammatical ontological terms such as subject or predicate. These terms are indeterminate, meaning they are taken in their broadest sense: « a subject (a being), a property (a predicate) ». This is a a generic formulation of the topos.
The topos expresses a structure common to a set of enthymemes. Unlike other topoi, the logical form of the topos of opposites is very simple.
According to Ryan’s formulation (1984, p. 97, cf. above), this basic form is as follows:
1A – If A is the opposite of B, and C the opposite of D,
then, if C is not predicated of A, then D is not predicated of B.
1B – If A is the opposite of B, and C is the opposite of D,
then, if C is predicated of A, then D is predicated of B.
The clause “— is not predicated” can be read as “is not true, acceptable, possible, etc.”.
According to etWalton & al. (2008, p 107), the argument « from opposites » has two forms:
Positive form:
The opposite of the subject S has the property P.
Therefore, S has the property non-P (the opposite of the property P).
Negative form:
The opposite of the subject S has the property non P
Therefore, S has the property P (the opposite of the property non P)
In practice, the « logical form » is obtained by replacing the indefinite terms (the variables), with letters. The original proposition is written in the standard form of the analyzed propositions, « A is C » (Ryan), or « S is P » (Walton). This shorthand is, very useful because it avoids the complicated formulations that are sometimes necessary to correctly express coreference.
A « logical form », in the strong sense, would be a form that could be used in a logical calculation. But the only operation here is the actualization of the generic form (topos) into a specified form (enthymeme).
2.2 Is the topos of opposites fallacious in itself?
The topos of opposites is logically fallacious
The phrase « is not predicated” can be read as “is not true, acceptable, possible etc. »
Applied to the logical implication, « A implies B« , the topos validates the conclusion « not P implies not Q« . A sufficient condition is mistakenly considered to be necessary and sufficient. So, the conclusion is not « quasi-logical », but simply false, as a case of a negation of the antecedent (modus tollens), see Deduction.
The topos of opposites is conditionally valid
Consider an opaque box: 1) It contains two kinds of objects, cubes and spheres. 2) These objects are either red or green (or exclusive). 3) objects of the same shape have the same color.
An observer pulls an object out of the box: it is a ball, and it is green.
In this case, a ball is a non-cube, and a non-green object is red. We can safely conclude that the balls are green; and that the non balls (cubes) are non green (i.e., red).
2.3 The topos of the opposites in literature
The topos of the opposites can be found in literary passages, where it serves as poetic oratorical amplification without losing its argumentative value of confirmation.
In Milton’s Paradise Lost, [1667], Satan leads the war against the angels, and has just suffered a cruel defeat. He calls “his potentates to council”, and explains to their assembly how a new weapon of his invention — gunpowder and cannons — will enable them to take their revenge.
He ended, and his words their drooping cheer
Enlighten’d, and their languish’d hope reviv’d
Th’invention all admir’d, and each how he
To be th’inventor mifs’d; so easy’ it feemed
Once found, which yet unfound moft would have thought
Impossible.
Milton, Paradise Lost, [1667], Book VI, 498-501; (My italics) [1].
The same conclusion applies to Columbus’ egg: « what seemed impossible before seems easy after. »
2. How does the topos apply?
In the preceding cases, the topos is quite easy to apply, because it operates on the basic linguistic structure “A is B” (as in the previous cases), which can be easily transformed into “Non A is non B”.
The topos is also easy to identify, when the final formulation of the argumentation “A is B, therefore not-A is not-B”, makes the relationship between the opposites transparent.
In other cases, the topos is more deeply embedded in the discourse, and its perception and reconstruction are more complex. In all cases, simple or complex, an argument is needed to show that a given passage corresponds to such and such a specific type of argument, see waste; argument scheme. For example, how can we decide whether the following passage is structured by the topos of opposites (i.e., corresponds to an occurrence of the topos of opposites)?
It took billions of years and ideal conditions before humans appeared on the planet, maybe one global warming will be enough to make it disappear. (Original formulation)
This is clearly an inferential structure, moving from a categorical statement about the past to a restricted statement about the future:
E1, maybe E2
The corresponding Toulminian structure is « Data, SO, Modal, Claim. » The two related statements have the same structure, and express consecutions. This parallelism bodes well for the occurrence of the topos of the opposites.
The structure to be considered for the operation is not the simple grammatical structure « S is P », but rather the consecutive structure:
« Conditions, Result« , « C resulted in R« , or « C (resultative) R. »
Do these C and R contain opposite predications about opposite subjects?
“It took billions of years and ideal conditions before humans appeared on the planet.”
It took B before A = B was necessary for A.
Billions of years and ideal conditions ==> (resulted in) humans appearing on the planet.
CONDITION C1 ==> RESULT R1
“Maybe one global warming will be enough to make it disappear”.
Maybe W will be enough for D
One global warming ==> will make humans disappear from the planet.
CONDITION C2] ==> RESULT R2
The opposites are not to be sought in a simple predicative structure, but rather in the two parallel structures, “C [results in] R”. The results R1 and R2 are clearly opposites:
Humans appeared on the planet.
to make [humanity] disappear.
Are their respective conditions in the same relationship? Condition C2, “one global warming” cannot be self-evidently opposed to condition C1, “it took billions of years and ideal conditions.” Nevertheless, their argumentative orientations are clearly opposed:
(i) C1, it took billions of years and ideal conditions before …
— Billions of years leads to conclusions like “that’s a long time”
— ideal conditions leads to conclusions like “it’s rare, difficult to obtain”
— The construction “it takes X(time) to do Y” is oriented toward “it’s a lot (of time)”.
These three orientations converge to give rise to the global conclusion, “This is a very complex process.”
(ii) Conversely, C2 is oriented toward a class of conclusions of the type: “this is a very simple process”:
— The determiner “one” is oriented towards uniqueness, “just one”, and simplicity.
— Will be enough is oriented toward limitation, such as “not more than”, or “less than expected”, for a given performance.
If this reconstruction is acceptable, then the following argumentative structure is attributed to the discourse:
It was really complicated to produce R,
so, maybe, it will be very easy for R to disappear.
These examples also suggest that the classical Aristotelian formulation of the topos may be oversimplified.
3. Trivial and non-trivial conclusions provided by the topos
The use of the topos of opposites is a semantic reflex. Reasoning from opposites is a basic way of thinking, much like causal reasoning, or reasoning by analogy or by definition. Reasoning from opposites may seem to produce commonplace conclusions, empty because analytical reformulations of the original proposition, when both terms are equally obvious.
Nevertheless, even in this case the topos helps to clarify the meaning of the words, which is no less necessary in philosophy than in general disputes:
Temperance is beneficial; for licentiousness is hurtful. (Aristotle, Rhet., II, 23; RR, p. 355)
There are, however, cases in which the “opposite reflex” may, or must, be inhibited: If a prayer says “Peace to those who love you”, should we apply the topos and conclude something like “War to those who don’t”?
Let us consider the following arguments based on the opposites:
If war is the cause of our present problems, then peace is what we need to set things right. (Ibid.)
Those who plunged the country into crisis may not be the best people to lead us out of it.
We cannot trust the same failed market mechanisms to successfully steer the country out of this crisis (after Linguee, 25-10-2015).
These conclusions are countered with the argument that « we failed because of a lack of determination and radicalism »:
If we are in trouble, it is because we just have only fought a limited war; this limited war is the cause of our current difficulties, an all-out war is what we need to put things right again; only an all-out victory will bring us peace.
Our policy has not failed, you have prevented us from actually implementing it
The conclusion of the following example is not trivial:
For even not evil-doers should / Anger us if they meant not what they did / Then can we owe no gratitude to such / As were constrained to do the good they did us. (Aristotle, Rhet., II, 23; RR, p. 355)
The following one is also quite suggestive:
Since in this world liars may win belief, / Be sure of the opposite likewise – that this world / Hears many a true word and believes it not (id., p. 357).
The opposites reflex is a typical example of how argumentation leads us to see things from a different perspective, under a different formulation; or, as Grize would say, in a different light, see Schematization.
4. A transcultural topos
As a semantic reflex, the topos of opposites combines well with analogical reasoning. Like the topos a fortiori, the topos of opposites has cross-cultural validity. The following two examples come from the Chinese tradition.
Wang Chung, Four Things to be Avoided. [2]
There are four things which, according to public opinion, must be avoided by all means. The first is to build an annex to a building on the west side, for such an annex is held to be inauspicious, and being so, is followed by a case of death. Owing to this apprehension, nobody in the world would dare to build facing the west. This prohibition dates from days of yore. […]
On all the four sides of a house there is earth; how is it that three sides are not looked upon as of ill omen, and only an annex in the west is said to be unpropitious? How could such an annex be injurious to the body of earth. or hurtful to the spirit of the house? In case an annex in the west be unpropitious, would a demolition there be a good augury? Or, if an annex in the west be inauspicious, would it be a lucky omen in the east? For if there be something inauspicious, there must also be something auspicious, as bad luck has good luck as its correlate. […]
Han Fei Tzu. “Precautions within the palace”. [3]
Moreover, whether one is ruler of a state of ten thousand chariots or of a thousand only, it is quite likely that his consort, his concubines, or the son he has designated as heir to his throne will wish for his early death. How do I know this is so? A wife is not bound to her husband by any ties of blood. If he loves her, she remains close to him; if not she becomes estranged. The saying goes, “if the mother is favored, the son will be embraced”. But if this is so, then the opposite must be, “if the mother is despised, the son will be cast away.”
5. A contrario
Latin contrarius, “contrary”. Two constructions can be used to refer to the argument, with the same meaning:
— the Latin preposition a: argument a contrario sensu, “by the opposite meaning”
— or, less commonly, the Latin preposition ex: “complecti ex contrario” “conclude on the basis of the opposite meaning” (Cicero, quoted in Dicolat, art. Complector).
S. Latin labels
The label “argument a contrario” can be used with the meaning of “inversion”, to refer to the various kinds of argumentations based on contradiction, S. Contradiction.
Argumentation from the opposites, as defined in law, corresponds to one kind of argumentation a contrario:
A discursive process according to which given a legal proposition asserting an obligation (or other normative qualification) of a subject (or a class of subjects), in the absence of any other express provision, we must exclude the validity of another legal proposition asserting the same obligation (or other normative qualification) with respect to any other subject (or class of subjects)” (Tarello 1972, p. 104).
Thus, if a provision requires all young men, who have reached the age of 20, to perform their military service, it will be concluded, a contrario, that young girls are not subject to the same obligation. (Perelman 1979, p. 55)
When a rule explicitly refers to a category of things, then it does not apply to the things that do not belong to that category. The rule applies only in the defined domain, to all the specified things, and only to them.
This is an application of Grice’s rule of quantity, which states that the speaker must provide just the necessary amount of information, no more and no less, see Cooperative principle.
This rule assumes that the legal system of law is well designed and stable, see systemic principle. In a period of social change and revision of the law, the argumentation a pari will be opposed to argumentation on the opposites. Women fighting for gender equality will refuse to contrast their status with that of men, and will demand that laws be applied a pari, be they beneficial (voting rights) or quite possibly less attractive (military service).
There is no paradox in the fact that a pari / a contrario argumentation can be applied to the same material situation. Legal issues are not unanimous, and cannot be resolved by the automatic application of an algorithm; their discussion involves historical considerations, values and affects.
[1] Edinburgh: Donaldson.
[2] Wang Chung, Four Things to be Avoided. In Lun-hêng, “Balanced Discussions”, Book XXIII, Ch. III, 68. Translation and notes by Alfred Forke, Leipzig, 1906. Reprinted by Paragon Book Gallery, New York, 1962. (p. 793-794)
Quoted from http://classiques.uqac.ca/classiques/wang_chung/lunheng/wangchung_lunheng.pdf
[3] Han Fei Tzu. Basic Writings. Section 17, “Precautions within the Palace”. Translated by Burton Watson. New York, London, Columbia University Press, 1964. P. 84-85.