The word proposition may be a synonym of proposal, “the point to be discussed” or “demonstrated” (MW, art. Proposition). A proposition may be developed in a complex argumentative discourse, justifying the briefly expressed concrete proposition itself. S. Argument – Conclusion.

In classical logic, a proposition is an autonomous statement. Propositional logic considers concatenations of unanalyzed propositions P, Q, R…. Predicate logic considers a proposition analyzed in two terms, the subject and the predicate, “S is P”.

1. Term

In logic, a distinction is made between categorematic and syncategorematic terms. Categorematic terms function as subject names or concept names (predicates). Used without further clarification, the word term refers to a categorematic term.
Syncategorematic terms include negation, binary logical connectives (“&”, and, etc.) and quantifiers (“∀”, all, etc.). They cannot function as subject or concept names, they appear only in combination. They have no independent meaning; their meaning being defined by specific contribution they make to the meaning of the terms or proposition they combine with.

In grammar, a parallel distinction contrasts the so-called full words, having a full semantic content (verbs, substantives, adjectives, adverbs) and the so-called empty or grammatical words (such as linking words, discursive particles, auxiliaries…)

2. Predicate, variable, constant

A sentence may be represented by its pivotal element, the verb, accompanied by variables representing its complements. Variables are denoted ‘x’, ‘y’, or simply as empty places, “—”.

— Paul sleeps: To sleep is a one place predicate, written “— sleeps » or “x sleeps”. :
— Paul eats an apple: To eat is a two-place predicate, written “— eats —” or “x eats y”:
— Paul gave the apple to the lady in black: To give is a three-place predicate, written “— gives — to —” or “x gives y to z”.

The same object can be attached to an infinite number of predicates, for example “— is a car”; “— is a means of transport”; “— is an object that can be bought”; « — is a cause of pollution”… Discourse constantly creates new predicates, according to the interests of the speakers, as “— was ​​carried out on 10 June 2017”; “— is a car available for next Saturday’s trip”.

In the case of a predicate admitting several variables, one or more empty places may be occupied by a constant. The predicate is then said to be partially saturated, which corresponds to a new predicate, for example, where “Paul gives y (something) to z (somebody)”, ​​“x (somebody) gives y (something) to John”, “Peter gives y (something) to John”.

In ordinary language, variables are expressed by indefinite phrases and pronouns: any, all, some, a (person)…”.

Constants are denoted ‘a’, ‘b’; in natural language, they are expressed by referring terms or phrases:

— Proper names (Peter), permanently attached to individuals.
— Pronouns (this the other, the next one). Their referential anchoring is based both on deictic maneuvers and on definite descriptions whose reference can be retrieved from the context. S. Object of discourse
— Definite descriptions, or denoting phrases (the man with the green hat). The noun phrase can be complexified at will: the seated man, the man who pretends to look elsewhere.

This simple notation renders explicit the skeleton of the sentence and is the basis of a more detailed semantic analysis of both its internal structure and external position in the broader discourse to which it belongs. Argument schemes are currently expressed in such a semi-symbolic notation.

3. Proposition

In classical logic, a proposition is a judgment, which can take only two values, true (T) or false (F); a proposition cannot be “more or less” true or false. A proposition is only a way of telling the truth or the false, without any consideration upon its meaning and conditions of use.

A proposition is unanalyzed if no information on its internal structure is available. Logical connectives and the laws of their combination are defined on the basis of such unanalyzed propositions.

A proposition is analyzed if its internal structure is taken into consideration. Classical logic considers that the analytic structure of a logical proposition is basically “Subject is Predicate”, “S is P”:

— The subject refers specifically (if a constant) or generally (if a variable) to the elements of a universe of reference.
— The predicate says something about these elements.
— The proposition categorically (without condition) affirms or denies that the predicate accepts the subject.

Capital letters A, B, C… P, Q, R… are used to denote both unanalyzed propositions and the subject and predicate in analyzed propositions.

3.1 Quality and quantity of a proposition

The quality of a proposition refers to its two possible dimensions, affirmative or negative.

The quantity of the proposition varies according to whether the subject refers to a being, certain beings or all beings of the universe of reference.

Quantifiers express the quantity. The quantifiers such as all (all N), or some (some N) express quantities. According to their quantity, propositions are:

Universals: all poets
Particular: a poet; some poets

Particular does not refer to a constant, a specific, known, individual. In its traditional form, logic does not deal with propositions predicating something from a determined individual, such as “Peter” or “this poet« ; S. Syllogism:

The combination of quantity and quality produces four kinds of propositions:

A     universal affirmative All S are P.
E     universal negative No S is P.
I      particular affirmative Some S are P.
O     particular negative Some S are not P

Traditionally, affirmatives are denoted by the letters A and I (two first vowels of the Latin verb AffIrmo “I affirm”) and the negatives by the letters E and O (nEgO, “I deny”).

3.2 Converse propositions

The converse proposition of a given proposition is obtained by swapping subject and predicate. The subject of the original proposition is the predicate of its converse proposition and the predicate of the original proposition is the subject of its converse proposition.

The quality (affirmative or negative) of the two propositions is the same.

The negative universal E and its converse are equivalent (they have the same truth conditions, cf. infra §4.2, Logical Square):

No P is Q ↔ no Q is P.

The positive universal E and its converse are not equivalent

all P are Q ≠  all Q are P.

3.3 Distribution of a term

A term is distributed if it says something of all the individuals belonging to the reference set. If not, the term is undistributed.
The terms preceded by the quantifier all are distributed. The terms quantified by some, many, almost all … are undistributed.
For example, in a universal affirmative proposition A, “All Athenians are poets”:

— The subject term, Athenians, is distributed.
— The predicate term, poet, is undistributed; the proposition only says that “some poets are Athenians”.

The notion of distribution is used by the rules of evaluation of the syllogism, S. Paralogism.

3.4 The presupposition of existence

Some expressions such as “the unicorn”, “the present king of France”, “real-life dragons”, are misleading, insofar as they appear to be referring expressions despite the fact they do not refer to any existing being. This being the case, when such phrases are used as subjects of a proposition, this proposition cannot be said to be true or false, the present King of France is neither bald nor hairy. To avoid such perplexities, it is assumed that the universe of reference of the subject term is assumed not to be empty. S. Presupposition.

4. Immediate inference and logical square

4.1 Immediate inference

An immediate inference is a one-premise argument, inferring from one proposition to another:

All the A are B, so some B are A

The two terms of this single premise are found in the conclusion, only the quantity of the proposition changes. While syllogistic inference requires a medium term (middle term), “im-mediate” inference does not need such a transition term. It is debatable whether immediate inference is a kind of reasoning.

Immediate inference is an inference, not a reformulation. The reformulation relation presupposes the identity of meaning between the two utterances it links:

Some A are B, so some B are A (conversion, see §3.2).
All the A are B, so some B are A (subalternation, see infra).

In the first case, the immediate inference corresponds to an equivalence. This is not true, however, of the second.

4.2 Logical square

The logical square expresses the set of immediate inferences between analyzed propositions of the subject-predicate form according to their quality, affirmative or negative, and the quantity of their subject (A, E, I, O, see above).

 

These four propositions are linked by the following relations.

— Contrariety, between the affirmative universal A and the negative universal E. A and E are not simultaneously true, but may be simultaneously false. In terms of immediate inference, if one is true, then the other is false.

— Subcontrariety, between the particular affirmative I and the negative particular O. At least one of the two propositions I and O is true. They may be simultaneously true, but cannot be simultaneously false. In terms of immediate inference, if one is false, then the other is true

— Contradiction, between:

The universal negative E and the particular affirmative I.
The universal affirmative A and the particular negative O.

E and I cannot be simultaneously true or simultaneously false (only one of them is true). The same will be true for A and O. In terms of immediate inference, the truth of one immediately implies the falsity of the other, and vice versa.

­— Subalternation, between:

A and I, the universal affirmative and the particular affirmative.
E and O, the negative universal and the negative particular.

If the superaltern is true, its subaltern is true. Immediate inference:

Every S is P, so some S are P.

If the subaltern is false, its superaltern is false. Immediate inference:

It is false that some S are P, so it is false that every S is P.

The subaltern may be true and the superaltern false.

Moreover, propositions E and I are convertible; cf. supra, §3.2.

5. Immediate inference, quantifiers and terms

Immediate inference is an inference from a single premise. The two terms of the single premise are found in the conclusion (examples above). In the case of the syllogism^@, the inference proceeds from two premises and three terms. The middle term functions as a “mediator”, an intermediary, between the major term and the minor term. In the case of immediate inference, the conclusion is “not-mediated” by a middle term.

From a cognitive point of view, argumentation by definition assigns to an individual the properties characterizing the class to which it belongs. From a linguistic point of view, argumentation by definition assigns to an individual designated by a name, all the elements of the linguistic definition of this term. Argumentation by definition is therefore an immediate, substantial, semantic inference, on the meaning of the terms. Immediate inferences are formal; they are not made on the basis of full words, but on the basis of quantifiers. Both kinds of inference function as semantic reflexes in ordinary discourse, linking natural statements, according to ordinary semantic intuition combined with contextual references based on the laws of discourse and the cooperative principle.

Because of their seeming obviousness, the way we handle such these inferences often goes unnoticed. This does not mean, however, that the process is always error free. Taking the correct approach to such inferences is part of the argumentative competence.

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The Greek word [analogia] means “proportionality”, as the Latin proportio.

1. Proportion

A relation is a stable connection between two things:

shell : fish                       old age : life
glove : hand                    pilot : ship

A proportion is an analogy between at least two relations (not between individuals, as in categorical analogy); it implies at least four terms. Two pairs of beings are in a relation of proportion if, in their respective fields, they are bound by the same, or a similar relation.

shell : fish ~ feather : bird                   — cover the body of —
glove : hand ~ shoe : foot                   — protect the —
leader : group ~ captain : ship             — guide the —
old age : life ~ evening : day                — last moment of the —

The analogy of proportions is expressed through parallel syntactic structures:

(Since) a ship needs a pilot, any group needs a leader!

In arithmetic, a proportion is defined as the relation between two numbers, such as ‘17 / 27’. The same proportional relation binds two pairs of numbers a/b and d/d if they obey the following rule:

3/2 = 9/6, same proportion 1.5
a/b = c/d <=> ad = bc (a = bc/d, etc.)

The analogy between proportions corresponds to the linear equation with one unknown, that is to say, to the “rule of three”:

a / b = c / x where ax = bc, ax-bc = 0; and x = bc / a

In geometry, two similar figures have the same shape and different dimensions. Two congruent triangles have equal angles and proportional sides.

The process of understanding is the same in the case of mathematics as it is in argumentation. The reasoning by which the value of ‘x’ is mathematically extracted from the arithmetical proportion is the same as the argument which extracts the necessity of a leader from the analogy of proportion between a ship’s crew and a group of people more generally.

The analogy of proportion is at the basis of a specific kind of metaphor:

old age, evening of life.

The analogy of proportion is open to ironic self-refutation:

A woman without a man is like a fish without a bicycle.

2. Proportionality

Lat. ad modum argument, Lat. modus, “measure, “just measure”
NB: Besides “moderation”, the Lat. temperentia can mean “just measure, fair proportion”.

The argument of proportionality justifies a provision or an action by claiming that it is well proportioned to the facts, gradual. It is invoked a contrario in routine press releases such as:

(The association, the trade union, the government…) X condemns the disproportionate use of force used against…

Let us consider a situation of unrest, described by the current government as a seditious uprising, led by a handful of terrorists. The government organizes a large military presence to “show strength not to have to use it”. This strategy of psychological war may have perverse effects. In reality, the argument of proportionality allows calculations that defeat the desired effect:

The deployment of strength, far from minimizing the enemy, made it stronger. (Pierre Miquel, [The Algeria War], 1993[1])

This conclusion is based on the topos, “one does not use cannons to shoot flies”. A strong refutation of a (declared) weak position entails the same kind of paradox.

The argument of proportionality is a form of argument on the right measure, which can also be defined as the intermediate measure, S. Moderation.

The proportionality strategy can be used to avoid the risks posed by the escalation strategy.

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[1] Pierre Miquel, La Guerre d’Algérie. Paris: Fayard, 1993, p. 190.

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The proper name argument scheme corresponds to topic n° 28 of Aristotle’s Rhetoric, “another topic is derived from the meaning of the name. For instance, Sophocles says, ‘Certainly thou art iron, like thy name’.” (Rhet., II. 23, 1400b29, Freese, p. 323). The example is a pun on the proper name of the hero and the word meaning “iron”.

Unlike the nickname, which claims to refer to a characteristic of the individual, the proper name is not motivated; it does not mean its bearer. When the proper name (first name or last name) of a person is homonymous with a common name, the topic of the name attributes to the person the characteristics of the homonymous thing; he or she is re-categorized as a non-human being, which may be less-than-flattering. The name functions as an index from which truths about the person might be inferred. Aggravated by the infinite resources of paronomasia, and rhyme, proper names can be the basis for all kinds of derivations, particularly, although not exclusively in the school playground:

You are Peter [Lat. Petrus], and on this rock [Lat. petram] I will build my church.
(Matthew, 16:18)

June will be the end of May[1]

Being named Peter, and thus being like a rock, is being apt to be a foundation: the name is an aptonym, the character and destiny of the person are pre-inscribed in his or her name. Mr. Child is of course a pediatrician, or a teacher or perhaps he has a childish character; the aptonym reinforces the person’s suitability for his task or confirms the attribution of a trait of character. Referring to John R. Searle as Sarl, (French acronym for “Limited Liability Company”, Inc.) Derrida re-casts, fairly or not, Searle’s work as a kind of business.[2]. S. True Meaning of the Word; Ambiguity.

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[1] The slogan appeared during the campaign for general elections to be hold in June 2017, Mrs Theresa May serving as Prime Minister of the United Kingdom since 2016.

[2] Jacques Derrida, Limited Inc. Evanston, IL: Northwestern University Press, 1988.

The words to prove, a proof, probation, probatory come from the Latin probare and its cognate words; probare means “to make good; esteem, represent as good; make credible, show, demonstrate; test, inspect; judge by trial” (OED, Prove). All these meanings evoking a practical activity are still present in the use of proof in rhetorical theory.

1. Vocabulary of the arts of proof

The following words belong to the elementary lexicon of the arts of proof.

to argue; an arguer, an argument, an argumentation; argumentative
to demonstrate; a demonstration; demonstrative
to prove; a proof, a prover; probatory
to reason; a reason, a reasoner; reasoning; reasonable; rational
evidence; evidential

The following remarks deal with the articulations of the ordinary lexicon of the arts of proof.

Agent names — Some names are related to their root verbs with the meaning “person who (Verb)”; so are arguer; reasoner; prover. Demonstrator a derivative from to demonstrate_2 “show other people how something is used or done”.

This can be interpreted as a mark of a subjective involvement in the mechanism of proving, arguing, reasoning.

Verb complementation — In “Peter reasons about P”, P is the issue, the substance of the reasoning or of the argument. “Peter has demonstrated, or proved that P”, the P clause is true and expresses the conclusion of the demonstration. To argue admits both constructions:

Peter argues about P: P is the issue,
Peter argues that P: P is the claim, but to argue does not imply that its P clause is true.

Aspectual distinction — The relationship of argument to proof is grammatically an aspectual distinction, that of unaccomplished / accomplished. To argue is no more a semantically weakened form of to prove that to look for something is a weakened form to find something. The proof is the “terminator” of the argument.

Semantic orientation —Evidence, proof, argument and demonstration, however, can function in co-orientation, as quasi-synonyms in many contexts. The lawyer is engaged in a brilliant demonstration in which he brings conclusive evidence and convincing arguments. Such discursive practices put in continuity argument/evidence and proof, the proof being the end and finality of the argument: it is “a knock-down argument” (Hamblin 1970, p 249.). Arguments are oriented towards proof.

Position markers — These terms which may be regarded as quasi-synonyms in some contexts, may clearly appear as markers of argumentative positions in the context of a debate. In the judicial field, the judge hears the statements and arguments of the parties; each party brings (what they consider to be) proofs and rejects those brought by the opponent as quibbling. We are no longer dealing with synonyms, but anti-oriented antonyms. The difference between evidence/proof, argument, and quibble becomes a simple matter of perspective. The probative value is now no more than the positive assessment I give to my argument and I refuse to grant to that of my opponent.

A polite although decisive rebuttal will be proposed as a mere objection and a simple argument. Argument is then a “lexical softener” for proof, its use implies a distance, a lesser commitment of the speaker to the claim.

Dialogic Status — The distinction demonstration / proof / argument seems primarily sensitive to the presence or absence of counter-discourse. This is why the word argument is used to describe reasoned discourse at both ends of scientific activity, in learning activities, as well as in the sharpest controversies over open questions, where two discourses both perfectly equipped theoretically and technically, revert to the status of argument, simply because there is disagreement.

2. The proof between fact and discourse

Proofs are expressed in a language, natural or formal, and put forward in a discourse. Formal evidence brought by a hypothetical-deductive demonstration is often seen as the archetypical proof. Its counterpart in ordinary language would be the argument based on essentialist definition used in philosophy and theology. In other areas of activity, probationary speech requires a reference to the world, in which case, evidence is now seen as a fact. The proof is built by a series of experiences and calculus, as suggested by the concrete metaphors used to talk about evidence — to produce proof, to provide evidence, to bring a proof, to make a demonstration. This connection with reality makes the difference between proof and argumentation on one side and formal demonstration on the other.

The concept of proof as fact invokes non-discursive evidence of material realities, perceptible to sight and touch. The proof that I did not murder Peter is that he is alive, standing before you. Such situations seem to make language superfluous. Nonetheless, facts can become evidence through discourse alone. Evidence is relative to a problem, and discourse frames the situation in which the evidence solves the problem. Evidence may be silently brought before the relevant judges. If some facts “speak for themselves”, some other times they are not so “eloquent”, or even remain “silent” for many. One must speak for them, and discourse is required to make the material evidence visible. The cruel experience of Semmelweiss has certainly shown us that the de facto existence of seemingly indisputable facts does not foretell their acceptance (Plantin, 1995, chap. 7).

 “The Wolf and the Lamb” — The La Fontaine fable “The Wolf and the Lamb” (Fables, I, X) shows how innocent people can trust material evidence, and that material evidence does not carry the day.

The reason of the strongest is always the best,
As we’ll show just now.

Situation:

A lamb was quenching its thirst
In a pure water stream.
A fasting wolf came by, looking for adventure;
Attracted to this place by hunger.

The wolf starts with a violent reproach, as men do with their future victims

—What makes you so bold as to cloud my drinking?
Said this animal, full of rage,
You will be punished for your audacity.

The offense is assumed (you cloud my drinking). The request for explanation of motives (what makes you so bold […]?) appears to give the lamb the opportunity of explaining itself. Yet, the accusation is immediately followed by the sentence (you will be punished for your temerity). This incriminating speech is deeply mysterious, why does the wolf speak? It could simply take advantage of the food it was yearning for, and finally met, devouring the lamb like the lamb drinks the water. With exquisite courtesy, the lamb denies the presupposed fact and its denial is backed up by undisputable proof, S. Self-Evidence:

—Sir, answered the lamb, let Your Majesty
Not get angry.
But rather, let Her consider,
That I am quenching my thirst
In the stream
More than twenty steps below Her;
And that, consequently, in no way,
Am I clouding his beverage.

The lamb’s argument is conclusive, physical laws are such that the brook never flows upstream. But conclusive does not mean impossible to contradict:

—You do cloud it, said the cruel beast.
And I know you said bad things about me last year.

This second accusation is also rebutted in the same decisive way:

— How could I have done that, when I wasn’t born,
Answered the lamb; I am still suckling my mother

Idem for the third:

— If it wasn’t you, then it was your brother.
— I have none.

But the last accusation is irrefutable; the lamb is given no chance to refute it:

— Then it was a relative of yours;
For you have no sympathy for me,
You, your shepherds and your dogs.
I am told of that. I must avenge.

The conclusion is that good reasons do not change the course of history:

Thereupon in the dark of the forest
The wolf carries the lamb, and then eats it,
Without further ado.

3. Functional heterogeneity of the discourse of the proof

Whatever the field, the discourse of proof is functionally heterogeneous. Proof fulfills a number of functions:

— Alethic: it establishes the truth of a fact.

— Epistemic: it justifies a belief; it helps to stabilize and increase knowledge.

— Explanatory: it accounts for facts which are not self-evident, via their integration into a coherent discourse in the correct language, be it a demonstration, or a story accounting for what took place.

— Cognitive and even aesthetic: proof must be relatively clear, and, if possible, “elegant”.

— Psychological: it eliminates doubt and inspires confidence.

— Rhetorical: it is convincing.

— Dialectical: it eliminates the challenge, and closes the discussion.

— Social: it builds consensus, assuages the community affected by the problem, and strengthens its confidence in its technical capacities to produce evidence particularly, but not only, in the social and judiciary domain.

— Conversely, evidence excludes: those who accept proof consider that those who resist the proof must be mad, feeble minded, carried away by their passions.

4. Unity of the arts of proof

The arts of proof — reasoning, arguing, demonstrating, proving — share the following characteristics.

— A language and discourse: arguing, demonstrating, proving, all require a semiotic medium, a language developing in a discourse. The same can be said for reasoning, although the term focuses on the cognitive aspects of the process.

— An intention: Like every discourse, the flow of demonstrative, argumentative, probative, reasoned discourse is organized by an objective, i.e., an intention.

— A question: These processes start with a problem, an uncertainty, a doubt.

— An illation (derivation) process or inference: The notion of inference is primitive. In logic an inference is defined as the logical derivation of one statement from a set of premises. The intellectual process of inference contrasts with the intuitive approach, for which a truth is asserted directly (without mediation) on the basis of its direct physical or intellectual perception. In the case of inference, the truth is asserted mediately, that is indirectly, via data or assumptions expressed by statements and supported by underlying principles, the nature of which depends on the area concerned. S. Self-evidence.

— Argumentation, proof and demonstration are referring to something external; the development of discourse is more or less governed by the external world. Anything and everything can be said, but reality creates limits. The practice of proof and argument is not pure linguistic virtuosity, it must confront objects and events.

— Domain dependence. As argumentation, demonstration and proof are domain dependent. The modes of production of evidence differ according to the field, the kind of technical language used and the kind of experimental method used in the considered area. The establishment of large classes of scientific proofs is the task of epistemologists. Argumentation in natural language is characterized by its capacity to combine a large variety of heterogeneous proofs, corresponding to the various argument schemes.

5. Argumentation among the arts of proof

Perelman & Olbrechts-Tyteca’s New Rhetoric opposes “argumentation” to “calculation”:

The very nature of deliberation and argumentation is opposed to necessity and self-evidence […] The domain of argumentation is that of the credible, the plausible, the probable, to the degree that the latter eludes the certainty of calculation. ([1958], p. 1).

This position leads us back to the Aristotelian opposition between rhetorical “means of pressure” and scientific proofs, S. Demonstration, without considering the possibility of bridging the gap between the two discursive regimes, or of positioning them upon the same truth oriented scale. An increasing range of contemporary discourses, however, are mixed; they seek to articulate some scientific reasoning and data, along with social values and material interests. A contemporary challenge for argumentation studies is to find a way of dealing with such mixed data. This is true of all the varieties considered to be typically argumentative in the Treatise: “speeches [of politicians] … pleadings [of lawyers] … decisions [of judges] … treaties [of the philosophers]” (Perelman & Olbrechts-Tyteca [1958], p. 10).

The approaches of argumentation as a set of “discursive techniques” (Perelman, Olbrechts-Tyteca), as discourse orientation (Ducrot) or discursive microstructure, as dialogue or interaction, anchor the study of argumentation in ordinary linguistic practices, structured by rules and norms depending on the genre of discourse and on the frame of the situation. Argumentation studies are thus clearly distinguished from research in scientific methodology, and from the epistemological study of proof, demonstration, explanation or justification in mathematics, science, or philosophy, S. Demonstration.

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The speaker may choose to connect his or her own argumentative line to a counter-discourse that he or she knows or anticipates and, in any case, rejects. The prolepsis steals the argument from the mouth of the (real or fictitious) opponent, “I know (perhaps better than you) what you are going to say”. The counter-discourse is resumed with an indefinite degree of distortion, from a literal referenced quotation to a sketchy evocation of a possible objection, which may be framed as a self-refuting scarecrow, S. Speech Resumption At the very least, the quoted speech is extracted and re-adjusted in view of the new discursive environment, and its ethotic force is kept at bay. Through the magic of quotation, an intended refutation becomes a mere objection.

The degree to which the counter-discourse is rejected is itself variable. The counter-discourse may be radically rejected; dismissed as absurd (“do we intend to ruin all small savers? No, quite the contrary, and for many reasons…”), or maintained in full force, until further information becomes available. In this sense, the Modal-Rebuttal component of argumentation is a special case of prolepsis, S. Layout of argument.

The proleptic structure covers not only coordinated or subordinated pairs of statements but any discourse pattern whose configuration corresponds to the staging of two anti-oriented discourses, the speaker taking responsibility for one of them; it represents the maximum development of monological argumentation, S. Connective; Destruction; Concession; Refutation.

 

Several rhetorical terms refer to this same structure:

— The anteoccupation refers to a refutative structure, composed of a prolepsis, which evokes the position of the opponent, followed by an hypobole, which refutes this position or expresses the position supported by the speaker (Molinié 1992, [Anteoccupation]). Lausberg ([1963], § 855) terms this same strategy preoccupation (Latin prefixes pre-, ante- “in advance”).

— The procatalepsis and the metathesis refer to a discursive configuration by which the speaker “reminds listeners of past events, presents to them the facts to come, foresees objections” (Larousse, quoted in Dupriez 1984, p. 290; Metathesis has another quite distinct meaning, “swapping two sounds or letters of a word”).

1. Argument of progress

By definition, “progress moves forward”; the argument of progress valorizes the most recent as the best. If F1 and F2 belong to the same category, if F2 comes after F1, then F2 is preferable to F1.

The argument from progress rejects the authority of elders and their practices, which are deemed outdated; the contemporary practices which follow their model are dismissed as regressive, indeed repulsive.

Cats are no longer burnt on cathedral forecourts, animal fights were banned in 1833, owls are no longer nailed on the doors of the barns, and rats are no longer crucified as targets for darting. Whatever may be said in bullfight circles, bullfighting with killing is doomed. (Le Monde, Sept. 21-22, 1986)

The argument is organized upon the following operations. Firstly, bullfighting is categorized as a case of animal abuse, whereby it is allocated to the same category as burning cats, organizing cockfights, nailing owls to doors and crucifying rats. In a second step, the practices belonging to this category are listed in the chronological order in which they disappeared. This factual line is then extrapolated to lead to the conclusion that bullfights should also be condemned in view of society’s progress — and the sooner the better.

2. Argument of novelty

Lat. ad novitatem; novitas, “novelty; condition of a man who, the first of his family, reaches an eminent position (senator)” (Gaffiot [1934], Novitas). Novitas is opposed to nobilitas. Its argumentative orientation can be positive (the dynamic of the novitas is opposed to the decadent nobilitas), or negative: the homo novus, the “New Man”, coming out of nowhere, is held in suspicion.

2.1 Traditional orientation 

The argument of progress reverses the traditional view of the higher appreciation granted to the old, particularly in the religious sphere, “the novitas is […] the index of heresy” (Le Brun 2011, §1). The argumentative orientation of the judgment “this is a novelty!” has been reversed.

The argument of progress is opposed to the argument of decay of civilization, which attributes all virtues to the ancients.

2.2 Contemporary orientation

The contemporary interpretation links the argument of novelty to the argument of progress: “what has just come out” is “super” exciting, and “déjà vu” is of little value. This argument values ​​innovation over routine, and the new over the old. It underlies the call:

Be the first to adopt it!

According to this rule, the recently published handbook would be necessarily better than its predecessors, and, in politics, the newest candidate is already seen as the much-needed savior.

The syzygy is a different vision of progress, as a passage from an imperfect world to a perfect and immobile world.

3. Ancients and moderns

The argument of progress structures the eternal quarrel between the Ancients and the Moderns. In its radical form, the argument affirms the absolute superiority of the latter over the former, in the domains of arts and culture as well as the sciences. Ultimately, this superiority would be that of the modern individual over his or her ancestors. In a relativized form, the argument of progress is compatible with the individual superiority of the ancients, “we are dwarves on the shoulders of the giants”, although not taller, we can see further ahead. This is classically refuted by the objection that the lice on the head of the giant sees no further than the giant.

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The concept of presupposition can be approached as a logical or as a linguistic issue.

1. A logical issue

The problem of presupposition was first addressed within the field of logic. The logic of the analyzed proposition postulates that propositions such as “all As are Bs” have two truth-values, the true and the false. The problem arises when the reference of A and B is void (there are neither A nor B), as in “unicorns can fly (are flying beings)” or “no unicorn is a dragon”. In this case, is the proposition “all As are Bs” true or false? Let us consider the declaration “the king of France is bald”, as said in 1905. It is impossible to attribute a truth-value to this statement, since in 1905, and still today, the French Republic has no king (Russell 1905).

From the point of view of logical technique, it is sufficient to add the premises “there are As”, and “there are Bs”, or “there is one, and just one King of France”. An apparently mono-propositional statement such as “the king of France is bald” is then translated into logical language via the conjunction of three propositions, each having its own truth-value:

 “there is a King of France” & “there is only one King of France” & “he is bald”.

In 1905 or 2017, the first of the three propositions is false. It follows that the conjunction of logical propositions representing the statement “the king of France is bald” is simply false. This analysis was criticized for failing to reflect the linguistic intuition of the ordinary speaker, for whom the statements “there is a King of France” and “this King is bald” do not have the same status in the original sentence. This is true, but the objection is irrelevant, since formal logic does not aim to represent linguistic intuition, but wants to solve a technical problem, and this is what it does.

2. A linguistic issue

Ordinary statements can synthetize different judgments, having different semantic and discursive statuses.

2.1 The multi-layered structure of meaning

The presupposition is defined as an element of the semantic content of the utterance that resists negation and interrogation. The statement “Peter no longer smokes” presupposes that “Peter used to smoked”, and poses that “now, Peter does not smoke”. The negative statement “Peter has not stopped smoking” and the interrogative “has Peter stopped smoking?” share this presupposed content “Peter used to smoke”. Negation and interrogation deal with the posed content (“Peter smokes now”), and do not concern the presupposed content.

This multi-layered structure of sentences is one of the major features which differentiate statements made in ordinary language from logical propositions.

2.2 Presupposition as a speech act and the “many questions” issue

Ducrot redefines presupposition as a strategic action (an illocutionary act) made with the aim of influencing, that is to say, restricting the speech possibilities of the conversational partner. The act of presupposition is a discursive power grab by which the speaker performs “an act of legal value, and therefore an illocutionary act […] [this act] transforms the speech possibilities of the interlocutor, […] modifies the listener’s right to speak” (1972, p. 91).

Consider the following question:

Interviewer — What are you going to do to fight corruption within your own party?

The question presupposes that “there are corrupt people and practices within your party”. The interviewee is given a choice:

(i) Either he or she accepts the presupposed claim and gives an answer within the range of pre-formatted, expected answers such as:

Interviewee — I’ll exclude (suspend) all suspects (the members under investigation).

This answer respects the linguistic orientation of the question. It falls perfectly within the frame of dialogue as established by the first turn. The interviewee submits to the interviewer.

(ii) He or she might also reject the presupposed claim:

Interviewee — To my knowledge, there is no (proved) case of corruption within my party

This second answer reframes the routine consensual dialogue; the interviewee rejects the claim made by the interviewer, and the dialogue takes on a character, becoming uncompromising and polemical, opening an argumentative₂ situation structured by the issue “are there (proved) cases of corruption in the party?” The rejection of the presupposed assumption “[is] always regarded as aggressive: it personalizes the debate, which turns into a quarrel. […] To attack the opponent’s assumptions is to attack the adversary himself” (Ducrot 1972, p. 92). The presupposition seeks to impose an “ideological framework” (id., p. 97) on the later dialogue, that is, to direct the partner’s speech. S. Many Questions; Conditions of Discussion; Persuasion.

It goes without saying that presupposition phenomena are not limited to dialogue, but, as always, dialogue serves to clarify any issues. A monologue that would not respect its own presuppositions would be inconsistent, while, in a dialogue, the rejection of a presupposition is contentious. In reality, dialogue (i) develops under the same conditions as a monologue.

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The argument from the precedent corresponds to the topic n° 11 of Aristotle’s Rhetoric:

Another line of argument is founded upon some decision already pronounced, whether on the same subject or on one like it or contrary to it. (Rhet., II, 23, 11; RR, p. 365)

“Judgment” not only refers to the sentence of a court but to any assessment or decision taken in the past, in ordinary life as well as in the political sphere or in the legal domain. And if the cause has not been settled in a formal assembly, it may have been by such authorities as known fables, parables or examples, proverbs or celebrated verses (Lausberg [1960], § 426).

Judgments are made in the context of past judgments concerning cases “of the same type”, that is belonging to the same legal category, S. Categorization. The importance granted to the precedent is a requirement of continuity and consistency between decisions made in the past and the decision to make, a particular application of the non-contradiction principle. The structural coherence of the involved discursive field is thus strengthened, and guarded against any ad hominem charge addressed to the institution, S. Ad hominem.

In much the same way as the argument ab exemplo, the argument from precedent motivates a decision or interpretation by relying upon data or examples drawn from tradition. It is a conservative principle, which limits innovation in all domains in which it applies. As such, it combines well with arguments appealing to “the wisdom of our ancestors” (Bentham, 1824; S. Political argument; Authority; Progress.

The precedent principle progresses in the following stages:

(i) A problem, P1, a case about which a decision has to be made.
(ii) Research of similar problems and cases, resulting in
(iii) A categorization: this case is similar to a prior case P0; it falls within the same category as P0, S. Analogy (II); Categorization.
(iv) The decision, judgment, evaluation … E was made about P0;
(v) By application of the rule of justice, a similar judgment has to be made about P1. “Similar” means here the same judgment, a judgment proportional, or opposite; or, more simply, a judgment consistent with E.

The invocation of the precedent can be blocked at the second stage, where it can be argued that there are essential differences between P1 and the previous case P0.

The appeal to the precedent saves time and energy. The problem of judgment is automatically solved as soon as analogy is drawn between the problematic fact and an established fact.

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1. Pathetic argument

Pathetic as evaluative
A participant can dismiss an argument she utterly rejects as “a pathetic, pitiful argument” because childish, void or desperate. One can say “I find this argument pathetic” (evaluation), but not “I find this argument a pari”, only “In my view, this is an argument a pari” (description).
The label pathetic argument is evaluative and can be applied to any kind of argument scheme.

Pathetic as descriptive
The label “pathetic argument” can be descriptively applied to a variety of arguments based on negative or positive consequences. The conclusion is deemed impossible and rejected because it would frustrate the arguer; or taken for granted because agreeable to her.

I fear that P, so not-P.
I wish P, so P
It can’t rain on Sunday, our picnic would be ruined!
This is not possible, we couldn’t manage the consequences:

— Syldavia cannot suspend its payment, that is impossible, nobody knows what might happen, actually we wouldn’t know how to deal with such a situation.
— Such pollution is unthinkable, it would make thousands of victims.
— If this criticism were right, what would become of our discipline?

The pathetic argument applies to the field of knowledge a style of argument quite common in the field of practical action:

I wish that P, so I strive to achieve P, I pray for P, I try to bring about P.
I fear P, so I try to avoid, prevent P…

But wishing P is different from striving to achieve P. That kind of  argument can systematically be evaluated as pathetic that is, “naive and desperate”.

The pathetic argument is currently designated as the argument ad consequentiam or the appeal to consequences. Here, the pathetic argument is considered as just one particular kind of appeal to consequences.

Pathetic arguments are not pathemic arguments. Pathemic is a derivative from pathos; one can speak of a pathemic arguments to refer to ad passiones arguments, that is, to any emotion-based argument, such as appeal to anger, enthusiasm, pity, etc.
Pathetic, “pitiful”, it can only be considered as a sub-sort of the pathemic argument.

2. “Pathetic fallacy”

The label “pathetic fallacy” refers to the anthroTpomorphic attribution of human feelings to non-human, non-living beings; it condemns the use of the rhetorical figure of personification. The expression was coined by John Ruskin:

I want to examine the nature of the other error, that which the mind admits when affected strongly by emotion. Thus, for instance, in Alton Locke,
They rowed her in across the rolling foam
The cruel, crawling foam.
The foam is not cruel, neither does it crawl. The state of mind which attributes to it these characters of a living creature is one in which the reason is unhinged by grief. All violent feelings have the same effect. They produce in us a falseness in all our impressions of external things, which I would generally characterize as the ‘pathetic fallacy’.
John Ruskin, Of the pathetic fallacy, [1856][1]

The label pathetic argument is consonant with the label pathetic fallacy. The pathetic fallacy condemns the personnification of natural world, while the pathetic argument seems to consider that the natural world is subject to the human desires.Both moves blurs the boundaries between the human and the natural world.

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[1] In Modern Painters, vol. III, part IV, London: Smith Elder, p. 160. Alton Locke is a novel by Charles Kingsley (1850).

Within the framework of classical Aristotelian logic, a paralogism is defined as an invalid syllogism. These paralogisms of deduction are “arguments of traditional syllogistic form which break one or another of a well-known set of rules” (Hamblin 1970, p. 44).

1. Syllogism rules

Traditional logic has established the following rules, which make it possible to eliminate invalid syllogisms. The following syllogisms respect all the rules of the syllogism; they are valid.

A syllogism contains three terms.

From two negative premises, nothing can be concluded

no M is P
no S is M
No conclusion

If a premise is negative, the conclusion must be negative

no M is P                       the major premise is negative.
some S are M,
so some S are not P           the conclusion is negative

In a valid syllogism, the medium term must be distributed at least once

no M is P                       M is distributed (universal).
all S are M,
so no S is P                     the conclusion is valid.

If a premise is particular, the conclusion is particular

no M is P
some S are M                  the minor premise is particular.
So, some S are not P          the conclusion is particular.

2. Paralogisms

A paralogism is a syllogism that does not respect one or several preceding rules. Of the 256 modes of the syllogism, 19 modes are valid; therefore, a syllogism can be fallacious in 237 different ways. The question of whether it “seems” conclusive or not is irrelevant. The term paralogism designates nothing other than a mistaken calculation.

The following are key forms of syllogistic paralogisms. The first form corresponds to the paralogism of homonymy, the others to an inadequate distribution of qualities and quantities.

(1) Paralogism of four terms.
(2) Paralogism concluding from two negative premises.
(3) Paralogism drawing a positive conclusion from a negative premise.
(4) Paralogism of the undistributed middle term.
(5) Paralogism of universal conclusion from a particular major.
(6) Paralogism of universal conclusion from a particular minor.

Examples

— The following paralogism consists of four terms:

Metals are simple bodies.
Bronze is a metal.
* Therefore bronze is a simple body.

Bronze is not a simple body but an alloy. In the minor premise, bronze is said to be a metal because it looks like an authentic metal such as iron, it can be melted and molded, etc. In the major premise, metal is used with its strict meaning. Metal is homonymous, and the syllogism actually has four terms; S. Ambiguity.

— The following paralogism concludes from two negative premises:

Some B are not C              some rich are not arrogant
No A is B                              no poet is rich.
* Therefore No A is C *       no poet is arrogant.

— The following paralogism concludes universally from a particular major:

all A are B                            all men are mortal
no C is A                               no dog is man
* Therefore No C is B          * no dog is mortal.

In the major premise, “all men are mortal”, the major term, mortal, is not distributed: this premise says nothing of all mortals, but only of certain mortals, namely, that “they are men”. Yet the conclusion “No dog is mortal” claims something of all mortals: “no mortal is a dog”. So the major term is distributed in the conclusion and not in the major premise. The conclusion thus affirms more than the premise, which is impossible.

3. Evaluation using the rules of the syllogism

Syllogisms are traditionally evaluated on the basis of a system of rules (§1), in a step-by-step process:

— Check the number of terms, and propositions.
— Identify the middle term, the major term, and the minor term.
— Determine the quantity and quality of the premises and conclusion.
— Identify the distribution of terms.
— Check the organization of the distribution of terms: check that the middle term is distributed at least once. If the major term or the minor term is distributed in the conclusion, make sure that they are also distributed in the premises; etc.

This laborious method is based on the notion, at the very least unintuitive, of the quantity of the predicates. It shifts the analyst’s attention from the understanding of the structure and articulation of the syllogism, from what the syllogism asserts, to the fragmented application of a system of rules. It may develop the ability to apply an algorithm, but it is far from an everyday critical thinking process.

4. Evaluation with Venn diagrams

The use of Venn diagram provides a more intuitive and clear base for syllogism assessment. Three intersecting circles represent the three sets which correspond to the three terms. The assertion made by each premise is carried to the corresponding circle. If a premise asserts that a set (made up of a circle or a portion of a circle) contains no elements, that circle or the portion of a circle is blacked out (striped). If a premise asserts that a set (id.) contains one or more elements, a cross is placed in the circle or portion of a circle. A portion of a circle is therefore either black, has a cross, or remains white. When white, nothing can be said about it.

The data of the premises having thus been plotted on the diagram, the result can be compared with what the conclusion asserts, the diagram shows whether the syllogism is or is not valid.

Consider the syllogism:

Some rich people are not arrogant
No poet is rich
* No poet is arrogant

The three intersecting circles represent the rich (R), the poets (P) and the arrogant (A), respectively.

— “Some rich are not arrogant”: consider the circle of the rich and that of the arrogant; put a cross outside of their intersection: there are some people within this zone.
— “No poet is rich”: consider the circle of the poets and that of the rich, and blacken their intersection: there is nobody within this zone.
— Finally, look at the circle of poets and that of the arrogant people. The conclusion affirms that the intersection of the circle of poets with that of the arrogant is black; but we see that this is not the case; it is partly white. This syllogism is a paralogism.

Consider the syllogism:

No M is P
All S is M
Therefore No S is P

The three intersecting circles represent the M set, the S set and the P set.

— “No M is P”: the intersection of the circles M and P is black (empty).
— “Every S is M”: the non-intersecting zone of the circles S and P is black (empty).
— Looking at the S circle the P circle, we can see that the intersection is black (empty); this is precisely what the conclusion claims, “No S is P”. This syllogism is valid.

5. Paralogism of quantifier permutation

By generalization, the word paralogism can refer to any error made in applying the rules of formal logic. For example, the paralogism of quantification is an error committed when the existential and the universal quantifier are permuted:

All human beings have a father; so they have the same father

For every human H, there is a human F, such that F is the father of H
* Therefore There is a human being F such that for every human being H, F is the father of H.

The following passage may contain such a paralogism, albeit complicated by a fallacious verbiage that is to say an eloquent amplification, S. Verbiage:

And all the geniuses of science, including Copernicus, Kepler, Galileo, Descartes, Leibnitz, Buler, Clarke, Cauchy, speak like [Newton]. They all lived in true adoration of the harmony of the worlds and of the all-powerful hand that threw them into space and sustained them.
And this conviction is not based on impulses, like poets. Figures, theorems of geometry give it its necessary basis. And their reasoning is so simple that children would follow it. They establish, first, that matter is essentially inert. It follows that, if a material element is in motion, it is because another has constrained it; for every movement of matter is necessarily a communicated movement. They thus claim that since there is an immense movement in the sky, which carries away in the infinite deserts billions of suns of a weight which crushes the imagination, it is because there is an all-powerful motor. They establish, secondly, that this movement of the heavens presupposes the solving of the problems of calculation, which have required thirty years of study, etc.
Ém. Bougaud, [Christianity and the Present Times], 1883.

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[1] (My italics).
[1] Em. Bougaud, Le Christianisme et le temps présent, t. I. Paris: Poussielgue Frères, 5th ed., 1883.

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