Logical CONNECTIVES

Logical connectives articulate simple or complex well-formed propositions so as to construct well-formed complex propositions, or formulas. Propositional calculus studies logical syntax, that is the rules for constructing well-formed formulas. It determines, among these formulas, which are valid formulas (logical laws, tautologies).

Propositions are denoted by the capital letters P, Q, R… They are said to be unanalyzed, that is, taken as a whole, in contrast to the analyzed propositions “[Subject] is [Predicate]” considered in the predicate calculus.

A binary logical connective combines two propositions (simple or complex) P and Q into a new complex proposition “P [connective] Q”. Logical connectives (or connectors) are also called functors, function words or logical operators

The most common connectives are denoted and read as follows:

↔           equivalence, “P is equivalent to Q”,
→           implication, “if P then Q”
&             conjunction, “P and Q”
V           disjunction, “P or Q”
W           exclusive disjunction, “either P or Q (not both)”

Logical connectives are defined on the basis of the possible truth values given to the propositions they combine. A particular logical connective is defined by the kind of combination it accepts between the truth values of the component propositions.

1.   The truth table approach to binary connectives

A logical connective is defined by its associated truth table. The truth table of a “P connec Q” binary connective is a table with three columns and five rows.

— The letters P, Q … denote the propositions; the letters T and F denote their truth values: true (T) or false (F). P and Q are propositions, while truth and falsity are said of propositions, “P is True”, “P is False”; so, the corresponding abbreviating letters use a different typographical character.

P	Q	P connective Q
T	T	depending on the connective
T	F	depending on the connective
F	T	depending on the connective
F	F	depending on the connective

— Columns:

The truth values ​​of the proposition P are expressed in the first column
The truth values ​​of the proposition Q are expressed in the second column
The corresponding truth values ​​of the complex formula “P connec Q” are expressed in the third column.

— Lines:

The first line mentions all the propositions to be considered, P, Q and “P connec Q”.
The next four lines express the truth values of these propositions. Since each proposition can be T or F, there are four combinations to consider, each corresponding to a line.

1.1 Conjunction “&”

By definition, the conjunction “P & Q”

— is true if both P and Q are simultaneously true: line 2
— is false if one of them is false: line 3, 4; or both of them: 5.

This is expressed in the following truth table:

P	Q	P & Q
T	T	T
T	F	F
F	T	F
F	F	F

This truth table reads:

line 2: “when P is true and Q is true, then ‘P & Q’ is true”
line 3: “when P is true and Q is false, then ‘P & Q’ is false”
line 4: “when P is false and Q is true, then ‘P & Q’ is false ”
line 5: “when P is false and Q is false, then ‘P & Q’ is false ”

1.2 Equivalence, “ ↔ ”

The logical equivalence “P ↔ Q” reads “P is equivalent to Q”. This resulting proposition is true if and only if the original propositions have the same truth values.

Truth table of logical equivalence:

P	Q	P ↔ Q
T	T	T
T	F	F
F	T	F
F	F	T

By this definition, all true propositions are mutually equivalent, and all false propositions are mutually equivalent, regardless of their meaning.

1.3 Disjunctions: Inclusive “V”; Exclusive, “W”

The inclusive disjunction “P ∨ Q” is false if and only if P and Q are simultaneously false; otherwise, it is true.

Truth table of the inclusive disjunction:

P	Q	P V Q
T	T	T
T	F	T
F	T	T
F	F	F

 

The exclusive disjunction <P W Q> is true if and only if only one of the two propositions it connects is true. In all other cases, it is false.

Truth table of the exclusive disjunction:

P	Q	P W Q
T	T	F
T	F	T
F	T	T
F	F	F

1.4 Implication: “→”

The logical implication symbol “→” reads “P implies Q”. P is the antecedent of the implication and Q, its consequent.

Truth table of the logical implication:

P	Q	P → Q
T	T	T
T	F	F
F	T	T
F	F	T

This table reads:

line 2:       The true implies the true
line 3:       The true does not imply the false
line 4:       The false implies the true
line 5:       The false implies the false

Only truth can be logically derived from truth (line 1), whereas, everything can follow from a false proposition, a truth as well as a falsehood.

The connectives for equivalence, conjunction, inclusive disjunction and exclusive disjunction are symmetric, that is, for these connectives, “P connective Q” and “Q connective P are equivalent (convertible):

P ↔ Q         ↔             Q ↔ P
P & Q          ↔             Q & P
P V Q         ↔             Q ∨ P
P W Q          ↔             Q W P

The implication connective is not convertible; that is, “P → Q” and “Q → P” have different truth tables.

The laws of implication express the notions of necessary and sufficient conditions:

A  → B (is true)
A is a sufficient condition for B
B is a necessary condition for A

A causal relationship can be expressed as an implication. To say that if it rains, the road is wet, means that rain is a sufficient condition for the road to be wet, and that the road is necessarily wet when it rains.
The implication thus defined is called a material implication; it has nothing to do with Toulmin’s substantial logic.

The implication “P → Q” is false only when P is true and Q false (line 2). In other words, “P → Q” is true if and only if “not-(P & not-Q)” is true.

Line (3) asserts the truth of the implication “If the moon is a soft cheese (false proposition), then Napoleon died in St. Helena (true proposition)”. Like the other logical connectives, the implication is indifferent to the meaning of the propositions it connects. It takes into consideration only their truth-values.​​ The strict implication of Lewis tries to elminate this paradox by requiring that for “P → Q” to be true, Q must be deducible from P. This new definition introduces semantic conditions, in addition to the truth values. This explains why the word “implication” is sometimes used in the sense of “deductive inference”.

Systems of natural deduction are defined in logic (Vax 1982, Deduction). They have nothing to do with Grize’s Natural Logic.

2 Logical laws

Using connectors and simple or complex propositions, one is able to construct complex propositional expressions, for example “(P & Q) → R”. The truth value of such a complex expression is only a function of the truth of its component propositions. Truth tables can be used to evaluate these expressions. Some of them are always true, they correspond to logical laws.

2.1 “Laws of thought”

Binary connectors combine in equivalences known as De Morgan’s laws, which are considered to be laws of thought. For example, the connectives “&” and “V” enter into the following equivalences:

The negation of an inclusive disjunction is equivalent to the conjunction of the negations of its components:
¬ (P V Q) ↔ (¬P & ¬Q)

The negation of a conjunction is equivalent to the disjunction of the negations of its components:
¬ (P & Q) ↔ (¬P V ¬Q)

Case-by-case argumentation is based on inclusive disjunction.

2.2 Hypothetical (or conditional) syllogism S. Deduction

2.3 Conjunctive syllogism

The following statement expresses a logical law:

If a conjunction is false and one of its components is true, then the other component is false

[¬(P & Q) & P] → ¬Q

The corresponding three-step deduction is called a conjunctive syllogism:

¬(P & Q)           the major proposition denies a conjunction
P                      the minor affirms one of the two propositions
————
¬Q                   the conclusion excludes the other

An adaptation to ordinary reasoning:

No one can be in two places at the same time
Peter was seen in Bordeaux yesterday at 6:30pm (UT)
So, he was not in London yesterday at 6:30 pm. (UT)

Knowing that Peter is a suspect; that his interest is to hide that he was really in Bordeaux, and that the witness is more reliable than the suspect, we can conclude that Peter lied when he pretended to be in London at 6:30pm yesterday.

In the following example, the major of the disjunctive syllogism is the negation of an exclusive disjunction:

¬(P W Q)          a candidate cannot be admitted and rejected
¬P                   my name is not on the list of successful candidates
————
¬Q                   I am rejected

All these deductions are common in ordinary language, where their self-evidence ensures that they go unnoticed. It would be a mistake to ignore them on the pretext that, since these arguments are valid, they are not arguments.

3. Connectives in logic and in language

Introductory courses in logic make consistent use of ordinary language to illustrate both the capabilities and the peculiarities of logical languages. In general, logic can be “applied to ordinary language” (Kleene 1967: p. 67-73) as a tool for expressing, analyzing and evaluating ordinary arguments as valid or invalid reasoning. These translation exercises are as follows (id. p. 59):

I will only pay you for your TV installation only if it works  — translated as P → W
Your installation does not work  — translated as ¬W
So I will not pay you — translated as  ¬P

Using the truth table method this reasoning is then tested for validity, and declared valid.

To identify similarities and differences, natural language components and properties can be compared with their logical language counterparts. This allows us to better understand both types of languages. Such exercises are helpful in gaining a better understanding of logical or linguistic systems, and may also be useful in teaching argumentation. However, there are some additional facts which should be taken into one consideration when using this methodology.

(i) The previous exercise did not focus on the correct combination of the truth values of semantically independent propositions, as was the case of the logical argument about the moon and Napoleon (see §1.4 supra). The exercise introduces a strong condition on semantic coherence between the linked propositions, they belong to the same domain of practical action, in this case, TV installation.

(ii) Natural language connectives do not connect propositions in the way that logical connectives do. The former can be said to be between the two propositions, whereas the latter are syntactically attached to the second proposition. Logical connectives and natural language connectives have two different syntaxes.

As a consequence, the right scope of a linguistic connective is essentially defined by the sentence to which it belongs, whereas its left scope can be much larger, and may include an entire narrative, with various twists and turns:

So, the prince married the princess — The End —

Connectors are classically thought of as connecting two statements in a complete discourse, such as yet in:

the path was dark, yet I slowly found my way (google)

Still, in:

 It is good, yet it could be improved (d.c, Yet)

yet introduces a more complex scenario, and the previous example is not a complete discourse. Yet announces that more hints will follow, specifying the weaknesses of the task being evaluated.

(iii) In many cases, the logical reconstruction of ordinary reasoning must introduce new propositions that are said to be present but are left implicit in the discursive string under consideration. This string is then said to contain an “incomplete argument”, see Enthymeme.

(iv) Elementary logical reasoning does not cover all ordinary reasoning:

I ate three apples and two oranges, so I have had my five-fruit diet today

First, this seemingly crystal-clear reasoning is loaded with implicit knowledge, such as “apples are fruits,” “oranges are fruits,” and that “no orange is an apple”. “Three citrus fruits and two oranges” sum up as five fruits only if none of the mentioned three citrus fruits is an orange.

Second, the critical fact here is that the conclusion is based on an addition that is easier to solve in arithmetic than in a logical language. Toulmin’s layout would satisfy this condition by adding a warrant-backing system that refers to the laws of arithmetic.

(v) Logical connectives capture only a small part of the linguistic role played by natural language connectives. The connector “&”requires only that the conjoined clauses be true. This property is common to many ordinary words, and, but, yet … and to all concessive words:

The circumstances which render the compound true are always the same, viz. joint truth of the two components, regardless of whether ‘and’, ‘but’ or ‘although’ is used. Use of one of these words rather than another may make a difference in naturalness of idiom and may also provide some incidental evidence to what is going on in the speaker’s mind, but it is incapable of making the difference between truth and falsehood of the compound. The difference in meaning between ‘and’, ‘but’, and ‘although’ is rhetorical, not logical. Logical notation, unconcerned with rhetorical distinctions, expresses conjunction uniformly. (Quine 1959, p. 40-41)

In other words, elementary logical theory has no adequate concepts to deal with the phenomena of argumentative orientation, and imposes no obligation in this respect. Quine’s argumentative strategy is to minimize the problem and delegate it to rhetoric, which is seen as a dumping ground for problems left unsolved by logical analysis.

The word « and » carries with it subtle semantic conditions, such as a sensitivity to temporal sequence. If “P & Q” is true, then “Q & P” is true. But these two statements do not contain the same information, and this is no longer a matter of rhetoric, whatever the meaning of that word means:

They married and had many children.
They had many children and married.

One might think that, under certain conditions, this logical analysis introduces a third proposition “The events succeeded in this order”. For other conditions affecting the use of and, see Composition and division.

3. No subordination, but bilateral relations

There is no ideal way to imagine the relationship between logical language and natural language; everything depends on the theoretical and practical goals of the researcher, whether he is building a conversational robot, or developing a formal syntax for ordinary language, or teaching second-level argumentation courses.

Logic is an autonomous mathematical language, that can be constructed from some chosen segments of ordinary language. From the beginning, the teaching of logic can draw more or less heavily on the resources of ordinary language. The same is true for the teaching of everyday argumentation in relation to the resources provided by the logical language. The teacher is free to make pedagogical choices, and possible alternative approaches should be judged by their results, according to the standard methods used to evaluate educational methods.

CONDUCTIVE ARGUMENT

Conductive arguments are defined by Wellman as third type of argument, parallel to deduction and induction. Using the following examples (my numbering), he notes that, “it is tempting, therefore, to define a conductive argument as any argument that is neither deductive nor inductive” (1971, p. 51):

(1) You have to take your son to the circus because you promised.
(2) This is a good book because it is interesting and thought provoking.
(3) Although he is tactless and nonconformist, he is still a morally good man because of his underlying kindness and real integrity. (Ibid.)

Wellman distinguishes between three types of conductive arguments

(i) “A single reason is given for the conclusion” (id. p. 55), as in

(4) You ought to help him because he has been very kind to you.
(5) That was a good play because the characters were so well drawn. (Ibid.)

(ii) “In the second pattern of conduction, several reasons are given for the conclusion” (id., p. 56), as in:

(6) You ought to take your son to the movie, because you promised to do so, it is a good movie, and you have nothing better to do this afternoon.
(7) This is not a good book, because it fails to hold one’s interest, is full of vague description, and has a very implausible plot. (Ibid.)

(iii) “The third pattern of conduction is that form of argument in which some conclusion is drawn from both positive and negative considerations. In this pattern, reasons against the conclusion are included as well as reasons for it” (id., p. 57), as in

(8) In spite of a certain dissonance, that piece of music is beautiful because of its dynamic quality and its final conclusion.
(9) Although your lawn needs cutting, you ought to take your son to the movie because the picture is ideal for children and will be gone by tomorrow. (Ibid.)

The key feature of conductive reasoning seems to be condition (3), where, depending on the speaker, and given the same reasons, the pros may outweigh the cons or vice versa (Blair 2011). Given the same data, another speaker might reach the opposite conclusion.

(8.1) In spite of a certain dynamic quality and its final conclusion, that piece of music is ugly because of its dissonance.

The adjective certain seems to be attached to the connective in spite of, indicating that the speaker will not argue on the basis of this argument (will not identify with this voice), S. Interaction, Dialogue, Polyphony.

A conductive argument does not seem to be amenable to default reasoning. Their conditions of refutation are different. Default reasoning might be updated or changed as new information is accessed, while conductive reasoning does not depend on information as such. A conductive argument is typically concerned with values, either moral or aesthetic. The specific problem of conduction is the hierarchization, or balancing of values. While some pairs of values will be very difficult, if not impossible, to balance, others will be quite plausibly balanced. for example, sentence (8) can be plausibly transformed into (8.1), because the three implied values cannot, in my view, be hierarchized, while (9) invokes values that seem easier to balance:

(9.1) I know, the movie is ideal for children and won’t be showing in the cinema after tomorrow, but you ought to cut your lawn!

Cutting the lawn seems to be a task that can easily be postponed, in view of the children’s education and their legitimate satisfaction, which could be prioritized. So, in the case of (9), the consensus would be that the pros clearly outweigh the cons.

In any case, more complex interactional data might provide some indications of how dissenting speakers fare when dealing with competing values.

CONDITIONS OF DISCUSSION

The Treatise on Argumentation insists on the necessity and variety of “prior agreements” between participants to develop an argumentation — that is, an argument₁; no prior agreements are necessary to engage in an argument₂:

For argumentation to exist, an effective community of minds must be realized at a given moment. First, there must be agreement in principle about the formation of this intellectual community, and then about the fact of debating a particular question together: now, this does not happen automatically. (Perelman & Olbrechts-Tyteca [1958], p. 14)

Two different kinds of agreements are mentioned here, and, as the text points out, neither of them can be taken for granted.

1. Formation of speech communities

This first type is concerned with the realization of an “effective community of minds”, constituted on the basis of the free decision of the participants. It can be considered as an ideal form of argumentative communication. Its closest approximation may be philosophical or scientific friendly encounters.

Not all argumentative practices depend on the production of such a community. The court is a prototypical argumentative venue, and no prior voluntary agreement with criminals is required to ensure their timely appearance; if necessary, legal coercion may be used. Institutions that define specific forums, problems and rules of interaction determine the social and legal conventions that govern argumentative communities. The existence of these social infrastructures makes it possible to avoid the previous cumbersome negotiations between speech communities.

2. Agreement on the issue

To discuss an issue, must we first “agree to discuss this issue together”? As in the case of the types of agreements described immediately above, the different legal systems determine who has the legal right to determine the charges that will lead to the appearance of a particular party; the defendant does not necessarily agree to discuss the matter, but is summoned by the judge.

ln institutionally structured communities, preliminary discussions may be useful in determining the items to be discussed at a given meeting. But the agenda is not necessarily determined by the prospective participants in the discussion; it may be the prerogative of an individual in charge of the organization. On the other hand, the topic itself, may be reformulated during the meeting.

Intellectual communities are also social communities, even when they deal with questions of human existence in general. The disputability of a question is itself an argumentative exercise, in the same way as is the process of discussing the question itself. There are two distinct subquestions to be considered, first, a central one, the conditions for the “disputability” of the issue properly speaking, and second, if all the potential partners agree to discuss such and such an issue, a practical question has to be settled, the material conditions for the discussion itself – where, when, who will chair the discussion, etc. — not to mention the shape of the table.

The dispute over maximizing vs. minimizing the right to discuss defines what may be called the stasis of stasis.

2.1 Maximizing the right to discuss

In terms of content, one can either emphasize the principle of radical freedom of expression according to which any point of view can be affirmed and challenged, or one can emphasize the pragmatic conditions of such discussion. The first of the “Ten Commandments for Reasonable Discussants” states that,

Commandment 1, Freedom rule: Discussants may not prevent each other from advancing standpoints or calling standpoints into question. (van Eemeren, Grootendorst, 2004, p. 190)
S. Rules.

This is also the position taken by Stuart Mill:

If all mankind minus one, were of one opinion, and only one person were of the contrary opinion, mankind would be no more justified in silencing that one person, than he, if he had the power, would be justified in silencing mankind. (Mill, [1859], p. 76)

2.2 Conditioning the rights to discuss

Absolute freedom of speech would give free rein to racist speech, hate speech, collective verbal and non-verbal harassment of the individual chosen as the scapegoat of a group, etc., forms of speech that many would find unacceptable. If individuals are free to discuss anything privately, provided they can find partners willing to do so, actual speech communities impose conditions on social discussion. For example, the res judicata principle prevents the reopening of an issue that has already been decided, unless a new fact is to be considered.

Moreover, the proper functioning of a speech community must take into account the fact that it is not possible to discuss anything (condition on the subject, on the agenda), with anyone (condition on the participants), anywhere and anytime (material conditions on place and time), no matter how (according to what procedure), see Manipulation:

Some Truths Are Not for Common Ears. It is lawful to speak the truth; it is not expedient to speak the truth to everybody at every time and in every way.
Erasmus, [1524], On the Freedom of the Will. (no pag.) [1]

The Treatise is very sensitive to the “anybody” condition:

There are beings with whom any contact may seem superfluous or undesirable. There are some with whom one cannot be bothered to speak. There are also others with whom one does not wish to discuss things, but to whom one merely gives orders.
(Perelman & Olbrechts-Tyteca [1958], p. 15)

Aristotle limits the subjects of legitimate discussion to the endoxa, and rejects debates that question “everything”, that is, affirmations that in practice no one doubts:

Not every problem, nor every thesis, should be examined, but only
 one which might puzzle one of those who need argument, not punishment or perception. For those who are puzzled as to know whether one ought 
to honor the gods and love one’s parents or not need punishment, while those who are puzzled to know whether snow is white or not need perception. (Top., 11)

The uncontroversial refers to three kinds of evidence: sensory evidence, “snow is white”; religious evidence, “we must honor the gods”; and social evidence, “we must love our parents”; these statements are uncontroversial because it is inconceivable that anyone would argue otherwise — in Aristotle’s Athenian society of course. For an opinion to be worthy of doubt, it must, on the one hand, fall within the scope of the doxa. That is, it must be part of the defining beliefs of the community, or seriously held by some of its honorable members or a subset, see Doxa.

On the other hand, the doubt must be serious, that is motivated. Since argument is a costly activity, one must have a good reason to doubt. In other words, the person who wishes to question an accepted proposition bears the burden of proof.

In the same spirit, the theory of stasis categorizes as uncontroversial (a-stasic) misplaced, poorly formulated or intractable questions, or, conversely, questions whose answer is obvious, S. Dialectic; Self-evidence; Stasis; Argumentative question.

On the legitimizing effects of debate, see Paradoxes.

3. Agreements on what counts as an argument

Agreements on the community of speech and on the issue must be supplemented by agreements on beings, facts, rules and values ​​(Perelman, Olbrechts-Tyteca [1958], II, 1). Agreements here should determine what counts as an argument: the condition of truth; the relevance of the true statement to the defended conclusion; the relevance of the conclusion (defended by a true and relevant statement) for the debate itself, see Relevance.

When it is impossible to determine whether a statement is true, or relevant to a conclusion, or relevant to the debate itself, a general system of acceptance or tacit agreement is invoked. In serious global disagreements, partial agreements are difficult to reach; the disputants anticipate their opponent’s conclusion, knowing well that once the argument is accepted, the conclusion will quickly follow, hence the tendency to postulate disagreement as a governing principle, even upon what should be considered facts, see Politeness; Dissensus; Disagreement.

This “appeal to agreement” is actually based on an argument of perverse effects, considering that the absence of agreement would condemn the debate to an undesirable state of deepening disagreement, which might even lead to a collapse of the discussion (Doury 1997). In practice, two facts have to be considered. First, points of agreement and disagreement can be negotiated on the spot, during the discussion. Second, the lack of agreement does not preclude argumentation, it is sufficient for third parties to take the reins of the discussion. The judge’s decision, and more generally that of the third party, is often made on the basis of an argument rejected or ignored by one or both parties, see Roles. Judicial organizations intervene precisely when no agreement can be reached between the parties; as representatives of the ruling power, they dispense with agreements — not with arguments.

In general, if one agrees on the data and rules, the conclusion follows automatically; argumentation becomes demonstrative. But argumentation is a linguistic way of dealing with differences in a system of generalized disagreement and uncertainty. There is a crucial incompatibility between the material interests at stake: one can indeed divide the cake, but what is eaten by any one person cannot be shared with the other. Serious, deep, insoluble … disagreement between the parties, proponents and opponents, should be considered to be the basic condition of argumentation; that is why third parties play a key role in argumentative devices.

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[1] Quoted from Desiderius Erasmus, On the Freedom of the Will. Trans. by E. Gordon Rupp (no pag., no date). www.sjsu.edu/people/james.lindahl/courses/Hum1B/s3/Erasmus-and-Luther-on-Free-Will-and-Salvation.pdf (05-23-17).

CONCESSION

Concessions can be negotiated in an organized discussion, or presented as an expression of the speaker’s good will in a monological discourse.

1. Negotiated concession

In negotiated concessions, the arguer modifies his or her original position by lowering the original demand or by conceding a controversial subpoint to the opponent. Strategically, this move may amount to an orderly retreat, possibly for future benefit, in the hope that the opponent will do the same on to another point.

In Aristotelian logical-dialectical games the discussion is about the truth of a statement. The consequence is that it ignores concessions, as a violation of the principle of the excluded middle, statements being considered either entirely true, or entirely false; conclusively defended or not, see Dialectic. In contrast, concession is a key moment in the negotiation process of human affairs, understood as a discussion leading to a reasonable agreement (Kerbrat-Orecchioni, 2000).

By making concessions, the arguer acknowledges that the opponent’s point of view has some validity, while still maintaining the value of his or her own positions and conclusions. The arguer may believe that hisremaining arguments are:

— More persuasive, or of a different nature than the opponent’s
— Not strong arguments, but arguments based on personal values and deep beliefs (identity-based arguments).

The original position should thus be maintained against all odds, according to the formula “I do know, but still …”.

In everyday discussions, concessions are valued as manifestations of openness to others, and as constitutive of a positive ethos. Nevertheless, concessions can be ironic, see Epitrope.

2. Concession as a speech act

In grammar, concessive constructions “A(claim) + C(concession)” coordinate two statements with opposite argumentative orientations, while maintaining the overall orientation determined by the first claim A:

“although C, A”; “certainly C, but A”
“I concede, I understand C but I stand by A”.

C takes up or reformulates the opponent’s speech, or evokes the speech of a fictitious opponent; A reaffirms the speaker’s claim.

Social relations are indeed extremely tense these days, but we still need to continue restructuring the company.

Unlike a negotiated concession, linguistic concession is purely verbal. The speaker sets out:

— First, a virtual character or voice develops the argument that “social relations are extremely tense”, pointing to conclusions such as “stop restructuring of the company”,

—followed by a second argument, that takes the opposite position “we must continue restructuring the company”, and identifies with this second character. In Goffman’s words, the speaker is the animator of A, and the animator and principal of C. In other words, the speaker acknowledges the existence of arguments supporting an opposite conclusion, but at the same time refuses to conclude on this basis. The concession here is a simple acknowledgment of the fact that someone, somewhere, is saying, or could say something opposite to what the speaker claims. This amounts to a de-activation of the argumentative strength of the aforementioned argument. This kind of concession is not at all an expression of the good will of a reasonable negotiator, but a mere phagocytosis and castration of the opponent’s arguments

I know that, you already told me, no need to repeat it!

The two forms of concession can be superimposed, by rationalizing the linguistic concession. One assumes that linguistic concession occurs when the speaker has considered the opponent’s arguments and confronted them with his or her own (even if this examination often leaves no discursive trace), and that, in the end,  he thinks that his arguments are better. But since language takes for real and true what it signifies, a purely linguistic concession automatically produces a negotiated concession effect, whether or not this is really the case. This does not mean that linguistic concession is always mere lip service, but that negotiated concession can only be studied on corpora built for that purpose.

COMPOSITION AND DIVISION
WHOLE AND PARTS argument

Aristotle considers composition or “combination of words” and division to be verbal fallacies, that is fallacies of words, as opposed to fallacies of things or method, see Fallacies 2. They are discussed in the Sophistical Refutations (RS 4) and in the Rhetoric (II, 24, 1401a20 – 1402b5; RR p. 128).

The term argumentation by division is sometimes used to refer to case-by-case argumentation.

1. Grammar of composition and division

Composition and division involve the conjunction and, which can coordinate:

— Phrases:

(1) Peter and Paul came.                   (No and N1) + Verb
(2) Peter smoked and prayed.            No + (V1 and V2)

— Statements:

(3) Peter came and Paul came.            (N + V1) and (N1 + V1)
(4) Peter smoked and Peter smoked     (N + V1) and (N1 + V2)

In Aristotelian logical-grammatical terminology:

(3) and (4) are obtained by division from (1) and (2) respectively
(1) and (2) are obtained by composition from (3) and (4) respectively

The compound and divided statements are sometimes semantically equivalent and sometimes not.

(i) Equivalent — (1) and (3) on the one hand, (2) and (4) on the other hand are roughly equivalent, although it seems that (1), not (3), implies that Peter and Paul came together. In this case, composition and division are possible, and the coordination is used simply to avoid repetition.

(ii) Not equivalent — sometimes phrase coordination (composed statement) is not equivalent to sentence coordination (divided statement). The semantic phenomena involved are of very different kinds.

Peter got married and Mary got married.
≠ Peter and Mary got married.

If Peter and Mary are brother and sister, the custom being what it is, the composition is unambiguous. Without such information, the composition introduces ambiguity.

The operation of division can produce a meaningless discourse:

The flag is red and black.
* The flag is red and the flag is black.

B is between A and C.
* B is between A and B is between C.

Sometimes a syntactic operation applied to a proposition produces a paraphrase of that proposition. At other times, the same operation applied to another proposition having apparently the same structure as the first one produces a proposition that has no meaning, or whose meaning and truth conditions are completely different from those of the original proposition.

2. Aristotelian logic of composition and division

The study of paraphrase systems is a classical object of syntactic theory. Aristotelian logic regards composition and division as a problem of logic. As Hintikka (1987) has repeatedly pointed out, the Aristotelian notion of fallacy is dialogical, see Fallacy (I). The fallacious maneuver confuses the interlocutor, and this is exactly what happens with composition and division. The following case is one of the oldest and most famous illustrations of the fallacy of composition:

This dog is your dog (is yours); and this dog is a father (of several puppies).
So this dog is your father and you are the brother of the puppies.

The interlocutor is disoriented, and everyone finds it very funny (Plato, Euth., XXIV, 298a-299d, pp. 141-142). see Sophism.

Aristotle analyzes this kind of sophistical and sophisticated problem in the Sophistical Refutations and in the Rhetoric under the heading of “Paralogism of composition and division”. He shows that the question extends to a variety of discursive phenomena, under what conditions can judgments made on the basis of isolated statements be “composed” into a discourse in which the statements are connected? The discussion is illustrated by several examples , which, although their formulation may seem contrived, show the full scope of the interpretative issues that are raised

(i) Consider the statement: “It is possible to write while not writing” (RS, 4); it can be interpreted in two ways:

— Interpretation 1 composes the meaning: “one can write and not write at the same time” (ibid.), in the sense of: “one can (write and not write)”. This construction is misleading and absurd.
— Interpretation 2 divides the meaning; if one does not write one still retains the ability to write, viz: « one can know how to write while not writing », which is correct. Under certain circumstances, a person who can write cannot physically do so, e.g., if his hands are tied. The modal force is ambiguous between “having the ability to” and “having the possibility of exercising that ability”.

 (ii) The following example also uses the modal can, this time in its relation to time and circumstances. Consider the statement “if you can carry one thing, you can carry several” (RS, 4, 166a30: 11):

(1) (I can carry the table) and (I can carry the cupboard)

Therefore, by composition of the two statements into one:

(2) I can carry (the table together with the cupboard).

Which is not necessarily the case.

(iii) The fallacy of division is illustrated by the example “five is equal to three and two” (after RS, 4, 166a30, p.12):

— Interpretation (1) divides the meaning, i.e., it divides the utterance into two coordinated propositions, which is both absurd and fallacious:

(five equals three) and (five equals two).

— Interpretation (2) composes the meaning, which is correct:

Five is equal to (three and two)

In the Rhetoric, the notion of composition is discussed with several examples that clearly show its relevance to argumentation. The argument by composition and division “[asserts] of the whole what is true of the parts, or of the parts what is true of the whole” (Rhet, II, 24, 1401a20-30; RR, pp. 381), which makes it possible to present things from quite different angles. This technique of argumentation involves statements constructed around evaluative and modal predicates such as:

— is good; — is just; — is able to —; — can —;
— knows —; — said.

The following example is taken from Sophocles play, Electra. Clytemnestra has killed her husband, Agamemnon. Then their son Orestes kills his mother to avenge his father. Was Orestes morally and legally justified in doing so?

“‘T’is right that she who slays her lord should die’; ‘it is right too, that the son should avenge his father’. Very good: these two things are what Orestes has done.” Still, perhaps the two things, once they are put together, do not form a right act. (Rhet., II. 24, 1401a35-b5, RR, 383).

Orestes justifies what he has done by arguing that his two actions can be composed. His accuser denies the composition.

This technique of decomposing a dubious action into a series of praiseworthy, or at least innocent action, is arguably very productive. Stealing is simply taking the bag that is there, taking it somewhere else, and not putting it back in the same place. The division blocks the overall evaluation.

A second example clearly shows that fallacy and argument are two sides of the same coin:

If a double portion of a certain thing is harmful to health, then a single portion must not be called wholesome, since it is absurd that two good things should make one bad thing. Put thus, the enthymeme is refutative; put as follows, demonstrative “for one good thing cannot be made up of two bad things”. The whole line of argument is fallacious. (Rhet., Ii. 24, 1401a30, RR p.381-383)

The teetotallers begin by an agreeing that “drinking a lot makes you sick”, and they divide: “so having one drink makes you sick”. Permissive people follow the other line: “having a drink is good for your health”, and proceed by composition. Abstainers argue by division, and this is considered to be fallacious by permissive people. Permissive people argue by composition, and this is considered to be fallacious by abstainers.

3. Whole and part argument

The two labels “composition and division” and “part and whole” are considered equivalent in practice (van Eemeren & Garssen, 2009).

3.1 Whole to parts and division

The whole argument assigns to each of its parts a property that is proved on the whole:

If the whole is P, then each of its parts must be P.

If the country is rich, then each of its regions (inhabitants …) must be rich.
The Americans are rich, so this one must be rich; let’s ransom him!

The problem faced by the whole-to-parts argument is the same as that of the division argument: can the property evidenced on the whole be transferred to each of its parts?

3.2 Parts to whole and composition

The argument based on the parts assigns to the whole they make up the properties evidenced on each of its parts:

If every part of a whole is P, then the whole is P.
If every player is good, then the team is good (?).

The problem faced by parts to whole arguments mirrors that of the argument by composition: is the property evidenced by each part also evidenced by the whole?

4. Complex wholes and emergent properties

Accidental or mechanical wholes are composed of a set of unrelated objects in a neighborhood relation. Essential or complex wholes consist of the conjunction of the parts plus some emergent additional properties, that distinguishes them from an inert juxtaposition of components. The degree of complexity of the whole is superior to the simple arithmetical addition of its parts. This process is called the composition effect. Aristotle’s case of the superiority of the group over the individual alleged by is an example of such an effect, see Ad populum.

This issue is also found in rhetoric, where a distinction is made between metonymy and synecdoche, the former focusing upon neighborhood relations and the latter on relations between a complex whole and its parts.

Argument of COMPREHENSIVENESS
A completudine

The evolution of society can manifest itself by the emergence of legal cases that do not find clear solutions in the existing legal system, be it in national, international or human rights legislation (Tarello 1972, cited in Perelman 1977, p. 55).
Nevertheless, the judge has an obligation to judge, i.e., he or she has to give a verdict upon all the cases before him or her, S.. Silence. That is, he or she cannot refuse to decide a case by arguing that there is no law applicable to that case, or that no interpretation of an existing law can settle it.
In other words, the principle of completeness presupposes that the existing legal body of law, properly interpreted, can qualify each and every human action as permitted, tolerated, or prohibited.

Meta-principles such as the following supplement the legal system:

In civil matters, in the absence of specific law, the judge is bound to proceed according to equity. In order to decide according to equity, he must refer to natural law and to reason, or to received usages, when the primitive law is silent.
Fortuné Anthoine de Saint Joseph, [Concordance between the Foreign Civil Code and the Napoleonic Code], 1856.[1]

The argument of comprehensiveness [2] is parallel to the topos of the impotent legislator, the nature of things that makes the application of the law impossible, see Weight of Circumstances.

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[1] Fortuné Anthoine de Saint Joseph, Concordance entre les codes civils étrangers et le Code Napoléon, 2^nd ed. t. II. Paris: Cotillon, 1856. P. 460.
[2] Argument a completudine; Lat. completudo, “completeness”.

Argument from COMPARISON

Comparison is the process of determining whether or not two objects,, two situations, two systems… have some similarities or analogies. A process of comparison is involved in many argumentative activities, so the label argument by comparison (a comparatione) is used with different meanings.
These meanings correspond primarily with the argument: a fortiori; a pari;, by analogy; by example or exemplum.

Comparison and categorization — Comparison is the basis for the categorization-nomination process; the individual to be categorized is compared either with a known individual belonging to the category, or with the prototypical member defining the category. S. Justice

Intra-categorical comparison — Two beings belonging to the same category are identical from the point of view of that category. Nevertheless, they can still be compared in terms of:

— their non-categorical properties; S. Intra-categorical analogy.

— their position relative to a prototypical subcategory of that category. A rat and a whale, for example, are identical insofar as both are mammals; considering that the cow is a prototypical mammal, we can say that a rat, being nearer to a cow than to a whale, is “more” a mammal than a whale.

— Hierarchical categories,by definition, contain built-in comparisons: Bachelor, Master, and Doctorate are three types of academic degrees, listed by ascending order, see a fortiori argument.

Comparison and structural analogy — Establishing a structural analogy also involves a process of comparison.

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INVENTION and COMMON PLACES

The term commonplace corresponds to the Latin locus communis, which translates the Greek topos.

— Often reduced to a place (locus, pl. loci), an inferential commonplace is an inferential topic, or argumentation scheme.

— A substantive commonplace is an endoxon, that is, a formulaic expression of a common idea. Traditional rhetorical invention specialized in the argumentative use of substantive commonplaces.

1. Chapter Heads of Reality

According to Aristotle’s Categories (1b 25 sq.; Tricot, p. 5), events and reality are organized according to a basic ontology, whose ultimate components (categories) are:

Person, Action, Time, Place, Manner, Cause or Reason

The parameters of this is a Western ontology can vary from author to author.

According to Benveniste (1966, ch. VI), these parameters, which are supposed to reflect reality, are also closely related to the Greek language, particularly the system of sentence complementation and to interrogative words.

Category                         Question

Person focus                  Who?                                  Peter
Kind of action                What?                                 met Paul
Quantity                          How many times?          twice
Place                                Where?                              in Washington
Manner                            How.                                  reluctantly
Medium                           How?                                  on Paul’s instigation
Purpose, reason             Why?                                  to discuss their business

The systematic use of this interrogative grid is a survey method for gathering and organizing information about any event.

[Interrogatives] have already been recognized in different languages ​​for different purposes: such as, for speculative purposes, in scholastic Latin: cur?, quomodo?, quando? [why? how? when?]; or for military purposes in German, where the tetralogy Wer? Wo? Wann? Wie? is taught to all military recruits as the framework of information that every scout on a reconnaissance mission must be able to provide and report to their superiors. (Tesnière 1959, p. 194).

This method is known as ”Five Ws” : Who? What? Where? When? Why? –plus How? How many?

When applied to a particular field, these parameters correspond to words with full lexical meaning. For example, a classic guide to political decision-making includes questions such as:

“Honorable? Will the proposed measure be honorable or embarrassing to us?

See political arguments: two collections and infra, the parameters for portraying human beings.

In the Middle Ages, it guided confessors looking for sins, who were anxious not to overlook any (Robertson & Olson, 2017). We can speak of “inquisitorial” questions [1] , in the sense that an inquisition is defined as an “investigation, methodical, rigorous research” (TLFi, Inquisitoire). It is a cornerstone of ordinary Western thought.

The same type of questions also guide moral evaluations. For example an act such as “having carnal intercourse” is considered shameful if it is done “with forbidden persons” (with whom?), or “at the wrong time” (when?) or “in the wrong place” (where?) (Aristotle, 1383b 15-20; RR p. 279).

2. The Rhetorical “Technical” Method

The distinction between rhetorical and non-rhetorical elements,  i.e.  between what belongs to “rhetorical technique” and what does not, is a key aspect of this method. This distinction is nonintuitive, and surprising a priori. This is most evident at the beginning of the rhetorical process, the inventio, or the research of arguments. The grid of questions remains  operative, the radical change lies in how the answers are constructed.

These questions can be answered a posteriori, i.e., after a full documented investigation into the specifics of the case–the kind of work a police investigator is supposed to do. The inspector does fieldwork, the rhetor as such does not. The rhetor can answer a priori, on the basis of endoxa, or preconceived common ideas, that are “ruling ideas ».
In both cases, the collected material must be presented in a convincing discourse to the court and the public. Ultimately, it’s all a matter of language, the result of the concrete investigation makes all  the difference. In any case, rhetorical discourse is particularly powerful in creating doubt and shifting the burden of proof.
When material data is scarce—no witnesses, no contracts, not even a corpse—the case must still be discussed and this is where rhetoric comes in, in full force, not necessarily to manipulate people, but to clarify the situation and circumscribe zones of doubt avoiding for example, the condemnation of an innocent person, for example.

Giving undue prominence to stereotyped ideas in the construction of arguments, leads to strong and indignant criticism of rhetoric as a fallacious verbiage, see ornamental fallacy and §5 below.

Consider the argumentative question “Did Mr. So-and-So commit this horrible murder?”
— The question Who? “Who is the defendant, Mr. So-and-So?”. The subtopic Which country? provides the categorizing information: “Mr. So-and-so is Syldavian,” and likewise for all questions about the person.

— Endoxon about the Syldavians: The Syldavian category is associated with a set of defining endoxic predicates (“the Syldavians are like this”), each of which has a specific argumentative orientation.

The Syldavians are peaceful / bloodthirsty people.

These predicates provide an encyclopedic endoxic semantic definition of the Syldavian.

— The instantiation of the endoxic definition supports the conclusion:

The guilt of Mr. So-and-So is probable / improbable.

Other topical questions about the same Mr. So-and-So will provide different, possibly contradictory, perspectives that the opponent can use.
Such answers can help to organize a previous serious documentation, and a bunch of pre-established judgments  regardless of the outcome of any detailed investigation of the matter.

3. Portrait Based on Commonplaces

Each of these questions can become the source of several sub-questions that can be developed considerably, to produce a detailed grid of investigation. The results produced by this technique depend entirely on the method of inquiry used to answer the questions. An armchair argument where the ‘research’ is based on common sense and commonplaces will produce commonplace conclusions.

A rich set of detailed questions focuses on the key element of rhetorical scenarios: the person (Who?). Quintilian distinguishes the following facets in order to identify a person and compose an a priori rhetorical representation of that person, independent of any concrete information about the situation under discussion.

— “Birth, for people are generally considered to be similar in character to their fathers and forefathers, and sometimes derive motives for living an honorable or dishonorable life from their origins” (Quintilian IO, V, 10, 24 ).

To answer the subquestion “Birth?”, the inquiry about the family gathers information such as “he comes from a well-known honorable family”, or “his father was condemned.” The first piece of information provides arguments that allow one to apply rules such as “like father, like son”, or “he is a chip of the old block”,leading to conclusions such as:

He made a mistake, but his family provides all the necessary guarantees. Good blood cannot lie, he deserves a second chance.

The second piece of information leads to different conclusions:

The father was convicted, so the son has a heavy inheritance. Bring me more information about him!

The saying “the son of the miser is a spendthrift” contradicts the previous conclusion. If the father has a vice, the doxa does not attribute the corresponding virtue to the son, but rather the same vice or an opposite one.

—  “Nation?” (ibid.) and “Country?” (ibid., 25). The answers will introduce national stereotypes: “If he is Spanish, he is proud, if he is British, he is phlegmatic.” These conclusions, “he is proud, he is phlegmatic”, can be useful for the ensuing discussion,  “He is Spanish, so he is proud. He certainly reacted strongly to this personal attack.”

— “Sex? – For you would more readily believe a charge of robbery with regard to a man, and a charge of poisoning with regard to a woman” (ibid.) The prejudiced investigator will follow the commonplace suggestion: he will tend to look for a woman in the second case. A French book, “The Famous Poisoners” (Les Empoisonneuses Célèbres), is devoted exclusively to famous female poisoners.

—  “Age?”, “Education?”, “Bodily constitution? – For beauty is often used as an argument for libertinism, and strength for insolence. Contrary qualities are used to justify for contrary conduct” (id., 25-26). In other words, “He is handsome, he must be a libertine” is more credible, and considered as more probable than “He is handsome, therefore he must live an austere life.” If A is stronger than B, then “A is more aggressive than B” is likely. Therefore, if A and B fought, “surely, A attacked B. » In other words, A bears the burden of proof. These conclusions can be reversed by applying the paradox of plausibility: “Actually, B must have attacked A, because he knew that the evidence will be against A.”

— “Wealth? – For the same charge is not equally credible in reference to a rich man and a poor man, in reference to one who is surrounded with relations, friends and clients, and to one who is destitute of all such support” (id., 26). Commonplaces associated with social roles and positions come under this category. For example, an elderly man from the country, sitting on a bench in the setting sun, will certainly have deep thoughts about the present state of affairs, see rich and poor.

— “Natural disposition –  for avarice, passion, sensibility, cruelty, austerity, and other similar affections of the mind, frequently either cause credit to be given or to be withheld from an accusation” (id., 27). The murder was committed in a peculiarly cruel manner. Peter is cruel, therefore he is the murderer, see circumstances.

— “Manner of living – for it is often a matter of inquiry whether a person is luxurious, or parsimonious, or mean” (ibid.).

The following questions refer to arguments based on desires and motives (ibid.):

— “What a person affects, whether he wishes to appear rich or eloquent, just or powerful” (id., 28)

— “Previous doings and sayings” (ibid.), are used to find motives and precedents.

— “Commotion of the mind, […] a temporary excitement of the feelings, such as anger, or fear” (ibid.), see emotions.

— “Designs” (id., 29)

This set of commonplaces underlies portraits such as:

A man in his thirties. Canadian. West Coast. Athletic. From a well-known and respected family. Has never finished law school. Very friendly with his neighbors. Lives a conventional life. Works in a pharmacy, with limited prospects for the future.

This portrait could be read as a literary draft, as a police report. In any case, it is a set of potential premises.
Doxa-based argumentation uses pieces of information such as “the man is X”, relies on the stereotyped categories attached to X’s, “the X are like this”, and concludes that “the man is like this.” See categorization; cefinition.

4. Literature of Characters

This topology has a derived argumentative function and a direct aesthetic-cognitive function. It builds a bridge between argumentation and literature by providing a technique for constructing  portraits, through the genre of “characters”, such as those of the Greek Theophrastus. We are no longer in the realm of ethos as autofiction, but in the pure world of the ethopoeia, that is, the vivid fictional representation of a “character”, such as « the Miser” or “the Garrulous Person” through their conventional typical manners, discourse and actions. These decontextualized portraits can serve as authorized and respectable sources of information about the represented character and as preparatory exercises for real-life argumentation.
This combination constitutes a coherent educational, aesthetic and cognitive process of controlled writing and thinking—the very antithesis of any automatic writing.

5. “This Noxious Fertility of Common Thoughts” (Port-Royal)

When based solely on linguistic associations and doxa-based knowledge, this technique quickly produces fairly convincing, true-to-life images of things and events. These images are very difficult to refute, because they are merely expressions of shared preconstructed  knowledge. The vicious circle between persuader and persuadee is an example of such a situation, see persuasion.
Such compositions are the opposite of the in-depth characterizations of individuals, that can be developed in psychology or philosophy. They are a perfect stronghold for all positive or negative social prejudices.

Port-Royal condemned this « noxious fertility of the common thoughts » in the strongest terms:

Now, so far is it from being useful to obtain this sort of abundance, that there is nothing which more depraves the judgment, nothing which more chokes up good seed, than a crowd of noxious weeds ; nothing renders a mind more barren of just and weighty thoughts than this noxious fertility of common thoughts. The mind is accustomed to this facility, and no longer makes any effort to find appropriate, special, and natural reasons, which can only be discovered by an attentive consideration of the subject. (Arnauld, Nicole, [1662], III, XVII; p. 235).

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COLLECTION 4: CONTEMPORARY INNOVATIONS
AND STRUCTURATIONS

1. Chaïm Perelman & Lucie Olbrechts-Tyteca, A Treatise on Argumentation — The New Rhetoric, 1958

In The New Rhetoric — A Treatise on Argumentation (1958), Perelman & Olbrechts-Tyteca propose a sophisticated typology of arguments. Some twenty years later, in The Rhetorical Empire [L’Empire Rhétorique, 1977], Perelman takes up the essential elements of the 1958 typology, and makes some significant simplifications. In Juridical Logic [Logique Juridique, 1979] he presents a specific set of legal arguments.

1.1 The typology of the Treatise

According to Conley, the Treatise contains “more than eighty different forms of argument, and illuminating remarks on more than sixty-five figures” (1984, p. 180-181), and contrasts these achievements with “Toulmin’s renegade logic” (ibid.).

The “Forms of argumentation” are described in the third part of the Treatise, entitled “Techniques of argumentation”. They are presented as a set of “association techniques”, (Chap. 1 to 3), along with two other kinds of techniques, the “technique of dissociation” (Chap. 4), and the “Interaction of arguments” (Chap. 5). The latter chapter presents a number of dispositional techniques, and discusses the relative persuasive effects of different arrangements of arguments in a speech, i.e questions of classical “dispositio”.

1.2 The association techniques

The association techniques correspond to the classical argument schemes. They are classified under three categories:

Chap. 1. Quasi-logical arguments
Chap. 2. Arguments based on the structure of reality
Chap. 3. The relations establishing the structure of reality

“Quasi-logical arguments” (§46-59)

This category lists arguments which “lay claim to a certain power of conviction in the degree that they claim to be similar to the formal reasoning of logic or mathematics” (p. 192); this definition should be brought closer to the definition of a fallacious argument as “one that seems to be valid but is not so.” (Hamblin 1970, p. 12), see. Fallacies (1). The category includes the following argument schemes:

• • • 46-49 Contradiction and incompatibility
    • 50 Identity and definition
    • 51 Analyticity, analysis and tautology
    • 52 The rule of justice
    • 53 Arguments of reciprocity
    • 54 Arguments by transitivity
    • 55 Inclusions of the part in the whole
    • 56 Division of the whole into its parts
    • 57 Arguments by comparison
    • 58 Argumentation by sacrifice
    • 59 Probabilities

In The Rhetorical Empire, the chapter on “Quasi-Logical Arguments” essentially recapitulates the class as presented in the Treatise.

“Arguments based on the structure of reality” (§60-77)

From a linguistic point of view, he broad label “argument based on the structure of reality” can be interpreted as referring to arguments that exploit syntagmatic, or metonymic relations. Indeed, this category lists arguments “alleged to be in agreement with the very nature of things” (p. 191); these arguments “make use of [the structure of reality] to establish a solidarity between accepted judgments and others which one wishes to promote” (p. 261). The “causal link” and the “relation of succession” are fundamental to this category.

Arguments within this category include:

• • • 61-63 “Causal link”, “Pragmatic argument”
    • 63-73 discuss arguments in which the person is considered to be a causal agent, such as:
      • • 64-68 “Ends and means”, among which:
        • 65 “Argument of waste”
        • 66 “The Argument of direction”
        • 68-73 “The Person and his acts”, including:
        • 70 “Argument from authority”
        • 73 “The Group and its members”
    • 74-75 extend the notion of “relation of coexistence” to:
    • 74 “Act and essence”
    • 75 “The symbolic relation”
    • 76-77 present “more complex”, second level arguments:
    • 74 “Double hierarchy”
    • 75 “Differences of degree and of order”

The Rhetorical Empire, Chapter VIII, recapitulates the same class of arguments based on the structure of reality under different groupings:

— Relations of succession
— Relations of coexistence
— The Symbolic relation, the double hierarchy argument, argument about the differences of order.

“Relations establishing the structure of reality” §78-88

The inclusive label “Relations establishing the structure of reality” could be interpreted as referring to a set of arguments that exploit paradigmatic or metaphorical relations. This category of relations is defined on the basis of two of its prototypical members, arguments from “the particular case”, and “arguments by analogy”. The following argument schemes come under this category:

• • 78 “Argumentation by example”
  • 79 “Illustration”
  • 80-81 “Model and anti-model”
  • 82-87, On analogy
  • 87-88, On metaphor.

In the Rhetorical Empire, the title “establishing the structure of reality” is not retained; its contents are grouped under two distinct chapters:

Chap. IX, Arguments by example, illustration and model
Chap. X, Analogy and metaphor

This can be construed as a waiver of the distinction between arguments “establishing” the structure of reality, and those “based on” the structure of reality.

It might, however, also be argued that this couple of concepts does not characterize causal arguments in opposition to analogical ones, but indeed applies to both argument schemes. The successful use of an argument “based on” authority, for example, presupposes that the invoked authority has been previously “established”. This distinction is especially helpful in the case of arguments from authority, definition, causality and analogy.

1.3 The dissociation techniques

The basic difference between association and dissociation techniques is that the former operates on judgments; they “establish a solidarity between accepted judgments and others which one wishes to promote” (p. 261); they correspond to argument schemes. In contrast, dissociation techniques operate on “concepts” (p. 411; my emphasis): “[they] are mainly characterized by the modifications which they introduce into notions, since they aim less at using the accepted language than at moving towards a new formulation” (p. 191-192), see Dissociation, Distinguo; Persuasive Definition.

The two terms of the opposition association / dissociation are thus of a very different nature.

2. Toulmin, Rieke, Janik, An introduction to reasoning (1984)


Toulmin, Rieke, Janik consider nine «forms of reasoning» «most frequently to be met with in practical situations (1984, p. 147-155; p. 155).

1. analogy 2. generalization 3. sign 4. cause

5. authority 6. dilemma 7 classification 8. opposites 9. degree

In the argument from degree, « the different properties of a given thing are presumed to vary in step with one another » (id., p. 155)

Like the following one, this restricted group of argumentative schemes has a family resemblance with the classical lists derived from Cicero, see Collections 2.
They are good candidate for universality.

3. Kienpointner, Alltagslogik [Everyday Logic] 1992.

Kienpointner (1992, p. 231-402) synthetizes six contemporary typologies (Perelman, Olbrechts-Tyteca [1958] ; Toulmin, Rieke, Janik 1984 ; Govier 1987; Schellens 1987; van Eemeren, Kruiger 1987; Benoit, Lindsey 1987), summarized in the following table (1992, p. 246):

3.1 Rule-using argument schemes

Classificatory Schemes

Definition
Genus – Species
Part – Whole

Comparison Schemes

Equivalence
Resemblance
Difference
A fortiori

Opposition Schemes

Contradictories
Contraries
Relative terms
Incompatibility

Causal Schemes

Cause – Effect
Consequences
Reason
Means – End

3.2 Rule-establishing argument schemes

Argumentation by example
Inductive argument

3.3 Other schemes

Argument by example, illustrative argument
Arg. by analogy
Arg. by authority

4. Douglas Walton, Chris Reed, Fabrizio Macagno, Argumentation Schemes, 2008.

Walton, Reed and Macagno present an extensive and exhaustive survey including “a user’s compendium of argumentation schemes” (2008, pp. 308-346).

The schemes are consistently referred to as argument schemes, with the exception of (19), (20), (21), which are referred to as argumentation from values, from sacrifice, from the group and its members.

The following list mentions only the main schemes; they may include subtypes.

(1) Authorities: position, expertise, testimony, number (p. 309-314)

1. 1. 1. Argument from position to know
      2. Arg. from expert opinion
      3. Arg. from witness testimony
      4. Arg. from popular opinion, ad populum
      5. Arg. from popular practice.

Arguments (4) are based on what people generally believe, whereas arguments (5) are based on what people generally do.

(2) Example, analogy (p. 315-316)

1. 1. 6. Argument from example
      7. Arg. from analogy
      8. Practical reasoning from analogy

Arguments (7) concern beliefs; arguments (8) concern ways of doing things.

(3) Composition and division (p. 316-317)

1. 1. 9. Argument from composition
      10. Arg. from division

(4 ) Negation, opposition (p. 317-318)

1. 1. 11. Arg. from opposition (contradictory, contrary, converse, incompatible)
      12. Rhetorical argument from opposition

Negation-based argumentation schemes may or may not be logically valid or not; they are often not well defined.

(5) Alternative (p. 318-319)

1. 1. 13. Arg. from alternatives

This scheme concludes by eliminating a member of an alternative because of the requirement of the other member. It corresponds to a case-by-case argument between two cases.

(6) Classification (p. 319-320)

1. 1. 14. Arg. from verbal classification

“for all x, if x has property F, then x can be classified as having property G.”

The set F is contained in the set G.

1. 1. 15. Arg. from definition to verbal classification

If an individual a is defined (categorized) as a D, and if Ds in general have property P, then a has property P.

1. 1. 16. Arg. from vagueness of a verbal classification
      17. Arg. from arbitrariness of a verbal classification

Schemes 16. and 17. conclude with the rejection of an argument as “too vague” or “too arbitrarily defined” in some aspects. These cases can also be seen as an application of Grice’s cooperative principle.

(7) Persons, values, actions and sacrifice (p. 321-327)

1. 1. 18. Argument from interaction of act and person
      19. Arg. from values
      20. Arg. from sacrifice
      21. Arg. from the group and its members

These schemes consider a group whose members are said to share a quality Q, and attribute that quality to each member of the group. A member of a racist group can legitimately be assumed to be racist.

Not all the characteristics of its members can be composed and attributed to the group as such; a large set is not necessarily composed of large elements.

1. 1. 22. Practical reasoning
      23. Two-person practical reasoning

If you have an end, then you must accept the means and steps necessary to attain it.

1. 1. 24. Argument from waste
      25. Arg. from sunk costs

Pages 10-11 (id.) consider as synonyms the labels argument from waste, (with reference to Perelman & Olbrechts-Tyteca), and argument from sunk costs. Nevertheless, they are discussed here as two separate entries.

(8) Ignorance (p. 327-328)

1. 1. 26. Arg. from ignorance
      27. Epistemic argument from ignorance

This argument covers the case “if it were true, the newspapers would surely be talking about it” (id., p. 99)

(9) Cause, effect; abduction; consequence (p. 328-333)

1. 1. 28. Argument from cause to effect
      29. Arg. from correlation to cause
      30. Argument from sign
      31. Abductive argumentation scheme
      32. Argument from evidence to a hypothesis
      33. Arg. from consequences
      34. Pragmatic argument from alternatives

Scheme (34) is a special case of (33), the choice is between doing/not doing something and suffering/not suffering negative consequences.

(10) Arguments from threat, fear, danger (p. 333-335)

1. 1. 35. Argument from threat
      36. Arg. from fear appeal
      37. Arg. from danger appeal

Schemes (35), (36), (37) schematize different fear strategies.

1. 1. 38. Arg. from need for help
      39. Arg. from distress

(11) Commitments, ethos, ad hominem (p. 335-339)

40. Arg. from commitment
41. Ethotic argument
42. Generic ad hominem
43. Pragmatic inconsistency
44. Argument from inconsistent commitment
45. Circumstantial ad hominem

Scheme (44) distinguishes between committed and not really so.

Schemes (43) and (45) express forms of contradiction between personal commitments and actions.

1. 1. 46. Argument from bias
      47. Bias ad hominem

Patterns (46) and (47) are closely related. According to (46), the argument from bias says: “L is biased, so the conclusions are suspect”. According to (47), the “bias ad hominem”: “L is biased, so I do not trust him”. Biases are relative to a domain, but it is convenient to consider that the whole personality is biased; L has a “false mind”.

(12) Gradualism; slippery slope (p. 339-341)

1. 1. 48. Argument from gradualism

The comments (id. p. 114-115), show that this scheme can be compared to the slippery slope forms, (49) to (53). It expresses the sorite paradox, also mentioned in (52): “If you remove a grain from a pile of grains, you always have a pile; if you remove another grain, you still have a pile … up to what extent?”

1. 1. 49. Slippery slope argument
      50. Precedent slippery slope argument

The slippery slope argument is used to oppose an exception, on the grounds that the exception would open a line of precedent leading to something unacceptable.

1. 1. 51. Sorites slippery slope argument
      52. Verbal slippery slope argument

The slippery slope argument is used to reject the attribution of a property to an object on the grounds that this property is transmitted by contiguity up to an object that obviously does not or should not possess it. This is a variant of the argument to the absurd, based on a demonstration by recurrence.

1. 1. 53. Full slippery slope argument

(13) Rules, exceptions, precedent (p. 342-345)

1. 1. 54. Argument for constitutive-rule claim

Scheme (54) refers to rules of language (synonymy) and to principles of categorization in institutionally codified languages (“D counts as W”).

1. 1. 55. Arg. from rules
      56. Arg. for an exceptional case
      57. Arg. from precedent
      58. Arg. from plea for excuse

When faced with an exceptional case, the usual rule  may be waived (56) or modified (57). Excuses and extenuating circumstances may suspend the rule.

(14) Perception, memory (345-346)

1. 1. 59. Arg. from perception
      60. Arg. from memory

Schemes (59), (60) argue that one can reasonably believe in a given fact on the basis of the perception or memory of this fact.

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COLLECTION 3: TRADITION AND MODERNITY

1. Scipion Dupleix, Logic, or the Art of Speaking and Thinking (1607)
Jacques-Bénigne Bossuet, Logic for the Dauphin (1677)

These works probably have no particular historical significance, but they certainly give an idea of the terminology of the seventeenth century, which clearly resembles the Ciceronian system, see Collections (2).

As the title suggests, Bossuet’s Logic functions as a pedagogical guide to everyday argumentation: ‘Dauphin’ was the title given to the heir to the French kingdom.

Table:
— First column, Bossuet, 1677
— Second column, Dupleix, 1607

The order of the lines is Bossuet’s. For ease of reading, Dupleix’s order of has been changed, so that the same types of arguments are on the same line; the numbering corresponds to the order in Dupleix’s typology.

Bossuet, 1677	Dupleix, 1607
1. Etymology	3. Etymology
2. Conjugates	4. Conjugata
3. Definition	1. Definition
4. Division
5. Genus	5. Genus and Species
6. Species
7. Property
8. Accident
9. Resemblance 10. Dissemblance	6. Similitude, 7. Dissimilitude
11. Cause	13. Cause
12. Effects	14. Effects
13. What comes before1	10. Antecedents1
14. What accompanies1	9. Adjuncts or conjuncts1
15. What follows1	11. Consequents1
16. Contraries	8. Contraries
17. A repugnantibus3
	12. Repugnants
18. All and parts2	2. Enumeration of the parts2
19. Comparison	15. Comparison with things bigger, equal and smaller
20. Example, or Induction

(¹) S. Circumstances

(²) Bossuet’s topic n°18 (here, topic = topos, arg. scheme), “enumeration of the parts” is akin to the topic of definition. For example, what is a “good captain” is defined by enumerating his relevant qualities: brave, wise, etc. Dupleix’s topic n°2, “all and parts” is more related to composition and division

(³) Dupleix’s topic n°12, from “repugnants” refers to predication: “stone” and “man” are repugnant because “ — be a stone” cannot be said of man — whereas Bossuet’s topic n°17, “a repugnantibus”, refers to a kind of ad hominem.

Both typologies prioritize arguments that exploit the resources that contribute to the definition of a word or a concept, with a view to the future use of this definition in syllogistic reasoning. This enumeration of the core set of arguments is followed by the usual enumeration of argument schemes based on causality, analogy, comparison, peripheral circumstances, opposites and induction. This set will reappear under a new reorganization in the New Rhetoric.

2. John Locke, An Essay concerning Human Understanding (1690)
Wilhelm Leibniz, New Essays Concerning Human Understanding (1765)

In An Essay concerning Human Understanding John Locke briefly mentions “four sorts of arguments, that men, in their reasoning with others, do ordinarily make use of to prevail on their assent; or at least so to awe them as to silence their opposition” (IV, 17, “Of Reason”, § 19-22; p. 410). These four arguments are:

— ad verecundiam, S. Ethos; 
Modesty; Authority.
— ad ignorantiam, S. Ignorance.
— ad hominem, S. Ad hominem.
— ad judicium, S. Matter

In his New Essays Concerning Human Understanding, Leibniz comments on this list, and qualifies Locke’s abrupt and general condemnation by taking into consideration the circumstances; see the above mentioned entries. In addition, Leibniz adds a new kind of argument, the argument ad vertiginem, S. Vertigo.

This short list has nothing to do with the previous Ciceronian ones; its purpose is to contrast the first three fallacious arguments with the last one, the only one that “brings true instruction and advances us in our way to knowledge” (op. cit., p. 411). Mathematics and experimental sciences are introduced under the heading ad judicium. Contrary to the classical typologies, these arguments are not associated with a logic itself based on a natural ontology, but rather with the requirements of the scientific method, S. Fallacy. We are thus entering a new argumentative world.

3. Jeremy Bentham, The Book of fallacies (1824) see Political Arguments.