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Classical Backgrounds

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Abstract

This chapter sketches the origin as well as the further development of the disciplines of dialectic, logic, and rhetoric in antiquity. For the beginnings of dialectic and logic, the chapter turns in Sect. 2.2 to Zeno’s reductio technique and Plato’s three forms of dialectic, for those of rhetoric to the Sophists and the educator Isocrates.

The chapter discusses Aristotle’s contributions to all three disciplines mentioned. In Sect. 2.3 Aristotle’s theory of dialectic is discussed. The fundamental features of the ancient discussion procedure are explained, the construction of argumentation by means of topoi (argument schemes), and tactical issues concerning debates. Sect. 2.4 is devoted to Aristotle’s fallacy theory. The theory of topics of Cicero and Boethius is discussed in Sect. 2.5. Sect. 2.6 explains Aristotle’s syllogistic – a precursor of predicate logic. Sect. 2.7 deals with Stoic logic – a precursor of propositional logic.

Aristotle’s systematic reflections on rhetoric as the art of finding the appropriate means of persuasion are the topic of attention in Sect. 2.8. Sect. 2.9 deals with the classical system of rhetoric, which developed after Aristotle’s time. The system is illustrated by going systematically through the consecutive tasks a speaker has to accomplish in preparation of the actual performance of a speech. In Sect. 2.10, finally, the ancient achievements are tied in with later developments and shown to relate to the various approaches to argumentation developed in present-day argumentation theory.

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Notes

  1. 1.

    See Diogenes Laertius (1925). The work was written in Greek and has several titles in Greek and in Latin, for instance, in Greek, Bioi kai gnômai tôn en philosophiai eudokimêsantôn (Lives and opinions of the eminent philosophers), or simply Bioi philosophôn (Lives of philosophers), and in Latin, Vitae philosophorum (Lives of philosophers). In references we shall use the abbreviation “LP.”

  2. 2.

    The subsection on the beginnings of dialectic and logic draws on Kneale and Kneale (1962) and Wagemans (2009). The subsection on the beginnings of rhetoric draws on Kennedy (2001) and Pernot (2005).

  3. 3.

    See Diogenes Laertius, Lives of eminent philosophers VIII, 57; IX, 25, and Sextus Empiricus, Against the logicians I (= Adversus mathematicos VII), 6–8.

  4. 4.

    For a critical account of the chronological grouping of Plato’s dialogues see Plato (1997, pp. xii–xviii) and Kraut (1992).

  5. 5.

    Gill (2012, Chaps. 5–6) provides an elaborate account of this and many other divisions in Plato’s Sophist and Statesman.

  6. 6.

    See Cicero, Brutus 46–48, and Diogenes Laertius, Lives of eminent philosophers VIII, 57, respectively.

  7. 7.

    According to Schiappa (1990), there is no such thing as the rhetoric of the sophists, since the term is not attested in any texts prior to Plato (e.g., Gorgias 449c), who may have first coined the term in a polemic sense.

  8. 8.

    Antiphon of Rhamnus (in Attica), also known as Antiphon the Orator, may or may not have been the same person as the one known as Antiphon the Sophist.

  9. 9.

    On the sophistic idea of arguing on both sides of the issue, see, for instance, Mendelson (2002) and Tindale (2010).

  10. 10.

    For a commentary on the Phaedrus that has a strong emphasis on the rhetorical contents of the dialogue, see Yunis (Ed., 2011).

  11. 11.

    The distinction between the three basic genres is often thought to be a later intrusion devised in order to assimilate the work to Aristotelian standard theory. Quintilian (Oratorial education III.4.9) seems to attribute to the author only two basic genres: juridical (iudiciale) and deliberative (contionale).

  12. 12.

    An English translation can be found in Aristotle (1984, Vol. 1).

  13. 13.

    An English translation can be found in Aristotle (1984, Vol. 1) and in Aristotle (2012).

  14. 14.

    Our reconstruction of the academic dialectical discussion (or debate) is based on Moraux (1968), Slomkowski (1997), and the summaries in Krabbe (2012a) and in Hasper and Krabbe’s introduction to the Dutch translation of Sophistical Refutations (Aristoteles 2014).

  15. 15.

    The two distinct functions of questions that introduce an issue (problêmata) and questions that ask to concede a premise (protaseis) were curiously interchanged by Kneale and Kneale (1962, pp. 34–35) and also by van Eemeren et al. (1996, p. 38), but this was corrected in the Dutch translation. See Slomkowski (1997, p. 21, Note 60).

  16. 16.

    Propositions are acceptable (endoxos) if they are “accepted by everyone or by the majority or by the wise – i.e., by all, or by the majority, or by the most notable and reputable (endoxois) of them” (Aristotle 1984, Vol. 1, Topics I.1, 100b21–23). As the quote shows, this word applies not only to propositions but also to people. In Topics VIII.5 and VIII.6, Aristotle proposes, for the Answerer, some refined rules with respect to the acceptability of premises, which take into account that premises must be more plausible than the conclusion that is drawn from them. See Wlodarczyk (2000).

  17. 17.

    See Topics VIII.8.

  18. 18.

    Topics VIII.10, 161a9–12 and Soph. ref. 33, 183a21–26, and also Topics VIII.2, 158a25–26. See also Moraux (1968, p. 285).

  19. 19.

    In the passage here cited, we interpret didactic arguments as arguments characteristic of didactic discussions. Similarly, we interpret dialectical arguments as arguments characteristic of truly dialectical debate; critically examining arguments as arguments characteristic of critical examination dialogues (peirastic), a subtype of dialectical debate; and eristic arguments as arguments characteristic of eristic debate. Wolf (2010) provides an analysis of Aristotelian “argumentation forms” based on three criteria and yielding seven different forms.

  20. 20.

    Here one may add: “or merely appear to deduce a conclusion from acceptable premises.” See Topics I.1, 100b23–25.

  21. 21.

    In the rare case that neither the Questioner nor the Answerer holds that the Answerer is or is not knowledgeable in the field, but both try to find out what is the case, there is no difference of opinion. Consequently, the critical examination would not be argumentative, but still a kind of test.

  22. 22.

    This interpretation is corroborated by a passage in Aristotle’s Rhetoric (Rhet. I.1, 1355a24–29), which contains a reference to the Topics.

  23. 23.

    The interpretation of the last point is very uncertain.

  24. 24.

    See, for instance, de Pater (1965, 1968), Brunschwig in Aristote (1967, 2007), Sainati (1968), Slomkowski (1997), Smith in Aristotle (1997), and Rubinelli (2009).

  25. 25.

    See Solmsen (1929, pp. 171–175).

  26. 26.

    Rubinelli (2009, p. 20) distinguishes six “elements that can occur in the description of a topos”: applicability requirements, name, instruction, law, example, and purpose.

  27. 27.

    See Slomkowski (1997, p. 45).

  28. 28.

    For rhetoric, the relation between topoi and argument(ation) schemes has been analyzed by Braet (2005).

  29. 29.

    According to Slomkowski, a topos is a universal proposition that functions as a premise in a deduction (a hypothetical syllogism) (Slomkowski 1997, p. 67).

  30. 30.

    These two parts of a topos correspond to what de Pater calls proposition/formule probative (proposition de preuve) and règle/formule de recherche (1965, pp. 115–117; 1968, p. 166).

  31. 31.

    This topos served as the first example of a topos in de Pater (1968, pp. 164–165), and the example about ignorance in the quotation was analyzed by de Pater in the concluding section of his paper (pp. 185–188).

  32. 32.

    An accident may or may not belong to its subject (Topics 102b6-7). It is one of the four “predicables” Aristotle distinguishes in the beginning of the Topics. See example (5).

  33. 33.

    See Slomkowski (1997, pp. 141–142).

  34. 34.

    This formulation follows Aristotle’s text. An equivalent, but simpler, formulation would be as follows: if it is more likely that A is B than that C is B, then if C is B, A is B.

  35. 35.

    Differentia is not counted as a separate predicable, but treated under genus.

  36. 36.

    This term has a technical meaning in this context.

  37. 37.

    The theory of predicables is explained by Aristotle in Topics I.5–8. The global structure of the Topics is based on the predicables: Books II and III deal with topoi concerned with accident, Book IV with those concerned with genus, Book V with those concerned with property, and Books VI and VII with those concerned with definition.

  38. 38.

    See Brunschwig’s analysis in Aristote (1967, p. XLII).

  39. 39.

    This subsection is based on Krabbe (2009) and Wagemans (2009).

  40. 40.

    We do not want to suggest that Aristotle wrote the books of the Topics in this order; it may well have been the other way round.

  41. 41.

    A good argument must, according to Aristotle, have premises that are more acceptable and more familiar than its conclusion (Wlodarczyk 2000, p. 156).

  42. 42.

    Aristotle discusses tactics for the Answerer also in Sophistical refutations 17.

  43. 43.

    For the concept of solution (lusis), see the end of Sect. 2.4.

  44. 44.

    Greek: Sophistikoi elegchoi, Latin: Sophistici elenchi; also used as a title is On sophistical refutations (Greek: Peri tôn sophistikôn elegchôn, Latin: De sophisticis elenchis).

  45. 45.

    Besides, Aristotle discusses the fallacy of begging the question in Topics VIII.11, 161b11–18, and VIII.13, 162b31–163a13, and also in Prior Analytics I.24 and II.16 and in Posterior analytics I.3 (on circular proof). The fallacy of non-cause he also discusses in Prior Analytics II.17.

  46. 46.

    There is some discussion about the proper extent of a dialectical (versus a more logical) interpretation of the fallacies in Sophistical refutations (Hintikka 1987, 1997; Woods and Hansen 1997).

  47. 47.

    Aristotle seems to have only deductive arguments in mind here. Notice that these eristic deductions are actually no deductions at all; as little as sophistical refutations are refutations.

  48. 48.

    Presumably, an incorrect argument of type (2) seems to reach the required conclusion.

  49. 49.

    Eristic deductions in this group are indeed deductions.

  50. 50.

    For group (3), evidence that Aristotle would call them paralogisms is scanty.

  51. 51.

    See Topics I.1, Soph. ref. 8 and 11.

  52. 52.

    For more information about Aristotle’s list and the further contents of Sophistical refutations, we refer to Hamblin (1970, Chap. 2). For a brief exposition, see Woods (1999). The reader may also consult the handbook article on Aristotle’s early logic by Woods and Irvine (2004, esp. Sect. 12). A brief summary of Sophistical refutations can be found in Krabbe (2012). There are also useful introductions by translators (into other languages than English): Dorion (Aristote 1995), Fait (Aristotele 2007), and Hasper and Krabbe (Aristoteles 2014). Schreiber (2003) dedicated a critical monograph to Aristotle’s list, with detailed discussions of the separate fallacies, in which Schreiber reconstructs (and corrects) the Aristotelian system by showing how each fallacy arises from false presuppositions about language or ontology. Hasper (2013) proposes a reconstruction of Aristotle’s completeness claim (in Soph. ref. 8) for his list of fallacies by analyzing the dialectical task of achieving a refutation into a limited number of dialectical acts, like using statements, citing statements, asking questions, and drawing inferences, which each involve some correctness conditions. See on the concept of a sophistical refutation also Botting (2012).

  53. 53.

    Such classificatory insights must constitute the deductive proof (showing that there are exactly six kinds of sophistical refutation dependent on the use of language) that, as we saw, Aristotle alludes to in Soph. ref. 4, 165b27–30.

  54. 54.

    Examples of the contemporary fallacies of composition and division are, however, found in the Rhetoric (see Sect. 2.8).

  55. 55.

    Another way to analyse this case is to say that “what” and “it” are misinterpreted as referring also to quantities (Krabbe 2012, pp. 246–247). According to Krabbe (2012, p. 247, see also 1998), “the fallacy of form of expression, which may at first seem a bit outlandish, can be connected with the twentieth century discussion about Russell’s and Wittgenstein’s distinction between the apparent and the real logical form of a sentence and Ryle’s concept of a systematically misleading expression […].”

  56. 56.

    The meaning of accident varies, but here it may stand for just any property predicated without further specification of the mode of predication. The term property is here used nontechnically: it does not refer to the predicable so called.

  57. 57.

    See Soph. ref. 5, 166b28–36. The point is not that “man is different from Coriscus” would not be true but that, even if it is true, it does not follow from the premises.

  58. 58.

    Aristotle alludes to it in Soph. ref. 24, 179a34–35.

  59. 59.

    See Soph. ref. 5, 167a7–9.

  60. 60.

    Woods (1993) points out how the new meaning can be tied to the old meaning.

  61. 61.

    The word fallacies (paralogismoi) in the completeness claim obviously refers to the sophistical refutations and not to proofs with a false premise in science – group (4) in Topics VIII.12 (see above). The definition of refutation implied in Aristotle’s sketch of a completeness proof (Soph. ref. 8, 169b40–170a11) seems to be a refined version of that given in Soph. ref. 1 (Hasper 2013).

  62. 62.

    Some authors distinguish between reductio ad absurdum and reductio ad impossibile, but there is no uniform way in which they make this distinction. Yet it makes a difference whether the absurdity reached by the reductio is a logical contradiction or something merely accepted as false or extremely implausible. Aristotle (2012, Soph. ref. 5, 167b23) says that the fallacy of non-cause occurs “in deductions of an impossibility” (en tois eis to adunaton sullogismois).

  63. 63.

    To blame one specific premise, it must of course be assumed that the other premises – as well as the impossibility of the conclusion – are beyond suspicion and that the deduction is impeccable.

  64. 64.

    For instance, if the fallacy is brought about by the ambiguity of some term t, adding the premise that t has always the same meaning makes the argument unsolvable (except, of course, by demolishing this very premise).

  65. 65.

    The other three roots are (1) Aristotle’s criticism, in Rhetoric I.1, of conceptions of rhetoric “that one-sidedly concentrate on features which lie outside the actual case,” such as “the person of the disputant” (Nuchelmans 1993, p. 43); (2) Aristotle’s remarks about arguments starting from what is admitted by one’s opponent, such as the critical examination (peirastic) arguments mentioned in Soph. ref. 2; and (3) proofs relative to a particular person that can, for instance, be used against someone denying the law of noncontradiction, as in Aristotle’s Metaphysics IX.5.

  66. 66.

    This section is based on Rubinelli (2009) and Stump’s essays on the text in Boethius (1978).

  67. 67.

    The etymology given by Aelius linking assiduus with aere dando (more precisely with qui assem dat) is mistaken. Nevertheless, one of the meanings of assiduus is “resident” (ad + sedeo) and therefore “wealthy and subject to taxation.”

  68. 68.

    Their names are ex coniugatis (from conjugates), a genere (from the genus), a forma generis (from the form of the genus), a similitudine (from similitude), a differentia (from difference), ex contrario (from the contrary), ab adiunctis (from adjuncts), ab antecedentibus (from antecedents), a consequentibus (from consequences), a repugnantibus (from opposites/contradictions/incompatibilities), ab efficientibus rebus (from causes/producing things), ab effectis (from effects), ex comparatione maiorum (from comparison with something bigger), ex comparatione minorum (from comparison with something smaller), and ex comparatione parium (from comparison with something equal).

  69. 69.

    An English translation of this work is found in Aristotle (1984, Vol. 1).

  70. 70.

    In references “AnPr” (Analytica Priora) stands for the Prior Analytics.

  71. 71.

    Here assertoric stands for the non-modal character of the theory (the lack of qualifications such as “necessarily” and “possibly” as parts of premises and conclusions in its argument forms), and the term categorical is used to characterize the theory as a part of what is now known as predicate logic, in contrast with hypothetical (hypothetical syllogisms forming a part of propositional logic).

  72. 72.

    Aristotle’s modal syllogistic has been widely regarded as incoherent. For a recent attempt to give a coherent account of it, see Malink (2006, 2013).

  73. 73.

    Our exposition must be very brief. The reader who wants to know more about Aristotelian syllogistic may consult Aristotle’s text but also, for instance, Smith (1995), for a short introduction to Aristotle’s logic; Kneale and Kneale (1962), for a longer historical exposition; Boger (2004), for a lengthy essay on the assertoric syllogism; and Corcoran (1974), for a modern interpretation which “restores Aristotle’s reputation as a logician of consummate imagination and skill” (p. 85). Barnes (1995) contains a section with suggestions for reading (pp. 287–293, esp. p. 291) as well as an extensive bibliography (Barnes et al. 1995) mentioning (under III H) various modern interpretations of syllogistic, starting with that by Łukasiewicz (1957).

  74. 74.

    An English translation of this work is found in Aristotle (1984, Vol. 1).

  75. 75.

    The Greek word protasis, which in a dialectical context is sometimes translated as “premise” and sometimes as “proposition,” must here be translated in the latter way.

  76. 76.

    “Not to some” must be read as “to some not,” meaning the same as “not to all.”

  77. 77.

    The same six types were introduced in De Int. 8. In references “De Int.” stands for De interpretatione.

  78. 78.

    See De Int. 7.

  79. 79.

    Smith refers to AnPr I.23 and AnPr I.32–44. See also Kneale and Kneale (1962, p. 44). Of course, there will be some more types of statements in the theory if modality is taken into account. But, in any case, the reduction seems not to have been completed, for Aristotle admits that certain kinds of deduction cannot be reduced to his syllogisms (hypothetical syllogisms and reductio ad impossibile arguments, AnPr I.44).

  80. 80.

    To be on the safe side, when arguing from certain premises to a conclusion, indefinite premises should count as particular and an indefinite conclusion as universal.

  81. 81.

    The letters A and I were in medieval times chosen to label the two types of affirmative statements: they are the first two vowels of the Latin word affirmo (I affirm). Similarly, the letters E and O, which are the vowels of nego (I deny), were chosen to label the two types of negative statements.

  82. 82.

    Generally, Aristotle avoided self-predication (“Every S is an S,” etc.); see Corcoran (1974, p. 99).

  83. 83.

    For example, swan, predator, animal, stone, human being, featherless biped, white object, man who knew too much

  84. 84.

    That an A-statement implies the corresponding I-statement follows from the conversion rules for these statements, introduced in AnPr I.2 (see below). One may also reason that if “Every S is a P” is true, its contrary “No S is P” must be false, and hence the denial of the latter, “Some S is a P,” must be true. Analogously to this second way of reasoning, one may show that an E-statement implies the corresponding O-statement.

  85. 85.

    For other interpretations of the language of syllogistic, see Kneale and Kneale (1962, pp. 64–66).

  86. 86.

    The form of a pair of categorical premises is determined by establishing which of the four types of categorical statements (A, E, I, O) each premise represents and which cases of repeated occurrence of the same general term can be found in the pair of premises. Aristotle’s question is not aiming at conclusions that follow by virtue of the meaning of the general terms.

  87. 87.

    Similarly as in the case of pairs of categorical premises, the form of an argument is determined by establishing which of the four types of categorical statements (A, E, I, O) each premise or conclusion represents and which cases of repeated occurrence of the same general term can be found in the argument. Again, the question is not aiming at conclusions that follow by virtue of the meaning of the general terms.

  88. 88.

    Or, one could say: which of the arguments in the figures are, by virtue of their form, valid. Here it must be remembered that Aristotle’s definition of the syllogism (containing his idea of validity) differs from the modern approach in that according to Aristotle’s definition, syllogisms may not be circular or contain superfluous premises. It can be checked that two-premise arguments in the language of syllogistic that are not in the figures but are valid (in the modern sense of not admitting a counterexample) by virtue of their form, either have a superfluous premise (e.g., by repeating the other premise in the conclusion) or have inconsistent premises (and are valid merely on that account). The first two are not syllogisms, and, presumably, those that are merely valid on the ground of having inconsistent premises should not be counted as syllogisms either, so that all bona fide two-premise syllogisms must be found among those in the figures.

  89. 89.

    See Kneale and Kneale (1962, pp. 68–72).

  90. 90.

    Aristotle used to formulate syllogisms not as three separate sentences – as we do here – but as one conditional sentence. For the present example, a “more Aristotelian” formulation would be “If predator belongs to no swan and swan belongs to some birds, then to some birds, predator does not belong (or, predator does not belong to all birds).”

  91. 91.

    That an argument belongs to a syllogistic figure does not imply that it is a syllogism.

  92. 92.

    Notice that the vowels in such a name correspond with the types of categorical statements.

  93. 93.

    Remember that the fourth figure contains one form with a weaker conclusion than would be possible, which we already subtracted.

  94. 94.

    At a metalevel, since Aristotle’s proofs show that some argument form is a syllogism. But if general terms are substituted for variables, the proofs can also be read, at the level of the language of syllogistic, as showing the truth of their conclusions in that language.

  95. 95.

    Repetition is used to make the application of Ferio at the next line more perspicuous.

  96. 96.

    Aristotle’s term for direct in this context is deiktikos (ostensive, probative).

  97. 97.

    See Kneale and Kneale (1962, pp. 75–76).

  98. 98.

    The method does not work to exclude a conclusion of the form “Some P is not an S” in which P is the minor term. “Some P is not an S” actually follows from the pair of premises here given as an example. However, the method works to exclude the other three conclusions of the form PS, in which P is the minor. So the method may be used to reject seven invalid forms using only two assignments of terms to variables.

  99. 99.

    See Sect. 2.2, Note 1.

  100. 100.

    Greek title: Purrhôneioi Hupotupôseis, abbreviated as “PH” (Sextus Empiricus 1933–1949).

  101. 101.

    For this collection of writings (Sextus Empiricus 1933–1949, II–IV), various Greek and English titles are used, either for the whole or for a part: Against the mathematicians (Greek: Pros mathêmatikous), Against the professors, Against the dogmatists, Against the logicians, etc., but most often the Latin title is used: Adversus mathematicos, abbreviated as “AM.” The Books AM VII and VIII are Books I and II, respectively, of Against the logicians (Sextus Empiricus 1933–1949, II).

  102. 102.

    This section draws mainly on the monograph by Mates (1961), the briefer exposition by Kneale and Kneale (1962), the longer and more recent one by O’Toole and Jennings (2004), and – especially for the interpretation of the formal system – on Bobzien (1996) and Hitchcock (2002d, 2005b).

  103. 103.

    Other subsisting incorporeal entities were void, place, and time, whereas fictional entities may have belonged to yet another order of being (O’Toole and Jennings 2004, p. 461).

  104. 104.

    Mates (1961, p. 11), paraphrasing Sextus Empiricus, AM VIII.12.

  105. 105.

    We cannot here enter into the debate about whether the grammatical subject also expresses an incomplete lekton (see O’Toole and Jennings 2004, pp. 450–456).

  106. 106.

    Aulus Gellius, Noctes Atticae XVI.8, translation by Mates (1961, pp. 27–28). The definition can also be found in Sextus Empiricus, PH II.104, and in Diogenes Laertius, LP VII.65.

  107. 107.

    The word axiôma is clearly derived from the verb axiousthai, in the sense of “to be asserted/claimed” (O’Toole and Jennings 2004, p. 443) or perhaps in the sense of “to be evaluated” (as true or false).

  108. 108.

    These ways of being negative can all be combined: “It is not the case that no one is unkind.”

  109. 109.

    See Kneale and Kneale (1962, pp. 145–147), O’Toole and Jennings (2004, pp. 465–466), Sextus Empiricus, AM VIII.96-100, and Diogenes Laertius, LP VII.69-70. A proposition of the third kind is certainly true if a corresponding proposition of the first kind is true, but that cannot be the whole story, since “Dion is dead” can be true while it is impossible to refer to Dion by a demonstrative (Kneale and Kneale 1962, pp. 126–127, 154–155).

  110. 110.

    The principal connective is the (occurrence of a) connective that governs the entire proposition, not just a part of it.

  111. 111.

    Examples of the other kinds are the following: “Since it is day, it is light” (inferential), “Because it is day, it is light” (causal), “It is rather day than night” (indicating greater degree), and “It is not so much night as day” (indicating lesser degree). See Kneale and Kneale (1962, pp. 147–148).

  112. 112.

    No proposition conflicts with itself, not even a proposition that is logically false. Consequently, for each proposition A, the conditional “If A, cA” will be false (since ccA = A). Clearly the Stoic logic of conditionals is not classical: rather it is a connexive logic (Wansing 2010).

  113. 113.

    We agree with Hitchcock (2002d, p. 14), who assumes “that a disjunction is true if and only if one disjunct is true and each disjunct conflicts with each other disjunct” (the “quasi-connexive” account). Syntactically, a disjunct may be repeated in the sequence, but then, of course, the disjunction is false (since no proposition conflicts with itself).

  114. 114.

    However, Antipater of Tarsus, who was head of the Stoic school around 150 BC, “asserted that arguments with a single premiss can be constructed” (Sextus Empiricus, 1933–1949, II, Against the logicians II(= AM VIII).443).

  115. 115.

    The principle of conditionalization expressed in this passage of Sextus Empiricus is rendered as follows by Mates: “Some arguments are valid and some are not valid: valid, whenever the conditional whose antecedent is the conjunction of the premises and whose consequent is the conclusion, is true” (1961, p. 110).

  116. 116.

    Singular: anapodeiktos. The word is used here in a way unrelated to the term demonstrative (apodeiktikos) above. It can be translated as “undemonstrated” or as “indemonstrable.” We follow Mates (1961) and Hitchcock (2002d, 2005b) in translating it in the first way. As we shall see, some anapodeiktoi can be demonstrated in the Stoic formal system, e.g., those of the second type can be reduced to those of the first type, and vice versa. So we take anapodeiktos to mean: undemonstrated because not in need of demonstration (see Diogenes Laertius, LP VII.79).

  117. 117.

    Moreover, there is uncertainty about the interpretation of “conflict” and hence about the scope of “validity.” Can an argument with a superfluous premise be valid? Probably not, since Sextus Empiricus denies it (AM VIII.429, 431), but this is not immediately obvious from the definition of validity in terms of conflict stated above (Diogenes Laertius, LP VII.77).

  118. 118.

    Plural: themata.

  119. 119.

    In this respect, the Stoic formal system resembles a sequent calculus or a tableaux system in contemporary logic.

  120. 120.

    For instance, the second type of undemonstrated arguments includes also the instances of the form “If not-A then not-B, B/A,” etc. Also, conjuncts must be treated as equals, so that the third type includes also the instances of the form “Both A and B, B/Not-A,” similarly for disjuncts. Moreover, on the basis of other texts, the descriptions may be expanded to cover conjunctions and disjunctions with respectively more than two conjuncts or more than two disjuncts (Hitchcock 2002d, pp. 24–28).

  121. 121.

    Together, the last three themata did about the work of a cut rule in a sequent calculus.

  122. 122.

    Recall that ccA = A.

  123. 123.

    This reduction (or analysis) is provided by Sextus Empiricus, AM VIII.235–236. Although we only show the forms, we continue to speak of “arguments.”

  124. 124.

    See Bobzien (1996, p. 161, n. 54) and Hitchcock (2002d, p. 58, S14).

  125. 125.

    According to Hitchcock, who proposes a new reconstruction of the system, it is “surprisingly difficult” to find argument forms with only propositional variables and the logical operators of the system that are valid, but cannot be shown to be valid within the system. “The difficulty is surprising because the system at first glance has glaring deficiencies.” Further he deems it noteworthy that the system “allows one to prove the validity of those arguments with formally valid moods [argument forms] expressible in the system which we are inclined to use in real reasoning and argument” (2002d, pp. 67–68).

  126. 126.

    This section draws on Kennedy (2001) and Rapp (2010). See Rapp (2002) for a translation of Aristotle’s Rhetoric into German with detailed commentary, including discussions of secondary literature.

  127. 127.

    See also Aristotle’s definition in Topics VI.12, 149b26-27 of the rhetorician as someone who is able to see the available means of persuasion in any given case.

  128. 128.

    On the sources and background of the list of topoi in Rhetoric II, 23, see Rambourg (2011).

  129. 129.

    Notice that examples (rhetorical inductions) are here reckoned to be among the enthymemes (rhetorical deductions).

  130. 130.

    For detailed expositions of the system of rhetoric, see Lausberg (1998), Fuhrmann (2008), Martin (1974), and, from a historical perspective, Kennedy (1994, 2001) and Pernot (2005).

  131. 131.

    Throughout our discussion of the components of the system, we will mostly use the English name of the component at issue (followed at the first mentioning by (1) the Greek name and/or (2) the Latin name, in parentheses).

  132. 132.

    Woerther (2012) provides a new edition of the reports of Hermagoras’s work.

  133. 133.

    Sometimes ascribed to Quintus Cornificius.

  134. 134.

    Often rhetoricians treat the first subpart of the introduction as a separate part of the speech (pars orationis).

  135. 135.

    In Iliad 4.297–9, Nestor arranges his troops in that order: “And first he arrayed the horsemen with horses and chariots, and behind them the foot-soldiers, many and valiant, to be a bulwark of battle. But the weaklings he drove into the midst.” See also Perelman (1982, p. 148).

  136. 136.

    For a systematic description of the various tropes, figures, and kinds of style, see, for instance, Lausberg (1998).

  137. 137.

    In Sect. 2.3, we mentioned that the term topos may also have its origin in this mnemonic technique.

  138. 138.

    For a discussion of the art of memory, see Yates (1966).

  139. 139.

    See Stump (1989) for the place of dialectic in the development of medieval logic.

  140. 140.

    See Green-Pedersen (1984) for an extensive overview and discussion of medieval works on the topics; Butterworth (1977) for Averroes’s commentary on Aristotle’s Topics; Ebbesen (1981) for a study of post-Aristotelian and medieval commentaries on Aristotle’s Sophistical refutations; and Ebbesen (1993), Green-Pedersen (1987), and Pinborg (1969) for the theory of loci in the Middle Ages.

  141. 141.

    The other four liberal arts, which constituted the quadrivium, were arithmetic, geometry, astronomy, and music (harmonics).

  142. 142.

    See, for instance, Dutilh Novaes (2005), Spade (1982), Stump (1982), Yrjönsuuri (1993), and Yrjönsuuri (Ed., 2001).

  143. 143.

    Developments in Medieval and Renaissance dialectic are discussed in Mack (1993), Spranzi (2011), Moss and Wallace (2003), and Ong (1958).

  144. 144.

    For the state of affairs in the so-called Standard Treatment, see Sect. 3.5 of this volume.

  145. 145.

    The uniformity Hamblin observed in the way the fallacies are treated in the textbooks led him to dub this chapter “The Standard Treatment.” However, the uniformity in the textbooks is not as striking as Hamblin suggests. See Hansen (2002). For differences within the standard treatment in dealing with the argumentum ad hominem, see van Eemeren and Grootendorst (1993, pp. 54–57).

  146. 146.

    See McKeon (1987), Miller et al. (Eds., 1973), and Murphy (2001) for the development of rhetoric in the Middle Ages; see Mack (Ed., 1994), Mack (2011), Murphy (Ed., 1983), and Seigel (1968) for the development of rhetoric in the Renaissance.

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van Eemeren, F.H., Garssen, B., Krabbe, E.C.W., Snoeck Henkemans, A.F., Verheij, B., Wagemans, J.H.M. (2013). Classical Backgrounds. In: Handbook of Argumentation Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6883-3_2-1

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