The original logical works: do De topicis differentiis, De Divisione, and De hypotheticis syllogismis constitute substantive original contributions beyond commentary?

Boethius, answered from the texts and cited to the page.

The position in brief

The original logical works are substantive contributions to areas of logic where I had to think for myself, beyond translation and commentary. De topicis differentiis develops the theory of topical reasoning: the differentiae are the distinguishing features that classify argument-types (arguments from the cause, from the part, from the contrary, from definition, etc.).1

The classification gives us a taxonomy of argument-forms broader than the categorical syllogism, useful for evaluating arguments in dialectical and rhetorical contexts. De Divisione develops the theory of logical division: how to divide a genus into species, how to divide a whole into parts, how to divide accidents from substances. The work is brief but systematic; it shaped the medieval theory of definition.

De hypotheticis syllogismis is one of the few extant late-antique treatises on hypothetical syllogisms, drawing extensively on Stoic logic. The hypothetical syllogism (if A then B; A; therefore B) and its variants (modus ponens, modus tollens, disjunctive syllogisms) had been extensively developed by the Stoics but the texts had largely been lost; my treatment preserves substantial elements of the Stoic system that would otherwise be unrecoverable.

Together these works constitute the original logical contribution; they are not just commentary but systematic treatment of areas where the Greek tradition had not provided a worked-out account.2345

Sources

  1. Cicero's Topic from differentia can be understood either as the Topic from the whole in Themistius's division or as the Topic from a part; /1203C/ from the whole if the differentia from which the argument is taken is constitutive, and from a part if it is divisive. D ia g ra m I. (referred to in 1202B, as given in PL text) Themistius's Division In trin sic E x trin sic I n t e r m e d ia t e 1.
    De topicis differentiis, pp. 76–77
  2. When applied in the area of actions, the basic idea of ease becomes skill or proficiency; in the area of material things, it becomes wealth or abundance. The closest English word in range of meaning is 'competence,' I think; I have also translated the word as 'capability' and 'discipline' in some passages. 6.
    De topicis differentiis, pp. 99–100
  3. Hence, Differentiae must function to find arguments by aiding in the dis- 43. De top. liiff. 1184D7-14; ICT 279.2-6 (PL 1050B9-13).
    De topicis differentiis, pp. 196–197
  4. But not all Topics are equally well suited to discover all kinds of syllogisms. Boethius divides syllogisms in two ways: first, some are demonstrative and others dialectical; second, some are predica- tive and other conditional. In 1195A13-1196A3, Boethius explains briefly which Topics are suited for which kinds of syllogism. 11.
    De topicis differentiis, pp. 100–101
  5. But when he discusses the relationships that are the Differentiae, the relationships are those holding between a term in an enthymeme's premise and another term in that enthymeme's conclusion; see, for example, p. 61.21-25. See also Dialectica Monacensis, p. 528, where the point is discussed in some detail.
    De topicis differentiis, pp. 237–239

Where the argument is made

  • De topicis differentiis (On Topical Differences, trans. Stump Cornell 1978/2004) on the theory of topical reasoning
  • De Divisione (On Division, ed. and trans. Magee 1998) on logical division
  • De hypotheticis syllogismis (On Hypothetical Syllogisms, ed. Obertello 1969) on hypothetical syllogisms
  • De Syllogismo Categorico (On the Categorical Syllogism)
  • Introductio ad Syllogismos Categoricos (Introduction to Categorical Syllogisms)

How the argument was received

The original logical works were the basis of much medieval logic. De topicis differentiis was the standard medieval treatment of topics; the medieval theory of topics (Green-Pedersen 1984) is essentially the development of Boethius's framework. De Divisione shaped the theory of definition. De hypotheticis syllogismis was the standard treatment of hypothetical reasoning until the recovery of Aristotle's Prior Analytics in the twelfth century. Stump's translation work and Magee's editorial work exemplify the contemporary scholarly engagement; Speca's Hypothetical Syllogistic and Stoic Logic (2001) develops the relationship to Stoic sources. The works are still read primarily by specialists in medieval logic but their philosophical content remains substantive.