The Art and Obligation of Doubting: Dubitatio in the 13th Century

1. The Art and Obligation of Doubting: Dubitatio in the 13th Century Jaap Maat, Katherina Rybalko, & Sara L. Uckelman Institute for Logic, Language, and Computation University of Amsterdam 1st GPMR Workshop in Logic and Semantics, 28 June 2007

2. What is an obligatio A type of formalized disputation. Opponent and respondent. Opponent puts forward statements. Respondent can accept, reject, or doubt. Roots in Aristotle: The conceptual origins of obligationes can be found in the dialectical disputations in Aristotle's Topics. However, there is nothing like dubitatio in these disputations. Found in medieval logic from the 13th century.

3. Our tract: Oxford MS Canon misc 281, ed. by De Rijk in 1975 as Obligationes Parisienses Tentatively can be placed in early 13th century France. Early text, but apparently describes common practice existing for quite some time. Contains a straightforward presentation of obligations Has not been thoroughly studied so far Treats dubitatio relatively extensively

4. purpose of the obligatio: The aim of disputation is twofold: knowledge or belief of things simpliciter exercise or being exercised The 2nd aim is pursued in obligation. When there is an obligation about something, one argues not only about things true simpliciter, but also about the consequences according to the obligation. But if the obligatum is true, the respondent similarly does not attend to the truth or falsity of things except compared to the obligation. Whence belief or knowledge of the consequences of things is very much acquired by this type of disputation.

5. Structure of the text Types of obligatio Classification according to type of response: obligatio positio: concede depositio: deny dubitatio: doubt

6. Structure of the text Types of obligatio Classification according to type of initial statement: obligatio institutio rei veritas petitio certain uncertain

7. Structure of the text • types of obligatio positio - of determinate positio • - of certain rules for ponible posita • - six sophisms • - of indeterminate positio • - of the twofold mode of indeterminate positio dubitatio • whether dubitatio is an obligation or not • of certain rules • a sophism depositio - of its definition and rules - of special depositio - whether this should not be anobligation - a sophism

8. Dubitatio Whether dubitatio is an obligation or not Just as someone can be obliged to concede or deny, so one can be obliged to doubt. Contra: a wise man is not in doubt; there is no art in doubting; the response ‘prove it!’ is that of the ignorant Solution: this is true for absolute disputation, as discussed in the Topics. But in restricted or hypothetical disputation, doubting may be necessary and hence is artful. The author seems to set obligation apart from dialectical disputation as treated by Aristotle

9. General rules Everything antecedent to the dubitatum must be held true or doubtful, that is [not] false. (Omne antecedens ad dubitatum habendum est pro vero vel dubio, idest pro [non] falso) Everything following from the dubitatum must be held not false, that is true or doubtful. (Omne sequens ad dubitatum, habendum est pro non falso, idest pro vero vel dubio)

10. Comparison with other dubitatio rules Nicholas of Paris (?) (1230-1250) To every antecedent to the dubitatum it is to be responded “false” or “prove it!” and never “true”. Text discussed by Green (Sherwood ?): For the dubitatum and for its convertibles and for its contradictory and for its consequences, if they are false, and for its antecedents, if they are true, the response is doubtful. But if the antecedent is false, it must be denied, and the consequent, if it is true, must be conceded; and the same can be said of the antecedent and the consequent of things not convertible. And for irrelevant things the response is according to its quality.

11. Specific rules (1) 3. Certain things antecedent to the dubitatum are true, certain are false. (Antecedens ad dubitatum quoddam est verum, quoddam est falsum) Of enuntiables, some are antecedent to the dubitatum through themselves (per se), some are antecedent to the dubitatum with a conceded thing or conceded things or the opposite of a denied thing or opposites of denied things. (Enuntiabilium quoddam est antecedens per se ad dubitatum, quoddam cum concesso vel concessis vel opposito negati vel oppositis negati [sic] vel negatorum ad dubitatum)

12. Specific rules (2) Everything convertible with the dubitatum and every opposite of the dubitatum must be doubted. (Omne convertible cum dubitato et omne oppositum dubitati est dubitandum) 6. Every false antecedent of the dubitatum the opposite of which is not a true thing being doubted must be denied. (Omne falsum antecedens ad dubitatum cuius oppositum non est verum dubitatum, est negandum) 7. Of things following from the dubitatum, some are true, some are false. However every truth following from the dubitatum must be conceded, but every falsehood following from the dubitatum must be doubted. (Sequentium ad dubitatum aliud est verum, aliud est falsum. Omne autem verum sequens ad dubitatum est concedendum, sed omne falsum sequens ad dubitatum est dubitandum)

13. Specific rules (3) 8. Of things repugnant to the dubitatum, some are repugnant through themselves, some through an accident, such as through a consequence of the dubitatum. (Repugnantium dubitato quoddam est repugnans per se, quoddam per accidens, ut per consequens dubitati) 9. Of things repugnant to the dubitatum, some are contradictory opposites or convertible with them, some are contraries. (Repugnantium dubitato quoddam est oppositum contradictorie vel convertibile cum illo, quoddam contrarium)

14. Specific rules (4) 10. Everything repugnant to the dubitatum through itself and contradictorily must be doubted, repugnant in truth through itself and contrary must be held to be not true, as false, if it is known to be false, and as doubtful, if it is doubted. Also everything repugnant per accidens and contradictorily similarly must be held to be not true, also similarly for things repugnant per accidens and contrarily. (Omne repugnans dubitato per se et contradictorie est dubitandum, repugnans vero per se at contrarie habendum est pro non vero, ut pro falso, si sciatur esse falsum, et pro dubio, si dubitetur. Omne autem repgunans per accidens et contradictorie similiter habendum est pro non vero, repugnans autem per accidens et contrarie similiter)

15. Formalization (1) • We construct a function  which when given an O-statement returns an A-action. • First we fix the following: • V a function such that V(p) = T if the proposition is true in reality and V(p) = F otherwise. • d the dubitatum • We stipulate that ‘hold to be true’ is equivalent to ‘concede’, ‘hold to be false' equivalent to ‘deny' or ‘negate’, and ‘hold to be doubtful’ equivalent to ‘doubt’. We then define the following notation for A-actions: • C = ‘concede’ • D = ‘doubt’ • N = ‘negate’ (or ‘deny’)

16. Formalization (2) General rules: 1.  (d) = D (definitional) 2. if p  d, then  (p) ≠ N (rule 1) 3. if d  p, then  (p) ≠ N (rule 2)

17. Formalization (3) Special rules: 1. if p  d, then V (p) = T or V (p) = F (rule 3) 2. if d  p, then  (p) = D (rule 5) 3. if p = d, then  (p) = D (rule 5) 4. if p  d, if V (p) = F, if  (p) ≠ D, then (p) = N (rule 6) 5. if d  p and V (p) = T, then  (p) = C (rule 7) 6. if d  p and V (p) = F, then  (p) = D (rule 7) 7. if p  d (read 'p is repugnant to d') then it is one of these: if r  R1,  (r) = D. If r R2, R3, R4, if V (r) = F,  (r) = N and if V (r) ≠ F,  (r) = D (rule 10)

18. An example dubitatio Assume in rei veritas the Pope is in Rome, and that it is put forward “Either the Antichrist is black or the pope is in Rome”. O: The Antichrist is colored. R: Deny (because it is irrelevant and false). O: The Antichrist is not colored. R: Accept (opposite of something correctly denied). O: The Antichrist is not black. R: Accept (follows from something correctly accepted). O: The pope is in Rome. R: Accept (follows from the dubitatum) along with things correctly accepted or denied, and is true). Cedat tempus: The respondent did badly because ‘The pope is in Rome’ implies the dubitatum, and so should have been doubted.