Supplement to Ibn Sina's Logic

Appendix C: Categorical Syllogisms

C.1 Sources

Categorical syllogistic in Qiyās, Nağāt, and Išārāt

Mix (figure) Qiyās Nağāt Išārāt An. Pr.
XX (1) II.4, 108–111 62 I.7 (5) A4
XX (2) II.4, 111–116 63 I.7 (6) A5
XX (3) II.4, 116–121 64 I.7 (6) A6
LL (1, 2, 3) II.4, 121–122 65 A8
LX (1) III.1, 125–130 66 I.7 (5) A9
LX (2) III.1, 130–139
III.3, 151–156
67 I.7 (6) A10
LX (3) III.3, 156–159 68 I.7 (7) A11
MM (1) IV.1, 181–189 69 I.7 (5) A14
MX (1) IV.2, 190–198 70 I.7 (5) A15
ML (1) IV.3, 199–204 71 I.7 (5) A16
MM (2) IV.4, 205–213 72 I.7 (6) A17
MX (2) IV.4, 213–215 73 I.7 (6) A17-18
ML (2) IV.5, 216–222 74 I.7 (6) A19
MM (3) IV.6, 223–224 75 I.7 (7) A20
MX (3) IV.6, 224–225 76 I.7 (7) A21
ML (3) IV.6, 225–227 77 I.7 (7) A22

C.2 List of Productive Moods

When Avicenna identifies and discusses a mood explicitly (or at least refers to it in an unequivocal manner by identifying its premises and conclusion), I give the reference to book, chapter, page, and line numbers with no additional comment. On several occasions, however, Avicenna's analysis proceeds by generalization over the properties of a given figure and modal mix or is simply too concise to extract sufficiently detailed information on a given individual mood. For this reason, I distinguish below between moods whose productivity is not discussed extensively or explicitly but still clear from the context (implied) and moods whose productivity Avicenna is committed to either in virtue of external evidence from other parts of the corpus or in virtue of systematic reasons (not mentioned). In both cases, I still identify the relevant context where the discussion of such moods seems more naturally to belong. Line numbers are given according to the Cairo edition, except for pages where a new chapter begins: in those cases the edition numbers lines starting from the chapter title, while I count from the first line of the main text. The following list does not generally include derivative moods with a weaker conclusion, e.g., XXM, LLM, LMM.

C.2.1 XX

Barbara XXX X-BaC, X-AaB ⊢ X-AaC Qiyās, II.4, 109.16
Celarent XXX X-BeC, X-AaB ⊢ X-AeC Qiyās, II.4, 110.1
Darii XXX X-BaC, X-AiB ⊢ X-AiC Qiyās, II.4, 110.2
Ferio XXX X-BeC, X-AiB ⊢ X-AoC Qiyās, II.4, 110.2–3

Cesare* XXX X-CeB, X-AaB ⊢ X-AeC Qiyās, II.4, 114.5–115.16
Camestres* XXX X-CaB, X-AeB ⊢ X-AeC Qiyās, II.4, 115.17–116.2
Festino* XXX X-CeB, X-AiB ⊢ X-AoC Qiyās, II.4, 116.3–6
Baroco* XXX X-CaB, X-AoB ⊢ X-AoC Qiyās, II.4, 116.7–12
(only with X-proposition converting as itself, i.e., as strong as Ld1)

Darapti XXX X-BaC, X-BaA ⊢ X-AiC Qiyās, II.4, 117.6–12
Felapton XXX X-BeC, X-BaA ⊢ X-AoC Qiyās, II.4, 117.13–118.2
Datisi XXX X-BaC, X-BiA ⊢ X-AiC Qiyās, II.4, 118.3–5
Disamis XXX X-BiC, X-BaA ⊢ X-AiC Qiyās, II.4, 118.6–12
Bocardo XXX X-BoC, X-BaA ⊢ X-AoC Qiyās, II.4, 118.13–119.3
Ferison XXX X-BeC, X-BiA ⊢ X-AoC Qiyās, II.4, 119.4–8

C.2.2 LL

Barbara LLL L-BaC, L-AaB ⊢ L-AaC Qiyās II.4, 121.3–4 (implied)
Celarent LLL L-BeC, L-AaB ⊢ L-AeC Qiyās II.4, 121.3–4 (implied)
Darii LLL L-BaC, L-AiB ⊢ L-AiC Qiyās II.4, 121.3–4 (implied)
Ferio LLL L-BeC, L-AiB ⊢ L-AoC Qiyās II.4, 121.3–4 (implied)

Cesare LLL L-CeB, L-AaB ⊢ L-AeC Qiyās II.4, 121.3–4 (implied)
Camestres LLL L-CaB, L-AeB ⊢ L-AeC Qiyās II.4, 121.3–4 (implied)
Festino LLL L-CeB, L-AiB ⊢ L-AoC Qiyās II.4, 121.3–4 (implied)
Baroco LLL L-CaB, L-AoB ⊢L-AoC Qiyās II.4, 121.12–17 (proved)

Darapti LLL L-BaC, L-BaA ⊢ L-AiC Qiyās II.4, 121.2–122.4 (implied)
Felapton LLL L-BeC, L-BaA ⊢ L-AoC Qiyās II.4, 121.2–122.4 (implied)
Datisi LLL L-BaC, L-BiA ⊢ L-AiC Qiyās II.4, 121.2–122.4 (implied)
Disamis LLL L-BiC, L-BaA ⊢ L-AiC Qiyās II.4, 121.2–122.4 (implied)
Bocardo LLL L-BoC, L-BaA ⊢ L-AoC Qiyās II.4, 122.1-4 (proved)
Ferison LLL L-BeC, L-BiA ⊢ L-AoC Qiyās II.4, 121.2–122.4 (implied)

C.2.3 LX

Barbara LXL L-BaC, X-AaB ⊢ L-AaC Qiyās, III.1, 125.8–127.13
Celarent LXL L-BeC, X-AaB ⊢ L-AeC Qiyās, III.1, 129.5–7
Darii LXL L-BaC, X-AiB ⊢ L-AiC Qiyās, III.1, 129.11
Ferio LXL L-BeC, X-AiB ⊢ L-AoC Qiyās, III.1, 129.13

Cesare LXL L-CeB, X-AaB ⊢ L-AeC Qiyās, III.1, 131.7–9
Camestres LXL L-CaB, X-AeB ⊢ L-AeC Qiyās, III.1, 131.10
Festino LXL L-CeB, X-AiB ⊢ L-AoC Qiyās, III.3, 151.4–5
Baroco LXL L-CaB, X-AoB ⊢L-AoC Qiyās, III.3, 151.8–10

Darapti LXL L-BaC, X-BaA ⊢ L-AiC Qiyās, III.3, 156.6–8
Felapton LXL L-BeC, X-BaA ⊢ L-AoC Qiyās, III.3, 157.1–3
Datisi LXL L-BaC, X-BiA ⊢ L-AiC Qiyās, III.3, 157.12–13
(reading mūğiba for sāliba, at 157.13)
Disamis LXL L-BiC, X-BaA ⊢ L-AiC Qiyās, III.3, 158.3–13
Bocardo LXL L-BoC, X-BaA ⊢ L-AoC Qiyās, III.3, 159.6–16
Ferison LXL L-BeC, X-BiA ⊢ L-AoC Qiyās, III.3, 158.14–16

Barbara XLX X-BaC, L-AaB ⊢ X-AaC Qiyās, III.1, 127.14–129.4
Celarent XLX X-BeC, L-AaB ⊢ X-AeC Qiyās, III.1, 129.8–10
Darii XLX X-BaC, L-AiB ⊢ X-AiC Qiyās, III.1, 129.12
Ferio XLX X-BeC, L-AiB ⊢ X-AoC Qiyās, III.1, 129.14

Darapti XLX X-BaC, L-BaA ⊢ X-AiC Qiyās, III.3, 156.9–13
Felapton XLX X-BeC, L-BaA ⊢ X-AoC Qiyās, III.3, 157.4–11
Datisi XLX X-BaC, L-BiA ⊢ X-AiC Qiyās, III.3, 158.1–2
Disamis XLX X-BiC, L-BaA ⊢ X-AiC Qiyās, III.3, 158.14–16
Bocardo XLX X-BoC, L-BaA ⊢ X-AoC Qiyās, III.3, 159.1–3
(reading ğuzʾiyya for kulliyya, at 159.1)
Ferison XLX X-BeC, L-BiA ⊢ X-AoC Qiyās, III.3, 159.4–5

Cesare XLL X-CeB, L-AaB ⊢ L-AeC Qiyās III.1, 131.11–14
Camestres XLL X-CaB, L-AeB ⊢ L-AeC Qiyās III.1, 139.3–4
Festino XLL X-CeB, L-AiB ⊢ L-AoC Qiyās, III.3, 151.6–7
Baroco XLL X-CaB, L-AoB ⊢L-AoC Qiyās, III.3, 151.11–13

Barbara Ld1LL Ld1-BaC, L-AaB ⊢ L-AaC Qiyās III.1, 128.13–129.4
Celarent Ld1LL Ld1-BeC, L-AaB ⊢ L-AeC (not mentioned)
Darii Ld1LL Ld1-BaC, L-AiB ⊢ L-AiC (not mentioned)
Ferio Ld1LL Ld1-BeC, L-AiB ⊢ L-AoC (not mentioned)

Cesare Ld1LL Ld1-CeB, L-AaB ⊢ L-AeC Qiyās, III.1, 131.15–17
Camestres Ld1LL Ld1-CaB, L-AeB ⊢ L-AeC (not mentioned)
Festino Ld1LL Ld1-CeB, L-AiB ⊢ L-AoC (not mentioned)
Baroco Ld1LL Ld1-CaB, L-AoB ⊢ L-AoC (not mentioned)

Darapti Ld1LL Ld1-BaC, L-BaA ⊢ L-AiC (not mentioned)
Felapton Ld1LL Ld1-BeC, L-BaA ⊢ L-AoC (not mentioned)
Datisi Ld1LL Ld1-BaC, L-BiA ⊢ L-AiC (not mentioned)
Disamis Ld1LL Ld1-BiC, L-BaA ⊢ L-AiC (not mentioned)
Bocardo Ld1LL Ld1-BoC, L-BaA ⊢ L-AoC (not mentioned)
Ferison Ld1LL Ld1-BeC, L-BiA ⊢ L-AoC (not mentioned)

C.2.4 MM

Barbara MMM M-BaC, M-AaB ⊢ M-AaC Qiyās, IV.1, 181 7–9 (perfect, kāmil)
Celarent MMM M-BeC, M-AaB ⊢ M-AeC Qiyās, IV.1, 186.7–9 (perfect)
Darii MMM M-BaC, M-AiB ⊢ M-AiC Qiyās, IV.1, 178.13–14 (perfect)
Ferio MMM M-BeC, M-AiB ⊢ M-AoC Qiyās, IV.1, 178.13–14 (perfect)

Darapti MMM M-BaC, M-BaA ⊢ M-AiC Qiyās, IV.6, 223.3–5
Felapton MMM M-BeC, M-BaA ⊢ M-AoC Qiyās, IV.6, 223.5–6
Datisi MMM M-BaC, M-BiA ⊢ M1-AiC Qiyās, IV.6, 223.7–8
Disamis MMM M-BiC, M-BaA ⊢ M-AiC Qiyās, IV.6, 223.8–224.3
Bocardo MMM M-BoC, M-BaA ⊢ M-AoC Qiyās, IV.6, 223.8–14
Ferison MMM M-BeC, M-BiA ⊢ M-AoC Qiyās, IV.6, 223.5–6

No moods in the second figure (Qiyās, IV.4, 205–213)

C.2.5 MX

Barbara MXM M-BaC, X-AaB ⊢ M-AaC Qiyās, IV.2, 190.4–5 (evident, ẓāhir)
Celarent MXM M-BeC, X-AaB ⊢ M-AeC Qiyās, IV.2, 199.6–7 (evident)
Darii MXM M-BaC, X-AiB ⊢ M-AiC Qiyās, IV.2, 198.9–11 (evident)
Ferio MXM M-BeC, X-AiB ⊢ M-AoC Qiyās, IV.2, 198.9–11 (evident)

Darapti MXM M-BaC, X-BaA ⊢ M-AiC Qiyās, IV.6, 225.5–6 (implied)
Felapton MXM M-BeC, X-BaA ⊢ M-AoC Qiyās, IV.6, 225.5–6 (implied)
Datisi MXM M-BaC, X-BiA ⊢ M-AiC Qiyās, IV.6, 225.5–6 (implied)
Disamis MXM M-BiC, X-BaA ⊢ M-AiC Qiyās, IV.6, 225.5–6 (implied)
Bocardo MXM M-BoC, X-BaA ⊢ M-AoC Qiyās, IV.6, 225.5–6 (implied)
Ferison MXM M-BeC, X-BiA ⊢ M-AoC Qiyās, IV.6, 225.5–6 (implied)

Barbara XMM X-BaC, M-AaB ⊢ M-AaC Qiyās, IV.2, 199.7–8
Celarent XMM X-BeC, M-AaB ⊢ M-AeC Qiyās, IV.2, 199.7–8
Darii XMM X-BaC, M-AiB ⊢ M-AiC Qiyās, IV.2, 198.11–12
Ferio XMM X-BeC, M-AiB ⊢ M-AoC Qiyās, IV.2, 198.11–12

Darapti XMM X-BaC, M-BaA ⊢ M-AiC Qiyās, IV.6, 224.5–225.7
(discussed in connection with
Darapti XMX)
Felapton XMM X-BeC, M-BaA ⊢ M-AoC Qiyās, IV.6, 225.9 (implied)
Datisi XMM X-BaC, M-BiA ⊢ M-AiC Qiyās, IV.6, 225.11 (implied)
Disamis XMM X-BiC, M-BaA ⊢ M-AiC (not mentioned)
Bocardo XMM X-BoC, M-BaA ⊢ M-AoC Qiyās, IV.6, 225.9 (implied)
Ferison XMM X-BeC, M-BiA ⊢ M-AoC Qiyās, IV.6, 225.9 (implied)

Cesare* XMM X-CeB, M-AaB ⊢ M-AeC Qiyās, IV.4, 214.2–4
Camestres* XMM X-CaB, M-AeB ⊢ M-AeC Qiyās, IV.4, 214.4–6
Festino* XMM X-CeB, M-AiB ⊢ M-AoC Qiyās, IV.4, 215.5–7 (implied)
Baroco* XMM X-CaB, M-AoB ⊢ M-AoC Qiyās, IV.4, 215.5–7 (implied)
Baroco* MXM M-CaB, X-AoB ⊢M-AoC Qiyās, IV.4, 215.8–14
(only with X-proposition converting as itself, i.e., as strong as Ld1)

C.2.6 LM

Barbara MLM M-BaC, L-AaB ⊢ M-AaC Qiyās, IV.3, 199.1–2
(implied, dictum de omni)
Celarent MLM M-BeC, L-AaB ⊢ M-AeC Qiyās, IV.3, 199.1–2
(implied dictum de omni)
Darii MLM M-BaC, L-AiB ⊢ M-AiC Qiyās, IV.3, 199.1–2
(implied, dictum de omni)
Ferio MLM M-BeC, L-AiB ⊢ M-AoC Qiyās, IV.3, 199.1–2
(implied, dictum de omni)

Darapti MLM M-BaC, L-BaA ⊢ M-AiC Qiyās, IV.6, 226.5–6 (implied)
Felapton MLM M-BeC, L-BaA ⊢ M-AoC Qiyās, IV.6, 226.5–6 (implied)
Datisi MLM M-BaC, L-BiA ⊢ M-AiC Qiyās, IV.6, 226.5–6 (implied)
Disamis MLM M-BiC, L-BaA ⊢ M-AiC Qiyās, IV.6, 226.5–6 (implied)
Bocardo MLM M-BoC, L-BaA ⊢ M-AoC Qiyās, IV.6, 226.5–6 (implied)
Ferison MLM M-BeC, L-BiA ⊢ M-AoC Qiyās, IV.6, 226.5–6 (implied)

Cesare MLL M-CeB, L-AaB ⊢ L-AeC Qiyās, IV.5, 217.5–6 (implied)
Camestres MLL M-CaB, L-AeB ⊢ L-AeC Qiyās, IV.5, 216.8–9 (implied)
Festino MLL M-CeB, L-AiB ⊢ L-AoC Qiyās, IV.5, 222.13 (implied)
Baroco MLL M-CaB, L-AoB ⊢L-AoC Qiyās, IV.5, 222.13 (implied)

Barbara LML L-BaC, M-AaB ⊢ L-AaC Qiyās, IV.3, 202.3–204.1
Celarent LML L-BeC, M-AaB ⊢ L-AeC Qiyās, IV.3, 204.1–2 (implied)
Darii LML L-BaC, M-AiB ⊢ L-AiC Qiyās, IV.3, 204.14 (implied)
Ferio LML L-BeC, M-AiB ⊢ L-AoC Qiyās, IV.3, 204.14 (implied)

Cesare LML L-CeB, M-AaB ⊢ L-AeC Qiyās, IV.5, 216.1–4
Camestres LML L-CaB, M-AeB ⊢ L-AeC Qiyās, IV.5, 217.5–6 (implied)
Festino LML L-CeB, M-AiB ⊢ L-AoC Qiyās, IV.5, 222.13 (implied)
Baroco LML L-CaB, M-AoB ⊢L-AoC Qiyās, IV.5, 222.13 (implied)

Darapti LML L-BaC, M-BaA ⊢ L-AiC (not mentioned)
Felapton LML L-BeC, M-BaA ⊢ L-AoC Qiyās, IV.6, 227.3–4 (implied)
Datisi LML L-BaC, M-BiA ⊢ L-AiC Qiyās, IV.6, 226.11–13 (implied)
Disamis LML L-BiC, M-BaA ⊢ L-AiC Qiyās, IV.6, 226.15–17 (implied)
Bocardo LML L-BoC, M-BaA ⊢ L-AoC Qiyās, IV.6, 227.3–4 (implied)
Ferison LML L-BeC, M-BiA ⊢ L-AoC Qiyās, IV.6, 227.3–4 (implied)

C.3 Examples of proofs by reductio

Cesare MLL M-CeB, L-AaB ⊢ L-AeC
1. M-CeB Premise
2. L-AaB Premise
3. M-AiC Assumption for reductio
4. M-AoB 1, 3, Ferio MMM
5. ⊥ M-AoB contradicts L-AaB

Barbara LML L-BaC, M-AaB ⊢ L-AaC
1. L-BaC Premise
2. M-AaB Premise
3. M-AoC Assumption for reductio
4. X-AoC 3, assuming the possible to be actual
5. L-AoB 1, 4 Baroco LXL
6. ⊥ L-AoB contradicts M-AaB
Ferio LML L-BeC, M-AiB ⊢ L-AoC
1. L-BeC Premise
2. M-AiB Premise
3. M-AaC Assumption for reductio
4. X-AaC 3, assuming the possible to be actual
5. L-AeB 1, 4 Cesare LXL
6. ⊥ L-AeB contradicts M-AiB

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