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 |
