**THE
LOGIC OF CAUSATION**

*Phase One: Macroanalysis*

**Chapter
8 – ****Matricial
Analyses. **

2. Crucial Matricial Analyses in Figure 1.

3. Crucial Matricial Analyses in Figure 2.

4. Crucial Matricial Analyses in Figure 3.

**3. Crucial Matricial Analyses in Figure 2.**

**Evaluation of mood # 221.** (Similarly, *mutadis mutandis*, for **mood
# 231**.)

__Major premise__:
R is a complete and (complemented by S) a contingent cause of Q:

**(i) If R, then Q; **

(ii) if notR, not-then Q;

(iii) where: R is possible.

**(iv) If (notR + notS), then notQ; **

(v) if (R + notS), not-then notQ;

(vi) if (notR + S), not-then notQ;

(vii) where: (notR + notS) is possible.

__Minor premise__:
P is a complete and necessary cause of Q:

**(viii) If P, then Q; **

(ix) if notP, not-then Q;

(x) where: P is possible.

**(xi) If notP, then notQ; **

(xii) if P, not-then notQ;

(xiii) where: notP is possible.

__Putative conclusion__ is P a complete or (complemented by S) a partial cause of R?

NO! P is not implied to be a complete cause of R:

If P, then R? | denied by (vi) + (xi); |

if notP, not-then R | implied by (iv) + (vii) + (viii); |

where: P is possible | same as (x). |

Nor (complemented by S) a partial cause of R:

If (P + S), then R? | denied by (vi) + (xi); |

if (notP + S), not-then R? | open; |

if (P + notS), not-then R? | denied by (iv) + (viii); |

where: (P + S) is possible | implied by (vi) + (xi). |

Table 8.16. Evaluation of mood 221. | ||||

P | Q | R | S | see (i) + (iii), or (viii) + (x), or (xii) |

P | Q | R | notS | implied possible by (v) + (xi) |

P | Q | notR | S | implied possible by (vi) + (xi) |

P | Q | notR | notS | implied impossible by (iv) |

P | notQ | R | S | implied impossible by (i) or (viii) |

P | notQ | R | notS | implied impossible by (i) or (viii) |

P | notQ | notR | S | implied impossible by (viii) |

P | notQ | notR | notS | implied impossible by (viii) |

notP | Q | R | S | implied impossible by (xi) |

notP | Q | R | notS | implied impossible by (xi) |

notP | Q | notR | S | implied impossible by (xi) |

notP | Q | notR | notS | implied impossible by (iv) or (xi) |

notP | notQ | R | S | implied impossible by (i) |

notP | notQ | R | notS | implied impossible by (i) |

notP | notQ | notR | S | see (ii), or (ix), or (xi) + (xiii) |

notP | notQ | notR | notS | implied possible by (iv) + (vii) + (viii) |

**Evaluation of mood # 222.** (Similarly, *mutadis mutandis*, for **mood
# 233**.)

__Major premise__:
R is a complete and (complemented by P) a contingent cause of Q:

**(i) If R, then Q; **

(ii) if notR, not-then Q;

(iii) where: R is possible.

**(iv) If (notR + notP), then notQ; **

(v) if (R + notP), not-then notQ;

(vi) if (notR + P), not-then notQ;

(vii) where: (notR + notP) is possible.

__Minor premise__:
P is a complete and (complemented by S) a contingent cause of Q:

**(viii) If P, then Q; **

(ix) if notP, not-then Q;

(x) where: P is possible.

**(xi) If (notP + notS), then notQ; **

(xii) if (P + notS), not-then notQ;

(xiii) if (notP + S), not-then notQ;

(xiv) where: (notP + notS) is possible.

__Putative conclusion__ is P (complemented by S) a cause of R?

NO! P is not implied to be a complete cause of R:

If P, then R? | open; |

if notP, not-then R | implied by (i) + (xi) + (xiv); |

where: P is possible | same as (x). |

Nor (complemented by S) a partial cause of R:

If (P + S), then R? | open; |

if (notP + S), not-then R? | open; |

if (P + notS), not-then R? | open; |

where: (P + S) is possible? | open. |

Nor a necessary cause of R:

If notP, then notR? | denied by (v) + (xi), or (iv) + (xiii); |

if P, not-then notR? | open; |

where: notP is possible | implied by (v) or (vii) or (ix) or (xiii) or (xiv). |

Nor (complemented by S) a contingent cause of R:

If (notP + notS), then notR | implied by (i) + (xi); |

if (P + notS), not-then notR? | open; |

if (notP + S), not-then notR | implied by (v) + (xi), or (iv) + (xiii); |

where: (notP + notS) is possible | same as (xiv). |

Table 8.17. Evaluation of mood 222. | ||||

P | Q | R | S | see (i) + (iii), or (viii) + (x) |

P | Q | R | notS | see (i) + (iii), or (viii) + (x), or (xii) |

P | Q | notR | S | see (vi), or (viii) + (x) |

P | Q | notR | notS | see (vi), or (viii) + (x), or (xii) |

P | notQ | R | S | implied impossible by (i) or (viii) |

P | notQ | R | notS | implied impossible by (i) or (viii) |

P | notQ | notR | S | implied impossible by (viii) |

P | notQ | notR | notS | implied impossible by (viii) |

notP | Q | R | S | implied possible by (v) + (xi), or (iv) + (xiii) |

notP | Q | R | notS | implied impossible by (xi) |

notP | Q | notR | S | implied impossible by (iv) |

notP | Q | notR | notS | implied impossible by (iv) or (xi) |

notP | notQ | R | S | implied impossible by (i) |

notP | notQ | R | notS | implied impossible by (i) |

notP | notQ | notR | S | see (ii), or (iv) + (vii), or (ix) |

notP | notQ | notR | notS | implied possible by (i) + (xi) + (xiv) |

**Evaluation of mood # 224.** (Similarly, *mutadis mutandis*, for **mood
# 234**.)

__Major premise__:
R is a complete and (complemented by P) a contingent cause of Q:

**(i) If R, then Q; **

(ii) if notR, not-then Q;

(iii) where: R is possible.

**(iv) If (notR + notP), then notQ; **

(v) if (R + notP), not-then notQ;

(vi) if (notR + P), not-then notQ;

(vii) where: (notR + notP) is possible.

__Minor premise__:
P (complemented by S) is a partial and contingent cause of Q:

**(viii) If (P + S), then Q; **

(ix) if (notP + S), not-then Q;

(x) if (P + notS), not-then Q;

(xi) where: (P + S) is possible.

**(xii) If (notP + notS), then notQ; **

(xiii) if (P + notS), not-then notQ;

(xiv) if (notP + S), not-then notQ;

(xv) where: (notP + notS) is possible.

__Putative conclusion__ is P (complemented by S) a cause of R?

NO! P is not implied to be a complete cause of R:

If P, then R? | denied by (i) + (x); |

if notP, not-then R | implied by (i)+(ix), or (i)+(xii)+(xv); |

where: P is possible | implied by (vi) or (x) or (xi) or (xiii). |

Nor (complemented by S) a partial cause of R:

If (P + S), then R? | open; |

if (notP + S), not-then R | implied by (i) + (ix); |

if (P + notS), not-then R | implied by (i) + (x); |

where: (P + S) is possible | same as (xi). |

Nor a necessary cause of R:

If notP, then notR? | denied by (iv) + (xiv), or (v) + (xii); |

if P, not-then notR? | open; |

where: notP is possible | implied by (v) or (vii) or (ix) or (xiv) or (xv). |

Nor (complemented by S) a contingent cause of R:

If (notP + notS), then notR | implied by (i) + (xii); |

if (P + notS), not-then notR? | open; |

if (notP + S), not-then notR | implied by (iv) + (xiv), or (v) + (xii); |

where: (notP + notS) is possible | same as (xv). |

Table 8.18. Evaluation of mood 224. | ||||

P | Q | R | S | see (i) + (iii), or (viii) + (xi) |

P | Q | R | notS | see (i) + (iii), or (xiii) |

P | Q | notR | S | see (vi), or (viii) + (xi) |

P | Q | notR | notS | see (vi), or (xiii) |

P | notQ | R | S | implied impossible by (i) or (viii) |

P | notQ | R | notS | implied impossible by (i) |

P | notQ | notR | S | implied impossible by (viii) |

P | notQ | notR | notS | implied possible by (i) + (x) |

notP | Q | R | S | implied possible by (iv) + (xiv), or (v) + (xii) |

notP | Q | R | notS | implied impossible by (xii) |

notP | Q | notR | S | implied impossible by (iv) |

notP | Q | notR | notS | implied impossible by (iv) or (xii) |

notP | notQ | R | S | implied impossible by (i) |

notP | notQ | R | notS | implied impossible by (i) |

notP | notQ | notR | S | implied possible by (i) + (ix) |

notP | notQ | notR | notS | implied possible by (i) + (xii) + (xv) |

**Evaluation of mood # 241.**

__Major premise__:
R (complemented by S) is a partial and contingent cause of Q:

**(i) If (R + S), then Q; **

(ii) if (notR + S), not-then Q;

(iii) if (R + notS), not-then Q;

(iv) where: (R + S) is possible.

**(v) If (notR + notS), then notQ; **

(vi) if (R + notS), not-then notQ;

(vii) if (notR + S), not-then notQ;

(viii) where: (notR + notS) is possible.

__Minor premise__:
P is a complete and necessary cause of Q:

**(ix) If P, then Q; **

(x) if notP, not-then Q;

(xi) where: P is possible.

**(xii) If notP, then notQ; **

(xiii) if P, not-then notQ;

(xiv) where: notP is possible.

__Putative conclusion__ is P (complemented by S) a cause of R?

NO! P is not implied to be a complete cause of R:

If P, then R? | denied by (vii) + (xii); |

if notP, not-then R | implied by (ii)+(ix), or (v)+(viii)+(ix); |

where: P is possible | same as (xi). |

Nor (complemented by S) a partial cause of R:

If (P + S), then R? | denied by (vii) + (xii); |

if (notP + S), not-then R | implied by (ii) + (ix); |

if (P + notS), not-then R? | denied by (v) + (ix); |

where: (P + S) is possible | impl. by (i)+(iv)+(xii), or (vii)+(xii). |

Nor a necessary cause of R:

If notP, then notR? | denied by (iii) + (ix); |

if P, not-then notR | impl. by (i)+(iv)+(xii), or (vi)+(xii); |

where: notP is possible | same as (xiv). |

Nor (complemented by S) a contingent cause of R:

If (notP + notS), then notR? | denied by (iii) + (ix); |

if (P + notS), not-then notR | implied by (vi) + (xii); |

if (notP + S), not-then notR? | denied by (i) + (xii); |

where: (notP + notS) is possible | impl. by (iii)+(ix), or (v)+(viii)+(ix). |

Table 8.19. Evaluation of mood 241. | ||||

P | Q | R | S | implied possible by (i) + (iv) + (xii) |

P | Q | R | notS | implied possible by (vi) + (xii) |

P | Q | notR | S | implied possible by (vii) + (xii) |

P | Q | notR | notS | implied impossible by (v) |

P | notQ | R | S | implied impossible by (i) or (ix) |

P | notQ | R | notS | implied impossible by (ix) |

P | notQ | notR | S | implied impossible by (ix) |

P | notQ | notR | notS | implied impossible by (ix) |

notP | Q | R | S | implied impossible by (xii) |

notP | Q | R | notS | implied impossible by (xii) |

notP | Q | notR | S | implied impossible by (xii) |

notP | Q | notR | notS | implied impossible by (v) or (xii) |

notP | notQ | R | S | implied impossible by (i) |

notP | notQ | R | notS | implied possible by (iii) + (ix) |

notP | notQ | notR | S | implied possible by (ii) + (ix) |

notP | notQ | notR | notS | implied possible by (v) + (viii) + (ix) |

**Evaluation of mood # 244.**

__Major premise__:
R (complemented by P) is a partial and contingent cause of Q:

**(i) If (R + P), then Q; **

(ii) if (notR + P), not-then Q;

(iii) if (R + notP), not-then Q;

(iv) where: (R + P) is possible.

**(v) If (notR + notP), then notQ; **

(vi) if (R + notP), not-then notQ;

(vii) if (notR + P), not-then notQ;

(viii) where: (notR + notP) is possible.

__Minor premise__:
P (complemented by S) is a partial and contingent cause of Q:

**(ix) If (P + S), then Q; **

(x) if (notP + S), not-then Q;

(xi) if (P + notS), not-then Q;

(xii) where: (P + S) is possible.

**(xiii) If (notP + notS), then notQ; **

(xiv) if (P + notS), not-then notQ;

(xv) if (notP + S), not-then notQ;

(xvi) where: (notP + notS) is possible.

__Putative conclusion__ is P (complemented by S) a cause of R?

NO! P is not implied to be a complete cause of R:

If P, then R? | denied by (i) + (xi), or (ii) + (ix); |

if notP, not-then R? | open; |

where: P is possible | implied by (ii) or (iv) or (vii) or (xi) or (xii) or (xiv). |

Nor (complemented by S) a partial cause of R:

If (P + S), then R? | open; |

if (notP + S), not-then R? | open; |

if (P + notS), not-then R | implied by (i) + (xi), or (ii) + (ix); |

where: (P + S) is possible | same as (xii). |

Nor a necessary cause of R:

If notP, then notR? | denied by (v) + (xv), or (vi) + (xiii); |

if P, not-then notR? | open; |

where: notP is possible | implied by (iii) or (vi) or (viii) or (x) or (xv) or (xvi). |

Nor (complemented by S) a contingent cause of R:

If (notP + notS), then notR? | open; |

if (P + notS), not-then notR? | open; |

if (notP + S), not-then notR | implied by (v) + (xv), or (vi) + (xiii); |

where: (notP + notS) is possible | same as (xvi). |

Table 8.20. Evaluation of mood 244. | ||||

P | Q | R | S | see (i) + (iv), or (ix) + (xii) |

P | Q | R | notS | see (i) + (iv), or (xiv) |

P | Q | notR | S | see (vii), or (ix) + (xii) |

P | Q | notR | notS | see (vii), or (xiv) |

P | notQ | R | S | implied impossible by (i) or (ix) |

P | notQ | R | notS | implied impossible by (i) |

P | notQ | notR | S | implied impossible by (ix) |

P | notQ | notR | notS | implied possible by (i) + (xi), or (ii) + (ix) |

notP | Q | R | S | implied possible by (v) + (xv), or (vi) + (xiii) |

notP | Q | R | notS | implied impossible by (xiii) |

notP | Q | notR | S | implied impossible by (v) |

notP | Q | notR | notS | implied impossible by (v) or (xiii) |

notP | notQ | R | S | see (iii) or (x) |

notP | notQ | R | notS | see (iii), or (xiii) + (xvi) |

notP | notQ | notR | S | see (v) + (viii), or (x) |

notP | notQ | notR | notS | see (v) + (viii), or (xiii) + (xvi) |

**4. Crucial Matricial Analyses in Figure 3.**

**Evaluation of mood # 312.** (Similarly, *mutadis mutandis*, for **mood
# 313**.)

__Major premise__:
Q is a complete and necessary cause of R:

**(i) If Q, then R; **

(ii) if notQ, not-then R;

(iii) where: Q is possible.

**(iv) If notQ, then notR; **

(v) if Q, not-then notR;

(vi) where: notQ is possible.

__Minor premise__:
Q is a complete and (complemented by S) a contingent cause of P:

**(vii) If Q, then P; **

(viii) if notQ, not-then P;

(ix) where: Q is possible.

**(x) If (notQ + notS), then notP; **

(xi) if (Q + notS), not-then notP;

(xii) if (notQ + S), not-then notP;

(xiii) where: (notQ + notS) is possible.

__Putative conclusion__:
is P a complete or (complemented by S) a partial cause of R?

NO! P is not implied to be a complete cause of R:

If P, then R? | denied by (iv) + (xii); |

if notP, not-then R | implied by (iv) + (x) + (xiii); |

where: P is possible | implied by (vii) + (ix), or (xi), or (xii). |

Nor (complemented by S) a partial cause of R:

If (P + S), then R? | denied by (iv) + (xii); |

if (notP + S), not-then R? | open; |

if (P + notS), not-then R? | denied by (i) + (x); |

where: (P + S) is possible | implied by (xii). |

Table 8.21. Evaluation of mood # 312. | ||||

P | Q | R | S | see (i) + (iii), or (v), or (vii) + (ix) |

P | Q | R | notS | implied possible by (i) + (xi) |

P | Q | notR | S | implied impossible by (i) |

P | Q | notR | notS | implied impossible by (i) |

P | notQ | R | S | implied impossible by (iv) |

P | notQ | R | notS | implied impossible by (iv) or (x) |

P | notQ | notR | S | implied possible by (iv) + (xii) |

P | notQ | notR | notS | implied impossible by (x) |

notP | Q | R | S | implied impossible by (vii) |

notP | Q | R | notS | implied impossible by (vii) |

notP | Q | notR | S | implied impossible by (i) or (vii) |

notP | Q | notR | notS | implied impossible by (i) or (vii) |

notP | notQ | R | S | implied impossible by (iv) |

notP | notQ | R | notS | implied impossible by (iv) |

notP | notQ | notR | S | see (ii), or (iv) + (vi), or (viii) |

notP | notQ | notR | notS | implied possible by (iv) + (x) + (xiii) |

**Evaluation of mood # 314.**

__Major premise__:
Q is a complete and necessary cause of R:

**(i) If Q, then R; **

(ii) if notQ, not-then R;

(iii) where: Q is possible.

**(iv) If notQ, then notR; **

(v) if Q, not-then notR;

(vi) where: notQ is possible.

__Minor premise__:
Q (complemented by S) is a partial and contingent cause of P:

**(vii) If (Q + S), then P; **

(viii) if (notQ + S), not-then P;

(ix) if (Q + notS), not-then P;

(x) where: (Q + S) is possible.

**(xi) If (notQ + notS), then notP; **

(xii) if (Q + notS), not-then notP;

(xiii) if (notQ + S), not-then notP;

(xiv) where: (notQ + notS) is possible.

__Putative conclusion__:
is P (complemented by S) a cause of R?

NO! P is not implied to be a complete cause of R:

If P, then R? | denied by (iv) + (xiii); |

if notP, not-then R | impl. by (iv)+(viii), or (iv)+(xi)+(xiv); |

where: P is possible | impl. by (vii) + (x), or (xii), or (xiii). |

Nor (complemented by S) a partial cause of R:

If (P + S), then R? | denied by (iv) + (xiii); |

if (notP + S), not-then R | implied by (iv) + (viii); |

if (P + notS), not-then R? | denied by (i) + (xi); |

where: (P + S) is possible | implied by (vii) + (x), or (xiii). |

Nor a necessary cause of R:

If notP, then notR? | denied by (i) + (ix); |

if P, not-then notR | implied by (i)+(vii)+(x), or (i)+(xii); |

where: notP is possible | impl. by (viii), or (ix), or (xi) + (xiv). |

Nor (complemented by S) a contingent cause of R:

If (notP + notS), then notR? | denied by (i) + (ix); |

if (P + notS), not-then notR | implied by (i) + (xii); |

if (notP + S), not-then notR? | denied by (iv) + (vii); |

where: (notP + notS) is possible | implied by (ix), or (xi) + (xiv). |

Table 8.22. Evaluation of mood # 314. | ||||

P | Q | R | S | implied possible by (i) + (vii) + (x) |

P | Q | R | notS | implied possible by (i) + (xii) |

P | Q | notR | S | implied impossible by (i) |

P | Q | notR | notS | implied impossible by (i) |

P | notQ | R | S | implied impossible by (iv) |

P | notQ | R | notS | implied impossible by (iv) or (xi) |

P | notQ | notR | S | implied possible by (iv) + (xiii) |

P | notQ | notR | notS | implied impossible by (xi) |

notP | Q | R | S | implied impossible by (vii) |

notP | Q | R | notS | implied possible by (i) + (ix) |

notP | Q | notR | S | implied impossible by (i) or (vii) |

notP | Q | notR | notS | implied impossible by (i) |

notP | notQ | R | S | implied impossible by (iv) |

notP | notQ | R | notS | implied impossible by (iv) |

notP | notQ | notR | S | implied possible by (iv) + (viii) |

notP | notQ | notR | notS | implied possible by (iv) + (xi) + (xiv) |

**Evaluation of mood # 324.** (Similarly, *mutadis mutandis*, for **mood
# 334**.)

__Major premise__:
Q is a complete and (complemented by P) a contingent cause of R:

**(i) If Q, then R; **

(ii) if notQ, not-then R;

(iii) where: Q is possible.

**(iv) If (notQ + notP), then notR; **

(v) if (Q + notP), not-then notR;

(vi) if (notQ + P), not-then notR;

(vii) where: (notQ + notP) is possible.

__Minor premise__:
Q (complemented by S) is a partial and contingent cause of P:

**(viii) If (Q + S), then P; **

(ix) if (notQ + S), not-then P;

(x) if (Q + notS), not-then P;

(xi) where: (Q + S) is possible.

**(xii) If (notQ + notS), then notP; **

(xiii) if (Q + notS), not-then notP;

(xiv) if (notQ + S), not-then notP;

(xv) where: (notQ + notS) is possible.

__Putative conclusion__:
is P (complemented by S) a cause of R?

NO! P is not implied to be a complete cause of R:

If P, then R? | open; |

if notP, not-then R | impl. by (iv)+(ix), or (iv)+(xii)+(xv); |

where: P is possible | implied by (vi), or (viii) + (xi), or (xiii), or (xiv). |

Nor (complemented by S) a partial cause of R:

If (P + S), then R? | open; |

if (notP + S), not-then R | implied by (iv) + (ix); |

if (P + notS), not-then R? | denied by (i) + (xii); |

where: (P + S) is possible | implied by (vi) + (xii), or (viii) + (xi), or (xiv). |

Nor a necessary cause of R:

If notP, then notR? | denied by (v) + (viii), or (i) + (x); |

if P, not-then notR | implied by (i)+(viii)+(xi), or (i)+(xiii), or (vi)+(xii); |

where: notP is possible | implied by (v), or (ix), or (x), or (xii) + (xv). |

Nor (complemented by S) a contingent cause of R:

If (notP + notS), then notR? | denied by (v) + (viii), or (i) + (x); |

if (P + notS), not-then notR | implied by (i) + (xiii); |

if (notP + S), not-then notR? | denied by (iv) + (viii); |

where: (notP + notS) is possible | implied by (v) + (viii), or (x), or (xii) + (xv). |

Table 8.23. Evaluation of mood # 324. | ||||

P | Q | R | S | implied possible by (i) + (viii) + (xi) |

P | Q | R | notS | implied possible by (i) + (xiii) |

P | Q | notR | S | implied impossible by (i) |

P | Q | notR | notS | implied impossible by (i) |

P | notQ | R | S | implied possible by (vi) + (xii) |

P | notQ | R | notS | implied impossible by (xii) |

P | notQ | notR | S | see (ii) or (xiv) |

P | notQ | notR | notS | implied impossible by (xii) |

notP | Q | R | S | implied impossible by (viii) |

notP | Q | R | notS | implied possible by (v) + (viii), or (i) + (x) |

notP | Q | notR | S | implied impossible by (i) or (viii) |

notP | Q | notR | notS | implied impossible by (i) |

notP | notQ | R | S | implied impossible by (iv) |

notP | notQ | R | notS | implied impossible by (iv) |

notP | notQ | notR | S | implied possible by (iv) + (ix) |

notP | notQ | notR | notS | implied possible by (iv) + (xii) + (xv) |

**Evaluation of mood # 344.**

__Major premise__:
Q (complemented by P) is a partial and contingent cause of R:

**(i) If (Q + P), then R; **

(ii) if (notQ + P), not-then R;

(iii) if (Q + notP), not-then R;

(iv) where: (Q + P) is possible.

**(v) If (notQ + notP), then notR; **

(vi) if (Q + notP), not-then notR;

(vii) if (notQ + P), not-then notR;

(viii) where: (notQ + notP) is possible.

__Minor premise__:
Q (complemented by S) is a partial and contingent cause of P:

**(ix) If (Q + S), then P; **

(x) if (notQ + S), not-then P;

(xi) if (Q + notS), not-then P;

(xii) where: (Q + S) is possible.

**(xiii) If (notQ + notS), then notP; **

(xiv) if (Q + notS), not-then notP;

(xv) if (notQ + S), not-then notP;

(xvi) where: (notQ + notS) is possible.

__Putative conclusion__:
is P (complemented by S) a cause of R?

NO! P is not implied to be a complete cause of R:

If P, then R? | denied by (ii) + (xiii); |

if notP, not-then R | implied by (iii)+(ix), or (v)+(x), or (v)+(xiii)+(xvi); |

where: P is possible | implied by (ii), or (iv), or (vii) + (xiii), or (ix) + (xii), or (xiv) or (xv). |

Nor (complemented by S) a partial cause of R:

If (P + S), then R? | denied by (ii) + (xiii); |

if (notP + S), not-then R | implied by (v) + (x); |

if (P + notS), not-then R? | denied by (i) + (xiii); |

where: (P + S) is possible | implied by (ii) + (xiii), or (vii) + (xiii), or (ix) + (xii), or (xv). |

Nor a necessary cause of R:

If notP, then notR? | denied by (vi) + (ix); |

if P, not-then notR | implied by (i)+(ix)+(xii), or (i)+(xiv), or (vii)+(xiii); |

where: notP is possible | implied by (iii), or (vi), or (viii), or (x), or (xi), or (xiii) + (xvi). |

Nor (complemented by S) a contingent cause of R:

If (notP + notS), then notR? | denied by (vi) + (ix); |

if (P + notS), not-then notR | implied by (i) + (xiv); |

if (notP + S), not-then notR? | denied by (v) + (ix); |

where: (notP + notS) is possible | implied by (iii) + (ix), or (vi) + (ix), or (xi), or (xiii) + (xvi). |

Table 8.24. Evaluation of mood # 344. | ||||

P | Q | R | S | implied possible by (i) + (ix) + (xii) |

P | Q | R | notS | implied possible by (i) + (xiv) |

P | Q | notR | S | implied impossible by (i) |

P | Q | notR | notS | implied impossible by (i) |

P | notQ | R | S | implied possible by (vii) + (xiii) |

P | notQ | R | notS | implied impossible by (xiii) |

P | notQ | notR | S | implied possible by (ii) + (xiii) |

P | notQ | notR | notS | implied impossible by (xiii) |

notP | Q | R | S | implied impossible by (ix) |

notP | Q | R | notS | implied possible by (vi) + (ix) |

notP | Q | notR | S | implied impossible by (ix) |

notP | Q | notR | notS | implied possible by (iii) + (ix) |

notP | notQ | R | S | implied impossible by (v) |

notP | notQ | R | notS | implied impossible by (v) |

notP | notQ | notR | S | implied possible by (v) + (x) |

notP | notQ | notR | notS | implied possible by (v) + (xiii) + (xvi) |

**Evaluation of mood # 352.** (Similarly, *mutadis mutandis*, for **mood
# 363**.)

__Major premise__:
Q is a complete cause of R:

**(i) If Q, then R; **

(ii) if notQ, not-then R;

(iii) where: Q is possible.

__Minor premise__:
Q is a complete and (complemented by S) a contingent cause of P:

**(iv) If Q, then P; **

(v) if notQ, not-then P;

(vi) where: Q is possible.

**(vii) If (notQ + notS), then notP; **

(viii) if (Q + notS), not-then notP;

(ix) if (notQ + S), not-then notP;

(x) where: (notQ + notS) is possible.

__Putative conclusion__:
is P a necessary cause of R?

NO! P is not implied to be a necessary cause of R:

If notP, then notR? | open; |

if P, not-then notR | implied by (i) + (viii); |

where: notP is possible? | implied by (v), or (vii) + (x). |

Table 8.25. Evaluation of mood # 352. | ||||

P | Q | R | S | see (i) + (iii), or (iv) + (vi) |

P | Q | R | notS | implied possible by (i) + (viii) |

P | Q | notR | S | implied impossible by (i) |

P | Q | notR | notS | implied impossible by (i) |

P | notQ | R | S | see (ix) |

P | notQ | R | notS | implied impossible by (vii) |

P | notQ | notR | S | see (ii) or (ix) |

P | notQ | notR | notS | implied impossible by (vii) |

notP | Q | R | S | implied impossible by (iv) |

notP | Q | R | notS | implied impossible by (iv) |

notP | Q | notR | S | implied impossible by (i) or (iv) |

notP | Q | notR | notS | implied impossible by (i) or (iv) |

notP | notQ | R | S | see (v) |

notP | notQ | R | notS | see (v), or (vii) + (x) |

notP | notQ | notR | S | see (ii) or (v) |

notP | notQ | notR | notS | see (ii) or (v), or (vii) + (x) |