**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) |