8b Matricial Analyses cont'd - Logic Philosophy Spirituality

THE LOGIC OF CAUSATION

Phase One: Macroanalysis

Chapter 8 – Matricial Analyses.

1. Matricial Analysis.

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)

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