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THE LOGIC OF CAUSATION

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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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2016-01-21T06:41:56+00:00