Appendix B - List of Theorems

Summary

Theorem 4.1 (p. 81) T and CC entail that if a causes b, then everything causally connected to a and distinct from b is causally connected to b.

Theorem 4.2 (p. 81) Given T and CC, if a is distinct from b and not causally connected to b, then it is not causally connected to any cause of b.

Theorem 4.3 (p. 82) CC, I, and T entail A.

Theorem 4.4 (p. 84) CC and I imply that if a is causally connected to b and everything casually connected to a and distinct from b is causally connected to b, then a causes b.

Theorem 4.5 (p. 84) T, CC, and I entail CP.

Theorem 4.6 (p. 84) T, CC, and I entail CP.

Theorem 4.7 (p. 85) T, CC, CP, and A (asymmetry) imply I.

Theorem 5.1 (p. 107) DHI_g, PI_g, T_g, and PP_g imply AT_g.

Theorem 5.2 (p. 108) DHI_g, CC_g, T_g, and AT_g entail CP_g.

Theorem 5.3 (p. 108) DIg, PIg, Tg, and PPg imply ATg.

Theorem 5.4 (p. 108) DI_g, CC_g, T_g, and AT_g entails CP_g.

Theorem 5.5 (p. 108) DI_g, PI_g, CC_g, and T_g entail CP_g.

Theorem 5.6 (p. 109) Given CC_g and NIC_g, Ig_g is entailed by DI_g and PI_g.

Theorem 5.7 (p. 110) CC_g, PI_g, DI_g, and NIC_g entail I_g.

Theorem 6.1 (p. 135) SIM, CDCC, and I imply that individual causes will not be counterfactually dependent on individual effects and effects of a common asymmetric cause will not be counterfactually dependent on one another.