p(┌b∨¬a┐)−1+c>c−1+c. p(┌b┐)>2c−1. So we only get: Bc(ab)(Bc(a)Bd(b)), where Br(s) abbreviates p(┌s┐)>r and we have d=2c−1. So in general, attempted applications of distributivity create weakened belief operators, which would get in the way of the proof (very similar to how probabilistic Löb fails). However, the specific application we want happens to go through, due to a logical relationship between a and b; namely, that b is a weaker statement than a. This reveals a way in which the assumptions for Payor's Lemma are importantly weaker than those required for Löb to go through. So, the key observation I'm making is that weak distributility is all that's needed for Payor, and seems much more plausible for self-...]]>

p(┌b∨¬a┐)−1+c>c−1+c. p(┌b┐)>2c−1. So we only get: Bc(ab)(Bc(a)Bd(b)), where Br(s) abbreviates p(┌s┐)>r and we have d=2c−1. So in general, attempted applications of distributivity create weakened belief operators, which would get in the way of the proof (very similar to how probabilistic Löb fails). However, the specific application we want happens to go through, due to a logical relationship between a and b; namely, that b is a weaker statement than a. This reveals a way in which the assumptions for Payor's Lemma are importantly weaker than those required for Löb to go through. So, the key observation I'm making is that weak distributility is all that's needed for Payor, and seems much more plausible for self-...]]>

p(┌b∨¬a┐)−1+c>c−1+c. p(┌b┐)>2c−1. So we only get: Bc(ab)(Bc(a)Bd(b)), where Br(s) abbreviates p(┌s┐)>r and we have d=2c−1. So in general, attempted applications of distributivity create weakened belief operators, which would get in the way of the proof (very similar to how probabilistic Löb fails). However, the specific application we want happens to go through, due to a logical relationship between a and b; namely, that b is a weaker statement than a. This reveals a way in which the assumptions for Payor's Lemma are importantly weaker than those required for Löb to go through. So, the key observation I'm making is that weak distributility is all that's needed for Payor, and seems much more plausible for self-...]]>

p(┌b∨¬a┐)−1+c>c−1+c. p(┌b┐)>2c−1. So we only get: Bc(ab)(Bc(a)Bd(b)), where Br(s) abbreviates p(┌s┐)>r and we have d=2c−1. So in general, attempted applications of distributivity create weakened belief operators, which would get in the way of the proof (very similar to how probabilistic Löb fails). However, the specific application we want happens to go through, due to a logical relationship between a and b; namely, that b is a weaker statement than a. This reveals a way in which the assumptions for Payor's Lemma are importantly weaker than those required for Löb to go through. So, the key observation I'm making is that weak distributility is all that's needed for Payor, and seems much more plaus...]]>

p(┌b∨¬a┐)−1+c>c−1+c. p(┌b┐)>2c−1. So we only get: Bc(ab)(Bc(a)Bd(b)), where Br(s) abbreviates p(┌s┐)>r and we have d=2c−1. So in general, attempted applications of distributivity create weakened belief operators, which would get in the way of the proof (very similar to how probabilistic Löb fails). However, the specific application we want happens to go through, due to a logical relationship between a and b; namely, that b is a weaker statement than a. This reveals a way in which the assumptions for Payor's Lemma are importantly weaker than those required for Löb to go through. So, the key observation I'm making is that weak distributility is all that's needed for Payor, and seems much more plaus...]]>

p(┌b∨¬a┐)−1+c>c−1+c. p(┌b┐)>2c−1. So we only get: Bc(ab)(Bc(a)Bd(b)), where Br(s) abbreviates p(┌s┐)>r and we have d=2c−1. So in general, attempted applications of distributivity create weakened belief operators, which would get in the way of the proof (very similar to how probabilistic Löb fails). However, the specific application we want happens to go through, due to a logical relationship between a and b; namely, that b is a weaker statement than a. This reveals a way in which the assumptions for Payor's Lemma are importantly weaker than those required for Löb to go through. So, the key observation I'm making is that weak distributility is all that's needed for Payor, and seems much more plaus...]]>