Copyright (C) 2018 Dennis Joe Darland
R is the relation between words words and ideas. (previously P|R)
S is the relation between ideas and objects (ideas are a special case of objects).
I am only handling beliefs expressed in words here. I think beliefs only in ideas simpler, but harder to understand.
Below the “R” relation is the “P|R” relation of previous sections.
Q believes(“V”, “a”, “b”) =df
——————————————————————————
(E iv)(E ia)(E ib)
(E V)(E a)(E b)
R(“V”,iv)
R(“a”,ia)
R(“b”,ib)
belief_private(Q,iv,ia,ib)
S(iv,V)
S(ia,a)
S(ib,b)
———————————————————————————
P believes (“believes” “Q” “V”, “a”, “b”) =df
———————————————————————————
(E iv1)(E ia1)(E ib1)
(E V1)(E a1)(E b1)(E Q1)(E BL2)
[Note i prefix for ideas, 1 suffix for Q’s ideas 2 suffix for P’s ideas]
[Words in quotes – they share words]
[variables used – 1 suffix for Q – 2 suffix for P]
R(“V”,iv1) – for Q
R(“a”,ia1) – for Q
R(“b”,ib1) – for Q
R(“V”,iv2) – for P
R(“a”,ia2) – for P
R(“b”,ib2) – for P
R(“Q”,iQ2) – for P
R(“BL2,iBL2) – for P
[iBL2 is P’s idea of belief, iQ2 is P’s idea of Q]
[P’s belief about Q’s belief.]
belief_private(P,iBL2,iQ2,iv1,ia1,ib1)
[Q and P’s S relations]
S(iv1,v1) – for Q
S(ia1,a1) – for Q
S(ib1,b1) – for Q
S(iQ2,q2) – for P [I’ve suppressed this for simplicity – really R and S relations
S(iBL2,BL2) – for P involve P and Q – indicted as [Q] in places below.]
S(iv2,v2) – for P
S(ia2,a2) – for P
S(ib2,b2) – for P
[We only have variables for the objects of belief – they cannot (at least almost never) be referred directly to.][P asserts that the values if his variables are identical with Q’s.]
[P’s beliefs about Q’s R and S relations follow]
belief_private(P,R,[Q],”V”,iv1) & belief_private(P,S,[Q],iv1,v1)
& belief_private(P,=,v1,v2)
belief_private(P,R,[Q],”a”,ia1) & belief_private(P,S,[Q],ia1,a1)
& belief_private(P,=,a1,a2)
belief_private(P,R,[Q],”b”,ib1) & belief_private(P,S,[Q],ib1,b1)
& belief_private(P,=,b1,b2)
[I use = for identity.]
[Strictly I think the belief_private(P,R,[Q],”V”,iv1), belief_private(P,R,[Q],”a”,ia1) and belief_private(P,R,[Q],”b”,ib1) relations are not necessary.
Q’s beliefs could be in a different language – as long as ideas correspond to the same objects.]
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