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On 5/13/2024 9:31 PM, Richard Damon wrote:Right, if True(L, p) is false, then ~True(L, p) is true, and since p in L is defined as ~True(L, p) that means the claim that True(L, p) is false meanss you are saying that True(L, true) is falseOn 5/13/24 10:03 PM, olcott wrote:*You keep forgetting that you said this*>
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive p?No, so True(L, p) is false
and thus ~True(L, p) is true.
Which has NOTHING to do with the above, as we never refered to False(L,p).>*You keep forgetting that you said this*>>
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive ~p?No, so False(L, p) is false,
So True(L, x) always returns True or False for allSo.
inputs and False(L, x) defined as True(L,~x)
always returns True or False for all inputs.
TruthBearer(L, x) ≡ (True(L,x) ∨ False(L,x))
*To make this easier to understand*Which has NOTHING to do with True(L, p) where p is defined in L to be ~True(L, p)
True(English, "a fish") is false
False(English, "a fish") is false
TruthBearer(English, "a fish") is false
Thus "a fish" is rejected as a type mismatch error
for any system of bivalent logic, yet the predicates
still answer correctly.
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