Copyright (C) 2018 Dennis Joe Darland
Suppose W is a wwf (sentence)
Then W is a sequence of words (following certain rules).
I will suppose it in the Lukasiewica notation (no punctuation needed).
Then if for every word x in the sequence W
(E y) x P|R|S y
then W is true iff there is an exactly corresponding fact consisting of the sequence of y’s corresponding to the x’s.
If there are any words x in W for which there is no such y then W is false.
Also it is false if, even though the y’s exist, the corresponding fact does not exist.
If there were no sentences, then none would be true.
I think propositions trickier, but, also, if none existed, none would be true.
Facts just exist – they are not true or false.
For any true proposition W, for each idea x in W there would be (E z)x R|S z where the z’s are objects.
If for any sequence of ideas there is a sequence of objects and the R|S relation holds between the idea and objects, the person with it ideas would understand the proposition, which might be true. And which the person might believe.
Then if believe(Q, z1, z2, ,,,) then this belief is true if the corresponding proposition (z1,z2,, …) is true, i.e. corresponds to a fact (y1, y2, …).
There are other propositional attitudes analogous to belief.
There will be facts for which there are no corresponding sentences or propositions.
Return to Dennis Joe Darland