Proposition and Belief:
According to Russell there are some propositions which are neither atom nor molecular: They are not atomic because they contain more than one proposition and they are in molecular because their truth or falsehood is not determined by the constituent propositions for example the propositions. ‘I believe it will rain’, ‘I think he is trustworthy’, ‘I dare say you are unequal the task’ etc., are statements which express a certain state of affair and also somebody believing in
Following are the points of differences between atomic and molecular propositions and belie propositions:-
1. Atomic propositions contain a single verb only, whereas belief propositions must have at least two verbs.
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2. The atomic propositions are unanlyzable, whereas the belief propositions are analyzable.
3. The truth or falsehood of the molecular propositions is determined by the truth or falsehood of this constituent proposition, whereas it is not the case with belief propositions that their constituents
According to Russell facts are neutral in regard to truth and falsehood. However, the facts correspond to beliefs; desires etc. are true or false. In this respect these are same as logical propositions.
Propositional Functions:
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According to Russell propositional function is an indefinite expression, there are three types of propositional functions:
(1) Necessary,
(2) Possible, and
(3) Impossible
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The characters of Necessity, Possibility and Impossibility belong to propositional functions and not to propositions themselves.