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In this paper I shall set out to describe, according to Bertrand Russell the logical form of two inferences, I shall also speak about their validity. The inferences are: Sam ate the sandwich so someone ate the sandwich; Sam believes George Orwell wrote Animal Farm, Eric Blair is George Orwell so Sam believes Eric Blair wrote Animal Farm. In between I shall speak about why Russell views proper names as disguised descriptions. The logical form of the first inference Sam ate the sandwich so someone ate the sandwich follows Russell's logical form pattern of the phi is psi (this will be spoken about later). The logical form of the sentence Sam ate the sandwich so some one ate the sandwich, according to Russell is: There is at least one x such that x ate the sandwich and for every y if y ate the sandwich then y is x and x is Sam. The logical form of the sentence Someone ate the sandwich would be there exists at least one x such that x ate the sandwich.
The inference is valid because the conclusion follows from the premises and the conclusion can not seem false based on the premises. What led Russell to view proper names as disguised definite descriptors is the sentence The present King of France is bald. When examining the truth-value and logical form of this sentence Russell was confronted with a problem. We could say that the sentence is false if we were admitting that there is a present King of France and he is not bald. However assuming that the logical form that we assume of the sentence is correct, mainly the predicate not bald taken on by the present King of France, our false claim must be false since there is no present King of France. Thus Russell believed that the logical form of a sentence was more complex than what the surface form of a sentence depicted it to be.
This lead Russell to think of names as descriptions. Thus Russell explained the in sentences in the logical form of The phi is psi. Russell said if the phi is psi then there is a phi. There is at least one relative to the context of the sentence and it is psi. The theorem is stated as follows there exists at least one phi such that x is phi and for every y if y is phi then y is x and x is psi. Going back to our sentence The present King of France is bald we would say there exists at least one x such that x is bald and for every y if y is bald then y is x and x is the present King of France.
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