UC Davis

Consider the following pair of sentences:

(1a) Russell believed the proposition that mathematics reduces to logic.

(1b) Russell believed that mathematics reduces to logic. These two sentences cannot diverge in truth value: for any circumstance in which both sentences are evaluated, (1a) is true iff (1b) is.

By contrast, the following pair of sentences may well have different truth values:

(2a) Amy remembers the proposition that first order logic is undecidable.

(2b) Amy remembers that first order logic is undecidable.

Suppose that Amy took a class that covered decidability results. She may well remember what first order logic is and what it is to be decidable, and so remember the claim that first order logic is undecidable. So (2a) is true. But Amy may well have forgotten whether this claim is true or false. She recalls it being discussed, but can�t remember if it or its negation was proved. Then (2b) is false.

Let us call the phenomenon illustrated by the sentence pairs substitution failure. The puzzle I wish to address is: why do we get substitution failure with sentences involving some verbs of propositional attitude but not others?

(1a) Russell believed the proposition that mathematics reduces to logic.

(1b) Russell believed that mathematics reduces to logic. These two sentences cannot diverge in truth value: for any circumstance in which both sentences are evaluated, (1a) is true iff (1b) is.

By contrast, the following pair of sentences may well have different truth values:

(2a) Amy remembers the proposition that first order logic is undecidable.

(2b) Amy remembers that first order logic is undecidable.

Suppose that Amy took a class that covered decidability results. She may well remember what first order logic is and what it is to be decidable, and so remember the claim that first order logic is undecidable. So (2a) is true. But Amy may well have forgotten whether this claim is true or false. She recalls it being discussed, but can�t remember if it or its negation was proved. Then (2b) is false.

Let us call the phenomenon illustrated by the sentence pairs substitution failure. The puzzle I wish to address is: why do we get substitution failure with sentences involving some verbs of propositional attitude but not others?

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