The putative counterexamples to the " Fido "-Fido theory considered so far are all cases where an utterance retains meaning even though one of its putative constituents fails to refer. More embarrassing for the Fido " "-Fido theory, Fregean cases are instances where a subject assents to one statement and rejects it for another, even though the two statements differ only in the substitution of one term for another referring to the same thing. For example : A subject sees himself in the mirror, without realizing that it's himself he's seeing. The subject notices that the pants of the man he sees are burning. He exclaims : His pants are burning ! The subject thus expresses a certain belief about the person he sees, but this belief is different from the one he would express if he said, in the first person, I've got burning pants. In fact, the subject in the imagined situation does not believe that he himself has burning pants. If the Fido theory " "-Fido were true, the two statements should have the same content, since the only difference between them lies in the replacement of one of the two expressions by the other, and the two expressions themselves refer to the same individual (and should therefore have the same content according to the Fido theory " "-Fido). Since, in fact, the subject holds one of the statements to be true and the other to be false, this implies, if the subject in question is rational, that these two statements have different contents for him or her, from which it follows that the content of a term cannot be reduced to its reference. Hence the Freghean distinction between meaning and reference (meaning corresponding to the way in which the reference is presented). The subject thinks of the person he sees in the mirror (himself, in fact) in a mode of presentation different from the mode of presentation involved when he thinks of himself in the first person.
According to Frege, meaning, or mode of presentation, corresponds to properties of the object that we know it possesses, and through which we refer to the object. Meaning determines reference insofar as reference is the object that actually possesses the properties through which reference is aimed. The model here is that of defined descriptions. The same individual can be referred to under different descriptions, for example as the general who won the battle of Austerlitz, or the one who lost at Waterloo. However, the mode of presentation associated with a proper name such as Napoleon is more complex than this : in the minds of language users, the proper name evokes a whole body of shared knowledge about the bearer of the proper name. Rather than a single description, then, the mode of presentation associated with a proper name corresponds to a mental file comprising a multiplicity of descriptions.