The Philosophical Review/Volume 1/Summary: Frege - Ueber Sinn und Bedeutung
If equality is a relation between objects and not between names or signs for things, the proposition 'a = b' would not differ from 'a = a'. But the former is synthetic, the latter analytic. What we seem to express by 'a = b' is that the symbol 'a' denotes the same thing as 'b' and the relation is therefore affirmed of the symbols. But this relation is mediated through the connection of each of the symbols with the same thing. The difference of the symbols must correspond to a difference in the manner in which the thing denoted is given. We must then recognize in a name or symbol (which may consist of one or more words), over and above the object denoted (Bedeutung), its sense (Sinn) or meaning. If three straight lines, a, b, and c, intersect in a point, 'the point of intersection of a and b' will have the same denotation as 'the point of intersection of b and c' but not the same sense. The sense of such a name is always understood by every one who knows the language; a definite meaning is always attached to one sign: but a symbol may have no denotation, or more than one name may be used to denote the same object. In indirect speech symbols do not denote objects, but the meaning or sense of the speaker, or that which is commonly their meaning. The denotation of a word hi indirect speech is thus its usual sense.
We must distinguish both the denotation and the sense of a name from the representation (Vorstellung) connected with it. Not always even in the same persons is the same Vorstellung connected with the same sense. The Vorstellung is subjective, and so differs essentially from the sense of a name which can be common to several. The sense of a name, too, does not imply space and time relations, while these are always joined to a Vorstellung. We enquire now after the sense and denotation (Sinn and Bedeutung) of assertory clauses which contain a complete thought. The thought is the sense, not the denotation of such a proposition, and this latter must be found in its relation to reality. It is the striving towards truth which urges us onward from the sense of a proposition to what it denotes. One may be tempted to regard the relation of thought to truth as that of the subject to the predicate. But subject and predicate are in a logical sense portions of a thought, which is formed by their connection, but never in this way do we pass from a thought to reality. Subordinate clauses have generally no complete meaning attaching to them, and consequently do not denote objects. This arises either from the fact that in subordinate clauses the words have their indirect signification, or through the incompleteness of these clauses, which only express a thought when taken in conjunction with the rest of the proposition.
If we found that the value for knowledge of 'a = a' and 'a = b' differs greatly, this is explained by the fact that the sense of a proposition, i.e. the thought which it expresses, is not less important than its denotation. Although a and b both denote the same object, yet their sense can be different, and consequently the thought expressed in the proposition 'a = b' different from that expressed in 'a = a.' If we understand under judgment the advance from thought to its correspondence with truth, we can also say that the judgments are different.