Whether or not you subscribe to the logic of Fregean semantics, and by that I mean simply it’s operational rules, it’s an important theory to understand. It was influential in the philosophy of language and the philosophy of logic, and motivated a certain brand of philosophical style we call analytic philosophy.
This post won’t be much of a history lesson, though. Yours truly is too engaged to come up with new content, so I’ll simply review and recast my notes on the matter from classes and my other private studies.
The key to understanding the basics of Fregean semantics can be found in the distinction between sense and reference:
1. Sense: the mode of presentation of a proposition (i.e. how it is that the meaning of a proposition or concept is presented)
2. Reference: that to which the proposition is directed towards (i.e. what the proposition denotes, the object of the proposition, et cetera)
One simple way to think about it is to say to yourself that the sense of a proposition is akin to its intention, that is, in the philosophical sense of a proposition’s being about something. With regard to the reference, it is helpful to say to yourself that is akin to the denotation of the proposition, that is, the “to what” that the proposition is directed towards.
Fortunately, the distinction between sense and reference is easily exemplified. I’ll start with a graphical depiction. Consider three lines, a, b, and c and consider a point of intersection, P. Notice that although all propositions share the same reference (in virtue of their being directed towards the same entity, P) they do not share the same sense (in virtue of each proposition having a different mode of presentation).
See the full sized jpg file for a more concise explanation.