In order to better illuminate the potential problems of language that he hopes to solve, Gottlob Frege begins On Sense and Reference with a short exercise in logic, analysing two statements, being that “a=a” and that “a=b”. On the Kantian understanding of logic, Frege explains, the first sentence is knowable a priori, and would be labelled as “analytic”. The second statement, however, may not always be knowable a priori, but would be understood to ostensibly contain valuable information regarding the nature of “a” and “b”.
The problem with the relationship between these two statements is, as Frege explains, that if “a” and “b” are both different names that designate the same thing, then it would seem as though the statements “a=a” and “a=b” are, in some form of understanding, not altogether different in nature. In example, let “a” be designated as “The band called Nickleback”, and “b” be designated as “The most hated band in the world”. Therefore, the statement “The band called Nickelback = The band called Nickelback” would be obviously true, but similarly, the statement “The band called Nickelback = The most hated band in the world” is also true, and contains the exact same point of reference. In this sense, the statements can be understood to be identical in reference (Assuming that “The band called Nickelback” actually is “The most hated band in the world”, but this is fairly non controversial).
If this is the case, then the statement “Nickelback is the most hated band in the world” may not be intended to convey information about the band directly, but rather it conveys the knowledge that both names designate the same thing. If, Frege explains, we take “The band called Nickelback” and “The most hated band in the world” to be objects themselves, rather than signs that reference objects, then the statement that “The band called Nickelback is the band called Nickelback” is cognitively identical to the statement that “The band called Nickelback is the most hated band in the world”. Obviously, this is not true. The first statement can be knowable a priori, whereas the second statement would require the excruciating experience of listening to one of their albums.
Thus, we have what Frege explains as two different names with the same object, but with different senses of how they call out that object. Frege argues that the sense of a given name is usually understood by anyone with sufficient knowledge of the object it is describing, but that the sense of the word serves to highlight a specific or single aspect of the object being referenced. In our given example, then, the term “The band called Nickelback” might provide us with information on how to recognise that certain promotional material is tied to that band in particular, or where in a music store to avoid going (that being, a specific part of the “N” section) if one does not want to contaminate one’s music collection. Conversely, the term “The most hated band in the world” does not help us to avoid Nickelback’s music, for example, but gives us some insight into precisely why their music should be avoided.
To this end, we can now understand the key differences between the concepts of sense and reference, particularly as they are explained in On sense and reference. Reference, then, is concerned with what object is being picked out by a given name. Sense, then, refers to what aspect of that object is being highlighted, also giving clues as to how and why that object is being picked out. Further, Frege implies, if we had comprehensive knowledge of any given object, we could at once say if any given sense applies to that object. He does say that such knowledge is not attainable and, given our example in question, we might say that such a limitation of knowledge is preferable.
With regard to ideas, Frege draws four clear delineations between the form in which ideas take, and things of the outside world. Firstly, he claims that ideas are not experienced via the senses.
Frege gives an illustration of himself walking outside, seeing a green field. He sees that the field is green, but the idea of what green is, and his identifying the field as “green” is not a visual phenomena. Similarly, the idea that I should hate Nickelback does not arrive in my head by way of my ears or my eyes. I may hear the music, but the message “this is dreadfully bad music” arrives only after the hearing, by way of abstraction. My opinion of the music is separate and apart from the sound waves created by the music as they arrive in my ears.
Secondly, Frege points out that ideas are had. In his example of the field, Frege states that the field will exist, and the sun will shine on it, whether he is there or not. However, his idea of the “green-ness” of the field requires him to be there to experience it. In other words, the light as it reflects off the field exists regardless of an observer. But the idea of “green” exists in the mind of the observer, making sense of the sensory experience, in spite of being apart from it. Similarly, without any fame or published albums, Nickelback’s music would still consist of little more than a set progress of power chords disguising a low and gravelly voice. However, the idea that “this is dreadfully bad music” requires a third party to actually hear the cheap succession of power chords and low range of gravelly vocals.
Thirdly, Frege says that ideas need a bearer. Rather than existing as objective objects, an idea must reside in the mind of the person thinking it, and thus are subjective. To illustrate this point, Frege suggests that he and his companion consider a strawberry in the field they are observing. Frege sees a red object among the greenery of the field, but his colourblind friend does not. This raises some questions: Does his friend see the green leaves as red? The red strawberry as green? Or are both some other colour that Frege himself is unacquainted with? Both people may describe the strawberry as “red”, but they may experience it entirely differently. Similarly, Nickelback has had a large number of sold out concerts, and sold millions of records. Assuming these tickets and albums are not being purchased ironically, or for purposes of paper mache or recycling, we must conclude that there are those who hear Nickelback’s music and actually think that it is good. That they and I are hearing the exact sound waves is largely unquestionable. What, then, are we to make of the unthinkable fact that they heard music and think to themselves “this is amazing!” while I, meanwhile, look for some steel wool to jam into my ears? The answer being, as Frege suggests, that each idea resides subjectively in our respective heads.
Finally, Frege says that, because all ideas reside within the minds of those that hold them, no two ideas are alike. It would appear the is arguing that they are not numerically identical, in the sense that if they were, then for two people to be experiencing the same idea, then the idea must exist independently of both of them, in order for both of them to have access to it. Frege calls to mind a Lime Tree, and asks the question “Is that Lime Tree my idea?” He presents two options, the first being that the Lime Tree in question exists, and can be sensed by other people. In that case, the Lime Tree cannot be his idea, for it exists independently of him, rather than being born by him. He has an idea about the Lime Tree, certainly, but his idea is not the Lime Tree itself. If the Lime Tree in question does not exist, then the subject of the sentence “That Lime Tree” does not exist. In such a case, he is unwittingly referencing a work of fiction, and the Tree does not exist outside of his head to be thought of by another person. Similarly, I can ask the question “Is the badness of Nickelback my idea?” a question complicated by the fact that so many people share my opinions of their music. However, a similar exercise can be applied to Nickelback as to the Lime Tree. If Nickelback’s over reliance on power chords, overly simplistic rhyming structure, and barely legible growling vocals actually does exist outside of my own head, then these factors can be abstracted by other people, and thus the facts that lead to the opinion of Nickelback’s badness exist outside of my head. My idea that “this is truly dreadful music” is not the source of itself, but rather it is drawn from experiences outside of my, and forms in my head. The person sitting next to me will likely experience the same sensations, but those sensations will enter their head instead of mine, giving birth to a similar idea, but one that is numerically distinct from my own. We can also largely intuit this using information from the third distinction that Frege has drawn, in that we can (however unfortunately) posit a third party experiencing all of the same sensations as my own, and that of the person sitting next to me, but instead think “This is great!”
Thus does Frege delineate the concepts of Idea, Sense, and Reference from one another, in a practical fashion. Robert May, in The Invariance of Sense, suggests some concerns for these concepts as Frege outlines them. Most particularly, with the concept of sense.
Frege, May suggests, would say that each name used to reference a specific object will have it’s own sense, used to pick out a specific aspect of that object. May points out that some have argued that different people may also apply different senses to the same name. An example given is Noonan’s remark that different people may attribute different senses to the name “Aristotle” (Perhaps one might invoke his name as an authority in philosophy, and still another might invoke his name as indicative of a long dead civilisation or a field of thinking that is now long disused).
We have already considered how different people may hear the same sound sensations, and have wildly different ideas about the value of those sensations. It is a very small step in logic to say that they may then apply to a specific name, say, the name of a band. Similarly, whereas many people would take the name “The most hated band in the world” to mean “Nickelback”, still others might take the name “The most hated band in the world” to mean “The Spice Girls”, which presents a truly difficult judgement call to make.
May says that some people have interpreted Frege to allow for this kind of variability in the application of the concept of sense. He does also say, however, that he believes this interpretation to be largely an incorrect one. He effectively argues that, on a Fregian view, if two people are ostensibly speaking the same language, but use the same word in two different senses, then those two people may appear to be speaking the same language, but in actuality are not.
This presents a very rigid understanding of “Language”, with an invariance of thought on the relationship between names and the objects they reference, and in what senses they reference that object. For now, we can take solace in the fact that, in most English speaking countries, there is little variance in how people view the relationship between “The most hated band in the world” and “The band called Nickelback”.