I found the excerpt from Frege’s work interesting because it challenged me and made me think about fundamental assumptions that we make in language but may not realize. Some time ago, I learned about E-Prime, a version of English that does not use the verb to be. I thought it was very difficult to exclude this verb fully, so I read some E-Prime translations, and I found them curious. However, it was not until I read Frege when I comprehended the entire complexity of using the concept of identity in language and in reasoning.
Frege tried to introduce mathematical principles to logic because he thought that logic should be strict and precise like math. However, based on his work, one can say that math is squishy, too. For example, there are two figures: a and b; when we say that a equals b we might mean that their shapes and areas are the same, but it does not mean they are the same thing. However, we might also say that a equals b if they are the same thing, but it just so happened that different signs are used to designate one thing.
It shows that, by identity, we might mean different things, and indeed, according to Frege, “[i]dentity gives rise to challenging questions” (25). I liked one example particularly: if the lines a, b, and c intersect in one point, will the point of intersection of a and b be equal to the point of intersection of b and c? It is the same point, and the entity designated by these different words is one, but I do not think that the point of intersection of a and b will be equal to the point of intersection of b and c because the contexts are different.
Similarly, the morning star and the evening star (although both are Venus) are not the same things in a sense because they were given different names and different meanings and because they were seen in different parts of the sky at different times of the year.
Philosophers have been arguing about this a lot, but what is important to understand is that an object is not equal to the sign or word that we use to designate it.
Work Cited
Frege, Gottlob. “On Sense and Reference.” Zeitschrift für Philosophie und philosophische Kritik, vol. 100, no. 1, 1892, pp. 25-50.