Sense

Perhaps a simpler example will make this problem clearer. Frege gives the example of the previous names of Venus: the morning star and the evening star (1892a). Hopefully the reason for Venus having these two pseudonyms is clear. If I were to tell you, just having found out about Venus as a planet and how it appears from here on Earth, that the morning star is the evening star, that is, they are one and the same, to which you replied “the morning star is the morning star, the evening star is the evening star” in what sense is the same thought being expressed once by me and twice by you? Seemingly none at all. But if there is in fact only one star, then all of these sentences turn on the exact same set of circumstances whether they are true or not. It looks like we are dealing here with three distinct thoughts:

A is A

B is B

A is B

The problem is that if it is true that the morning star is the evening star, then whether I use one term or the other shouldn’t change the ‘thought’ because the names have no bearing on the circumstances that the three thoughts turn on regarding whether they are true or not.

Frege (1892a) offers another example. Imagine three lines, a, b, and c, that run from each of a triangle’s vertices to the midpoints of the opposites edges of the triangle. Of this situation, we can say that the point of intersection between lines a and b is the same point of intersection between b and c.

Now imagine you’ve lost your keys in the grass at a park. A passer by asks you what you are looking for and you tell him. He says he passed some keys lying in the grass back a ways, and you ask him to indicate where they are. After a bit of fruitless pointing, he indicates that starting at the picnickers over there, if you walk in a line towards the midpoint between the tree and the barbecue, you’ll find them right when the tree is on your left and the midpoint of the picnickers and the barbecue is on your right. Odd directions, to be sure, but admirable for their Cartesian precision. However, when you get over to the area you have (understandably) forgotten the details of where to start and which thing should be on the left or right. Your friend, though, points out it does not matter, just pick one of the three, head towards the opposite mid-point, and stop when you’re standing between something else and another mid-point. Long story short, you find your keys, right at the intersection of ABC, you also learn the geometry lesson from your friend (that all of these lines intersect at the same point). Now, assuming the direction giver didn’t know that all of the lines intersected at the same point, and was literally giving their best way of indicating the point where the keys were, in what sense could it be said that they were saying the same thing as your friend with their more abstract ‘pick any point and…’ direction? If the only resources we have is the physical world, and thoughts, it would seem the thoughts (or sentences) are equivalent. But it seems strongly here that there is a difference.

What differs is the manner in which the thought presents itself, the ‘mode of presentation’. Both the direction giver and your friend are saying the same thing about the same keys being in the same point in space, but they are presenting this fact in two different ways, one more general than the other. The road to them is different. This is not say that one has their idiom and the other has theirs, because separate idioms don’t necessarily imply a different thought, otherwise no one would ever have the same thought (because it seems arbitrary to demarcate — do different accents change the thought?). The difference between the direction giver’s and your friend’s presentations of the point where the keys lay would still be a difference in any idiom, or even language.

Frege (ibid) refers to this ‘mode of presentation’ as sense (Sinn), and argues that it is necessary to account for the difference between statements (and thoughts) like A = A, and A = B. If A and B are in fact equal, then they are just one thing, and whether we use one name or another should (in our simple, common sense ontology) make no difference. But there is, seemingly, an important difference, thus there must be something beyond words and objective things to account for this difference.

At the level of individual names (or phrases that would act as definite names, what Russell called ‘definite descriptions’) there is a sign, that has a referent (often an object), and the sign refers to the referent via a sense, a mode of presentation. The relation here is from many to one: many signs could pick out a single sense (as when a name of a city is translated), and many senses could refer to a single referent (such as ‘17’ and ‘9+8’). At the level of the sentence, the ‘sense’ of a sentence is a ‘thought’, and the reference of this thought is a truth value. Why a truth value? The reasons for this get a little complex, and have to do with the idea of substituting equivalent terms into a sentence. If terms are truly equivalent, then this should not alter what is being denoted by the sentence. But it is possible to perform a series of substitutions that seem to draw the sentence away from one state of affairs onto another, as long as each step renders a true sentence (see the slingshot argument). This means that every true thought has the same reference: the ‘true’.

However, the key point for our purposes is that these ‘thoughts’, the senses of propositions, are necessarily non-subjective. Frege contrasts them to ‘ideas’, which he seems to mean in the empiricist’s sense, as a cluster of past or present sensory data. These, owing to the subjective and private position from which they are engendered, can never be shared. Thus, there are as many ideas as people having them. However, it is important for our consideration of the question of counting thoughts that it was possible for two people to have the same thought, that two people could think or say the same thing. A moments consideration also shows us that if that were not the case, then language could not achieve its inter-subjective function (assuming, of course, with our simple ontology, that sentences express thoughts). A group of people will generally have different ideas that are called up by the name “The Statue of Liberty” (different images and associations); if there is any coincidence between these ideas then this itself would be mere coincidence. However, this myriad of different ideas has no bearing on this group of people being able to grasp that the sentence “The Statue of Liberty is on Liberty Island” is true while the sentence “The Statue of Liberty is on Staten Island” is false. And should there be disagreement about this, then we wouldn’t say that there is a just an insoluble difference of ideas, but rather that some portion of this group were simply wrong, given the senses and objects involved.

This leads Frege to assert that we don’t ‘have’ thoughts as much as ‘apprehend’ them. Sense, though accessible to language, precedes it, and provides it its condition for providing true and false sentences. The Pythagorean theorem is a thought (a sense) that has as its referent ‘the true’ and it sits there whether or not we have ever talked about it, or apprehended its truth. This makes thought sit in a ‘third realm’ between the public, objective, shared world, and the private, subjective world. Not a concrete physical occurrence, nor a pure mental idea, but something that allows the one to communicate with the other, the ‘in virtue of which’ we can encounter each other in language and discuss the world.