Frege Was From Venus

If you spend any time mucking around in the philosophy of language, you’re going to run headlong into Gottlob Frege at some point. Frege, round about the turn of the 20th century, was a key figure in the emerging fields of logic and the philosophy of mathematics, but he may well be best remembered for his contributions to the theory of meaning.

What is Meaning?

The basic question that any philosophy of language must address is this: What can we say about the meaning of a word (and — what perhaps amounts to the same thing — the meaning of a sentence)?

A first stab at analyzing this is to say that the meaning of a word is just what it points to — what it designates or refers to. For instance, the word (or name, in this case) “Herbie” refers to my cat, Herbie. (Make sure to get your head around the difference between a word and an object referred to by that word. We’ll have a post about this “use/mention” distinction soon. For now, just stay alert to the use of quotation marks to distinguish a word from its associated object.) The word “Herbie” points to the creature that is at the time of this writing tapping my leg with his paw, trying to get me to play with him. (I’ll be right back…)

Reference - Herbie

We can apply the same analysis to numbers. The ink-on-paper numeral “7” that you might write down in your checkbook or on a math test, refers to the actual number 7, which for the sake of argument we’ll take to be some object out there in the universe somewhere. Similarly, and perhaps easier to comprehend, the words “seven”, “siete”, “sept”, and “sieben” all refer to the number 7 as well (in English, Spanish, French, and German, respectively).

Reference 7

If this is the right picture, it would give us a convenient way to explain how “seven” and “siete” both mean the same thing: It’s because both words refer to the same thing.

Reference Ain’t Enough

If this were all there is to meaning, then “12” and “7 + 5” would mean the same thing, because they both refer to the number 12.

But as Kant famously pointed out (in his analytic/synthetic, a priori/a posteriori distinctions), these two words/phrases might well mean different things.

To see why, let’s look at the following statement: “12 = 12”.

Compare that with this statement: “7 + 5 = 12”.

The first statement doesn’t say much except that a thing is always identical with itself. The second says something significantly new about 12 (that it’s the sum of 7 and 5).

If this is true, then “12” and “7 + 5” do not have the same meaning; and if this is the case, then there has to be more to meaning than the idea of reference. You can see this difference more clearly if you look at these in a different context.

“I know that 12 = 12.” One can know this without knowing anything about addition.

“I know that 7 + 5 = 12.” To know this, one has to know something about addition.

This becomes even clearer with a more complex mathematical fact.

“I know that 812,285,952 = 812,285,952.”

“I know that 24,789 x 32,768 = 812,285,952.”

Anyone can utter the first sentence without any more knowledge than ‘everything is equal to itself’. But to say the second sentence with any sort of certainty, you’d have to have done some complex calculations (or had a calculator do them for you). There’s something about the second statement that is differently meaningful than the first.

The Morning Star and The Evening Star

The more usual example philosophers of language use is (happily for most of you) not mathematical.

The ancient Greeks, looking at the dark sky above them, noticed two very bright stars. One came up shortly after the sun went down in the evening, and was brighter than any other star around it; the other star came up shortly before the sun came up in the morning and was similarly bright. They named these two stars: “The Morning Star” and “The Evening Star”.

Well, maybe you saw this coming, but it turns out that these two stars were actually the same object: Venus. (Of course, not even a star after all, but a brightly reflective planet.) So here’s the referential picture the ancient Greeks had:

Morning Star / Evening Star Greeks

A few centuries later, astronomers gave us this picture instead:

Reference Venus

Now, if reference is all there is to meaning, then these two sentences would have the same meaning:

“The Morning Star is the Morning Star.”

“The Morning Star is the Evening Star.”

Because by just considering reference those two sentences translate to this one sentence:

“Venus is Venus.”

Reference Sentences

But clearly these sentences have very different meanings — the first sentence is obvious to anyone, even those without any knowledge of astronomy; the second sentence is something that one would only know by virtue of synthesizing some significant piece of astronomical knowledge, namely that “The Morning Star” and “The Evening Star” both refer to the same heavenly body: Venus.

Frege’s Solution

So hopefully you’ll agree that reference can’t be all there is to meaning.

Frege’s idea was that while reference is important to meaning, there is another important dimension to meaning as well, which he called sense. He called the sense of a term the “mode of presentation” of the referent. So while “the Morning Star” and “the Evening Star” both refer to the same thing, they have different senses: the sense of “the Morning Star” is something like “the bright star that rises in the early morning”, while the sense of “the Evening Star” is something like “the bright star that rises in the early evening”. Same reference; different sense.

On this scheme, when we say “the Morning Star is the Evening Star”, we’re comparing senses, not references, and this is why it’s a statement of new knowledge (synthetic, a la Kant) and not just an obvious truth (analytic, a la Kant). “The Morning Star is the Morning Star” is comparing two things that not only have the same references, but the same senses. And this is semantically not interesting.

Sense Without Reference

One interesting consequence of Frege’s philosophy of language is that it turns out that not everything with a sense has a reference.

“The novel written by Richard Nixon” has a sense — it presents an idea to us in a clearly understandable way — but has no reference — Nixon never (as far as I know) actually wrote a novel. So in fact the meaning of a sentence might not have to rely at all on reference. “The novel written by Richard Nixon is long and boring” has a meaning even though the subject of the sentence doesn’t exist. We’ll take up this interesting idea in a future post.

What is True Depends on What is the Truth

This is a follow-up to Alec’s nicely written post on realism and its varieties. I put forth in the comments section the idea that what one believes to be the case with regards to realism v. anti-realism is going to color what one takes to be true in the world. Or, at the very least, what one considers to be a candidate of truth in the world. Here is why that is (and note that this is not merely my opinion, but is an established line of argument and belief among metaphysicians).

Realism, as Alec eloquently stated, is the view that the world is a particular way in a mind-independent fashion. Anti-realism is the view that the world is mind-dependent, and so derives many, perhaps all, of its features because of how it is perceived. Those are very quick takes on the two views and should not be satisfactory in and of themselves to anyone. Again, I refer you to Alec’s post.

Depending on which of the views you hold, your idea of what is true (or at least what you believe to be true) need not change, but what makes something true (its truth conditions) does change. Why might this be? First, let’s talk about the common sense view of truth.

Suppose a person makes the following utterance, “snow is white.” That utterance has a truth value. It is true if snow is white, and it is false if snow is any color other than white. How do we go about determining if it is true? Well, we go and look at snow. “Look”, you might say, if you live somewhere other than NYC or Chicago, “there is some snow, and it is white.” Hurray! We have verified its truth status. Or, dum dum dum, have we?

If you are a realist, you think that there are properties in the world that we can discover. This does not just mean that we can encounter snow, but that when we encounter snow, we can learn something about it, such as it being cold, malleable, crunchy, and white. If those are characteristics that we cannot discover or encounter, there is no way we can determine the truth value of any statements that make reference to such characteristics. The utterance, “snow is white”, is true only if snow is actually white. We laugh at a child who says, “snow is brown” because we know that snow is not brown (even in NYC, snow is white until it hits the dirty, dirty ground there). This is called the correspondence theory of truth. An utterance is true if it corresponds with what is actually the case in reality. “My keys are in the bowl by the door” is only true if my keys are in the bowl that is by the door. If they are in a dish, if they are in the kitchen, if I have no keys at all, the utterance is false because it does not correspond with how things actually are in reality. Hopefully you can see why a realist is drawn to the correspondence theory (though the two are not necessarily conjoined).

But I suspect you can also see why the anti-realist is not going to favor a correspondence theory of truth. For the anti-realist, most of what we believe to be the case about the world is due to how our minds project or create certain features or characteristics of what we perceive. For the anti-realist, the utterance of “snow is white” is expressing an opinion since there is no objective characteristic of ‘white’ in the world; there is only the experience that I refer to as ‘being white’. Whiteness, then, is a mind-dependent characteristic. It exists only because our minds create it. What does that do to the truth value of the utterance then? Well, as there is no objective reality to compare the utterance to, we cannot rely on the correspondence theory. Even if there were an actual characteristic of being white in the world, how could we ever know what that characteristic was like when our perceptions are so unreliable? And yet, the anti-realist does not want to say that there is no such thing as truth. Instead, what determines truth is something different from correspondence. It is called the coherence theory of truth. For the anti-realist (for many of them, at least), our mind-dependent experiences build up a large collection of beliefs about what we think the world is like. Since we cannot say what the world is actually like, we judge truth based on how well an utterance coheres (fits in) with our collection of beliefs. We want our collection of beliefs to be as coherent as possible. Note that coherence here does not merely mean understandable or rational, it means something larger: that our collection of beliefs not contain contradictions. We do not want to believe that we are both standing in the rain and we are not standing in the rain. We do not want to believe that snow is white together with snow is not white. (Of course, we can believe variations of those, but the contradictions are smoothed away by adding unspoken caveats to the utterance. For example, “snow is white” need not contradict “snow is not white” if we have the unspoken belief that the second utterance is about NYC snow which is changed or altered snow. “I am standing the rain” need not contradict “I am not standing in the rain” so long as we have the unspoken belief that I am standing beneath an umbrella which means that I am in the rain without being rained upon.)

Truth and Language
This can quickly become an issue of semantics or philosophy of language and so worth another, different post. Briefly, though, we know what we mean when we say what we do. When I point at snow and say, “snow is brown”, I do not literally mean that I believe snow is brown. Instead, I mean that snow, in such and such a state or condition (whatever condition is present, perhaps), is brown. If someone, maybe Alec, who knows, were to ask me, “do you mean to say that you think snow is brown?” I can honestly and reasonably say, “That is not what I meant when I said, ‘snow is brown.’ I meant that the snow here is brown, by which I meant to say, this is some really dirty snow.’” There is the demonstratrive sense of the utterance, by which I point and so indicate a particular batch of snow. Think of the old example about eskimos having eighteen different words for snow. That is a ridiculous example, I think, meant to suggest that eskimos like snow so much they talk about it a lot. But guess what? We non-eskimos have lots of different words for snow too: snow, wet snow, dry snow, soft snow, heavy snow, light snow, sleet, hail, etc. Wait a minute, you might exclaim, those are just the word ‘snow’ with an adjective in front of it. Yep — many of our words are like that. In fact, many words are like that: compound concepts captured in one word. What does ‘slush’ mean, if not icy rain? What is ‘beautiful’ aside from ‘pretty’ preceded by some number of ‘very’s?

Back to the topics at hand though, for an utterance to be true for the anti-realist, then, just means that the utterance fits in with my already accepted beliefs. “Snow is white” is true if what I call ‘snow’ is associated with the characteristic that I call ‘white’, and it means nothing beyond that. So, which theory of truth is correct? The realist theory is not correct, as there is no way to verify if what we have said actually corresponds with what is actually the case in the world. There is the experience I have whenever I come across a sensation that I label ‘white’, but why think that particular experience matches up with the way the world truly is? Perhaps I am color blind. Perhaps I am hallucinating. But you are not, the realist might contend. But how do you know that I am not? Can you prove that you are sensing the world as it actually is? If you could, there would be no anti-realist camp.

The anti-realist theory is not true either though, at least not obviously so. Coherence is an important attribute for any system of beliefs. For any system of beliefs, we want there to be as few outright contradictions as possible. Yet, why think that coherence alone is enough to establish truth? Someone who is schizophrenic or just simply insane might have a very coherent view of their experiences, but it only seems coherent to them because they are crazy. The schizophrenic person believes he hears voices separate from his own; he may even believe he sees people talking to him. We consider him sick though, because he is experiencing what no one else is or can. We say that the schizophrenic is wrong, not because his beliefs are not coherent, since many of them are (perhaps even as many of his beliefs cohere as do our own), but because he has beliefs that do not correspond to reality, to what we think is actually true. A claim, by the way, the schizophrenic will agree with once he is on successful medication.

What is the upshot of all this? Well, the realist maintains that our intuitive conception of truth is based on correspondence, not coherence, and the anti-realist maintains that we can never know whether our beliefs correspond with anything external to the mind, but that we can determine if our beliefs cohere with one another. Which you favor seemingly depends on what you think is real (though, to be fair, some suggest that what you think is real depends on what you think makes something true). However, it more often depends on what you think you justify as being true. That, however, has to do with straight up epistemology, and so must wait for another post.