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.


I haven’t used Zotero in a couple of years, but I thought I’d revisit it. It’s a great tool for philosophy essay writers.

It’s a free browser plugin (originally for Firefox, but now available for Chrome as well) that helps researchers wrangle bibliographic info in a central location. Once you’ve gathered your references, you can easily include them in Word or OpenOffice with the Zotero word processing plugins.

Check out the official intro video for a nice overview:

Or if you’re old-school, you can actually read about it here.

The Philosopher of the Pool

I ran across this old stereoscopic picture in a random walk through the interwebs just now. Titled “The Philosopher of the Pool”, it got my mind running down lots of interesting tracks as to what could have dubbed this man with so grand a title.

Philosopher of the Pool

The truth is often not as grand as the fictions of the mind. But there are aspects of the truth here that certainly are fascinating. While information regarding this man is scant, I did find this (I’ve bolded what I think is the most interesting paragraph, but the whole story is worth a read):

In the annals of the little town of Pardeeville, picturesquely situated on the Fox River and two lakes, John Merrill, a settler from New Hampshire, who was related to S.S. Merrill, an early resident of Milwaukee, and to Henry Merrill, sutler at Old Fort Winnebago, occupies a conspicuous niche.

In John Merrill’s life were many unique incidents. He had a fair education, was widely read of an ingenious turn of mind, with a bent for natural science. While living in New Hampshire he wrote a book entitled “Cosmogony or Thoughts on Philosophy” which contained a refutation of Isaac Newton’s theory of gravitation. Mr. Merrill contended that the center of the earth consists only of space and that our globe consists is composed of various layers, earth, air, and water in regular order. He held that at each pole there is a large hole, and that into the one at the North Pole the ships of missing Artic explorers sank. He described the agricultural activities of the inhabitants of the interior of our planet and the way in which the sun’s rays reached the region…

Mr. Merrill’s manuscript was polished and copied with pen and ink by a woman resident of Pardeeville and printed in pamphlet form in New Hampshire. Many copies were sold in those early days especially in his native state, where he owned a celebrated nook in the White Mountains called the Pool. It was situated at Franconia Notch, at the foot of Mount Lafayette, in a canyon on the Pemigewasset River. Each summer after settling in Pardeeville he made a trip to his pool, where from tourists he gathered a harvest of dollars for the use of his boats.

Naturally John Merrill did a flourishing business in his books, as well as his boats. He gave lectures on his theory before many famous persons, including a number from abroad, and he wrote a letter to Queen Victoria and sent her a copy of his scientific work.

One eventful day he received what purported to be a reply from the ruler of the British Empire. A copy was made by a printer in New Hampshire and is in the possession of Charles W Merrill of Pardeeville, John Merrill’s grandson. It is yellowed by age. The original is supposed to have been lost or inadvertently destroyed after the death of John Merrill at the home of his daughter in Pardeeville.

The printed copy read as follows:

Royal Despatch of her Majesty to Ho. John Merrill, Flume House NH – Her Seal & N
By Lord Napier British Minister Aerial Mansior
High Picacoddy Royal Ramparts, Thames Tunnel July 4th Anno Domini 1857,Albertus Princeps

To his August Highness Hon John Merrill director of the pool, artic philosopher, practical philanthropist etc, etc

Monsieur: I am commissioned by her most gracious majesty’s royal high butler to communicate to your obsequious highness the most transatlantic compliments of Alid el Kader; and to acknowledge the receipt of your most learned, antiloquent and circumambient state document dated Aug 28, 1854; which has been under profound consideration of the grand lama ever since. The grand lama fully concurs in your new views of the hole in the earth; and believes it was caused by a derangement of the north pole — affected by the scintillations of the hyperborean aurora borealis, which have ” shaken the bark of Sir John Franklin from outside into the inside of the pole,” as you say.

The grand lama takes this opportunity to express to your obsequious highness the great satisfaction which the most grand butler of her majesty feels after the perusal of so learned a document and begs to salute you as a man of transcendental prognostications.

By royal command and my own royal pleasure. Signed in the grand culinary department with a royal goose quill.

By Albert

What could be thought of a document like that? Among the early Pardeevillians it aroused considerable amazement; on the part of some, hilarity. It is left to the reader to guess its source. Although a few unsuspecting individual marveled at the peculiarity of the royal phraseology, it was generally y considered as being the composition of jokesters, who in some way had learned of the sending of the book and letter to Queen Victoria. As to whether the original document showed evidence of having been sent from England, Charles W Merrill is unable to say. He remembers, however, that it bore impressive looking seals and other fancy touches. The supposed reply may have been the production of American college students who heard of the letter to Queen Victoria and who took great pains to make the document resemble an official one from a European monarchy.

In 1888 an eastern newspaper und the caption “The Philosopher of the Pool” printed a complimentary mention of John Merrill with the following letter from him:

Mr. Editor: Please say to my friends that I have retired from The Pool, after being there 34 years, and concluded to spend the rest of my days on the homestead in Pardeeville, Wis. Where I can sit and see the 100 acres of crops almost ready for harvest. Crops never looked better. Give my best and respects to all, till we meet in heaven. I am almost home. This is my eighty-seventh year. Am well, only old age says stay with my children. Yours in love, JOHN MERRILL

The editor adds: Thus after having paddles his skiff so many years, the old philosopher drops his oars with this plaintive strain, and thus too, a rugged landmark, second only in importance to his more aged rival, the “Old Man of the Mountains,” disappears from view.

The author philosopher died in 1892 at the age of 90 years and was buried in the Pardeeville cemetery. On his monument is inscribed a map of our globe, on which he spent so much time and thought. He is remembered as one of the picturesque figures in Wisconsin history.

The Milwaukee Journal Sunday September 23, 1928