Some thinkers, including those in the twentieth-century tradition of Analytical Philosophy, say that Gottlob Frege founded the modern philosophy of language with his 1892 article “Sense and Reference.”² Or more, Frege laid the basis for the application of mathematics, logic, and algorithmic thinking that is the basis of modern computing.³

For an article that is supposed to be foundational, this one is notable for its haziness, and often remarked to be such by the very philosophers of language who deem it foundational.⁴ It is nevertheless a useful starting point for our discussion of the notion of “particular things” or “instantiations,” because it sits in a place where we want to make some distinctions that Frege half makes or fails to make.

Here is our paraphrase of the article, addressing the elemental raw material of meaning upon which we want to start to build our transpositional grammar. There are things in the world to which we may refer – referents. We give them a sense, or a meaning-to-us. The process of making sense, of reference, connects the sense we are making to the thing we are making sense of, a referent.

So, to Frege’s example, there is a bright star in the sky in the evenings that we call the Evening Star. And there is bright star in the morning we call the Morning Star.⁵ The ancients didn’t realize it, nor do people today who don’t know astronomy, but this is the same star. And in another sense it is not even a star. It is the planet Venus. We have the same referent but different senses. The astronomical referrer has added a layer of inferential reasoning to come to their more scientific senses.

When two people speak of Venus, they not only have the same referent; they have also achieved the same sense. Then we might say, using direct quotes, that the bright star in the evening that we sometimes call the “Evening Star” is in fact the planet called “Venus,” which is the same as the “Morning Star.”⁶ By placing these words inside inverted commas, our referents now have become our sense and we are speaking grammatically – to use this word in the broad way we do in this book, as a process of thinking reflectively about the function of our meaning.

Here Frege is talking about exactly the things that interest us for a transpositional grammar, mainly the connection between our externalizable practices of thinking (and to the words “Morning Star,” “Evening Star,” and “Venus,” we also want to add visualizing, and objectifying, and embodying and other meaning forms) and the world to which these meaning-making practices refer. But pushing the analysis beyond this, Frege becomes vague.

Frege calls the elemental unit of reference, the process of making sense of a referent, a “proper name,” a “definite object.”⁷ But, in English proper names (nouns) are capitalized. “The planet” is also a “proper name” for Frege, though not in our regular understanding of this phrase in traditional grammar. In Frege, there is no definition of “proper name,” so its distinction from other semantic units can be based on no more than intuitive recognition of the existence of singularly determinate objects.⁸

Frege encounters several symptomatic problems. He has an “Aristotle” problem, where there can be a number of senses given to this proper name: the student of Plato, the teacher of Alexander the Great, the person born in Stagira, but “so long as the referent remains the same, such variations in sense may be tolerated.”⁹ But tolerability is a very rough and ready measure. Here, Frege is eliding practices that we will later in this part call attribution of quality (studentness, teacherliness, biographical description, and an infinity of such possible attributions) that add meaning to an instantiation, but do not define the instantiation. The word “Aristotle” and his marble bust are both instantiations, before we add however many of their qualities and his.

So, we need not despair of making sense of “Aristotle,” which Frege does to this extent that so many of his senses of the person may be possible: “Comprehensive knowledge of the referent would require us to be able to say immediately whether every given sense belongs to it. To such knowledge we never attain.” In a transpositional grammar, the specifiability of a singular referent is not to be confused with the infinite range of describable qualities that might be attributed to that referent.

Then, Frege has an “Odysseus” problem. The sentence “Odysseus was set ashore in Ithaca while sound asleep,” has no reference.¹⁰ Homer or his people (we may presume) made it up. However, this highlights something for us about human design. We can conjecture possibilities in the form of referents that may later be discovered to exist (the elementary Higgs Boson particle for instance¹¹), or we may fail to find them because they don’t exist or we can’t find them. Or we can imagine things that may be fictional, or half-fictional in the nice way that fictions are always part-true in their characteristic manner of indirectness. Such modes of reference should not give us trouble. In fact, these varied modulations of reference can be specified in our transpositional grammar as ontology.^§MS3.1

Next, Frege has a fundamental problem with something variously translated from his German as “identity” or “equality.”¹² This is the opening sentence of his now-famous article: “Identity gives rise to some challenging questions which are not altogether easy to answer.” At the end of this sentence, a footnote points to this: “I use this word strictly and understand ‘a=b’ to have the sense of ‘a is the same as b’ or ‘a and b coincide’.”¹³ Evening Star/Morning Star; “a” can be substituted for “b.” Venus can substitute for both. “What else,” he asks, “but the truth value could be found, that belongs quite generally to every sentence concerned with the referents of its components and remains unchanged by substitutions of the kind in question?”¹⁴

We can see two transpositions here, but we are not sure Frege can: one is sense for referent, the thing you see in the sky with one of these three names for it; and the other is sense for sense, or one word for another. But none of these transpositions is ever a matter of identity or equality. Different senses reflect different frames of reference, and in the case of the two stars versus the planet, profoundly so.

And the thing you see in the sky is not in any sense the same as the word. The perceptible thing has a visual and spatial meaning, and the word a spoken or written meaning. Nor is it just the word that is the meaning. Both are acts of meaning, seeing and speaking. Acts of meaning transposition are different in their processes and meaningful effects. We may trace genealogies that account for the similarities in the design process that makes for transposition, but the source and the meaning transposed to another destination are never the same.

And another major problem for us in Frege: what is the difference between the “sense” of his “proper name” and the sense that defines a concept? He issues a “warning against apparent proper names having no referents” because “this leads to demagogic abuse … ‘The will of the people’ can serve as an example; for at any rate there is no generally accepted referent for this expression.”¹⁵ However, herein lies a fundamental difficulty – “the will of the people” is a concept, not a proper name.

Of course, “the will of the people” as a general concept is always deserving of considerable qualification, in every moment of its specification, as well as the generality of the process. Here is a sentence we have just made up: “The will of the people was expressed in the German Election of 1933.” What to make now of this “proper name”? Frege mixes two things where we want to make a fundamental distinction. We will name this as the distinction between an “instance” and a “concept.”

On these (it seems) shaky foundations, Frege builds an elaborate logical-mathematical superstructure of inference and truth conditions so things like planets and stars can get sorted. This superstructure is designed to be capable of inferential reasoning that will address “truth values.”

A very short version of the story that follows runs like this: Frege builds a logical-mathematical edifice in his monumental two-volume Basic Laws of Arithmetic. Bertrand Russell writes him a letter, pointing out that his system is radically incomplete.¹⁶ Frege acknowledges this, in an appendix to his Volume 2. “Hardly anything more unfortunate can befall a scientific writer than to have one of the foundations of his edifice shaken after the work is finished. This was the position I was placed in by a letter of Mr. Bertrand Russell, just when the printing of this volume was nearing its completion.”¹⁷ Then, with Alfred North Whitehead, Russell constructs a three-volume monument, Principia Mathematica, famously proving after 362 pages that 1 + 1 = 2.¹⁸ In 1931, Kurt Gödel demonstrates that their mathematical/logical system is also radically incomplete, and perhaps that all such systems must always be incomplete.¹⁹ The paths to transposition are not straightforward, even in their mechanical extension through the rule-based equivalences of logic and mathematics.

Frege was by reputation an austere person, a mechanic of reason who did not give much away about his personal views and life. He taught Gershom Scholem, who became a scholar of Jewish mysticism, and was a close friend of Walter Benjamin. Frege’s most significant translator and interlocutor into the world of Anglophone academe was Jean van Heijenoort, former Soviet leader Leon Trotsky’s bodyguard, secretary, editor, and translator in the years of his exile from 1932 to 1939, and one of artist Freda Kahlo’s lovers.²⁰

Another great Frege exegete was Analytical Philosopher and anti-racism activist Michael Dummett. Late in his career, Dummett discovered Frege’s diary which shows him “to have been a man of extreme right-wing political opinions, bitterly opposed to the parliamentary system, democrats, liberals, Catholics, the French, and above all, Jews, who he thought ought to be deprived of political rights and, preferably, expelled from Germany. When I first read that diary … I was deeply shocked, because I revered Frege as an absolutely rational man, if, perhaps a not very likeable one.”²¹

Scholem and van Heijenoort may never have come to know Frege in the sense Dummett came to know him. But the context of his meaning does help us with Frege’s sense of “the will of the people.”

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² Gottlob Frege, 1892 [1948], “Sense and Reference,” The Philosophical Review 57(3):209–30.

³ Jean-Luc Chabert, ed., 1994 [1999], A History of Algorithms, translated by C. Weeks, Berlin, Germany: Springer, p. 455.

⁴ Colin McGinn, 2015b, Philosophy of Language: The Classics Explained, Cambridge, MA: MIT Press, pp. 5–18; Michael Dummett, 1973, Frege: Philosophy of Language, New York, NY: Harper and Row; John McDowell, 1977, “On the Sense and Reference of a Proper Name,” Mind LXXXVI(342):159–85; Mark Textor, 2011, Frege on Sense and Reference, London, UK: Routledge, pp. 103ff.

⁵ Gottlob Frege, 1892 [1948], “Sense and Reference,” The Philosophical Review 57(3):209–30, pp. 212, 215.

⁶ Ibid., p. 211.

⁷ Ibid., p. 210.

⁸ Michael Dummett, 1973, Frege: Philosophy of Language, New York, NY: Harper and Row, pp. 54–55.

⁹ Gottlob Frege, 1892 [1948], “Sense and Reference,” The Philosophical Review 57(3):209–30, p. 210.

¹⁰ Ibid., p. 215.

¹¹ http://www.sciencealert.com/cern-discovers-higgs-like-particle

¹² Susanna Schellenberg, 2012, “Sameness of Fregean Sense,” Synthese 189(1):163–75.

¹³ Gottlob Frege, 1892 [1948], “Sense and Reference,” The Philosophical Review 57(3):209–30, p. 209.

¹⁴ Ibid., p. 217.

¹⁵ Ibid., p. 222.

¹⁶ Robert Brandom, 1994, Making It Explicit: Reasoning, Representing and Discursive Commitment, Cambridge, MA: Harvard University Press, pp. 436–37.

¹⁷ Gottlob Frege, 1893/1903 [2016], Basic Laws of Arithmetic, Oxford, UK: Oxford University Press.

¹⁸ Alfred North Whitehead and Bertrand Russell 1910/1912/1913 [1927], Principia Mathematica, Cambridge, UK: Cambridge University Press, Volume 1, p. 362.

¹⁹ Kurt Gödel, 1931 [1962], On Formally Undecidable Propositions of Principia Mathematica and Related Systems, Volume 38, translated by B. Meltzer, New York, NY: Basic Books.

²⁰ Anita Burdham Feferman, 1993, From Trotsky to Gödel: The Life of Jean Van Heijenoort, Natick, MA: A.K. Peters; Jean van Heijenoort, 1978, With Trotsky in Exile: From Prinkipo to Coyoacán, Cambridge, MA: Harvard University Press.

²¹ Michael Dummett, 1973, Frege: Philosophy of Language, New York, NY: Harper and Row, p. xii.

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Cope, Bill, and Mary Kalantzis. 2020. Making Sense: Reference, Agency and Structure in a Grammar of Multimodal Meaning. Cambridge UK: Cambridge University Press, pp. 79-83. https://doi.org/10.1017/9781316459645

Gottlob Frege’s "Sense and Reference" §MS1a