Scientific Knowledge -- Analysis of Fregean vs Russelian accounts based on the Principle of Compositionality

Final Paper for Philosophy of Language Class

Introduction

Analytic Philosophers in the late 19th and early 20th centuries were deeply concerned with the exploration of sentences expressing propositions that lead to scientific knowledge. Perhaps rightfully so, for most of the renowned philosophers from the time including Frege and Russell were both logicians and mathematicians as well. Even with the passage of time, the questions they pondered on are still relevant today: How do we differentiate between sentences that contribute to scientific knowledge and sentences that do not?

In this paper, I will focus on certain types of sentences, ones that refer to entities that do not exist, like “Harry Potter” or “a unicorn.” These kinds of sentences, as we will see, force us to understand and analyze them through multiple layers of analysis, and perspectives. The complexities in these sentences will be analyzed using competing theories by Frege and Russell. While Frege and Russell both present a basis to define sentences that express propositions leading to scientific knowledge, their accounts are fundamentally different. In this paper, the accounts will first be carefully laid down and then assessed in terms of a principle called “The Principle of Compositionality.” Ultimately, this paper argues the following: Sentences like “Harry Potter flew in a broomstick” that involve propositions about non-existing referents are challenges to scientific knowledge, and while Russell and Frege both give different and competing cognitive accounts of such sentences(“false”, and “lacks truth value” respectively), Frege provides a better solution to the problem by upholding the principle of compositionality.

Sentences Leading to Scientific Knowledge

Before we start, I would like to acquaint the readers with the project that this paper is interested in. The project of this paper is the analysis of what Frege and Russell were concerned about in the analysis of truth. Both Frege and Russell heavily focus their analysis of truth on scientific knowledge. Frege (1892, p. 63) states, “The question of truth would cause us to abandon aesthetic delight for an attitude of scientific investigation.” In “Thought: A Logical Inquiry” (1918, p. 289), he argues that while it is the task of science to discover truth, the kind of logical inquiry he is interested in is to discern laws of such truth. Russell then follows on, along and after Frege, in multiple papers (1905, 1917, 1919) taking upon the responsibility of considering what it is that we know. In this paper, we are concerned about a similar investigation based on arguments presented by Frege and Russell. Just like Frege and Russell, we are interested in defining sentences that express propositions that lead us to scientific knowledge.

For the same project, Frege makes an important distinction between thoughts and ideas. Frege (1918, p. 292) defines thought as something for which the question of truth arises. He then describes ideas to be the product of the inner world of sense impressions, imaginations, sensations, feelings, and wishes (ibid., 299). While ideas are members of our inner world, the outer world being made up of physical materials, Frege designates thoughts to a third realm (ibid., 299). For Frege, thoughts need no bearer to the contents of the consciousness to belong (ibid.). All this points to a desire to define knowledge objectively and scientifically, irrespective of subjective opinions, feelings, or collectively “ideas”, people might have about the world. Given that Russell was an active interlocutor with Frege in the debate, we can safely assume that the context that the discourse was happening in also involved the analysis of sentences leading to scientific knowledge.

Scientific knowledge involves justification through scientific theories. Such scientific theories, being the product of language, involve sentences. To account for the meaning of these sentences, we require a methodological principle to avoid ambiguity and proper acquaintance with scientific knowledge. One such methodological principle is the Principle of Compositionality(PoC). PoC (2022), can be defined as the following: “The meaning of a complex expression is determined by its structure and the meanings of its constituents.” In simple terms, the PoC states that the meaning of a whole expression is determined by the meaning of its parts. I would like to argue that this principle is particularly helpful in the context of scientific knowledge we are seeking to explore. With the PoC in hand, we have two advantages. First, we have a way of building large sentences effectively. We can mean what we want to express using small building blocks that are all agreed upon by the scientific community. Second, as interlocutors, we can easily understand what large sentences mean by breaking the large sentences into small constituents and adding up their meanings. Formal logic is an excellent demonstration of how using the PoC can help us communicate effectively. In formal logic, the truth value of the whole sentence is a function of the truth value of its parts. With this, I want to convince the reader that the PoC as a principle is of utmost importance to the project at hand, i.e., defining sentences expressing propositions that lead to scientific knowledge.

Challenges to Scientific Knowledge and accounts for the challenge

We now move on to discuss what needs to be accounted for by any theory that properly solves the project under discussion. Let us take an example of such a sentence that needs to be accounted for before we discuss the specifics:

P: “Harry Potter flew in a broomstick”

Note that I will be using P in the place of “Harry Potter flew in a broomstick” throughout the paper. From a scientific standpoint, the sentence P clearly cannot be true. It is because Harry Potter is a fictional character and it does not exist. With Frege, we are concerned with scientific knowledge through thoughts expressed using sentences. A sentence involving a fictional character cannot be true in the context of our project since we are concerned about the scientific investigation of the world. For our example, Harry Potter cannot fly, as it doesn’t exist in a scientific sense, and therefore P cannot amount to truth. Logically speaking, P has to be either false or it should lack any truth value. This fact needs to be accounted for by any theory that aims at attempting the project under discussion.

Frege tackles this project using his idea of sense and reference. For Frege, the sense of an expression is a part of thought that has cognitive value or mode of presentation associated with that expression (1914, p.44 & 1892, p.57). Reference is then, the entity about which something is being said (ibid.). For example, when we say, “Sylvia Plath wrote dark poems”, and “The author of “The Bell Jar” wrote dark poems”, the subject is the same and thus we are referring to the same entity i.e., Sylvia. However, since the mode of presentation is different (Sylvia vs The author of “The Bell Jar”), what is different for Frege is their senses. When we focus exclusively on proper names, Frege would then define names to be signs, both complex or simple, that express a sense which purports to determine a definite object (1892, p.57). What we are first interested in here is how Frege deals with expressions like “Harry Potter”. Since “Harry Potter” purports to determine a definite object, Frege would allow us to call it a proper name. However, he has a special distinction for those proper names that purport but fail to determine a definite object (1892, p.62). They are commonly referred to as empty names. On a sentence level, Frege postulates that the sense of a sentence is the thought or the proposition it expresses. The reference of the sentence is then the truth value of the proposition it expresses (ibid, p.63).

Now, we can apply the methodological principle i.e., the PoC we laid out earlier to analyze the account of Frege for our example sentence P. In a Fregean account, both the sense of a sentence and the reference of a sentence can be analyzed using the PoC. Thus for P, since every component has its sense (mode of presentation), the sentence as a whole has a sense as well. The sense of P is the proposition expressed by P. Things take an interesting turn as soon as we enter the realm of referents. In P, “Harry Potter” is an empty name as it doesn’t have any reference in the outer world. Now, using PoC, if one of the constituents of an expression doesn’t have a reference, the whole expression cannot have a reference (The reference of the whole is a function of the reference of the parts). Hence, the sentence P as a whole doesn’t have a reference as well. Since the reference of a sentence is its truth value, sentence P doesn’t have any truth value. This is how Frege accounts for the fact that P cannot be true.

Next, we move on to Russell’s analysis of the same problem. Russell defines a name to be a simple symbol whose meaning can only occur as a subject and that denotes something (1919, p.50). A proper name would then be a name that denotes a particular individual. For Russell, an expression like “The author of The Bell Jar” would not count as a name, as it is divisible. Furthermore, in our sentence P, “Harry Potter” would not count as a name, as it does not denote a particular individual. He calls such expressions definite descriptions. And Russell posits that sentences containing definite descriptions should be understood in their existential form (ibid., p.53). For the sake of simplicity, let us take an example, “The A is B”. Here, let us suppose that “The A” is a definite description. Then for Russell, the logical form of the sentence would vaguely resemble the following: There is one and only entity called A, and something that is A is B. This logical form can be seen as a function, referred to as a propositional function (1919, p.53). This function takes any value as an input, and if the function is satisfied returns “true” as output, and if the function is not satisfied returns “false” as its output. For clarity, let us check how Russell’s idea of propositional function deals with our sentence P. In Russell’s analysis, sentence P can be roughly analyzed as the following: There exists a one and only entity called Harry Potter and the entity flew in a broomstick. Now, since an entity called Harry Potter does not exist, the function returns the value “false”. This is how Russell accounts for the fact that P cannot be true.

It is now clear how Frege and Russell attempt and, to a reasonable degree, succeed at solving the challenge at hand. The sentence P could not be true for our project, and while Frege showed that it lacks truth value, Russell showed that it is merely false.

Analysis of Fregean and Russellian Account

We now focus this part of the paper on analyzing both the accounts we briefly laid out in the earlier section. At the end of this section, I intend to convince the reader that based on what has been built until now, the Fregean account is a comparatively better solution to the project in hand than the Russellian account.

Firstly, let us analyze why the Russellian account of the sentence P is a problematic one. Russell points out that a proposition gets its truth value after its propositional function spits out a truth value when an input is inserted into the function. For example, in the sentence P, the propositional function would be of the form: There exists one and only entity called Harry Potter, and that entity flew in a broomstick. Since no entity satisfies the function, the function returns “false” as its output. For Russell, the definite description “Harry Potter” in itself, however, does not have meaning. Russell (1905, p.480) states, “This is the principle of the theory of denoting I wish to advocate: that denoting phrases never have any meaning in themselves, but that every proposition in whose verbal expression they occur has a meaning.” Here, by “denoting phrases” Russell refers to both definite and indefinite descriptions. So, for Russell, a proposition gets its meaning only after the propositional function is inserted with an input value. And a denoting phrase in the proposition acts only to give the propositional condition its logical form. “Harry Potter” in P acts only as to denote the condition that one and only entity called Harry Potter exists, and that condition can be evaluated only when the whole proposition is expressed. Russell (1905, p. 481), gives a similar example. “I met a man” can be analyzed as “I met x, and x is human.” Russell(ibid.) then states the following, “This leaves “a man” by itself, wholly destitute of meaning, but gives meaning to every proposition in which verbal expression “a man” occurs.” So, for Russell, even a description that denotes the existence of an actual referent, like a “man”, does not have a meaning. Since we are talking about the expression “Harry Potter”, which does not even have a referent, it is clear that “Harry Potter” doesn’t have a meaning in P. However, as we discussed earlier, Russellian analysis leads us to conclude that the sentence P, as a whole though, does have a meaning and is false. Now, I would like to point out that this is contradictory to the general spirit of the PoC. According to the PoC, we cannot have a sentence have its meaning if one of its components does not have meaning, as the meaning of the whole is a function of the meaning of its parts. Russellian account of P breaks the spirit of the PoC. I would like to remind the readers that upholding the PoC was one of the crucial parameters we set out at the onset of this paper.

Now, on the other hand, the Fregean account is itself built in the spirit of the PoC. In sentence P, since one component, “Harry Potter”, does not have a reference, the entire sentence does not have a reference as well and therefore lacks any truth value. We have already discussed in length about the Fregean account in relation to the PoC in the earlier section.

The question we are interested in asking at the crux of these analyses is the following: Which account gives us a better worldview at defining sentences that express propositions leading to scientific knowledge? To answer this question, let us analyze Russell’s account a little further. With Russell’s account, we can assign a truth value, i.e., false, to statements like P, which have non-existent referents. So, if I utter a similar statement, “I saw a unicorn”, a Russellian analysis would vaguely be the following: I saw an entity X that exists, and X is a horse, and X has one horn(keeping the object of the sentence at the focus of the analysis). Now, since no existing “X” can satisfy the logical form expressed by the sentence, Russell would tell us that the sentence is false. And that resonates a lot with what we would intuitively think the truth value should be. Since I did not see a unicorn, a sentence like “I saw a unicorn” makes most sense to be false because a unicorn does not exist. Even intuitively speaking outside of the Russellian realm, “I saw a unicorn” makes an existential claim, i.e., it must exist for us to see it. Russell’s heavily existential-based logical form does justice to our intuition. Turning to Frege, Frege would say that the sentence “I saw a unicorn” does not have a reference, and thus it lacks any truth value, as we discussed earlier. Now, this might come up as unintuitive, and even unacceptable for some readers. Some might wonder, how is it worth defending a theory if it cannot even assert false to a sentence like “I saw a unicorn” when clearly no unicorn exists?

I would like to push back on such questions and try to remind the readers that while Russell does give us a way to assert “false” as a truth value to sentences like P and “I saw a unicorn”, it does so at the cost of PoC, which we took as a fundamental basis for scientific knowledge. On the other hand, Frege, while does not give us as intuitive of an ability to determine the truth value by concluding that such sentences lack truth value, he encodes the PoC at the center of this account. I hope the readers can now see the two sides that the particular discourse in this paper hinges upon. On one side, we have a Russellian account which violates the PoC yet gives us a way to assert “false” to statements like “I saw a unicorn”, which is more intuitive in this particular case. On the other hand, we have a Fregean account that preserves the PoC while giving a slightly unintuitive assessment of the truth value of such sentences. Both sides of the discourse have their strengths and weaknesses. First, I argue that the strength of the Fregean account clearly outweighs the strength of the Russellian account. In the same argument, I aim to show that the weakness of the Fregean account is not particularly relevant to the premise of this paper and it does not affect the merit of the account.

The Fregean account’s strength is the preservation of the PoC. Since we took the PoC as the basis for judging the sentences that express propositions leading to scientific knowledge, the Fregean account is clearly meritorious in this regard in comparison with the Russellian account. The strength of the Russellian account that we have identified for sentences like P is that it helps us assert “false” to sentences like P. Since we are aiming for scientific knowledge, I would like to argue that the distinction between “false” and “lacks truth value” is not as important as long as we are asserting “truth” to propositions expressed by true statements. As I mentioned at the onset of the paper, sentences like P are challenges that need to be accounted for by any meritorious account. Sentences like P cannot be true. Now, whether they are designated “false” or “lacks truth value” is not so important, as long as they are not designated the truth value “true”. The primary purpose of the project is to help us define sentences and classify them based on whether they can or can not lead to scientific knowledge. What we assign to the sentences that do not lead to scientific knowledge then turns out to be a matter of convention/taste for the project. Russell does give us a theory with better taste, for it also matches our intuition to assert “false” to sentences like “I saw a unicorn”. Russell (1905, p. 482) himself asserts the following regarding Frege’s account: “But this procedure, though it may not lead to actual logical error, is plainly artificial, and does not give an exact analysis of the matter.” But the cost it takes for Russell to reach the non-artificial solution breaks the fundamental basis the project was built upon. Frege might have given us a less tasteful account, but it holds the most fundamental pillar of the project: the PoC. I want to again remind the readers, with the risk of being redundant, that the PoC is crucial for the scientific method, as it is a methodological principle and helps us both form large sentences and understand large sentences. It is of no wonder then that this paper argues that the Fregean account clearly outweighs the Russellian account of the problem at hand.

Possible Objections and Conclusion

With the argument tabled and presented, there can be a few objections to the thesis of this paper. One such objection I can see is the over-reliance of the paper on the necessity of the sentences to follow the PoC. Some might even argue that there could be cases where PoC might hinder us from getting to sentences that might have led us to scientific knowledge. For example, tachyons are hypothetical particles in Physics that can travel faster than the speed of light. With Fregean analysis and PoC applied, any sentence involving “tachyons” lacks truth value. That might be limiting for certain readers. However, I would like to argue that instead of being limiting, the Fregean analysis paired with the PoC underscores the importance of empirical evidence and observation. Furthermore, the PoC is fundamentally helpful in forming those hypotheses effectively in the first place. Scientific knowledge then can be attained after empirical evidence is found on these hypotheses that initially lack any truth value. So, the thesis stands unweathered by such an objection.

To conclude, the challenge we started with at the beginning of the paper was to define sentences that expressed propositions leading to scientific knowledge. We were particularly interested in sentences like “Harry Potter flew in a broomstick” which involve propositions about non-existing referents. We laid out that the PoC was a fundamental basis for judging any account that can classify our example sentence in any other cognitive basis of truth value other than “true”. We then discussed and analyzed the Fregean and Russellian accounts, and since the Fregean account upholds the PoC while the Russelian account doesn’t, we concluded that the Fregean account is a better solution to the project. Further discourses on the matter might involve questions like whether there could be other methodological principles than the PoC that can lead us to scientific knowledge more tastefully than the Fregean account, but with the preservation of the principle, unlike Russell.

References:

Bertrand Russell (1905): “On denoting”. Mind, Vol. 14, No. 56, pp. 479-493

Bertrand Russell (1917) “Knowledge by acquaintance and knowledge by description”, Proceedings of the Aristotelian Society, 1910-1911. Reprinted in his Mysticism and Logic (London: George Allen & Unwin Ltd.: 1917). Reprinted then in Totowa, New Jersey: Barnes & Noble Books, 1951, pp. 152-167.

Bertrand Russell [1919] (1993) “Descriptions”. An extract from Chapter XVI of his Introduction to Mathematical Philosophy. London: Allen & Unwin. Reprinted in A.W. Moore, (ed.), Meaning and Reference, Oxford University Press, pp. 46-55.

Gottlob Frege [1892] (1952): “On sense and reference.” In Translations from the Philosophical Writings of Gottlob Frege. P. Geach and M Black (eds.) M. Black (trans.) Blackwell Publishing, pp. 56-78.

Gottlob Frege [1914] (1993) “Letter to Jourdain”. An extract from an un- dated letter, published in Frege’s Philosophical and Mathematical Correspondence, Gottfried Gabriel, Hans Hermes, Friedrich Kanbartel, Christian Thiel, and Albert Veraart (eds.), abridged for the English edn. by Brian McGuiness, and trans. Hans Kaal, Oxford, Blackwell, 1980. Reprinted in A.W. Moore, (ed.) Meaning and Reference, Oxford University Press, pp. 43-45.

Gottlob Frege [1918] (1956). “The Thought: A Logical Inquiry”. Mind, Vol. 65, No. 259, pp. 289-311.

Szabó, Zoltán Gendler. (2022). “Compositionality.” In The Stanford Encyclopedia of Philosophy (Fall 2022 Edition), edited by Edward N. Zalta & Uri Nodelman. URL: https://plato.stanford.edu/archives/fall2022/entries/compositionality/.