Analytic Philosophy and Language

One of the more “mainstream” ideas newcomers to Western philosophy encounter is the so-called split between “continental” and “analytic” theory. Like most ideological debates, a totalizing account of the conflict can be stretched as far back as the interpreter wants (one such interpretation I found easy to follow was this post by PhilosophyNow that traces things, as always, back to Kant) and can be broadened in scope to encompass all kinds of things; alleged analytic and continental philosophers seem to butt heads on their underlying assumptions, their methods, their politics, whether they prefer pineapple on pizza, and so on.

In this post, though, I want to look one particular aspect of analytic philosophy that has defined the 20th century movement: a critical analysis of the relationship between language and thought. For one thing, it’s a testament to how far-reaching the transformations undergoing mathematics were across academia at the time—some of the most well-known analytic philosophers of the time like Russell were mathematicians, and the mission to ground the field in a solid logical foundation sparked a renewed interest in  the formal logic that Aristotle first developed over two thousand years ago. But the main reason I decided this debate is worth dedicating a full post to is because the exact questions we’re pursuing surrounding the limits of thought and breaking out of a formal system are mirrored in analysts’ treatment of language.

To be sure, the idea that the structure of consciousness determines and limits our engagement with the real world isn’t new, going back to German idealism, and yes, to Kant and his separation of noumena (things-in-themselves) and phenomena (our experience of those things); but the study of language undertaken by Frege and his successors didn’t just place a unique focus on language’s role in this determinism, it prompted a study of language as an entity in itself, one that may or may not constrain pure thought but definitely sets the boundaries and categories of how we express it.

Frege’s Revolution of Logic

In many ways, the privileged role of logic in analytic philosophy is a natural response to the revolution logic as a field underwent thanks to the work of Gottlob Frege. Any undergraduate math major who’s taken a proof-based class is already familiar with Frege’s work; his predicate logic outlined in Begriffsschrift and Grundgesetze can be seen in everything from our logical quantifiers to the way we structure proofwritng. Because of this, I’ll keep the summary of his work short and selective to the parts we’re most interested in.

• Well-formed Formulas as Functions: in Frege’s “predicate calculus,” all sentences break down into functions that take in particular objects as arguments.
• Sentences as Building Blocks: all sentences denote “truth values,” i.e. can be either True or False. Some key special functions are the “truth-functionals,” the familiar “if-then, and, or, not, iff,” which combine component sentences like building blocks and produce new sentences with new truth-values.
• Quantifiers: this is a big break from Aristotle’s foundational theory; the existential and universal quantifiers defined by Frege are “second-order”—they’re applied to functions and objects the same way—and can be applied to all arguments of a function the same way, with no distinction between “subjects” and “objects” of a sentence.
• Rules of Inference: all of these prior elements are building blocks of Frege’s “syntax”: along with these, Frege defined the “grammar”: sets of logical axioms and rules of inference by which new sentences can be inferred from others.

How much each of these components differed from Aristotle’s original logical system isn’t really important; the takeaway is that, taken together, Frege’s flexible system opened the door to applying formal logic to areas of discourse it was previously seen as too rigid to fit.

But besides its direct role as a language of discourse, I’d also like to look at the ideological project implied in Frege’s work, what philosopher Robert Brandom calls “semantic logicism.” In analytic philosophy, he argues, philosophy is cast as an analysis of the structure of thought rather than the psychological structure of thinking, and in this endeavor “logical vocabulary is accorded a privileged role.”

The first ideological claim is one well-supported by Frege in his other monumental work “Über Sinn und Bedeutung”: here, he makes the famous distinction between a sentence’s “reference,” or its formal truth-value based on the singular referents of its composite objects, and its “sense,” or the cognitive significance of these objects and the ways they’re strung together in context. This is the reason, for instance, we view the sentences “10 = 10” and “10 = 3 + 7” as saying different things; technically, both of these are just identity statements with the same reference, but we have a different mental image of “3 and 7” than we do of a singular “10”: in this sense, the second phrasing reveals these images to be aspects of the same thing. Frege’s work, then, reveals an awareness and attempt to separate out these two aspects of natural language.

Frege’s stance on the second claim is more ambivalent and something he only explicitly addresses in the preface to Begriffsschrift. Here, he compares the relationship of formal to natural language to that between the microscope and the eye—the former is a specialized tool that excels in contexts that demand precision, but precisely for this reason unsuitable for the diverse use-cases of the latter. This suggests that Frege sees formal languages such as his own as tools, useful for enhancing rather than strictly expanding the domains of our analysis and only in particular contexts. We can see this pragmatic worldview in Frege’s own application of his language, which primarily concerned mathematics and his (ultimately failed) attempt at reducing the theory of numbers to his logical axioms.

But Frege also expresses a dissatisfaction with “the inadequacy of language” in expressing ideas; such inadequacies, he claims, are almost unavoidable because of how closely tied language is to our thoughts, that it is thus “one of the tasks of philosophy to break the domination of the word over the human spirit.” And it’s not hard to read the Begriffsschrift as a proposed foundation of this task with how much it emphasizes the unity of mathematics and semantics, the way its quantifiers and functional propositions map to analyses of sentences in linguistics—all this points to a view of natural language as a broken tool, a device in need of fixing.

Russell and Language as Ontology

If Frege’s cautious ambitions for logical analysis opened the door to an ideology of “semantic logicism,” Bertrand Russell’s subsequent work not only flung that door wide open but pushed these ambitions as far as they could go, with the two components of his logical atomism mapping onto and extending the ideological claims of semantic logicism.

The first is a metaphysical and ontological one—that it isn’t just thought but reality itself that has an underlying logical structure, composed of a set of irreducible “atomic facts” with particular properties and a set of external relations that connect them into larger “complexes.” We can immediately see how this model privileges logic in a way that isn’t just epistemological, but ontological: it implies that the structure of the universe can be mapped one-to-one onto some “perfect language,” where every possible relationship, scientific or otherwise, is well-defined down to the level of atomic axioms.

It’s natural, then, that the second argument Russell’s atomism makes is for a proposed method of deciphering this language of the universe, a strategy he referred to as “analysis.” Again, the particulars of analysis are less important to us than its relation to language; while early Russell in his Principles of Mathematics gave examples of using the grammar of natural-language sentences as guides to their propositional structure, this optimism quickly fades and is replaced by the general sentiment that natural language is too vague to have any sort of one-to-one correspondence with reality. In other words, natural language isn’t just what an eye is to a microscope—it’s a grainy old camera with decades of lens distortion, epistemically limited and ontologically corrupt.

Wittgenstein and the Limits of Language

To me, it’s Frege’s epistemological and Russell’s ontological ambitions that really define the relationship of modern analytic philosophy to language—it structures the reasoning by which we learn about the world, and the world is itself structured in a way that fits a logical form of this reasoning. But it would feel disingenuous of me not to at least mention the philosopher whose early works seemed to epitomize these contemporary ambitions—even as it’s still debated whether this reading really captures the depth of what he was trying to say. Of course, I’m talking about Wittgenstein, and specifically the second half of his Tractatus Logico-Philosophicus.

To be sure, at a glance the Tractatus seems to fall in lockstep with its predecessors: the text is structured as a list of propositions mirroring a logical argument, and the first half of them establish a “picture theory” that appears to be a twist on Russell’s logical atomism—every state of affairs in reality is “pictured” by a set of propositions in language, these propositions are truth functions of “elementary propositions,” which in-turn correspond to atomic states of affairs, and so on.

One noteworthy difference for us is that Wittgenstein explicitly argues that all languages, natural or formal, possess the same logical form, and that formal language just happens to express it more clearly. In a sense this can be read as subsuming Frege’s categories of “sense” and “reference” under the same umbrella, arguing they ultimately possess the same scaffolding.

But what really distinguishes the Tractatus is where it takes this analysis; the latter half inverts the idea that “logic is…a mirror-image of the world” to get that “the limits of language mean the limits of my world” (TLP 5.6)—in other words, if logic pictures reality and there are things that logic can’t picture, then we can’t speak meaningfully about those things.

Those things turn out to be statements about the logical form, which in this picture theory Wittgenstein interprets to be claims about the world as a whole…essentially all the propositions of metaphysics, and to a lesser extent ethics and aesthetics. To use Wittgenstein’s wording, if well-formed propositions within the language have “sense” then the propositions of metaphysics are not well-formed, are “nonsense.”

Logical Positivism: Is Metaphysics Nonsense?

It might be this fateful choice of words that’s part of why the Tractatus was hailed by other analytic philosophers as the tradition’s most radical work; this reading effectively affirms the supremacy of logical analysis as the only path to philosophical truth, draws the battle lines between the meaningful propositions of logic and the “nonsense” of metaphysics and other fields outside the strict constraints of language.

This was the interpretation of the “Vienna Circle,” a sort of philosopher’s book club founded by Moritz Shlick and featuring Bertrand Russell that collectively defined the analytic tradition of the 20s and 30s; their interpretation of Wittgenstein came to be known as “logical positivism,” or the belief that any proposition that didn’t have a well-defined truth-value under all conditions within its logical system was meaningless, explicitly taking “nonsense” as a pejorative.

But is this pejorative connotation actually justified within the Tractatus? As skepticism mounted towards a dogmatic adherence to semantic logicism, and particularly towards the Vienna Circle’s positivism, philosophers like Elizabeth Anscombe—eventually even Shlick himself—began to recast the Tractatus’s stance towards “nonsense” that existed outside of language not as one of dismissal, but of reverence. And once again, a lot of the support for this reinterpretation can be found in phrasing and tone rather than the formal structure of any particular proposition…which for a text like the Tractatus I find hilariously ironic.

While yes, the first half of the Tractatus outlines the structure of its logical atomism in a very formal, systematic fashion, the second half that deals with the edges of this theory is much more contemplative in tone, pondering the unity of ethics and aesthetics and the origins of fate in an acceptance of this limitative character of language. And while his fellow analysts—particularly his former teacher Russell—were typically avowed atheists, Wittgenstein was much more ambivalent on the nature of spirituality and had even criticized typical atheistic arguments against theology as “misguided”. So, while the discussions of metaphysics in the same terms as religion might read as dismissal to a staunch analyst, could they instead reflect a similar ambivalence from Wittgenstein on the nature of metaphysics?

Then there’s the fact that Wittgenstein doesn’t just refer to metaphysics as “nonsense”—he also uses the term “mystical,” imbuing it with a transcendental rather than dismissive connotation. And the place where he uses it is even more telling: in the final stretch of propositions he writes, “There is indeed the inexpressible. This shows itself; it is the mystical” (TL 6.522).

This proposition does something very strange in the context of the Tractatus’s “picture theory”: it asserts that there are things that are outside the limits of language and thus the limits of the world…and yet they still exist. The Fregean “sense” that was discarded earlier in the Tractatus reasserts itself at the boundaries of language, a layer of meaning to metaphysical statements that cannot be spoken, only shown.

In short, where the Vienna Circle’s reading of Wittgenstein sharply defines the divide between analytic and continental philosophy, this “ineffability” reading suggests a sort of continuity, that the border of logic where analytic philosophy ends is where continental philosophy begins. And as the idealism of logical positivism has largely faded today and the work of contemporary analysts has been focused on applying the tools of formal language to parse current debates across fields of supposedly “continental” philosophy, I think this appraisal is the best way to look at the language of both traditions today.

Part 2: Speculations and Looking Ahead

Well, look at that…one moment I was just planning to mention Wittgenstein in passing, and now I’ve spent the last half of the post ranting about him. If you’re following this series of posts on consciousness just know that’s going to become a running theme. Hopefully that standalone section of the post was a thorough enough history-of-philosophy discussion—it’s not really my style, but I think it’s important to lay out some of the philosophical underpinnings of this project, and it’s one of those buzzword topics that I’ve only recently read enough philosophy to try making sense of. Still haven’t gotten around to Kant though…

Anyways, in this section I’m going to do a little firing off the hip, touching on two of the ideas covered earlier and connecting them to our broader questions about language, consciousness and how we create and expand our frameworks of meaning. If any of those topics interest you, stick around!

A Second Look at Frege’s Formal Language

The first thing I wanted to zoom in on is Frege’s notion of “the domination of the word over the human spirit,” which he cites as the reason the inadequacies of natural language are so difficult to see. Here Frege appears to lean into the view of natural language as bodily—its structure is so embedded in our thoughts that fitting one’s thoughts into that structure requires no more conscious thought than stretching the muscles needed to raise one’s hand.

But like the limbs of our body, there are moments where that distance seemingly makes itself felt; transformative experiences we can’t put into words, where a name or phrase is on the “tip of the tongue,” where we’re writing a blog post and have to keep typing and retyping a sentence that just doesn’t sound right (I’m still not fully sold on this use of ellipses)…in these moments there’s a separation between intention and action, between “pure thought” and its expression in language.

In Martin Stockhof’s paper “Hand or Hammer? On Formal Semantics and Natural Languages in Semantics,” he calls this assertion of the existence of pure thought that we can aspire to and measure the efficacy of our language against the “Availability Assumption”; what’s more, he argues Frege implicitly invokes this when weighing the explanatory power of natural and formal languages.

Stockhof uses this claim to assert a contradiction between Frege’s ideology and the reasoning by which he reaches it: if the essence of our thoughts is already accessible independent of our language, then why would we need formal language to avoid the logical errors of its natural counterpart? At most formal language is an instrumental tool that makes this thinking more easily accessible, or avoids transmitting such logical errors in interpersonal communication, but the idea that our inner selves are also dominated by an erroneous and error-prone language can’t follow from this imposed distance between language and thought.

Now I’m going to lay my cards on the table; I’d like to collapse this distance, to argue that language fundamentally structures thought in the manner early Wittgenstein alludes to, even if that structuring doesn’t take place at the level of conscious awareness. The idea that our thoughts arise logically from a determinate set of laws cuts deep to the root of my metaphysical intuitions, and the idea of using tools from mathematical logic to study consciousness is just too exciting to refuse. But that means I have to contend with the flipside of the difficulties raised by Stockhof—if our language is intrinsic to our thoughts, then how do we actually spot the gaps from within that formal system, measure its explanatory power against some external ideal we can’t conceptually access?

It’s that specific question I’m planning to study further, and that means we can finally get back to some math; specifically, I’m planning to look into a branch of mathematical logic called Model Theory that specifically studies how the form of a language constrains its domain of representation (think “provability” within a formal system…Godel’s theorem!)…and yes, expect another diatribe on Wittgenstein as the philosophical basis of this train of thought.

Does Language Mirror the Brain?

The other reason I’d like to maintain the assumption of language as intrinsic to thought is because of the second train of thought I want to explore, this time on how the linguistic structure of the thoughts we produce can reflect on the architecture of the brain that produces them.

Right off the bat, this analysis of a general “linguistic structure” worth studying opens up a can of worms in the study of natural language: it invokes the assumption that all languages share a common essential structure, the linguist Noam Chomsky’s controversial “universal grammar.” I could probably spin off a whole series of posts examining the ways this claim has been interrogated across philosophy, linguistics, and neuroscience, but for now I’ll just say that, as I understand it, Wittgenstein makes a mild form of this Chomsky-esque assumption when he asserts that all languages possess a shared logical form. And while I personally consider this premise to be fairly reasonable on its own, any further statements about shared properties of language that we’d like to trace to a shared “hardware” in the brain would have to first qualify this assumption.

Once again, though, I’ll lay out my cards and say that despite the postmodernist in me I’d like this romantic universality of language to hold, not just because of my fondness for logic but because it opens up another interesting avenue of exploration, an analysis of how cognitive structures—whether at the anatomical or data-structural level—map onto the structures seen in artificial intelligence research today.

No, this isn’t me announcing my pivot from blogging to starting a venture-capitalist-coded AI podcast. But the relationship between computer software and hardware seems to me like the perfect case study into how any hypothetical universal structures of language might reveal their physical underpinnings. And since I’m stuck relearning the basics of coding again thanks to graduation requirements, I figure it’s a good way to put all those hours of C++ to use instead of coding the dozenth string comprehension algorithm for class…
Tl;DR I have an overactive imagination, and despite the turbulent emergence of the analytic tradition onto the philosophical scene, it’s given us a lot of rabbit holes to dive down. Hope you stay for the ride!

References

• Duke, G. (2009). Dummett and the Origins of Analytical Philosophy. The Review of Metaphysics, 63(2), 329–347. http://www.jstor.org/stable/40387695
• Zalta, Edward N., “Gottlob Frege”, The Stanford Encyclopedia of Philosophy (Summer 2025 Edition), Edward N. Zalta & Uri Nodelman (eds.), URL = <https://plato.stanford.edu/archives/sum2025/entries/frege/>.
• Irvine, Andrew David, “Bertrand Russell”, The Stanford Encyclopedia of Philosophy (Winter 2024 Edition), Edward N. Zalta & Uri Nodelman (eds.), URL = <https://plato.stanford.edu/archives/win2024/entries/russell/>
• Stokhof, M. Hand or Hammer? On Formal and Natural Languages in Semantics. J Indian Philos 35, 597–626 (2007). https://doi.org/10.1007/s10781-007-9023-7
• Gottlob Frege, et al. “Begriffsschrift.” Jena, Friedrich-Schiller-Universität, 1979.
• Wittenstein, Ludwig. Tractatus Logico Philosophicus. Lanham, Start Publishing LLC, 2012.
• Dąbrowska E. (2015). What exactly is Universal Grammar, and has anyone seen it?. Frontiers in psychology, 6, 852. https://doi.org/10.3389/fpsyg.2015.00852
• Jones, Kile. “Analytic versus Continental Philosophy | Issue 74 | Philosophy Now.” Philosophynow.org, 2009, philosophynow.org/issues/74/Analytic_versus_Continental_Philosophy.
• Greenstreet, Stuart. “Wittgenstein,Tolstoy and the Folly of Logical Positivism | Issue 103 | Philosophy Now.” Philosophynow.org, 2014, philosophynow.org/issues/103/WittgensteinTolstoy_and_the_Folly_of_Logical_Positivism.