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Introduction
Hello! In our previous lesson, we explored the dramatic shift in Ludwig Wittgenstein's philosophy, moving from the rigid picture theory of meaning in the Tractatus to the flexible concept of meaning as use in the Philosophical Investigations. We saw how he abandoned the idea that language has a single, essential function (to represent reality) and instead embraced the metaphor of language as a toolbox, with words serving countless different purposes.
Today, we will build directly on that foundation to address the learning outcome: Explain the concepts of 'language-games' and 'family resemblance' with examples. These two concepts are the core machinery of Wittgenstein's later philosophy, providing the "how" for his "meaning is use" doctrine. They explain how language functions in practice and how we manage to use general terms without needing the strict, universal definitions that philosophers from Plato to Frege had sought.
This lesson is central to understanding the "linguistic turn" and will be particularly relevant to your interest in the philosophy of mathematics, as Wittgenstein later applies these same ideas to concepts like "number" and "proof."
1. Language-Games: The Context of Meaning
In the last lesson, we heard the slogan, "the meaning of a word is its use in the language." But what does "use" mean here? For Wittgenstein, language is not something we use in a vacuum; it is always interwoven with human activities. He coined the term language-game (Sprachspiel) to refer to these instances of language-in-action.
A language-game can be as simple as an order and its execution, or as complex as a scientific debate. The key idea is that words get their meaning from the role they play within these structured activities.
To see this in action, let's start with one of Wittgenstein's most famous simple examples.
Language Games and Private Language
The scholar Lars Hertzberg provides a clear explanation of one of Wittgenstein's foundational examples from the Philosophical Investigations: the 'builders' game'. This simple scenario powerfully illustrates what a language-game is.
Please read the section titled 'The builders’ game'. Focus on how the words 'Block!', 'Pillar!', etc., are meaningful not because they are labels, but because they are integrated into a shared activity.
As the builders' game shows, the meaning of "Slab!" is not an abstract definition but is constituted by the whole activity of the builder calling it out and the assistant bringing the correct stone. The utterance is a move in the game, like a move in chess.
Wittgenstein emphasized that there are "countless" such games, not just the three traditional categories of assertions, questions, and commands. His list in the Philosophical Investigations (§23) includes:
- Giving orders and obeying them
- Describing the appearance of an object
- Reporting an event
- Speculating about an event
- Forming and testing a hypothesis
- Telling a joke
- Translating from one language to another
- Asking, thanking, cursing, greeting, praying
The purpose of philosophy, in this view, is not to create a 'better' language, but to describe these games clearly to dissolve confusions that arise when we mix them up—for instance, by treating a moral or aesthetic utterance as if it were a scientific report.
Ludwig Wittgenstein's Philosophy - John Searle & Bryan Magee (1987)
In this discussion, John Searle elaborates on the language-game concept, explaining why Wittgenstein chose the analogy of a 'game' and what it reveals about the nature of language as a rule-governed, human activity.
Watch from 15:10 to 19:04. Pay attention to the three key reasons for the 'game' analogy: it's an activity, it's conventional (rule-governed), and it's something we operate within, without an external foundation.
Test your understanding!
Think about the everyday activity of ordering a coffee at a café. Describe this as a language-game. What are some of the key "utterances" or "moves"? What are the implicit "rules"? How do words like "latte," "large," or "to-go" get their meaning within this specific game?
Show answer
In the "ordering coffee" language-game:
- Players: The customer and the barista.
- Context/Setting: A coffee shop.
- Objective: For the customer to receive a desired coffee and for the barista to be paid for it.
- Moves/Utterances:
- Customer: "Can I get a large latte to-go?" (The opening move)
- Barista: "That'll be £3.50." (A counter-move, requesting payment)
- Customer: Taps card (A non-linguistic move, but part of the game)
- Barista: "What's the name for the order?" (A move to manage multiple orders)
- Barista: "Large latte for Alex!" (A move to complete the transaction)
- Rules (Implicit):
- The customer speaks first.
- The order must use terms the barista understands (e.g., "latte," not just "milky coffee").
- Payment follows the statement of price.
- The customer waits for their order to be called.
- Meaning as Use: The word "latte" doesn't just name an object. Its use here is a specific request for a particular action from the barista (combine espresso with steamed milk in a certain way). "Large" is a command to use a specific cup size. "To-go" is an instruction about the type of cup to use. Their meanings are entirely embedded in this activity and would be different in another language-game (e.g., a "coffee tasting" game, where "latte" might be used as a descriptive label for comparison).
2. Family Resemblance: The Logic of General Terms
The language-game concept explains the context of meaning. But it raises a new problem. If meaning is use, how do we understand general terms? Consider the word "game" itself. We use it to talk about chess, football, poker, and peekaboo. What single thing do they all have in common that makes them "games"?
The traditional philosophical impulse, from Plato onwards, is to search for a common essence or a strict definition. For a mathematician like Frege, a concept without a sharp boundary wasn't a concept at all. Wittgenstein radically breaks from this tradition.
Wittgenstein argues that there is nothing that all games have in common. To see why, let's turn to his own words.
Imagine a language-game in which someone is ordered to ...
The following is an excerpt from Wittgenstein's Philosophical Investigations, containing the classic passages where he introduces and explains the concepts of 'game' and 'family resemblance'.
First, read §65, where Wittgenstein explicitly frames the problem. Then, read §§66-67 carefully. Follow his instruction: 'Don't say: "There must be something common..."—but look and see'. Observe how he moves between different types of games, noting that features appear and disappear.
As Wittgenstein shows, instead of a common essence, we find "a complicated network of similarities overlapping and criss-crossing." He calls this family resemblance.
Think of the members of a family. One person might have the family nose and eyes, another the nose and chin, a third the chin and gait. There is no single feature that every member possesses, yet we see a clear resemblance that connects them all. So it is with the instances of a concept like "game."
- Chess and poker are both rule-governed, competitive.
- Poker and patience both use cards.
- Football and throwing a ball against a wall both use a ball.
The connections are indirect and overlapping. This is a profound shift from the search for necessary and sufficient conditions that has defined much of Western philosophy.
Great Minds - Part 5 - The Latter Wittgenstein: The Philosophy of Language
To solidify this idea, watch this clip where Michael Sugrue contrasts Wittgenstein's approach with Socratic essentialism, and another where John Searle unpacks the 'family resemblance' concept.
First, watch from 16:13 to 20:58. Sugrue does an excellent job contrasting the Socratic demand for a single definition ('what is virtue?') with Wittgenstein's method of looking at examples. Then, watch from 29:02 to 32:07 where he explains how the 'family resemblance' idea holds concepts like 'game' or 'chair' together.
3. Implications: Life with Blurred Edges
If concepts are defined by family resemblance, it means most of our concepts have "blurred edges." There isn't a sharp line where "game" stops and "not-game" begins. Is a professional gambler really "playing"? Is a baby playing peekaboo engaged in a rule-governed activity?
For Frege, such vagueness was a disaster. For Wittgenstein, it's not a flaw to be fixed but simply a feature of how language works. An "indistinct photograph" is still a photograph, and sometimes it's exactly what we need.
Let's read Wittgenstein's defense of this inexactness.
Imagine a language-game in which someone is ordered to ...
In this final excerpt from the Investigations, Wittgenstein directly addresses the objection that concepts with 'blurred edges' are not concepts at all, using his famous analogy of the indistinct photograph.
Read §§68-71. Pay close attention to his critique of Frege in §71 and his argument that 'inexactness' does not mean 'unusable'. The key is that we can draw a boundary for a special purpose, but none is drawn in advance.
This pragmatic view is powerful. We don't need a perfect, timeless definition of "game" to use the word successfully every day. We give examples, and others learn to go on in the same way. This process of "going on" is what we'll explore next.
Test your understanding!
In the Investigations (§67), Wittgenstein says, "the kinds of number form a family in the same way." Drawing on your background in mathematics, how would you explain this claim? In what way are natural numbers, integers, rational numbers, real numbers, and complex numbers related by family resemblance rather than by a single, shared essence?
Show answer
This is a fantastic application of the concept. While modern mathematics often defines these number systems via set-theoretic constructions (e.g., integers as equivalence classes of pairs of natural numbers), Wittgenstein is looking at how the concept of "number" evolved and how we use it.
A family resemblance account would look like this:
- There is no single property that all these systems share that we could call the "essence" of number. For example, not all numbers are used for simple counting (like naturals), not all have a clear successor (like reals), and they aren't all ordered on a line (like complex numbers).
- Instead, they are related by overlapping features. We extend the concept of "number" from one domain to the next by preserving some features while dropping others.
- Naturals to Integers: We extend the idea of discrete units and operations like addition, but we add the concept of negatives (additive inverses) to ensure closure under subtraction. We lose the idea of a fixed starting point (0 or 1).
- Integers to Rationals: We preserve the algebraic field properties (addition, multiplication, inverses) but now ensure closure under division. We lose the property of having a unique "next" number.
- Rationals to Reals: We extend the concept to fill in the "gaps" on the number line, ensuring properties like the least upper bound property (completeness). We lose countability. The "feel" of a real number is very different from that of a rational.
- Reals to Complex: We extend again to ensure algebraic closure (e.g., so that has a solution). We preserve field properties but lose the property of being totally ordered.
Each step feels like a natural extension of "number" because it's analogous to the previous system in crucial ways (it solves a problem, it allows certain operations), but it also introduces new properties and leaves old ones behind. The "strength of the thread" connecting them is the overlapping of these many fibres, not one single fibre running through the whole length.
Conclusion
In this lesson, we have unpacked the two central concepts of Wittgenstein's later philosophy, which provide the mechanism for his "meaning as use" theory.
Key Takeaways:
- Language-games are the structured, rule-governed activities in which language is embedded. A word's meaning is its role within a specific game.
- The term "game" is an analogy for an activity that is conventional and rule-governed, not something frivolous.
- General terms like "game" or "number" are not defined by a single common essence.
- Instead, their instances are united by a network of "overlapping and criss-crossing" similarities, which Wittgenstein calls family resemblance.
- This implies that most of our concepts have blurred edges, a feature that Wittgenstein saw not as a flaw but as essential to their practical use.
Preview of the Next Lesson:
We've talked a lot about language-games being "rule-governed." But this raises a difficult question. If there are no strict definitions and concepts have blurred edges, how do we know if we are following a rule correctly? How do I know that my use of "green" matches yours? This leads to one of the most debated parts of Wittgenstein's work: the rule-following considerations and their deep skeptical implications for meaning itself. We will tackle this in our next lesson.