The Limits of Language
Tractatus Logico-Philosophicus · Language Games · Family Resemblance · Forms of Life
Ludwig Josef Johann Wittgenstein (1889–1951) was an Austrian-British philosopher, widely regarded as one of the most important thinkers of the twentieth century. Born into one of the wealthiest families in Europe — the Wittgensteins were Viennese industrial magnates of steel and banking — he gave away his entire inheritance and lived with austere, almost monastic simplicity.
His life traced an extraordinary arc: engineering student in Manchester, aeronautics researcher, student of Bertrand Russell at Cambridge, soldier and prisoner of war in World War I, village schoolteacher in rural Austria, architect in Vienna, hermit in Norway, and finally professor at Cambridge. He is the only major philosopher to have produced two fundamentally different and deeply influential philosophical systems in a single lifetime.
Tractatus Logico-Philosophicus (1921) · Philosophical Investigations (1953, posthumous) · On Certainty (1969) · The Blue and Brown Books · Remarks on the Foundations of Mathematics
The "early" Wittgenstein of the Tractatus held that language mirrors logical structure. The "later" Wittgenstein of the Investigations rejected this entirely: meaning is use, language is a multiplicity of games, and philosophy's task is therapeutic — to show the fly the way out of the fly-bottle.
The Tractatus (1921) is one of the most compressed and ambitious works in the history of philosophy. Written in austere, numbered propositions, it attempts to draw the limits of meaningful language — and thereby the limits of the world itself.
A proposition is a logical picture of a fact. Just as a picture represents reality by sharing its logical form, a meaningful sentence depicts a possible state of affairs. The elements of the proposition correspond to the objects in the world; their arrangement mirrors reality's structure.
The world consists of facts, not things. Facts are combinations of simple objects (atoms). Every complex proposition can be analysed into elementary propositions, each of which pictures an atomic fact. Truth is correspondence between picture and reality.
The most important distinction in the Tractatus. What can be said are propositions of natural science. But the logical form that makes picturing possible cannot itself be pictured — it can only be shown. Ethics, aesthetics, and the meaning of life belong to what shows itself.
1. The world is all that is the case.
2. What is the case — a fact — is the existence of states of affairs.
3. A logical picture of facts is a thought.
4. A thought is a proposition with a sense.
5. A proposition is a truth-function of elementary propositions.
6. The general form of a truth-function.
7. Whereof one cannot speak, thereof one must be silent.
The Tractatus is not merely a work of logic — it is, as Wittgenstein insisted to his publisher, fundamentally an ethical book. Its deepest point is what it does not say. Everything that matters most lies beyond the limits of language.
Ethics, aesthetics, the meaning of life, the existence of the self, the feeling that the world exists at all — these are not propositions of natural science. They cannot be said, only shown. They are not nonsense because they are trivial, but because they transcend the limits of what language can picture.
"The subject does not belong to the world: rather, it is a limit of the world" (5.632). The metaphysical subject is like the eye that sees but is not part of its visual field. Solipsism, strictly carried through, coincides with pure realism.
"My propositions serve as elucidations in the following way: anyone who understands me eventually recognises them as nonsensical, when he has used them — as steps — to climb beyond them. He must, so to speak, throw away the ladder after he has climbed up it" (6.54). The Tractatus consumes itself.
"If there is any value that does have value, it must lie outside the whole sphere of what happens and is the case" (6.41). Value cannot be a fact in the world. The ethical will changes not the facts of the world but its limits — the world of the happy person is different from that of the unhappy person.
"Whereof one cannot speak, thereof one must be silent."
— L. Wittgenstein, Tractatus Logico-Philosophicus, 7After publishing the Tractatus, Wittgenstein believed philosophy was finished. He became a schoolteacher, a gardener, an architect. But by the late 1920s, cracks appeared in the Tractatus system that he could not ignore.
"This is both red and green all over" is necessarily false — but not a logical contradiction. The Tractatus demanded that all necessity be logical. Colour incompatibility revealed that logical atomism could not account for the internal relations between concepts. Elementary propositions were not independent.
Conversations with the Vienna Circle (Schlick, Waismann) and encounters with Brouwer's intuitionism sharpened Wittgenstein's doubts. The demand that every meaningful proposition be verifiable against atomic facts was too rigid. Mathematics, colour, time — vast regions of meaningful language resisted the picture theory.
The Tractatus assumed language had one essential function: to picture facts. But everyday language does far more — commanding, joking, greeting, cursing, praying, thanking. The idea that all language shares a single logical form was itself the deepest error. Language has no essence, only overlapping uses.
"The more narrowly we examine actual language, the sharper becomes the conflict between it and our requirement. The conflict becomes intolerable."
— L. Wittgenstein, Philosophical Investigations, §107The Philosophical Investigations (1953) is the central work of the later Wittgenstein. Written as a series of interlocking remarks rather than a deductive system, it dismantles the picture theory and replaces it with a radically different vision of language, mind, and philosophy.
Meaning is not a matter of picturing facts but of use in a practice. Language is a multiplicity of "games" — each with its own rules, purposes, and criteria of success. There is no single essence of language, only a family of overlapping activities.
Concepts are not defined by necessary and sufficient conditions but by a network of overlapping similarities — like the resemblances between members of a family. No single feature is shared by all instances of "game," "language," or "number."
How do we follow a rule? No rule determines its own application — any action can be interpreted as following a rule. Understanding is not a mental state but a practice, embedded in shared forms of life and agreement in action.
"For a large class of cases — though not for all — the meaning of a word is its use in the language" (§43). Meaning is not a thing (an image, a mental object) but a function of how a word operates within a language game. Don't ask for the meaning; ask for the use.
The concept of Sprachspiel (language game) is Wittgenstein's central tool for dissolving philosophical confusion. A language game is language interwoven with action — words are instruments, not labels.
"I shall also call the whole, consisting of language and the actions into which it is woven, the 'language-game'."
— L. Wittgenstein, Philosophical Investigations, §7Consider the concept "game": board games, card games, ball games, Olympic games, war games, language games. What do they all have in common? Wittgenstein's answer: nothing. There is no single essence — only a complicated network of overlapping and criss-crossing similarities.
One of the most debated arguments in twentieth-century philosophy. Wittgenstein argues that a language understandable by only a single individual — a language referring to the speaker's private sensations, in principle inaccessible to anyone else — is impossible.
Suppose I try to give a name "S" to a private sensation, consulting only my inner experience. There can be no criterion of correctness: whatever seems right to me is right — which means there is no distinction between right and wrong at all. Without a public check, there is no rule — and without a rule, no language.
Imagine everyone has a box with something in it called a "beetle." No one can look into anyone else's box. The word "beetle" functions in language regardless of what is in any particular box — even if the boxes are empty. The thing in the box drops out of consideration. Sensation words get their meaning from public criteria, not inner objects.
Wittgenstein is not denying that people have inner experiences. He is denying that inner experience could be the foundation of language. Pain is real; but "pain" does not mean "my private sensation." It functions within a public language game of pain-behaviour, sympathy, and response.
The private language argument strikes at the heart of Cartesian philosophy: the idea that each person's knowledge begins with their own private mental states. For Wittgenstein, meaning is essentially public and social. The community of language-users is bedrock.
"This was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule" (§201). The rule-following considerations are among the deepest in the Investigations.
Consider the rule "add 2": 2, 4, 6, 8 ... 1000, 1002. But someone might continue: 1000, 1004, 1008. They claim they are following the rule, interpreted differently. No finite set of examples determines a unique continuation. No mental act of "grasping" the rule can fix its application in advance. Interpretation cannot be the basis of rule-following, since interpretations themselves require rules.
"There is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call 'obeying the rule' and 'going against it' in actual cases" (§201). Rule-following is a practice, not a mental act. It rests on training, custom, and agreement in form of life — not on some further fact that guarantees correctness.
"It is not agreement in opinions but in form of life" (§241). That we all continue the series 2, 4, 6, 8 in the same way is not justified by a further rule — it is the bedrock on which justification rests. At some point, explanations come to an end: "This is simply what I do" (§217).
Saul Kripke's Wittgenstein on Rules and Private Language (1982) radicalised the paradox: there is no fact about a person that constitutes their meaning one thing rather than another. Kripke's "sceptical solution" appeals to community agreement. Whether this is Wittgenstein's own view remains fiercely debated.
In Part II of the Investigations, Wittgenstein explores seeing-as: the experience of seeing something as something. The famous duck-rabbit figure can be seen as a duck or as a rabbit — but the drawing itself does not change.
The shift from seeing it as a duck to seeing it as a rabbit is the "dawning of an aspect." It is not a new perception (the retinal image is unchanged) and not merely a new interpretation (it is experienced). It lies between thought and perception — a category the Cartesian tradition cannot accommodate.
I can continuously see the figure as a rabbit (someone who has never seen a duck might always see it so). The philosophical interest lies in the change: the moment of "Now I see it as ...!" This reveals that perception is concept-laden — what you can see depends on what concepts you possess.
Wittgenstein imagines someone "aspect-blind" — unable to experience the shift. Such a person could still use language, identify objects, function normally. What they would lack is a dimension of experience connected to imagination, metaphor, and the sense of significance.
Lebensform — form of life — is one of Wittgenstein's most evocative and least defined concepts. Language games are embedded in forms of life: the shared patterns of activity, reaction, and natural response that constitute the bedrock beneath justification.
"What has to be accepted, the given, is — so one could say — forms of life" (PI, p. 226). Forms of life are not theories or hypotheses. They are the background against which our practices of speaking, acting, and judging make sense. They are what we do not question because they make questioning possible.
"If I have exhausted the justifications I have reached bedrock, and my spade is turned. Then I am inclined to say: 'This is simply what I do'" (§217). At the foundation of all reasoning lies not a self-evident truth but a practice — something we do, not something we believe.
Forms of life include the natural facts about human beings: that we feel pain, express it in characteristic ways, respond to others' pain with concern. "Commanding, questioning, recounting, chatting, are as much a part of our natural history as walking, eating, drinking, playing" (§25). Language is rooted in biology and culture alike.
Forms of life cannot be justified from outside — there is no Archimedean point. Philosophy cannot dig beneath them. It can only describe them. "Philosophy may in no way interfere with the actual use of language ... It leaves everything as it is" (§124). The philosopher's task is not to explain but to see clearly.
Wittgenstein's last work, written in 1950–1951, responds to G. E. Moore's attempt to prove the external world by holding up his hands: "Here is one hand, and here is another." Wittgenstein's response transforms epistemology.
Certain propositions stand fast for us — not because we have verified them, but because they are the hinges on which our inquiries turn. "The earth has existed for a long time," "Objects don't disappear when unobserved," "I have a body" — these are not knowledge-claims but the framework within which knowledge-claims are possible.
"The mythology may change back into a state of flux, the river-bed of thoughts may shift. But I distinguish between the movement of the waters on the river-bed and the shift of the bed itself" (§97). Some certainties are so deep they form the channel through which thought flows. They can shift — but not by argument.
Moore was right that we are certain — but wrong to call it knowledge. "I know I have two hands" is not an empirical claim; it is a grammatical remark about the framework of empirical inquiry. To doubt it is not to be philosophically rigorous but to have lost one's footing in language altogether.
"Doubt itself rests only on what is beyond doubt" (§519). Doubt is a language game that requires a background of certainty. Universal doubt is incoherent — to doubt everything is to have abandoned the practice of doubting. Descartes' cogito fails because the language in which it is expressed already presupposes what it claims to establish.
The shift from early to late Wittgenstein is not merely a change of doctrine but a transformation of what philosophy is. The Tractatus sought to delimit thought from above; the Investigations works from within, describing the terrain of ordinary language.
Wittgenstein's philosophical development can be understood as a movement away from the programme of his two great teachers — Gottlob Frege and Bertrand Russell — and toward a vision of philosophy that would have been unrecognisable to either of them.
Sought a logically perfect language — a Begriffsschrift — purified of the ambiguities of ordinary speech. Logic as the foundation of arithmetic. Sense and reference as the basis of a systematic theory of meaning. The later Wittgenstein rejects the very idea that ordinary language needs "reform."
Russell's logical atomism held that language, properly analysed, mirrors the structure of reality. Philosophy's task is logical analysis — revealing the hidden form beneath misleading grammar. The early Wittgenstein radicalised this; the later Wittgenstein abandoned it entirely. There is no hidden logical form to uncover.
Ordinary language is perfectly in order as it is (§98). Philosophy is not a theory but an activity — the therapeutic dissolution of confusions that arise when "language goes on holiday" (§38). There is nothing to discover; everything lies open to view. "The work of the philosopher consists in assembling reminders for a particular purpose" (§127).
"Philosophy is a battle against the bewitchment of our intelligence by means of our language."
— L. Wittgenstein, Philosophical Investigations, §109J. L. Austin, Gilbert Ryle, P. F. Strawson, and others at Oxford developed Wittgenstein's insight that philosophical problems arise from misunderstandings of ordinary language. Ryle's The Concept of Mind (1949) dismantled the Cartesian "ghost in the machine" using recognisably Wittgensteinian methods.
Saul Kripke's Wittgenstein on Rules and Private Language (1982) generated an enormous secondary literature. The rule-following paradox has influenced debates in philosophy of mind, language, mathematics, and even law. It remains one of the most discussed arguments in analytic philosophy.
Iain McGilchrist draws heavily on the later Wittgenstein in The Master and His Emissary. Wittgenstein's emphasis on context, aspect-seeing, the limits of explicit rules, and the priority of the lived whole over analytical decomposition aligns with McGilchrist's account of right-hemisphere cognition.
The "therapeutic" reading (Cora Diamond, James Conant, Alice Crary) holds that Wittgenstein's goal is not to advance philosophical theses but to dissolve the urge to philosophise in the traditional sense. Philosophy cures itself of the diseases it has created. "The philosopher treats a question; like an illness" (§255).
Quietism: Does therapeutic philosophy leave everything as it is, abandoning
the explanatory ambitions of philosophy?
Relativism: If meaning is use and forms of life are ultimate, is there
no standpoint from which to evaluate rival frameworks?
Science: Cognitive science and formal semantics have achieved what
Wittgenstein said was impossible — systematic theories of meaning and mind.
Anthropology (Winch), political theory (Pitkin), aesthetics, philosophy of religion, philosophy of psychology, AI research. The Tractatus shaped logical positivism; the Investigations helped destroy it. Few thinkers have so thoroughly reshaped the landscape of philosophy — twice.
"The real discovery is the one that enables me to break off philosophising when I want to. The one that gives philosophy peace, so that it is no longer tormented by questions which bring itself in question."
— L. Wittgenstein, Philosophical Investigations, §1331889 – 1951 · Vienna · Cambridge · Norway · Ireland
"Tell them I've had a wonderful life."