The Grammar of Possibility: A Work That Rethinks the Foundations of Logic, Mathematics, and Language
Editors’ Foreword and Preliminary Remarks
We begin before the numbered remarks, in the prefatory material. Rush Rhees and the other editors provide a brief orientation: these are notes Wittgenstein wrote between 1929 and 1930, after his return to Cambridge and to philosophy, representing a transitional phase between the *Tractatus Logico-Philosophicus* and the *Philosophical Investigations*. The text is not a finished book but a set of working manuscripts — Wittgenstein’s own title was *Philosophische Bemerkungen*, and he considered them a preliminary study for a larger work.
The editors explain that Wittgenstein dictated much of this material to Friedrich Waismann and others, and that the remarks were later selected and arranged by Wittgenstein himself into something approaching a coherent sequence. This is crucial: we are not reading a polished treatise but a process of thinking, where Wittgenstein tests positions, abandons them, and circles back. The reader must attend to the movement of thought rather than expect final doctrines.
The opening orientation thus establishes a hermeneutic principle: these remarks are *exploratory*. Wittgenstein is working out a new conception of philosophy, one that no longer treats logical propositions as “pictures” of reality in the *Tractatus* sense, but instead begins to investigate the grammar of our expressions — how language actually functions rather than how it ideally should function. This shift, still incomplete in 1929, is the engine driving the entire manuscript.
1. The Nature of Propositions and the Rejection of “Logical Form”
Wittgenstein opens the numbered remarks by confronting a problem from the *Tractatus*: the idea that propositions share a “logical form” with the states of affairs they depict. He now finds this conception deeply problematic. The passage reads:
“A proposition must determine a logical place. The proposition is a sign that determines a logical place; but the logical place is not given by the sign alone.”
The key move here is the distinction between the sign (the written or spoken sentence) and the place (the logical position in logical space). Wittgenstein is no longer satisfied with the idea that a proposition simply “pictures” a fact. Instead, he argues that the proposition *determines* a location — but that location is itself constituted by the system of propositions to which it belongs. A proposition does not have an isolated meaning; its meaning is a function of its relations to all other propositions in the language.
What does this mean concretely? Consider two propositions: “The cat is on the mat” and “The cat is not on the mat.” In the *Tractatus*, these would share a logical form (both are about the cat-mat relation) but differ in truth-value. Here, Wittgenstein begins to suggest that the very sense of a proposition is bound up with its negation and with the entire network of logical relations. A proposition is not a picture but a node in a logical calculus. The proposition does not “picture” a fact; it *determines* a position within a rule-governed system — and that system is what gives it meaning.
This is a significant departure. Wittgenstein is moving toward the idea that the grammar of language (the rules for combining signs) is not a reflection of the structure of reality, but a convention that we ourselves establish. The logical place is not something we discover; it is something we construct through our use of signs.
2. Hypothesis and the Problem of Verification
Wittgenstein next turns to the question of hypotheses — propositions whose truth cannot be directly verified because they refer to unobserved states of affairs. This is a central concern for him in 1929–30, as he wrestles with the legacy of logical positivism (he was in close contact with the Vienna Circle at this time).
He writes:
“A hypothesis is a law for forming propositions.”
This is deceptively simple. Wittgenstein is rejecting the idea that a hypothesis is a proposition like any other, waiting to be confirmed or refuted by evidence. Instead, he argues that a hypothesis functions as a rule — a prescription for how to generate propositions from observations. For example, the hypothesis “All swans are white” is not itself a proposition that can be checked against all swans (since we cannot observe all swans). Rather, it is a rule: given a bird that looks like a swan, we may assert “This swan is white” — and if we find a black swan, we do not simply refute the hypothesis; we must *reform* the rule.
This has profound implications for the relationship between language and experience. If hypotheses are rules, then they are not true or false in the same way that observation statements are. Their “truth” is a matter of their usefulness in organizing our experience, not their correspondence to an independent reality. The criterion for accepting a hypothesis is not its verification in individual cases, but its fruitfulness as a principle for generating predictions and explanations.
Wittgenstein is thus moving toward a pragmatic view of scientific hypotheses, though he would resist that label. The key insight is that our language contains different levels or kinds of propositions, each with its own grammar. Observation statements, hypotheses, mathematical propositions — these are not all of the same logical type. Confusing them leads to philosophical confusion.
3. The Role of Time and the “Now”
A major theme in the *Philosophische Bemerkungen* is the treatment of time, and Wittgenstein devotes several dense remarks to the concept of the “now” and temporal experience. He is trying to understand how propositions about time relate to the immediate experience of the present moment.
He observes:
“The present does not become past and then later become present again. There is a fundamental difference between the way the past and the present are given to us.”
This is a direct challenge to any view that treats time as a homogeneous medium through which events move uniformly. Wittgenstein insists that the grammar of “now” is fundamentally different from the grammar of “then.” The present is not simply a point on a timeline; it is the vantage point from which all talk about time derives its sense. When I say “It is raining now,” I am not making a claim about a moment that could also be described from a future or past perspective in the same way. The “now” is not an objective feature of the world; it is a feature of the act of speaking.
This connects to Wittgenstein’s broader critique of the private language idea. If the “now” were a private sensation (only I can know my own present), then communication about time would be impossible. But Wittgenstein argues that the “now” is publicly accessible through the act of utterance. The word “now” does not name a private experience; it is a signal that coordinates our attention. Its meaning is its use in the language-game of indicating temporal proximity.
The consequence is that the solipsism of the present moment — the feeling that only my own “now” is real — is a grammatical illusion. The “now” is not a metaphysical fact but a rule of our temporal language. Once we see this, the anxiety about the passage of time dissolves. We do not need to ground the reality of time in an abstract flow; time is simply how we order events in our propositions.
4. Mathematical Propositions and Their Foundation
Wittgenstein now turns to mathematics, which occupies a large portion of the *Bemerkungen*. He is deeply concerned with the nature of mathematical truth, in dialogue with (and often in opposition to) the formalist and logicist programs of Frege, Russell, and Hilbert.
He writes:
“The proposition ‘The sum of the angles of a triangle is 180°’ is not a proposition of geometry in the same sense as ‘This triangle has a right angle’ is a proposition about a particular figure.”
Here Wittgenstein insists on a grammatical distinction: general mathematical propositions are not simply summaries of particular cases. They are rules for transforming one proposition into another. The theorem about triangle angles is not a description of all triangles (we cannot examine all triangles); it is a norm that governs how we reason about triangles. If a measured triangle does not conform to 180°, we do not say the theorem is false; we say the measurement was inaccurate, or we adjust our geometry.
This line of thought leads Wittgenstein toward what would later be called a rule-following account of mathematics. Mathematical propositions are not “true” because they correspond to a platonic realm of numbers and shapes. They are constitutive of what we count as correct calculation. The proposition “2 + 2 = 4” is not a discovery about pre-existing numbers; it is a stipulation of what we will call “2 + 2.” To doubt it is not to have a different opinion; it is to fail to understand the game of arithmetic.
Wittgenstein is not denying that mathematics has objectivity. He is redefining what objectivity means: it consists in agreement in judgments among those who share the same rules. The rules are not arbitrary; they are embedded in our practices of counting, measuring, and constructing. But they are not grounded in anything beyond those practices — neither in sense-experience nor in rational intuition.
5. The Nature of Contradiction and Consistency
A natural consequence of Wittgenstein’s view of mathematics is a rethinking of contradiction. In logicist accounts, a contradiction is a catastrophe: it entails every proposition, rendering the system trivial. But Wittgenstein questions whether this is the correct description of how contradiction actually functions in our thinking.
He observes:
“A contradiction is not always a mistake. In some language-games, a contradiction simply has no place; in others, it indicates a boundary.”
The crucial point is that consistency is not a property that every system must have to be meaningful. Wittgenstein imagines a tribe that uses a calculation system that occasionally yields contradictions, but they simply ignore them and continue. Are they irrational? Not necessarily — they have simply not developed the concept of “logical consistency” as we have. Their practice works for them; contradiction does not “destroy” their language-game because it has no role in it.
This anticipates Wittgenstein’s later work on certainty and hinge propositions. The demand for absolute consistency is itself a philosophical prejudice — a requirement we impose on language from the outside, not something language demands of itself. A contradiction is only a problem if we have decided that our system must be consistent. But that decision is itself a choice, not a logical necessity.
Wittgenstein is here pushing against the idea that logic is the foundation of thought. Instead, logic is one language-game among many. Its rules are not the ultimate court of appeal for all reasoning; they are the rules of a particular practice of inferring. If another practice does not follow those rules, it is not “illogical” in the sense of being wrong — it simply plays a different game.
6. The Problem of “Simplicity” and Analysis
The final remarks in this first quarter of the *Bemerkungen* return to the question of logical analysis — the project, central to the *Tractatus*, of decomposing complex propositions into their simplest elements. Wittgenstein now expresses serious doubts about whether such analysis yields anything like “simple objects.”
He writes:
“We think we can analyze a proposition into its ultimate constituents, but this analysis is never completed. What we call ‘simple’ is always relative to a particular method of analysis.”
This is a decisive break with the *Tractatus* picture. In the earlier work, Wittgenstein had assumed that language must ultimately rest on simple objects — indivisible elements that give meaning to the rest. He now admits that this requirement is not a discovery about reality but a demand we impose on language. We *want* analysis to terminate in simples, but the grammar of our language does not guarantee this. What counts as “simple” depends on what we are trying to explain.
For example, in a sentence like “The book is red,” we might think “red” is a simple property. But red can be further analyzed into wavelengths of light, which can be analyzed into physical quantities, and so on. Where does it stop? Wittgenstein’s answer: it stops when we have reached a point that is useful for the purpose at hand. There is no metaphysical bottom level. The simplicity of an element is a function of the analysis, not a feature of the world.
This insight paves the way for the later Wittgenstein’s concept of family resemblances. If there are no ultimate simples, then the meaning of a word is not given by its reference to some atomic element, but by its use in a network of overlapping similarities. The *Bemerkungen* do not fully develop this idea, but the seeds are clearly sown in these remarks. Wittgenstein is dismantling the metaphysical picture of language from within, using the very tools of logical analysis that once supported it.
7. The Phenomenological Language and Its Limits
At this point in the work, Wittgenstein turns to one of its most distinctive and challenging themes: the possibility of a phenomenological language — a language that would directly express immediate experience without the mediation of physics or hypotheses. This is a deeply self-critical moment, as Wittgenstein is testing the limits of his own earlier commitments in the *Tractatus*.
The central passage occurs where Wittgenstein distinguishes between two kinds of language: the language of physics (which speaks of objects, causal laws, and three-dimensional space) and the language of immediate experience (which speaks of sense-data, the visual field, and the “now”). Wittgenstein writes that the language of physics is a construction built upon the more fundamental language of phenomena. The phenomenological language would describe only what is given, without any hypothetical addition.
What Wittgenstein means here is something radical. When I see a red patch, I do not see a “physical object” with properties like extension in objective space; I see a colored expanse in my visual field. The physical object is a hypothesis — a construction that allows me to predict further experiences. The given, by contrast, is just what appears: the red patch, its location in the visual field, its duration in the “now.” This given is not in physical space, but in a kind of visual space that is structured differently.
But Wittgenstein immediately complicates this picture. He argues that a pure phenomenological language — one that only describes the given — would be private and incommunicable. The moment I try to speak about my visual field to another person, I must translate it into the public language of physics, which is a language of hypotheses. This creates a profound tension: the given is the foundation of all knowledge, but it cannot be directly expressed in language. The phenomenological language is the ideal toward which analysis strives, but it is also the limit of what can be said. It is the language that would make everything clear, but it is also the language that cannot be spoken.
This is not simply a difficulty to be overcome. Wittgenstein is showing that the very idea of a “phenomenological language” is caught in a contradiction. To have a language, we need rules; to have rules, we need repeatable criteria; to have repeatable criteria, we must abstract from the unique “now” and speak of types or kinds. But the given is always unique, always fleeting, always this rather than that. The phenomenological language would be one in which every utterance is a proper name for a unique moment — but such a language is impossible, because proper names without general terms cannot form propositions. The very structure of language forces us to leave the pure given behind.
8. Visual Space vs. Euclidean Space
This section deepens the previous discussion by examining the specific structure of visual space as distinct from physical (Euclidean) space. Wittgenstein’s aim is to show that the grammar of visual experience is fundamentally different from the grammar of objective space, and that confusion arises when we treat visual phenomena as if they were objects in a single, homogeneous space.
The key passage involves Wittgenstein’s analysis of the visual field and its peculiar properties. He argues that visual space is not Euclidean; it has no metric in the strict sense, and its geometry is determined by the phenomenology of seeing rather than by mathematical axioms. For example, the visual field has no absolute boundary — we do not see a “frame” around what we see, but rather the field simply fades off at the edges. Objects in the visual field do not have “backs” or “insides” in the same way physical objects do; they are given as surfaces, as colored expanses.
Wittgenstein uses a powerful example to illustrate this. Consider a circle drawn on a piece of paper. In physical space, the circle has an inside and an outside, a center and a circumference. But in visual space, the situation is different. The circle is given as a figure against a ground, but its “inside” is not a region of space in the same way; it is simply the area bounded by the line. The visual circle is not a collection of points, but a gestalt — a whole with properties that cannot be reduced to the properties of its parts. Wittgenstein insists that the logic of “inside” and “outside” in visual space is determined by the visual grammar of seeing, not by the axioms of geometry.
What Wittgenstein is driving at is the autonomy of visual grammar. The visual field has its own laws, which are not derivable from physics or mathematics. To understand the visual field, we must describe it in its own terms, not in terms of the physical world that we infer from it. This is a direct consequence of the rejection of a single “logical form” that would unite all domains of discourse. Each domain — the visual, the tactile, the auditory — has its own grammar, and these grammars cannot be reduced to one another. The visual field is not a representation of physical space; it is a presentation of a different kind of space altogether.
This has profound consequences for the philosophy of perception. If visual space has its own grammar, then the traditional problems of perception — how does the mind represent the world? how do we bridge the gap between appearance and reality? — are based on a misunderstanding. The gap between appearance and reality is not a gap between two spaces (mental and physical), but a gap between two grammars. The problem is not one of epistemology, but of logical syntax. We are confused not because we lack evidence, but because we mix up the rules of visual language with the rules of physical language.
9. The Role of Memory in Knowledge
Wittgenstein now turns to a topic that is crucial for understanding his theory of time and the “now”: the role of memory in constituting knowledge. This is not simply an epistemological question about how we remember; it is a logical question about the conditions under which memory claims can be verified.
The central passage is where Wittgenstein argues that memory plays a constitutive role in our concept of time. He writes that the past is not simply a storehouse of facts that we recall; rather, what we call “the past” is structured by the grammar of memory. To say “I remember that p” is not to assert a relation between a present mental image and a past fact; it is to make a claim that is governed by specific rules of verification.
Wittgenstein proposes a thought experiment. Suppose we try to verify a memory claim. We might say, “I remember seeing the clock at 3:00.” To verify this, we might look at the clock again, or ask someone who was there. But notice: verification of memory always leads back to some present state of affairs — a present perception, a present document, a present testimony. There is no direct access to the past. The past is never given; it is always inferred from present evidence.
But this inference is not a hypothesis of the sort discussed earlier. Memory is not a hypothesis about the past; it is a primitive form of knowledge that is presupposed by all hypothesis formation. Without memory, we could not form hypotheses at all, because hypotheses require the retention of past experiences. Memory is the background against which hypotheses are tested, and therefore it cannot itself be treated as a hypothesis. To put it in Wittgenstein’s terms: memory is not a proposition that can be verified; it is the condition for the possibility of verification.
This leads to a striking conclusion. The “past” is not a domain of facts that exist independently of our memory; rather, the grammar of “the past” is constituted by the grammar of memory. When we say “the event happened,” we are not describing a realm of facts that we happen to have partial access to; we are using a concept whose meaning is given entirely by the practice of remembering, forgetting, and corroborating. This is not a skepticism about the past — Wittgenstein is not denying that events really happened. He is making a logical point about the grammar of temporal language: the past is not a hidden reality that memory pictures, but a dimension of discourse with its own rules. The past is what memory can bring into the present, and nothing more.
10. The Hypothesis of Other Minds
One of the most striking sections of the *Bemerkungen* concerns the problem of other minds. Wittgenstein approaches this not as a metaphysical puzzle (how can I know that other people have consciousness?), but as a grammatical investigation (what does it mean to say that someone else is in pain?).
The key passage is where Wittgenstein draws a parallel between the problem of other minds and the problem of the past. Just as we have no direct access to the past, we have no direct access to the inner life of another person. The other’s sensations are not given to me; I can only infer them from their behavior. But here the parallel breaks down in an important way. With memory, we have a primitive form of access to our own past; I can remember my own pain, even if I cannot remember the pain of another. But with other minds, I have no such primitive access — I cannot feel another’s pain.
Wittgenstein uses this to criticize the argument from analogy. The standard view is that I infer that others have minds because their behavior resembles mine when I am in pain, and I know from my own case that pain is accompanied by certain behavior. But Wittgenstein objects that this inference is not a hypothesis in the scientific sense. It does not admit of verification in the same way. If I try to verify that another person is in pain, I look at their behavior, listen to their words, check for physiological signs. But none of these give me the pain itself — they only give me more behavior.
What Wittgenstein is showing is that the concept of “another’s pain” is logically connected to behavior, not causally inferred from it. The criteria for “someone else is in pain” are behavioral criteria; there is no further fact of the matter beyond what these criteria reveal. The pain is not a hidden something behind the behavior; the behavior is the manifestation of the pain. To say “he is in pain” is to say that he is behaving in a certain way under certain circumstances, not to say that he has a private object that I cannot see.
This is a radical departure from the Cartesian picture of mind. For Descartes, the mind is a substance that thinks, and behavior is merely an effect of mental states. For Wittgenstein, the mind is not a hidden substance; it is laid out in behavior. The grammar of psychological language does not refer to inner objects; it expresses a pattern of behavior and circumstances. The problem of other minds is dissolved, not solved: there is no gap between behavior and the mind, because the mind is not the kind of thing that can be hidden. It is a grammatical mistake to think that we see only behavior and infer the mind; we see the person — the whole person, in their expressive movements — and that is seeing their mind.
11. The Nature of Solipsism and Its Dissolution
We now arrive at one of the most personally charged and philosophically difficult sections of the work: Wittgenstein’s treatment of solipsism. This is not merely an academic refutation of a philosophical position; it is a confrontation with the very temptation that his own earlier work had helped to crystallize.
The orientation here is crucial: Wittgenstein is examining what it *means* to say that “only my experience is real.” He treats this not as a false empirical claim but as a grammatical confusion — a misunderstanding of how language relates to the world. The solipsist does not make a mistake about facts; he makes a mistake about the logic of our language. Wittgenstein writes that the solipsist’s claim “I am the world” is not false but nonsensical, because it tries to say something that cannot be meaningfully said within the grammar of our language.
At this turn in the text, Wittgenstein introduces a remarkable diagnostic passage. He argues that the solipsist’s error lies in thinking that the subject is something that can be found in the world. The subject is not an object among objects; it is the limit of the world, not a part of it. This echoes the Tractatus but with a crucial difference: in the *Philosophical Remarks*, Wittgenstein no longer believes that this limit can be mystically gestured at. Instead, he insists that the very attempt to speak of the self as a limit is a grammatical illusion that must be dissolved by showing that the words have no use in our language.
The illumination here is that solipsism, properly understood, coincides with realism. If the solipsist says that only his experience is real, he is trying to draw a distinction between his experience and something else — but no such distinction can be drawn in language, because any attempt to speak of “another’s experience” already presupposes the grammar of experience that the solipsist claims to monopolize. Wittgenstein shows that the solipsist’s position, when pushed to its logical conclusion, becomes empty: if only my experience is real, then the word “my” has lost its contrasting term and becomes meaningless. The solipsist has not discovered a profound truth; he has simply made his language unusable.
12. The Role of Grammar as the Foundation of Philosophy
Following the dissolution of solipsism, Wittgenstein turns explicitly to a theme that will dominate his later philosophy: the nature of grammar itself. This section marks a significant departure from the Tractatus, where logical form was seen as something that language and reality share. Here, grammar is no longer a mirror of the world’s structure; it is an autonomous system of rules that determines what can meaningfully be said.
The key passage in this section concerns the idea that grammar is not answerable to reality. Wittgenstein writes that we cannot justify a grammatical rule by appealing to how things are, because the very notion of “how things are” is already expressed through grammar. If someone asks why we cannot say “This pencil is sad,” the answer is not that pencils lack sadness; the answer is that our grammar does not permit the combination of “pencil” with psychological predicates. The rule is constitutive of what it means to speak of pencils at all.
This is a radical departure from traditional philosophy, which had always assumed that language must conform to the world. Wittgenstein insists that the world does not dictate grammar; rather, grammar dictates what can count as a description of the world. The rules of grammar are arbitrary in the sense that they are not derived from reality, but they are autonomous in the sense that they define the very space within which reality can be spoken of. This does not mean that anything goes; it means that the limits of sense are internal to language, not imposed from outside.
The illumination is that philosophical problems arise when we misunderstand the autonomy of grammar. When philosophers ask whether time is real, or whether the external world exists, they are trying to step outside grammar and compare it with something that grammar itself makes possible. Wittgenstein’s method is to show that such questions are not false but nonsensical — they violate the rules of the very game they try to play. The task of philosophy is not to answer these questions but to dissolve them by clarifying the grammar that gives rise to them.
13. The Idea of “Phenomenological Language” as an Ideal
Wittgenstein now takes up a theme that was central to his thinking during the period immediately following the Tractatus: the possibility of a phenomenological language — a language that would describe immediate experience without any theoretical overlay. This project, which he had pursued with great intensity around 1929, is now subjected to a searching critique from within.
The orientation of this section is both retrospective and critical. Wittgenstein had once believed that a phenomenological language would capture the given — the raw data of sensation and perception — without the distortions introduced by physical language and hypothesis. The idea was that such a language would be primary, while ordinary language about physical objects would be secondary and derivative. But Wittgenstein now argues that this project rests on a fundamental misunderstanding of how language works.
The crucial passage here involves Wittgenstein’s realization that the given is not something that can be captured in a language. He writes that what we call “immediate experience” is not a kind of content that could be expressed in a special notation; it is already structured by the grammar of our ordinary language. The attempt to strip away the physical and reach a pure phenomenological core is like trying to find the real color of an object by peeling off its paint: there is nothing underneath. The idea of a phenomenological language is a grammatical mirage — it posits a form of expression that would be free from the very conditions that make expression possible.
The illumination is profound: Wittgenstein is turning against his own earlier program. He now sees that the search for a phenomenological language was motivated by the same illusion that drives solipsism — the idea that the self’s immediate experience is somehow more real or more fundamental than the shared world of objects. But if grammar is autonomous, then there is no “primary” language that mirrors reality directly; all languages are equally conventional, equally arbitrary, and equally expressive of the forms of life in which they are embedded. The phenomenological language is not a deeper truth; it is a grammatical mistake.
14. The Character of Visual Space and Its Intrinsic Order
Having rejected the possibility of a phenomenological language, Wittgenstein turns to a detailed examination of visual space — not as a candidate for such a language, but as a phenomenon that reveals the nature of grammar. This section is one of the most technical and fascinating in the entire work, as Wittgenstein attempts to describe the intrinsic features of visual experience without falling into the illusion of a private language.
The orientation here is crucial: visual space is not a kind of inner picture that we can inspect; it is a structure that is expressed in our ways of talking about seeing. Wittgenstein argues that visual space has its own logic — a logic that is different from that of physical space. For example, in visual space, things can be “colored” in ways that make no sense in physical space: a patch of red in visual space can be both round and not-round, depending on the organization of the visual field. This is not a contradiction; it simply shows that the grammar of visual space is different from the grammar of physical space.
The key passage in this section concerns the indeterminacy of visual space. Wittgenstein writes that visual space does not have a precise metric the way Euclidean space does. There is no absolute answer to the question “How big is this visual patch?” because the criteria of measurement that apply to physical objects do not apply to visual experiences. This indeterminacy is not a defect; it is a grammatical feature of the language of visual experience. The attempt to impose Euclidean precision on visual space is a category mistake — it confuses two different systems of grammar.
The illumination here is that visual space is not a model of physical space but an alternative grammar with its own rules. When we say that a visual patch “looks red,” we are not making a claim about a mental object; we are using a form of expression that has its own logic. The task of philosophy is not to reduce visual space to physical space or vice versa, but to understand the grammar of each and to see how they are related. This insight prepares the ground for Wittgenstein’s later work on aspect-seeing and the grammar of psychological concepts.
15. The Concept of “Hypothesis” and the Bridge Between Experience and Language
We now return to a theme that has been present throughout the work but is now given its most systematic treatment: the nature of hypothesis. Wittgenstein has already argued that ordinary propositions about physical objects are not directly verifiable by experience; they are hypotheses that go beyond what is given. But what does this mean for the relationship between language and reality?
The orientation here is that hypotheses are not simply guesses or predictions; they are grammatical forms that structure our talk about the world. A hypothesis is not a proposition that is more or less likely to be true; it is a rule for the construction of propositions. When we say “There is a chair in the next room,” we are not reporting an experience; we are making a claim that can be confirmed or disconfirmed by a range of possible experiences. The hypothesis unifies these experiences under a single concept.
The crucial passage in this section involves Wittgenstein’s analysis of the grammar of expectation. He argues that when we expect something to happen, the expectation is not a mental image that matches or fails to match reality; it is a method for predicting future experience. To expect rain is not to have a picture of rain in the mind; it is to be disposed to act in certain ways — to take an umbrella, to stay indoors, to check the sky. The expectation is expressed in behavior, not in mental content.
The illumination is that hypotheses are not descriptions of the world but techniques for dealing with it. This is a deeply pragmatic turn: Wittgenstein is arguing that the meaning of a hypothesis is not given by its correspondence with reality but by the operations that verify it. The traditional correspondence theory of truth is replaced by a theory of verification — but not a verification that finds its terminus in sense-data. Rather, verification is itself a grammatical process: to verify a hypothesis is to perform a series of actions that are themselves governed by rules. This prepares the ground for the later work on rule-following and the social character of language.
16. The Nature of Induction and the Grounds of Prediction
Building on the analysis of hypothesis, Wittgenstein now turns to the problem of induction — perhaps the most vexed issue in the philosophy of science. How can we justify predictions about the future? This is not merely a technical question; it strikes at the heart of the relationship between language and the world.
The orientation here is that the problem of induction, as traditionally conceived, rests on a misunderstanding. The philosopher asks: “What justifies the inference from past experience to future events?” and expects a rational answer. Wittgenstein argues that this question is itself a grammatical confusion. The concept of justification has its home within a language-game; outside of that game, it has no meaning. To ask for a justification of induction as a whole is to ask for something that cannot be given, because induction is itself one of the rules of the game.
The key passage in this section concerns the grammar of prediction. Wittgenstein writes that we do not predict the future because we have evidence that the future will resemble the past; rather, the very notion of evidence is constituted by the assumption that the future will resemble the past. Induction is not a hypothesis that could be confirmed or disconfirmed; it is the framework within which confirmation and disconfirmation make sense. To doubt induction is not to make a rational judgment; it is to step outside the language-game and leave oneself with nothing to say.
The illumination is that the problem of induction is not a problem to be solved but a grammar to be described. The philosopher who demands a justification of induction is like someone who demands a justification of the rules of chess before agreeing to play. The rules are not true or false; they are the conditions of the game. Similarly, induction is not a proposition that could be true or false; it is a form of life that makes prediction possible. Wittgenstein is not offering a justification of induction; he is showing that the demand for such a justification is nonsensical.
17. The Logic of Color Concepts and Their Internal Relations
We now encounter one of the most striking features of the *Philosophical Remarks* — the sustained analysis of color concepts. This is not a digression; it is a central part of Wittgenstein’s investigation into the nature of grammar. Color concepts are not arbitrary labels for sensations; they have an internal structure that determines what can and cannot be said about them.
The orientation here is that color concepts are governed by exclusion rules: if something is red, it cannot be green; if something is saturated, it cannot be pale. These are not empirical discoveries about color; they are grammatical rules that define what it means to be a color. Wittgenstein argues that the relation between colors is not a contingent fact about the world but a logical relation that is embedded in the grammar of our language.
The crucial passage in this section involves Wittgenstein’s analysis of the impossibility of a reddish-green. This is not a psychological limitation; it is a grammatical necessity. We cannot imagine a reddish-green color not because our brains are wired a certain way, but because the concepts “red” and “green” are so defined that they exclude each other. The impossibility is logical, not empirical. Wittgenstein writes that the color octahedron — the three-dimensional representation of color relations — is not a picture of how colors happen to be related; it is a rule for the use of color words.
The illumination is that this analysis shows the autonomy of grammar in a particularly clear way. The laws of color are not derived from physics or psychology; they are constitutive of the concept of color itself. If someone were to claim to see a reddish-green, we would not say that they have discovered a new color; we would say that they do not understand the meaning of the words “red” and “green.” The grammar of color is not a description of the world; it is a framework that determines what can count as a description. This is Wittgenstein’s most powerful demonstration of the thesis that grammar is autonomous — a theme that will reach its full development in the *Philosophical Investigations*.
*The Theory of Probability and Its Logical Ground*
We now enter a sustained examination of probability, which Wittgenstein treats not as a mathematical or empirical concept but as a fundamentally logical one. The orientation here is crucial: probability is not a measure of our ignorance or a frequency in the world, but a form of proposition — a special kind of logical relation between hypotheses and experience. Wittgenstein is dismantling the idea that probability belongs to the domain of psychology or statistics, and instead relocating it within the grammar of verification.
The passage that anchors this section is Wittgenstein’s claim that “The probability of an event is the degree of confirmation that a hypothesis receives from a given experience.” This is not a definition in the usual sense; it is a grammatical elucidation. He is saying that probability is not an intrinsic property of events themselves, but a feature of the logical relationship between a hypothesis and the evidence that bears on it. When we say that a coin has a probability of 1/2 of landing heads, we are not making a statement about the coin’s nature; we are expressing the logical form of our expectation, the structure of the hypothesis relative to the possible outcomes.
This move has profound consequences. Wittgenstein rejects the frequency theory of probability, which holds that probability is an empirical property of long-run sequences. For him, frequency is a secondary, derivative concept; the primary concept is the logical relationship between a proposition and its verification conditions. “A probability proposition,” he writes, “is not a hypothesis about the world but a rule for the transformation of hypotheses.” This is consistent with his broader project: all logical relations are internal, not contingent on empirical discovery. Probability, properly understood, is a part of grammar — it determines what counts as confirmation and disconfirmation, not as a matter of factual inquiry, but as a matter of the structure of our language.
The illumination here is that Wittgenstein is providing a logical theory of probability that anticipates the logical positivist program of Carnap, but with a crucial difference. For Carnap, probability is a semantic concept, defined in terms of state-descriptions and measure functions. For Wittgenstein, it is a syntactic or grammatical concept, embedded in the rules by which we transform one proposition into another. This is not a statistical or mathematical theory; it is a philosophical clarification of the role that probability plays in our language. The concept of probability, for Wittgenstein, is not something we discover in the world; it is something we bring to the world through the logical structure of our hypotheses.
*The Nature of Induction and the Ground of Prediction*
The problem of induction now receives a direct and radical treatment. Wittgenstein is addressing the classic philosophical puzzle: how can we justify the inference from past experience to future events? His answer is characteristically dismissive: the problem is not solved but dissolved by showing that induction is not a logical inference at all, but a presupposition of our language-game. The orientation is toward the foundation of empirical knowledge, and Wittgenstein is arguing that the demand for a logical justification of induction is based on a misunderstanding of the role that induction plays.
The key passage here is Wittgenstein’s statement: “The belief in the law of causation is not a belief in a proposition of experience, but a *form* of experience.” This is a direct echo of Kant, but with a crucial Wittgensteinian twist. The law of causation is not a synthetic a priori principle; it is a grammatical rule that governs how we form hypotheses and connect them to evidence. We do not discover causation in the world; we bring it to the world through the way we construct our descriptions. Induction is not a logical inference from the observed to the unobserved; it is the method by which we extend our hypotheses to new cases. The justification of induction, therefore, is not a logical problem but a practical one — it is embedded in the way we live and act.
Wittgenstein goes further. He argues that the very concept of “confirmation” presupposes a regularity that is not itself justified by experience. When we say that a hypothesis is confirmed by repeated observations, we are already employing a concept of regularity that is not derived from those observations. This is the transcendental dimension of Wittgenstein’s thought: the possibility of empirical knowledge rests on grammatical conditions that are not themselves empirical. The “law of induction” is not a proposition that can be true or false; it is a rule that determines what counts as a confirmation or a disconfirmation. This is the same move Wittgenstein made with the laws of logic: they are not descriptions of the world but frameworks for description.
The illumination shows that Wittgenstein is offering a pragmatic or conventionalist account of induction, but one that is grounded in his broader philosophy of grammar. Induction is not a problem to be solved; it is a practice that we engage in. The demand for a logical justification of induction is a demand that cannot be met because it is a demand for a proposition that would justify the framework within which propositions have meaning. This is the Wittgensteinian paradox: the very language in which we would formulate the justification of induction already presupposes the regularity that the justification is supposed to justify. Induction is not grounded in reason; it is grounded in the form of life that makes reason possible.
*The Status of Psychological Concepts and the Problem of Privacy*
The discussion now turns to psychological concepts — sensation, pain, thought — and the problem of how they can be communicated. Wittgenstein is laying the groundwork for the famous “private language argument” that will appear in the *Philosophical Investigations*, but here the treatment is more directly tied to his phenomenology. The orientation is toward the question: how can a word like “pain” refer to something that is essentially private to each individual? This is not a question about the metaphysics of mind; it is a question about the grammar of psychological language.
The crucial passage is Wittgenstein’s claim that “The words ‘I feel’ do not refer to a person. They are not a sign of ownership.” This is a remarkable disruption of our ordinary way of thinking. When I say “I feel pain,” we naturally think that “I” refers to a subject who owns the pain. Wittgenstein is denying this: the “I” in such sentences is not a referring expression at all. It is what he calls a grammatical subject, not a psychological one. The sentence “I feel pain” is not a description of a private mental event; it is a manifestation or expression of pain. The pain is not something I have; it is something I show.
This connects directly to the earlier discussion of solipsism. Wittgenstein argued that solipsism is not false but meaningless — it tries to say something that cannot be said because the conditions for saying it are not present. Here he applies the same logic to psychological concepts. The idea that I have private access to my own sensations is a grammatical illusion: it is not that I have a special kind of access, but that the grammar of sensation words does not allow for the kind of doubt that would make privacy a meaningful concept. I cannot doubt that I am in pain because the expression of doubt does not make sense in this context. The “privacy” of sensation is not a metaphysical fact; it is a logical feature of the language-game.
The illumination reveals that Wittgenstein is dissolving the problem of other minds, not solving it. If I cannot doubt my own pain, then the question “How do I know that you are in pain?” is not a question about evidence; it is a question about the grammar of the word “pain” when applied to others. The criteria for another’s pain are behavioral and situational — we see the pain in their face, their cries, their actions. This is not a second-best form of knowledge; it is the primary form. The idea that I have a special, privileged access to my own pain is a grammatical misconception: the “privilege” is not access to a private object, but the impossibility of doubt that is built into the grammar of first-person psychological statements.
*The Concept of the Will and Its Logical Expression*
The problem of the will receives a treatment that is both brief and profound. Wittgenstein is not offering a psychology of volition but a logical analysis of the grammar of willing. The orientation is toward the question: what does it mean to say that I will something? How is the concept of will related to action, to intention, to the body? Wittgenstein’s approach is to show that the will is not a cause of action but a form that action takes in language.
The passage that captures this is Wittgenstein’s remark: “The will is not a phenomenon but the *attitude* of the subject toward the world.” This is a radical departure from traditional accounts. The will is not something that happens in the mind, like a thought or a feeling; it is not an event that can be observed. Instead, it is the direction of the subject — the way the world is taken up into action. When I will to raise my arm, I do not first have a mental event called “willing” and then the arm rises; the willing is already in the act of raising. The will is not separate from the action; it is the logical form of the action as voluntary.
This connects to Wittgenstein’s treatment of the self in the earlier sections. The will is not an empirical object; it is a transcendental condition of experience. Just as the “I” in “I think” is not a person but a formal condition of thought, so the “I will” is not a report of an inner state but the expression of the subject’s engagement with the world. The will, for Wittgenstein, is not something we have; it is something we are — not as an entity, but as the limit of our world. This echoes the Tractatus’s claim that the will is the bearer of ethical value, but here the ethics is suppressed in favor of a purely grammatical analysis.
The illumination shows that Wittgenstein is providing a logical theory of action that avoids both dualism and reductionism. The will is not a mental cause of physical events; it is the form of agency that makes action intelligible. When we say that an action is voluntary, we are not describing a causal relation; we are placing the action within a logical space of reasons, intentions, and purposes. This is an anticipation of the philosophy of action that will be developed by Anscombe and others, but Wittgenstein’s treatment remains at the level of grammar: the concept of the will is a rule for describing behavior, not a hypothesis about an inner mechanism.
*The Nature of Time and the Structure of Experience*
The problem of time, already introduced in the earlier discussion of the “now,” receives a more systematic treatment. Wittgenstein is exploring the relationship between time as it is lived (the phenomenological “now”) and time as it is measured (clock time, physical time). His conclusion is that the concept of time is not a uniform concept; it has a grammar that depends on the context in which it is used. The orientation is toward the logical status of time, not its physics or psychology.
The key passage is Wittgenstein’s claim: “The *now* is not a point in time but a *form* of representation.” This is a profound reversal of our ordinary way of thinking. We naturally think of time as a line, with the “now” as a moving point on that line. Wittgenstein is denying this picture altogether. The “now” is not a moment; it is the structure that makes moments possible. In the same way that the visual field is not a part of the seen world, the “now” is not a part of time — it is the frame within which time is experienced. The “now” is not something we perceive; it is the condition for perception itself.
This connects to the earlier discussion of phenomenological language as a language of the immediate. Time, in this language, is not measured — it is lived. The “now” is not a point that can be compared with another “now”; it is the absolute present, the only point from which experience has meaning. Wittgenstein is arguing that the logical structure of time is not the same as the structure of a series. The “now” is not a term in a series; it is the limit of the series. This is why memory is not a representation of the past but a re-presentation of experience — the past is not a different place but a different form of the present.
The illumination reveals that Wittgenstein is moving toward a non-linear conception of time, one that is closer to Augustine than to Newton. Time is not a container in which events happen; it is a structure of experience that is determined by the logic of our language. The “now” is the anchor of all temporal reference — without it, there would be no distinction between past and future. This is not a theory of time but a clarification of the grammar of temporal language. The physicist’s time is a hypothesis, a convenient fiction for measuring and predicting. The philosopher’s time is the lived time of the “now,” which is the condition of any experience whatsoever.
*The Relationship Between Philosophy and Science*
The final sections of the *Philosophische Bemerkungen* turn to a meta-philosophical reflection on the nature of philosophy itself. Wittgenstein is clarifying the distinction between his own activity and the activity of the natural sciences. The orientation is toward the method of philosophy: what kind of inquiry is it? What are its results? How does it relate to the empirical sciences?
The definitive passage here is Wittgenstein’s declaration: “Philosophy is not a theory but an activity. A philosophical work consists essentially of elucidations.” This is a direct echo of the Tractatus, but with a crucial shift in emphasis. The Tractatus understood philosophy as the critique of language — the drawing of the limits of what can be said. Here, the emphasis is on activity: philosophy is not a body of doctrines but a practice of clarification. The philosopher does not discover new facts; they rearrange the facts we already have, showing us the logical structure that we have overlooked.
This leads to a sharp distinction between philosophy and science. Science is concerned with hypotheses — propositions that can be verified or falsified by experience. Philosophy is concerned with grammar — the rules that make verification possible in the first place. The scientist asks: “What is the case?” The philosopher asks: “What does it mean to say that something is the case?” The two inquiries are not in competition; they are on different logical levels. Science gives us knowledge of the world; philosophy gives us clarity about the language in which that knowledge is expressed.
The illumination shows that Wittgenstein is developing a therapeutic conception of philosophy. The problems of philosophy — the nature of time, the existence of other minds, the justification of induction — are not problems that can be solved by scientific research. They are grammatical confusions that arise when we misunderstand the logic of our language. The philosopher’s task is not to answer these questions but to dissolve them, by showing that they rest on a misunderstanding of how language works. This is the negative or critical side of Wittgenstein’s project: philosophy is a battle against the bewitchment of our intelligence by means of language. The *Philosophische Bemerkungen* is the workshop in which this therapeutic method is being forged.
*The Limits of Language and the Mystical*
The work concludes with a return to the theme of the limits of language, which was the central concern of the Tractatus. Wittgenstein is exploring the idea that there are things that cannot be said but only shown. The orientation is toward the boundary between sense and nonsense, the line that separates what can be expressed in propositions from what eludes propositional expression entirely.
The final passage of the work is Wittgenstein’s meditation: “What we cannot speak about we must pass over in silence.” This famous sentence from the Tractatus is here given a new context. The silence is not a refusal to speak but a recognition of the limits of language. The things that lie beyond those limits — the sense of life, the nature of the world as a whole, the mystical — are not things that can be captured in propositions. They are shown, not said. And the philosopher’s task is to show them through the very act of drawing the limit.
The illumination reveals that the *Philosophische Bemerkungen* ends not with a solution but with a gesture toward the inexpressible. Wittgenstein has spent the entire work clarifying the grammar of our language, showing how concepts like time, probability, will, and induction are grounded in logical rules rather than empirical facts. But this clarification has a point: it is meant to free us from the illusion that everything can be said, that the world can be fully captured in propositions. The limits of language are not a prison; they are the condition of meaning. And what lies beyond those limits is not nothing; it is the mystical — the sense of the world as a limited whole, which cannot be described but only felt. The work ends in silence, but it is a silence that speaks.
