Notes on Wittgenstein’s Tractatus Logico-Philosophicus

Wittgenstein’s Tractatus Logico-Philosophicus

• What can be said at all can be said clearly, and what we cannot talk about we must pass over in silence.

• The world is not a totality of things, only a totality of facts. The totality of facts is all that is the case, and the case is the world.

• Facts in logical space are the world.

• Facts are the existence of states of affairs. A state of affairs is a combination of objects (things). Things are constituents of states of affairs.

• If a thing can occur, the possibility of it occurring in a state of affairs is already given.

• There is no object that we can imagine that can’t be combined with other objects in state of affairs.

• Knowing an object, means knowing all its possible occurrences in state of affairs; a new possibility cannot be discovered (a new object is discovered).

• When all objects are given, all possible states of affairs are also given.

• Objects contain the possibility of all situations. The form of an object is the possibility of it occurring in a state of affairs. Objects are simple and make up the substance of the world.

• Substance is what makes possible a picture of the world. Substance of the world is the form of an object, and not any material properties. Material properties are represented only by propositions, which are based on objects.

• Objects can be different even when they have the same logical form.

• Objects need a distinguishing element to enable us to distinguish them from others.

• Substance is the form and content of objects; objects must be unalterable if the world is to have substance. The configuration of objects is what is changeable.

• States of affairs contain objects in relation to each other; these relations are the structure of states of affairs or the structure of facts.

• The world is the totality of existing states of affairs, which also determines states of affairs that do not exist.

• Reality is the existence and non-existence of states of affairs. The sum-total of reality is the world.

• We picture facts to ourselves as models of reality. Pictures contain representatives of objects as elements of the picture. A picture is a fact.

• Elements of a picture are related to each other in a structure; called pictorial form. Pictorial form is the possibility that elements of the picture are related in the same way as things are related. A picture reaches out and becomes attached to reality.

• Pictorial form is what the picture has in common with reality; it has in common its logical form.

• A picture displays its pictorial form. Every picture is a logical one and logical pictures can depict the world.

• A picture depicts reality by representing a possibility of existence or non-existence of states of affairs.

• A picture is a possible situation in logical space that either agrees or disagrees with reality (true or false).

• A picture represents its sense by means of its pictorial form. Agreement or disagreement of a picture’s sense (or pictorial form) with reality is its truth or falsity. A picture must be compared to reality to determine its truth or falsity.

• A logical picture of facts is a thought.

• We can picture states of affairs to ourselves; we make them thinkable.

• Totality of true thoughts is a picture of the world.

• A thought includes the possibility of what is thought and what is thinkable.

• Thought can never be illogical; they always have their own logic. We could not say what an “illogical” world would look like.

• It is impossible to represent in language anything that contradicts logic.

• A proposition is a thought expressing what can be perceived by the senses.

• A projection of a possible situation is a perceptible sign of a proposition.

• A proposition is a propositional sign that is projected.

• A propositional sign is a fact and is determined by how words stand in relation to one another.

• A proposition contains the form but not the content of its sense (words are empty and listeners fill in the sense).

• A proposition is articulate and not a blend of words. Only facts express a sense.

• Objects of thought correspond to elements (simple signs) of the propositional sign of a proposition.

• Simple signs are called names.

• A name is a representative of an object and an object gives names meaning.

• The configuration of simple signs in a propositional sign corresponds to the configuration of objects in a situation.

• Objects can only be named. Signs represent objects. I can only speak about objects, I cannot put them into words. Propositions can only say how things are, not what they are.

• The possibility of simple signs determines sense.

• A complex is given by its description; a proposition about a complex is made up of propositions about constituents of the complex.

• A proposition has only one complete analysis.

• A name is a primitive sign. Elucidations explain the meaning of primitive signs and are propositions.

• A name has meaning only in a proposition. A part of a proposition is an expression or symbol. An expression/symbol is a mark of a form and its contents.

• The expression is constant in a class of propositions and everything else is variable.

• Expressions amongst different propositions are variable; called a propositional variable.

• An expression has meaning only in a proposition.

• A class of propositions have the same value of propositional variable. The value is stipulated and describes those propositions.

• Symbols are perceived as signs.

• Signs can be common to two different symbols.

• Modes of signification indicate common characteristics of symbols.

• The same word can have different modes of signification and so belong to different symbols. For example, is as a sign for identity and existence. This generates fundamental confusions in philosophy and elsewhere. These are avoided by using sign-language with logical syntax.

• A proposition has essential (enabling the proposition to express its sense) and accidental (the way the propositional sign is produced) features.

• The sense that a group of propositions have in common is their essential feature.

• The essential feature of a group of symbols is the purpose they have in common.

• The name of an object is what is common among symbols that signify the object.

• When we determine one thing arbitrarily, another thing is necessary.

• The possibility of a mode of signifying is more important than a particular mode of signifying; it discloses something about the essence of the world.

• Symbols can be substituted when what signifies in a symbol is common to those symbols.

• A proposition determines a place in logical space. This space exists because of the existence of the constituents and the sense of the proposition.

• This logical place is a propositional sign with logical co-ordinates; it is a possibility that something can exist in it.

• One proposition determines one logical space; but it gives the whole of logical space.

• A thought is a propositional sign that is applied; it is a proposition with a sense.

• The totality of propositions is language. Language expresses every sense.

• Language disguises thought, it is clothing that hides the body of thought underneath.

• Most propositions and questions in philosophy are not false but nonsensical; they arise from failure to understand the logic of language.

• Philosophy is a critique of language; the apparent logical form of a proposition need not be the real one.

• A proposition is a picture of reality and a model of reality as we imagine it. The pictorial character is not impaired by apparent irregularities; irregularities still depict what they express.

• A record, musical notes, sound waves are constructed to the same logical pattern. There is an internal relation between language and the world.

• The logic of depiction contains the possibility of all imagery and expression.

• A proposition is a picture of reality, which represents a situation. A proposition shows its sense, or how things stand, if it is true.

• A proposition restricts reality to yes or no. It must describe reality completely.

• A proposition is a description of a state of affairs. It describes reality by its internal properties. It constructs a world using a logical scaffold.

• Understanding a proposition means to know what is the case if it is true; it is still understandable without knowing if it is true. You understand by understanding the constituents.

• The meaning of simple signs (words) needs to be explained to be understood. However, with propositions we make ourselves understood.

• Propositions can communicate a new sense from old expressions. Propositions communicate/represent a situation by connecting to the logic of the situation by means of a logical picture.

• Names stand for different things. Combining names presents a state of affairs.

• Objects have signs as their representatives. But the logic of facts cannot be represented. Propositions are pictures of situations only because they are logically articulated (the logic of facts can only be represented if we step outside of logic and view it from the outside, which is impossible).

• Propositions must contain equal numbers of parts as the situation.

• Reality is compared with propositions. A picture is true or false if it is a picture of reality. However, propositions still have a sense that is independent of facts; they can be understood without knowing if they are true or false.

• An analogy of truth: imagine a black spot on a white piece of paper. The shape of the spot can be described by saying, for every point on the paper, whether it is white or black. A black spot is a positive fact and a white spot is a negative fact. I must know when a spot is black or white. Determining when a spot is black is the sense of a proposition.

• A proposition has no sense if nothing corresponds to it (it says only a point is indicated) and it has no truth value (“black” or “white”)

• Every proposition must already have a sense.

• Negated propositions have a logical place different to the proposition that negates it.

• Propositions represent the existence and non-existence of a state of affairs. The totality of true propositions is natural science.

• Philosophy is not a natural science; it logically clarifies thoughts by elucidation; it is not a doctrine but an activity.

• Philosophy sets limits to natural science and what can/cannot be thought and what can/cannot be said.

• Propositions cannot represent logical form (logical form can only be represented if we step outside of logic and view it from the outside, which is impossible); they mirror logical form.

• Language cannot represent/express logical form. Propositions and language display logical form but cannot represent logical form. What can be shown cannot be said.

• There are internal and external properties of objects and states of affairs. Internal property of a fact is a feature of the fact.

• Internal properties of propositions represent the internal properties of possible situations.

• Language expresses the existence of an internal relation between possible situations. It does this by expressing the internal relation between the propositions that represent the situation.

• Formal concepts are formal properties. Formal concepts contain objects and are expressed by signs. The expression of formal properties is by means of certain symbols. Symbols of a concept are indicated by the sign of a formal concept.

• Expression of a formal concept is a propositional variable.

• Propositional variables signify the formal concept. Values of the variable signify the objects under the concept. Every variable is the sign for a formal concept; every variable is a constant form that all values have and is the formal property of values.

• It is nonsensical to speak of the total number of objects. Logical forms are without number.

• To ask whether a formal concept exists is nonsensical because no proposition can answer it.

• The sense of a proposition can agree or disagree with the possibility of existence or non-existence of states of affairs.

• Elementary propositions (the simplest proposition) assert the existence of states of affairs. They consist of names. Names are simple symbols.

• Elementary propositions cannot be contradicted by other elementary propositions; that’s what makes them elementary.

• Analysis of propositions uncovers elementary propositions.

• The world contains objects and states of affairs whether it is infinite or not.

• If an elementary proposition is true the state of affairs exist; if false, it doesn’t exist.

• If all elementary propositions are given, and their truth or falsity is also given, the world is completely described.

• Truth-possibilities of elementary propositions express the possibilities of existence and non-existence of states of affairs.

• Propositions agree or disagree with truth-possibilities of elementary propositions; propositions are true or false according to truth-possibilities of elementary propositions; expressed as the truth-conditions of propositions.

• It is impossible for a proposition to state itself that it is true.

• Extremes of truth-conditions are: tautological (proposition is true for all truth-possibilities of elementary propositions) and contradictory (proposition is false for all truth-possibilities of elementary propositions).

• Tautologies and contradictions say nothing, they have no truth-conditions. But they are not nonsensical. They are not pictures of reality since tautologies admit all possible situations and contradictions admit none.

• Truth-conditions of propositions are the range of possible facts expressed by the proposition.

• A proposition is like a solid body restricting freedom of movement of other propositions.

• General form of propositions: this is how things stand; a variable.

• If I’m given all elementary propositions, I’m given all propositions.

• A proposition is a truth function of elementary propositions.

• Truth-grounds are the truth-possibilities of a proposition; they form the truth-arguments of a proposition that make that proposition true.

• If the truth-grounds of a group of propositions are the same as a certain proposition, then the truth of that proposition follows from the other propositions. This is seen in the shared structure of the propositions.

• A proposition affirms every proposition that follows from it.

• Two propositions oppose each other if there is no proposition (with a sense) that affirms them both.

• Every proposition that contradicts another negates that proposition.

• Propositions that follow from a proposition can be deduced from the first proposition. All deductions are made a priori.

• One elementary proposition cannot be deduced from another.

• The events of the future cannot be inferred from the present; there is no causal connection; only a logical connection.

• Freedom of will consists in the impossibility of knowing the future from the present.

• A proposition is neither probable nor improbable; it simply occurs or it doesn’t.

• Structures of propositions stand in internal relations to one another; this is an operation from other propositions (other proposition for the base of the operation).

• An operation is an expression of the relation between the structures of propositions.

• Truth-operations are operations of truth-functions of elementary propositions; formed from elementary propositions as bases.

• An operation gives expression to the difference between the forms of propositions.

• Operations can cancel each other out.

• All propositions result from truth-operations on elementary propositions.

• Truth-functions are produced out of elementary propositions by truth-operations.

• Truth-operations are applied to truth-functions of elementary propositions. This generates another truth-function of elementary proposition, or a proposition.

• Every proposition is the result of truth-operations on elementary propositions.

• Truth-functions are truth-operations on elementary propositions.

• All propositions of logic say nothing.

• With a proposition comes the result of all truth-operations.

• Logic has primitive logical signs. In logic the general and specific are the same.

• The general propositional form is the essence of a proposition. The essence of a proposition is the essence of all description, and hence the world. It is a description of the general primitive sign in logic.

• If a sign is possible, it signifies. Whatever is possible in logic is also permitted.

• Logic is a priori since it makes illogical thought impossible.

• The positive proposition presupposes the existence of the negative proposition.

• If objects are given, then all objects are given; if elementary propositions are given, then all elementary propositions are given.

• Situations are expressed by a tautology, a proposition with sense or a contradiction.

• The world is described by generalised propositions.

• Generalised propositions are composite; the totality of elementary propositions is the same in generalised proposition.

• To say two things are identical is nonsense; to say one thing is identical to itself is to say nothing.

• To perceive a complex means to perceive its constituent parts are related to one another.

• Elementary propositions consist of names.

• A question decided by logic means it is possible to decide.

• Logic is prior to every experience.

• There is no hierarchy to elementary propositions; we only see what we construct.

• Empirical reality is limited by the totality of objects and the totality of elementary propositions.

• Hierarchies are and must be independent of reality.

• All propositions in everyday language are in perfect logical order.

• The limits of my language mean the limits of my world.

• Logic pervades the world. Limits of the world are logic’s limit.

• We cannot say in logic what the world has in it and what it does not; excluding certain possibilities requires logic to go beyond the limits of the world – the limits of a thing are only seen if you can step outside the thing and see it from the other side. Logic can only think logically; language can only articulate logically. The world, being limited by language, can only be logically constructed if it is to have sense. The world only includes logical objects; therefore, nothing logical is excluded from a necessarily logical world.

• We cannot think what we cannot think; what we cannot think we cannot say either.

• The world is my world; the limits of language mean the limits of my world.

• The world and life are one. I am my world.

• There is no such thing as a subject that thinks ideas. The subject does not belong to the world; it is the limit of the world. The eye cannot see itself, only its limit.

• There is no a priori order to things.

• The philosophical self is the limit of the world.

• The propositions of logic are tautologies and say nothing; this shows the formal, logical, properties of language and the world.

• Propositions of logic represent the scaffold of the world; they have no subject matter.

• Proof of logical proposition is a tautology generated from tautologies.

• Logic is a mirror image of the world.

• Language itself provides the necessary intuition.

• Exploration of logic means the exploration of everything subject to a law; the rest is accidental.

• Newtonian mechanics imposes a unified form on the description of the world. It covers the world with a fine square mesh (other meshes are possible). Different meshes correspond to different systems for describing the world.

• Describing the world with meshes tells us nothing about the world; only that it is possible to describe it by this means.

• There are no grounds for believing that the simplest eventuality will be realised.

• It is a hypothesis that the sun will rise tomorrow; we do not know.

• There is no necessity making one thing happen because another has happened; there is only logical necessity.

• The world is independent of my will.

• There is only logical necessity; also, there is only logical impossibility.

• The sense of the world must lie outside the world. In the world, everything is as it is. There is no value in it. All that happens and is the case is accidental.

• What is non-accidental must lie outside the world. Propositions of ethics is impossible. Ethics cannot be put into words.

• Good or bad exercise of the will alters only the limit of the world; this cannot be expressed by language.

• At death the world does not alter, it comes to an end. We do not live to experience death.

• Eternal life, timelessness belongs to those who live in the present.

• There is no guarantee of temporal immortality of the human soul.

• The solution of the riddle of life in space and time lies outside space and time.

• How things are in the world is a matter of complete indifference for what is higher. God is not in the world.

• Facts set the problem, not the solution.

• How things are in the world is not mystical, but that it exists at all is mystical.

• When the answer cannot be put into words, neither can the question. If the question can be put into words, so can the answer. Riddles do not exist.

• Doubt can exist only where a question exists, only where something can be said.

• Problems of life are left untouched when all scientific questions are answered.

• Solution of the problem of life is the vanishing of the problem.

• There are things that cannot be put into words.

• Method in philosophy: philosophy says nothing except what can be said, which is the propositions of natural science; which has nothing to do with philosophy.

• Philosophy demonstrates failure to give certain meanings to certain signs in propositions.

• Wittgenstein’s propositions, when they are understood, are nonsense; they should be used to climb beyond them. His propositions should be transcended.

• What we cannot speak about we must pass over in silence.