Thursday, January 3, 2008

Notes on the Tractatus Logico-Philosophicus

Ludwig Wittgenstein’s (1889-1951) Tractatus logico-philosophicus is a difficult book. But this should not prevent us from examining its important insights. This work is an attempt to grapple with Wittgenstein’s first book, the only one published during his lifetime. Although the goal of the Tractatus in constructing a logically perfect language is a mission impossible, it yields important philosophical points of view explaining the relationship between language, logic, and reality worthy of our philosophical scrutiny.We have lifted several epigrams from the Tractatus. An explanation follows each epigram.

1. The world is all that is the case.

The world is the sum total of all state of affairs. Truth belongs to the world, and what is beyond it cannot be expressed. To express the meaning of the world means to express what can be said about it.For logical atomists, reality consists of objects. “Only objects exist, and ideas are mere mental copies of objects.” (PA) Multiplicities have to be admitted since this is the actual state of affairs of things.The statement also expresses the limitation of human knowing. Since the world is all that is the case, the object of human knowledge is limited to what can be known in the world.Thus, what can only be meaningful is the world and everything that can be said about it. The world exists like a compendium of facts, and language, that tool that describes what the world is like, presents the world into a form that makes communication and understanding possible.

1.1 The world is the totality of facts.

This totality is revealed in language by means of atomic propositions. A proposition, says Wittgenstein, is a picture of reality. Propositions picture facts. The meaning of a proposition, then, comes from the fact it pictures. Whatever is pictured is in the picture. Language, logically speaking, is factual. Language, according to the philosophy of logical atomism, must be founded on logic and mathematics. The fact that the world has a logical order can only mean that language can only be logical, if it is to be construed as meaningful. The world, in this sense, and its logical order, can only be revealed linguistically.

1.13 The facts in logical space are the world.

Logical space here refers to the conditions for the possibility of existence or non-existence of facts. What can be said or expressed about the world is the existence or non-existence of facts situated in infinite logical possibilities. These facts constitute the sense of the world. Sense is anything that can be said about the world, and what can be said about it is determined by the facts so constituted in different states of affairs.

2. What is the case – a fact – is the existence of states of affairs.

The existence of states of affairs refers to the truth-condition of the world. What is true or factual is that only states of affairs exist. The world in this sense is made up of the different states of affairs of things. Reality is the sum total of all these states of affairs.

2.01 A state of affairs (a state of things) is a combination of objects.

States of affairs reflect the truth-conditions of objects. States of affairs refer to the way things are together with the facts that constitute them. Facts and their relations to objects characterize the over-all make up of the world.A fact is a quality added to an object. Let us make an example. In “a small red patch”, the patch is characterized as “small” and “red”. So we ask, what kind of thing is it? “red” and “small”. That it is “red” and that it is “small” constitute the states of affairs of the patch. Thus, states of affairs show the different conditions of the various things in the world. A room, for instance, can be “overcrowded”, “dimly lit”, “spacious”, etc.

2.02 Objects are simple.

Objects are simple because they are the basic stuff of the world. An object is that which is not yet predicated of something. If we take a closer look at reality, the world is made up of objects. Hence, “objects make up the substance of the world.”(TLP) Simplicity for an object here means the capacity to be predicated of something. A “flower”, as an object, is a simple reality. It becomes a complex thing when we talk of “magnolias”, “cattleyas”, “tulips”, etc. because of the distinct characteristics of each of these flowers.

2.0232 In a manner of speaking, objects are colorless.

Here, Wittgenstein explains what an object is. As a basic unit of reality, it is not predicated of anything. It is independent of any factual characterization. When it is predicated of something, it is only in such time that it becomes a thing. Facts characterize an object. When a patch contains some color, it becomes a thing.

2.024 Substance is what exists independent of what is the case.

What is the case is the existence of facts. Substance exists independent of facts. A “chair” as a substance is not necessarily brown. The one we use in school is a chair, the one we have at home is a chair, the one we have in the theater is a chair, etc., and so there are many types of chairs, but there is one and only one concept we understand as “chair”. This is because a chair does have one and only one substantial definition.Moreover, objects constitute the substance of the world, and as such objects contain the possibilities of the world. An object can possess different factual characterizations. That it can be characterized as such and such is contained in its possibility as an object.

2.0251 Space, time, and color are forms of objects.

Objects can be here or there, old or new, black or white. A car can be red, blue, or black. But although we see different colors, we see only one substance there, that of a car. We don’t see different cars, what we see are differently-colored cars. This is because a car can have many forms, and forms vary by virtue of the facts we attach to objects.

2.063 The sum total of reality is the world.

What is real? What is real is the existence of state of affairs. The world consists of facts. Facts constitute the reality of the world. What is not factual, that which is beyond the sense of logical thinking, is nonsense.Bertrand Russell believes that language can be broken down into atomic or elementary propositions. The sum total of these atomic propositions is the world. He calls them atomic because they are the most basic (following chemistry - an atom is the smallest particle of matter). What can be said about the world can be said by means of propositions. Language is no more than the collection of all atomic propositions. Language, therefore, as a repository of what can be said about the world, is the repository of what reality is.

2.1 We picture facts to ourselves.

Thinking is like picturing something. Since the world is factual, thinking about the world means thinking of a factual world.Thoughts are expressed linguistically. Since we picture facts to ourselves, the only way by which these facts can be pictured is by means of language. I do this when I make propositions. Picturing, in this sense, is a linguistic activity. Language is a tool. We use it to express facts to ourselves. To tell someone about what a chameleon is, I have to describe such in words. I paint a picture of such by means of words.

2.12 A picture is a model of reality.

A model is like a re-creation in our minds about the way a certain thing is. A diorama is a model of a building or of a certain structure. It is not the structure itself, but it brings us into the meaning of the structure. The meaning being the sense, the point of how a thing looks like. It is not the thing but it helps us perceive the thing. We look at reality by modeling the words we utter to the actual world. Meaningful words are models of reality. My language is based on my world. Wittgenstein has shown that the limits of our language show the limits of our world. For instance, it is impossible for me to speak in the Russian dialect because I’ve never heard nor conversed in Russian. More than that, this implies that there are concepts in a language which I may not understand simply because I do not live in the context of that form of language. As an example, the statement “~(J v A) v [(S v K)] v ~(J v A)” may prove too much to someone who does not have any formal training in symbolic logic. This does not mean, however, that language can’t be learned. What I am trying to emphasize is the fact that I can only deal with a language where I can picture the meaning of the signs such a language have.

2.13 In a picture objects have the elements of the picture corresponding to them.

A picture displays the sense of objects. Henceforth, a picture cannot be a mere copy. It must be an authentic copy. Whatever is in the picture must be a definite description of what it models. It may not perfectly describe the thing it pictures, but there is always an enough approximation that makes identification possible. Otherwise, such can’t be the picture of something.

2.131 In a picture the elements of the picture are the representatives of objects.

The elements of the picture refer to the configuration of the properties of the picture. These elements refer to the varying conditions that objects can have. These variations are reflected in the picture so that objects are properly represented in the picture.

2.141 A picture is a fact.

Language correctly describes the world in terms of factual statements since the world is a factual one. These factual statements are pictures of state of affairs. Language, as a picture of the world, is factual. Otherwise, language would not be able to say anything about the world.What is a fact? A fact is whatever that can be predicated of something. A thing is therefore no more than the facts that constitute it. Facts in this regard describe the kind of thing a thing is. Things always have factual content, this factual content being their state of affairs. In the proposition “There exists one and only one x such that this x is both man and mortal,” the facts man and mortal are the state of affairs of x.A proposition with one particular fact is called a monadic fact. A proposition with two particulars is called a dyadic fact. A proposition with three particulars is called a triadic fact. (PA)In p(x.y.z) the variables x, y, and z represent facts. This we can translate to “my notebook is small, red, and new.”Monadic: p is small or p(x)Dyadic: p is small and red or p(x.y)Triadic: p is small, red, and new or p(x.y.z)

2.151 Pictorial form is the possibility that things are related to one another in the same way as the elements of the picture.

Pictorial form can be elucidated by way of the following:That the elements in the picture measure up to the way things are situated in logical space.The elements, being the properties that configure the things in the picture, show the similarity between the logical possibilities of the picture and that of reality.The way things are related to each other in a particular situation, say the way fruits are arranged in a table can be observed as the same condition one sees in a picture, if such a picture were to be a true picture of such reality.

2.1512 That is how a picture is attached to reality; it reaches right out to it.

A picture is a copy of reality. A picture brings us to reality. A picture then does not lie. An ugly picture is a result of the ugly reality it has pictured. Thus, what is pictured is always seen in the picture. A picture always speaks for itself. A picture represents reality. It shows the truth condition of a thing. It shows the states of affairs of things.

2.16 If a fact is to be a picture, it must have something in common with what it depicts.

A picture is a fact (TLP). It is only in such an instance that a picture may correctly represent reality. Since reality is factual, a picture must also be factual. For instance, if I picture a stone in my mind, I am thinking of the stone’s correlation with reality. If I am thinking of a bird made of stone, I cannot be thinking of a bird in flight since a bird that is made of stone (statues, etc.) can never fly. To find something in common with reality means that a picture reveals something that is logically connected to what is real.

2.161 There must be something identical in a picture and what it depicts, to enable the one to be a picture of the other at all.

What is identical in a picture and what it depicts is factual content. What is in the picture, what is in my mind, is the actual condition of what I am looking at or perceiving. To think of something that does not exist is not thinking at all. If I picture a griffin, I am not picturing something real. It is not a real picture. But I can create it in my imagination. However, its sense cannot be established since it does not actually exist. It is not a fact. There can be no identity since it cannot be compared with something. A griffin is not something. It is but an idea where I have combined an eagle and a lion. Its ontological status cannot be established. Thus, in thinking about a griffin, I am really thinking of a lion with the head and wings of an eagle. Without the reality of these two creatures I would never create in my imagination the idea of a griffin. On the one hand, it is called a griffin since I have assigned it a name. It is no more than that.

2.181 A picture whose pictorial form is logical form is called a logical picture.

Pictorial form refers to the arrangement of the elements in the picture. It prescribes the connectedness of the different elements in the picture. This connectedness is logical. This connectedness ensures that the picture is a logical one. A picture, if it is to depict a logical world, must be faithful to the logical structure of the world.When I think of something, my thought follows a logical order. I can only think or picture out something correctly if my thinking adheres to the terms of logic. An illogical world is unthinkable, as we have shown above.

2.182 Every picture is at the same time a logical picture.

Because I can only picture a logical world, my picture of the world is a logical one, if and only if I make the right propositions. Language, as a picture of the world, acts as a logical picture, since it is structured in such a way that it has factual content that in turn gives language its sense. Only “logical pictures can depict the world.”(TLP) This is because the world has a logical structure. Logic serves as the backbone in the way we think and express the meaning of the world. Thus, language, if it is a correct expression of the world, must be grounded on logic.

2.201 A picture depicts reality by representing a possibility of existence and non-existence of state of affairs.

A picture, or a proposition for that matter, either affirms or denies the existence or non-existence of state of affairs. What is real is to be tested by the propositions we make. What makes sense is that which is answerable by a yes or a no. The possibility of being able to say yes or no rests on the actuality or possibility of certain state of affairs. It does make sense when it can’t be answered. This is because “a picture contains the possibility of the situation that it represents.”(TLP)

2.21 A picture agrees with reality or fails to agree; it is correct or incorrect, true or false.

Sense, logically speaking, is reducible to a true or false question. A picture then is true if it pictures what is real, false if it does not. Thus, says Wittgenstein, “what a picture represents is its sense.”(TLP) In language, a proposition is true if it agrees with reality, false if it does not. Wittgenstein affirms this by saying that “the agreement or disagreement of its sense (the proposition) with reality constitutes its truth or falsity”. (TLP)

2.223 In order to tell whether a picture is true or false we must compare it with reality.

Following Russell’s theory of descriptions, acquaintance is the only way to know if an assertion is valid or not. It is not valid if we are not acquainted with its constituent parts. If there is no acquaintance, there is no sense. Here, we affirm the empiricism of the Tractatus. If a statement does not contain any truth, it is no more than a sentence whose words mean nothing. If a statement confirms something about the world, then it is saying something. It makes sense. The importance of verification is due to the fact that “it is impossible to tell from the picture alone whether it is true or false.”(TLP)

3. A logical picture of facts is a thought.

It might be important to analyze the meaning of thought here. Thought is the product of the process of thinking. When we think of something, we have a thought about something. What we are concerned of is the content of our thoughts. For Wittgenstein, we can only think about facts. The reason for this is the fact that the world is all that is the case. Hence, we can only think of a factual world, a world that is there. Thinking is thinking about whatever is “in” the world. True thinking is factual thinking. The process of thinking begins with perception since it is only through the senses where we gather the raw data that our minds assemble to form a thought.

3.001 ‘A state of affairs is thinkable’: what this means is that we can picture it to ourselves.

What we think of are the state of affairs of things. Thinking is picturing. I am thinking in terms of the pictures that I can make in my mind. To think of a chair then is to picture a chair, say its shape, color, weight, etc. If I think of a happy life, happiness is not as simple as thinking about a chair. But still, I can picture it in my mind, since I have observed how people behave when they are happy.

3.01 The totality of true thoughts is a picture of the world.

My thoughts are no more than a picture of the world. If for instance, I think of a tikbalang, a creature that is half-man and half-horse, the possibility of my being able to think about it is the fact that I have seen a man and a horse and that I know the concept of half. A tikbalang in this sense cannot be true, and I can come up with such a thought only because I can think of a man and a horse as conjoined objects. I can’t think of something beyond. I can only think in terms of the world I inhabit.

3.03 Thought can never be anything illogical, since, if it were, we should have to think illogically.

We can never imagine an illogical world since our minds are conditioned in such a way that it can only think in terms of the logical order of the world. It is impossible to draw an illogical world. If we think illogically, it does not mean that the world is illogical. It only means that there is something wrong in the process of thinking. What becomes illogical then is not the world, but the way we think.

3.031 It is impossible to represent in language anything that contradicts logic…

Logic serves as the backbone of language. It acts as its skeleton. The structure of language follows the structure of logic. Language, in this sense, is only meaningful when it has a logical order. This is because language reflects the world. For language to properly picture the world, it must be grounded on the true condition of the world.

3.1 In a proposition a thought finds an expression that can be perceived by the senses.

“A proposition is a statement in which anything whatsoever is affirmed or denied.”(IL) Let us examine this definition. First, a proposition is a statement. But a proposition cannot just be any statement. Let us consider the following: 1. My God! 2. Who am I? 3. I am 21 years old.Statement number one does not state a fact. A proposition cannot just be a mere expression of an emotion. Rather, it must affirm or deny something. What it affirms or denies is a fact. A proposition, therefore, is always a factual statement. Consider statement number two. The second statement is not a proposition because it does not declare anything. It simply asks. There is nothing whatsoever in it. If, however, we consider statement number three, common sense tells us that it does say something. It declares a fact. It states a truth-condition. If a proposition says something true, then it affirms something about reality. If it states something false, then it denies something about reality. Knowledge is nothing but the sum total of all factual statements. If we are to judge the value of our assertions, it is good to note that science as a discipline dwells on the facts of human experience and not on speculation. In looking for the cure of certain diseases, the scientist relies on hard data and never on mere speculation. In law, for instance, the only way to establish the guilt or innocence of an accused is through the evidences presented in court. The judge cannot simply make a guess on the merits of the case. He has to rely on facts.

3.11 We use the perceptible sign of a proposition as a projection of a possible situation.

The method of projection is to think the sense of the proposition.Projection here refers to the capability of perceiving the sense of something. When we project a certain meaning, we refer to the sign of a proposition in order to know what it tries to project. Projection here means picturing. A painting, for instance, projects a certain situation. A painting is compared with reality. The painter projects what is real in a painting. What is projected is the meaning or the sense of the proposition. The word directs my attention to the sense of an object. For instance, to understand what the color red means, the sign/word “red” directs me to a color sample, a thing that is red. Only then can I get the sense of the sign.

3.12 I call the sign with which we express a thought a propositional sign.

Let us examine the proposition “This is poison.” What is the meaning of the proposition? We refer to the sign “this” and “poison”. By “this”, we mean a definite object, though such an object is not described significantly. But there is a sign and it refers to something. And so I know where it is. Next, we think of the sign “poison”. By poison, we know that it is a dangerous and a fatal substance. The thought in the proposition “This is poison” therefore is that “This thing is dangerous and fatal”. If we translate the proposition into variables, say let x be the representation for “This” and “y” the representation for poison, we can have the propositional sign “X is Y.” Here, the proposition being a sign is made clearer. X stands for something and Y represents something. Language then is a mere representation. It represents our thoughts.

3.14 A propositional sign is fact.

Propositions are statements of state of affairs. For it to be a true expression of such, propositions too must be factual. This means that its contents must be based on facts. The following must be considered regarding the proposition as a fact (PL):most everyday facts are ultimately atomic.a sentence, being the physical structure of a proposition, is a physical fact.Since a sentence is an internally structured fact, it is said to picture the world. Let us consider replacing words with objects. In the proposition, “Rodolfo Dumlao read Alice in Wonderland,” we can make this representation:Rodolfo Dumlao = plateRead = paperAlice in Wonderland = stonePicturing “Rodolfo Dumlao read Alice in Wonderland” is like putting the stone on top of the paper and the paper on top of the plate. Thus,Rodolfo Dumlao read Alice in Wonderland.Plate Paper StoneWords in this regard correspond to individual objects. As Fr. Thomas Green has stated above, since most everyday facts are atomic, they can be replaced by individual words that we consider as atomic propositions representing atomic facts.

3.142 Only facts can express a sense, a set of names cannot.

Let us examine the word “dog”. The word “dog” does not mean anything if there is no actual dog. The sense of the word comes from the fact it represents. The name then is insignificant to the existence of a state of affairs. A dog can be called “zift” instead of “dog”. The word “dog” has some meaning because of the real dog. Thus, “a name means an object. The object is its meaning.”(TLP)

3.22 In a proposition a name is the representative of an object.

The word “dog” represents the actual dog in the statement “My dog is barking.” What is its importance? This is what Wittgenstein calls the ostensive meaning of words. Words point out or direct us to the objects they represent. If I say “yellow”, what I mean is that I am talking about a color sample, yellow. If I need to tell someone what kind of color yellow is, I have to direct his attention to something that is yellow. Without the word yellow I may not be able to direct him to such color.

3.221 Objects can only be named. Signs are their representatives. I can only speak about them: I cannot put them into words. Propositions can only say how things are, not what they are.

Propositions do not tell us the ontological status of things. Propositions only reveal the truth-condition of things, their state of affairs. Only factual conditions are revealed by propositions. Their being, or the reality that they are such and such in essence, is beyond the task of logic.

3.25 A proposition has one and only one complete analysis.

Language can be reduced ultimately into atomic propositions. Let us examine the statement “Rodolfo Dumlao crossed the Atlantic”. To analyze the statement, we have to determine the entities present in the proposition, which, in this case, are “Rodolfo Dumlao” and “crossed the Atlantic.” Its formal translation into an analytic statement should be: That there is one and only one Rodolfo Dumlao which we can represent as A and that A crossed the one and only one ocean called the Atlantic which we can represent as B. The relationship can be stated as “There is one and only one A which crossed the one and only one B” or ArB, “r” representing the way A is related to B. This example above is the one and only one complete analysis of the statement “Rodolfo Dumlao crossed the Atlantic”.Following Russell’s theory of descriptions, for us to understand the statement ArB, the constituents A and B must be understood. Understanding them means we are acquainted with such realities.In Russell’s point of view, all propositions in language must be reduced to atomic propositions. In a logically perfect language, there is a corresponding atomic proposition to each fact. This correspondence is one to one.

3.328 If a sign is useless, it is meaningless.

A word as a sign is meaningful because of its use. Since the word “zift” is not in use, it does not mean anything. Meaning comes from use. It is not the word, but what the word signifies. If a word does not refer us to something, it becomes a worthless sign. A sign functions as if it directs us to the object.

3.5 A propositional sign, applied and thought out, is a thought.

The picture-theory of meaning, in summary, explains that language ultimately is all about the propositions we make, and these propositions constitute our true thoughts of the world. In the Tractatus, logic serves as the backbone of our way of speaking. To make sense means to be logical. A.J. Ayer once said that an illogical world is unimaginable. Since the world fits the criterion of logic, our thought must also possess such a criterion to be meaningful. Language must be a reflection of a true thought. The collection of all atomic propositions, statements that pass the criterion set by atomists, would compose what can properly be called our true thoughts of the world.

4.001 The totality of propositions is language.

Language, in Russell’s point of view, is nothing but the sum of all atomic propositions. Language reveals the world, or more appropriately, picture the world. This language must be a logical one, for it is a necessary requirement for language to be logical so that it can picture a world that is logical. The implication of this is the rejection of any language that does not pass the criterion of logic. Such a language will have to be dismissed as nonsensical. We can cite an example. Let us examine the statement: “God is love.” For a statement to be meaningful, we must be able to derive several observation-statements for it to be logically valid. In the statement “God is love”, we may say that “God is good”, “God is just”, etc. But these statements can never be validated. So in this case, the statement “God is love” is not within the limits of logic.

4.01 A proposition is a picture of reality.

A proposition states something about the state of affairs of things. Since the world is a collection of facts, a proposition about the world is a picture of the world. Reality is factual since the world is factual. The purpose of a proposition is to reveal reality. A proposition is attached to reality. It shows the sense of reality. It tells us what is and what is not.

4.023 A proposition must restrict reality to two alternatives: yes or no.

As we have stated above, a proposition is true if it affirms something, false if it does not. If we examine the statement “God is love”, there is no empirical data that would affirm or deny the statement. The statement, in this regard, is a mere statement. It is not a proposition. It offers no knowledge about the world, and the state of affairs of things. Meaningfulness is based on factual content. Without it, a statement is absurd. This is because, according to Wittgenstein, “reality is compared with propositions.”(TLP)

4.25 If an elementary proposition is true, the state of affairs exists: if an elementary proposition is false, the state of affairs does not exist.

A proposition is true if it is a picture of a fact. It is false when it does not picture a fact. Its sense then comes from the fact that it pictures. Meaning then is always factual. Meaning is derived from the state of affairs of things. My language contains the sense of my world.