A proposition describes of a matter of fact.

A proposition must restrict reality to two alternatives: yes or no. In order to do that, it must describe reality completely. A proposition describes of a matter of fact. Just as a description of an object describes it by giving its external properties, so a proposition describes reality by its internal properties. A proposition constructs a world with the help of a logical scaffolding, so that one can actually see from the proposition how everything stands logically if it is true. One can draw conclusions from a false proposition.

To understand a proposition means to know what is the case if it is true. (One can understand it, therefore, without knowing whether it is true.) It is understood by anyone who understands its constituents. When translating, we do not translate each sentence of one language into a sentence of the other, but merely translate the constituents. (And the dictionary translates not only substantives, but all the parts of speech and it treats them all in the same way.) The meanings of simple signs (words) must be explained to us if we are to understand them. With sentences, however, we make ourselves understood. It belongs to the nature of a sentence that it should be able to communicate a sense new to us.

A sentence is an image of reality: it shows its sense.

A sentence is both an image and a model of what we think reality is. At first sight, the (printed) sentence does not seem to be an image of the reality it treats. But neither do written notes seem at first sight to be an image of a piece of music, nor our phonetic notation (the alphabet) to be an image of our speech. And yet these sign languages prove to be images, even in the ordinary sense, of what they represent.

Obviously, we perceive the proposition (aRb) as an image. In this case the sign is a likeness of what it denotes. And if we penetrate to the essence of this representation, we see that it is not impaired by seeming irregularities (such as the use of ♯ and ♭in musical notation). For these exceptions also depict what they are meant to express; only in another way. A gramophone record, the musical idea, the written notes, and the sound-waves, all relate to one another in the same internal relation that holds between language and the world. They are all constructed according to a common logical pattern.

There is a general rule by means of which the musician can obtain the symphony from the score, and which makes it possible to derive the symphony from the groove on the gramophone record, and, using the first rule, to derive the score again. It constitutes the inner similarity between such entirely different constructs. And that rule is the law of projection which projects the symphony into the language of musical notation. It is the rule for translating this language into the language of gramophone records.

The possibility of all imagery, of all vividness of expression, is contained in the logic of depiction. In order to understand the nature of a sentence, consider hieroglyphic script, which depicts the facts that it describes. Alphabetic script developed from it without losing what was essential to depiction. We can see this from the fact that we understand the sense of a propositional sign without its having been explained to us.

A sentence is an image of reality: for if I understand a sentence, I know the situation that it represents and I understand it without having had its sense explained to me. It shows its sense, it shows how things stand if it is true; and it says that they do so stand.

A thought is a sentence that made sense.

Thoughts are sentences that make sense. In their entirety, they constitute language. Mankind constructs languages that allow one to express any sense without needing to have much of an idea what each particular word means or how that is so. This is also just how one speaks, without knowing how individual sounds are made. Natural language is a bodily function and no less complicated than that body. It is not humanly possible to directly obtain the logic of natural language from itself.

Language disguises thought, so that one cannot infer, from the outward form of the clothing, the form of the thought clothed by it. This is so, because the outward form of the clothing is designed for entirely different purposes than to let the form of the body be recognized and the tacit conventions that are part of understanding natural language are so complex.

Most of the statements and questions to be found in philosophical works are not false; they just make no sense. Consequently we cannot give any answer to questions of this kind, but can only point out that they do not make sense. (They belong to the same class as the question whether the good is more or less identical than the beautiful.) Most of the propositions and questions of philosophers arise from our failure to understand the logic of our language and it is not surprising that the deepest problems are in fact not problems at all.

All philosophy is a 'linguistic critique' (though not in Mauthner's sense). Russell's achievement was to show that the apparent logical form of a proposition need not be its real one.

A propositional sign, applied by thinking it, is a thought.

The sentence determines a location in logical space. The existence of this logical location is established by the mere existence of the components, by the existence of a sentence that makes sense. The sentence and the logical coordinates together constitute a logical location. The geometric and logical location are alike in that both allow something to exist.

Although the sentence is allowed to determine only one location in logical space, nevertheless, it must already establish the whole of logical space. (Otherwise negation, logical sum, logical product, etc., would introduce more and more new elements in co-ordination.) The logical framing of an image determines its logical space, while the sentence extends through the whole of logical space.

Any valid symbolic language must be translatable.

A proposition possesses essential and accidental features. Accidental features are those that result from the particular way in which the propositional sign is created, while essential features enable it to make sense. So what is essential in a particular proposition is what all propositions that can express the same sense have in common. And in the same way, what is generally essential in a symbol is what all symbols that can serve the same purpose have in common.

So one could say: All symbols that signify an object have its actual name in common. Thus, it would follow that no particular composition is essential to a name.

There is indeed something arbitrary in the notations we use, but this is not arbitrary: That once we have fixed on one thing arbitrarily, then something else must necessarily be the case. (This lies in the nature of notation.) A particular notation may be unimportant but that it is possible is always important. And that is generally so in philosophy: again and again the individual case turns out to be unimportant, but the possibility of each individual case discloses something about the nature of the world.

Definitions are rules for translating from one language into another. Any valid symbolic language must be translatable into any other in accordance with such rules: This they all have in common. What denotes in a symbol is what is common to all the substitute symbols that the rules of logical syntax allow.

For instance, what all notations for the truth function have in common can be expressed in this way: They all have in common that the notation '~p' ('not p') and 'p ∨ g' ('p or g') can replace any of them. (This characterizes the way in which a specific notation can disclose something general.)

The sign of a complex is not resolved arbitrarily upon analysis; its resolution would not be different when it is incorporated in a different sentence structure.

Russell's Paradox

In 'theory of types' Russell had to consider the meaning of signs when establishing the rules for them. This is an error. We can dispose of Russell's paradox as follows: No proposition can make a statement about itself, because a propositional sign cannot contain itself. (That is the whole of the 'theory of types').

The reason why a function cannot be its own argument is that the function sign already contains the prototype of its argument, and it cannot contain itself.

Let us suppose that the function F(fx) could be its own argument. In that case, we would have propositions such as: 'F(F(fx))' where the outer function F and the inner function F must have different meanings. This is because the inner one has the form ϕ(f(x)) and the outer one has the form ψ(ϕ(fx)).

Only the letter 'F' is common to the two functions, but the letter by itself signifies nothing. This immediately becomes clear if instead of 'F(Fu)' we write '(∃φ) : F(φu) . φu = Fu'.

The rules of logical syntax must be self evident, once one knows how each individual sign signifies.

The sign is that aspect of a symbol perceivable by the senses.

Two different symbols can share a sign (written or spoken etc.) yet still signify in distinctly different ways. However, a common characteristic of two different objects can never be indicated by using a single sign with two different modes of signification. For the sign, of course, is arbitrary. We could just as well choose two different signs instead, and then where would the common significance be?

In everyday language it is common for the same word to have different modes of signification and thus belong to different symbols. By the same token, two words that have different modes of signification are commonly employed in sentences in what is superficially the same manner. Thus the word 'is' figures as the copula, as a sign for identity, and as an expression for existence. 'Exist' figures as an intransitive verb like 'go', and 'identical' as an adjective. We speak of something, but also say something's happening. (In the sentence, 'Green is green' - where the first word is the proper name of a person and the last an adjective - these words do not merely have different meanings: they are different symbols.)

In this way the most fundamental confusions are easily produced (the whole of philosophy is full of them). In order to avoid such errors, we must use an object language that prevents them. It must do so by not using the same sign for different symbols and by not using signs that have different modes of signification in a superficially similar way. A notation, therefore, that observes logical grammar and has logical syntax. (The conceptual notation of Frege and Russell is such an object language, though, it is true, it fails to exclude all mistakes.)

In order to recognize a symbol by its sign we must mind that it be used in a manner that makes sense. The sign only determines a logical form in conjunction with its logical, syntactic use. If a sign is not needed, it has no meaning: That is the point of Occam's maxim. (If everything acts as if it has meaning, then it does.) The meaning of a sign should never play a role in establishing logical syntax; it must be possible to do it by merely describing expressions.

Only a sentence makes sense; only in the context of a sentence does a name have meaning.

Wittgenstein now explicitly defines the word expression as any part of a sentence that characterizes its sense. (The sentence itself is also an expression.) In terms of making sense, expression is all that sentences can have in common. An expression denotes both a form and a content.

Prerequisite for an expression are the forms of all the sentences in which it can appear. That makes it a common, characteristic attribute of a class of sentences. Thus, an expression will be exemplified by the general form of the sentences that it characterizes. Once in this form, the expression will be constant while all else can vary.

Thus, an expression will be embodied by a variable whose values are all the sentences containing it. (In the limiting case, the variable will have a constant value and the expression will be one sentence.) Wittgenstein calls such a variable a "propositional variable". Because an expression has meaning only in a sentence, all variables can be construed as propositional variables. (Including variable names.)

If we declare a component of a sentence as a variable, the resulting sentence is now variable and constitutes a class of sentences all of which are values of that variable sentence. In general, this class will also depend on what we mean, according to our arbitrary conventions, by components of that sentence. But even if we turn all the signs with arbitrary meanings into variables, such a class will still exist. Only now the class no longer depends on convention, but solely on the nature of the sentence. This nature fulfills the conditions of a logical form - a logical prototype. What values that propositional variable may take must be specified, and that specification is what constitutes the variable.

Specifying the values of a sentential variable is to specify the sentences whose common characteristic the variable is. The specification is a description of these sentences, so it will only deal with symbols, not their meaning. The sole requirement is that the declaration be a mere description of symbols and state nothing about what is signified. How the sentences are described is not essential.

Like Frege and Russell Wittgenstein construes a proposition as a function of the expressions contained in it.

What signs do not say, their application shows.

It is possible to use a sentence to express a thought in such a way that the elements of the propositional sign correspond to objects of consideration. Wittgenstein calls these elements 'simple signs' and such sentences 'completely analyzed'. When employed in sentences, simple signs are called names. A name refers to an object and that object is its meaning ("A" is the same sign as "A").

The configuration of the simple signs in the propositional sign corresponds to the configuration of the objects in the situation. The name stands in for the object in the sentence. So I can only name objects of consideration; signs stand in for them. I can only speak about them, I cannot speak them. A sentence can only say how a thing is, it cannot say the thing itself.

Requiring that simple signs be possible amounts to requiring that sense be determinate. When a sentence deals with a complex, it stands in an internal relation to the sentence that deals with the constituent of the complex.

A complex can only be given by its description, which will be right or wrong. A sentence that mentions a complex which does not exist will still make sense, it will just be false. One can tell that an element of a sentence signifies a complex because it introduces an indeterminacy. We know that the sentence in which it occurs has not determined everything yet. (The notation for generality contains a prototype, after all.) The synopsis of a symbol for a complex into a simple symbol can be expressed by a definition.

The complete analysis of a sentence is unique. A sentence expresses what it does in a definite, explicit manner: the sentence is articulated. A name cannot be further analyzed by a definition: it is a primitive symbol. Every defined sign symbolizes via the signs that defined it; and those definitions show how. Two signs, one primitive and the other defined by means of primitive signs, cannot signify in the same manner. Names cannot be analyzed by means of definitions because no sign has a meaning on its own.

What is not expressed in signs, their application shows. What signs slur over, their application enunciates. The meaning of primitive signs can be made explicit by means of elucidations, which are sentences that contain them. Thus they can only be understood if the meanings of those symbols are already kown.

Thought expresses itself perceptibly in a sentence.

We use the perceptible sign (sounded or written etc.) of a sentence to project a possible situation. That projection is accomplished by thinking the sense of the sentence. Wittgenstein calls a sign which expresses a thought a propositional sign. And so, a sentence is a propositional sign that relates to the world in a projection.

A sentence includes all that is needed to project, but not what is projected. That is, the possibility of what is projected, but not that itself. So a sentence does not already contain its sense, but does contain the means to express that sense. ("The content of the sentence" means the content of a sentence that one can make sense of.) A sentence includes the form of its sense, but not the sense itself.

The propositional sign consists of its elements, words, which relate to each other in it in a definite way. The sentence is articulated; it is not a medley of words. (Just as a musical theme is no medley of tones.)

The propositional sign is a fact. Only facts can make sense, a class of names cannot. That the propositional sign is a fact, is obscured by its usual form as written or printed. (Thus it was possible that Frege called the proposition a compound name.)

The nature of the propositional sign becomes very clear if, instead of lexical symbols, we think of it as composed of material objects (such as tables, chairs, books). The spatial relation of these things then expresses the sense of the proposition.

Not: "The complex sign 'aRb' says that a is in relation R to b." but: That 'a' is in relation R to 'b' says that aRb. One can describe situations, not name them. (Names are like points. Sentences are like arrows; they have a sense.)

We cannot think anything illogical.

The logical image of facts is thought. For: 'A matter is conceivable' means we can picture it. A thought implies that what is thought about could be; for what is conceivable is also possible. The entirety of true thoughts is an image of the world.

We cannot think anything illogical, since otherwise we would have to think illogically. It was said once that God can create all things except those that are contrary to logic. But, in the event, we cannot tell what an illogical world would look like.

One cannot create something 'contrary to logic' in language just as we cannot create the coordinates of a figure counter to the laws of space in geometry; or give the coordinates of a point that does not exist. We can, of course, portray matters of fact that contravene the laws of physics spatially, but none that would contravene the laws of geometry.

To be true a priori, the thought itself must imply its truth. We could only know that a thought was true a priori if its truth were discernible without an object of comparison.

An image depicts its sense.

What the image and what it depicts have in common is the logical form of representation. An image depicts reality by presenting a possible way that matters of fact may be the case or not. It presents a possible situation in the realm of logic and implies that the situation it presents is possible. It corresponds to reality or not; it is correct or incorrect; true or false. The image portrays what it portrays, independently of its truth or falsehood, by means of its representational form.

What an image depicts is its sense. Whether or not its sense is congruent with reality constitutes true or false. So in order to tell whether an image is true or false, we must compare it to reality. It is not possible to determine from the image alone whether it is true or false; there is no a priori true image.

We imagine the facts.

The mental image that we conceive portrays a situation in logical space in which some matters of fact are the case and others not. That image is itself a fact. That figment of our imagination is a model of reality because the elements of it correspond to objects. What makes it an image is that its elements relate to each other in a specific way. That, in turn, presumes that the objects depicted relate so as well. Let us call this relationship between its elements the structure of the image and whatever the elements are made up of its form of representation. That the objects to relate to each other as the elements of the image do is made possible by the form of representation.

The image relates to reality in that the former extends to the latter. It is laid against reality like a ruler is. Only the end points of the graduating lines touch the object being measured. Viewed like this, the representational relation that makes it an image is also a property of the image. This relation is established by assigning elements of the image to objects. These relations are, as it were, the sensors of the elements of the image with which the image is in touch with reality.

A fact must, in order to be an image, have something in common with what is depicted. Something in the image and the imaged must be the same so that one can be image of the other. What the image must have in common with reality in order to depict it - properly or not - is its form of representation.

The image can depict every reality whose form it has. The spatial image all that is spatial, the colored image all that is colored, etc. An image cannot, however, represent its representational form; it embodies it. Because an image presents its object externally (its point of reference is its form of representation), it represents the object correctly or incorrectly. The image cannot, however, place itself outside its representational form.

What every image, in whatever form, must have in common with reality, in order to depict it - correctly or incorrectly - is logical form, the form of reality. If the representational form is logical, then the image is called a logical image.

Whereas not every image is, for example, spatial, all images are also logical. Thus, a logical image can depict the world.

In a matter of fact, objects intertwine like links in a chain and relate in a specific way.

The way its objects relate in the matter of fact is its structure, it is its form that makes that structure possible. The structures of its matters of fact make up the structure of a fact.

The entirety of matters of fact that are the case is the world and also determines which matters of fact are not the case. Whether matters of fact are the case or not constitutes reality. (We also call their being the case a positive and their not being the case a negative reality.) Matters of fact are independent of each other, so from one matter of fact which is the case or not, we cannot conclude whether another is.

All of reality is the world.

An object is simple.

Every statement about a complex can be resolved into a statement about its constituents together with the propositions that describe the complex completely.

Objects constitute the substance of the world, so they cannot be complex. If the world had no substance, then that a sentence makes sense would have to depend on whether another was true. It would then be impossible to design an image of the world that could be true or false.

However different an imagined world is from the real one, it must have something - a form - in common with it. This fixed form consists of objects. The substance of the world can only determine a form and not material properties, for those are only embodied by propositions - only formed once objects adopt a configuration. (By the way, objects are colorless.) Two objects with the same logical form - irrespective of their external properties - differ from each other only in that they are distinct.

Either something has has unique properties, in which case we can distinguish it from the others by a description, and then refer to that; or there are several things that have all properties in common, so that it is impossible to refer to any particular one of them. For, if a thing is not distinguished by anything, then I cannot distinguish it, else it would be distinguished.

Substance is that which exists independently of that which is so. It is form as well as content. Volume, time and color are object forms. Only if there are objects, can the form of the world be durable. What is durable, what is, and the object are one. The object is what is durable, permanent; the configuration is what is changeable, impermanent. A configuration of objects constitutes a matter of fact.

A matter of fact is a compound of objects.

It is in the very nature of any thing (any object of consideration whatever) to be a part of a matter of fact. There is no happenstance in logic, so a thing can only occur in a specific matter of fact, when that possibility has its precedent in the thing itself. We would call it happenstance if, in the case of a thing that can stand entirely on its own, a fitting situation in a matter of fact would be found after all.

Something in the realm of logic cannot be merely possible. Logic deals with every possibility and treats all possiblities as its facts. Just as we cannot conceive of a material object without the space it takes up, or an event without time, so we cannot consider any thing without the possibility of its relating to others. If I can associate an object with with a matter of fact, then I cannot think of it without the possibility of this association.

A thing stands on its own in that it can occur in all possible matters of fact. But this is a way to relate to a matter of fact, a form of dependence. (It is impossible for words to occur in two modes, both alone and as part of a sentence.)

If I know a thing, then I also know all the ways it occurs in matters of fact (they all must lie in the nature of the object); it cannot be possible to find an additional, new way. In order to know an object I may not need not know its external properties, but I do need to know its internal properties. So, once all objects are given, all possible matters of fact are given as well.

It is as if every thing is located in a space of possible matters of fact. I can consider this space empty, but not the thing without the space. A geometric object must be situated in infinite space. (A point in space is location as an argument.) The speck in the visual field, though it need not be red, must have some color. It has, so to speak, color space about it. Notes must have some pitch, objects of the sense of touch some hardness, etc.

Objects make matters of fact possible and how an object can be part of a matter of fact is determined by its form.

There is no enigma.

If a question can be framed at all, it can be answered. So if one cannot put the answer into words, then neither can one ask the question.

Scepticism is not irrefutable, but rather, it obviously makes no sense as it tries to raise doubts where no questions can be asked. For doubt can exist only where a question exists, a question only where an answer exists, and an answer only where something can be said.

We feel that even when all possible scientific questions are answered, the problems of life will be entirely untouched. Of course, there is nothing left to ask about then; and precisely that is the answer. One can tell that the problem of life is solved when it vanishes. (Isn't this why those to whom the meaning of life became clear after a long period of doubt were then unable to say what that meaning consists of?)

There is, after all, what is inexpressible. It simply shows itself - it is a mystery.

The correct method in philosophy would really be the following: say nothing except what can be expressed objectively, such as propositions of natural science, that has nothing to do with philosophy. Whenever someone wanted to say something metaphysical, demonstrate that certain signs in his propositions have no meaning. Although that person would not feel that we were teaching him philosophy, this alone would be the valid method.

Whoever has read and understood my propositions sees at the end that they have become pointless, when by them he has transcended them. (He must, so to speak, discard the ladder he has ascended on.) One must master these propositions for a correct view of the world.

Wittgenstein's Preface

Training in science and mathematics is a prerequisite to understanding the Tractaus; it is not a textbook for liberal arts majors. Its purpose was soon served. Wittgenstein's student, Alan Turing, went on to develop the Universal Turing Machine and thus become a founder of the computer age. It is no surprise that the man who broke the Enigma code would be an understanding reader of the Tractatus.

The Tractatus shows that the problems of nineteenth century philosophy reduced to misunderstanding the logic of natural language. One could phrase the whole point of the book as: There is no enigma. What can be said at all can be said clearly, and whereof one cannot speak, thereof one must needs remain silent.

The aim of the Tractatus is to mark the bounds of what can be expressed. But to do that, we have to view the boundary from both inside and outside. This can only be done in thought. Thought itself is unbounded. For, to mark the bounds of thought, we would have to think on both sides of the boundary. We would have to think what cannot be thought. The boundary will therefore be set within language and whatever statement lies beyond will simply not make sense.

Wittgenstein had received an extremely sophisticated education; no expense had been spared. By all accounts, he also combined a brilliant mind with intensity of purpose. No wonder Frege and Russell were impressed. Having read and understood their pioneering efforts, he had all he needed to do original work. It makes no difference to original thinkers whether or not what they think has been thought already.

Expecting a prisoner of war to write a polished monograph on philosophical logic makes so little sense that all commentators stand in awe of his achievement. Who would be so presumptuous and try to meet his high expectation by improving the Tractatus? Who has claimed that transgressing the limits he marked makes sense?

Wittgenstein's thinking has become a part of our culture. That is the value of this work. I consider the Tractatus unassailably definitive. How little of what preceded him is needed to pursue modern thought!

Second Reading

After the first reading has given an overview, we can now examine the individual reasonings. One would expect that most convince immediately, but that will only highlight difficult proofs and controversial aspects that don't seem understandable.

This is where Wittgenstein's numbering system really comes in handy. It allows one to mark a place in the text while at the same time indicating at what level difficulties occur. Taking advantage of this modular structure allows us to pick and choose. We are not required to read in sequence from beginning to end.

My guess is that Wittgenstein had no choice but to totally fragment his work in this way. Only such a "Zettelwirtschaft" would allow a combat soldier to continue thinking about anything at all. In my opinion, this explains why he was unable to publish his work. There was no way he could escape the habits he had acquired.

Whereof one cannot find the words to speak, thereof one must needs remain silent.

All propositions result from successive applications of negation.

The propositions of logic are tautologies. Thus, logical statements assert nothing and are used solely for analysis.

Logic is not a body of doctrine, but a reflection of the world. Thus, logic is transcendental.

Mathematics is a logical method, so a mathematical statement does not express a thought. In life, after all, it is never the mathematical proposition that we need, rather we use it only in inferences from non-mathematical propositions to others that are likewise non-mathematical.

The exploration of logic means the exploration of all regularity. That gives all propositions equal significance. Philosophical logic cannot be used to give meaning to life. Nevertheless, philosophy is not an enigma. If no answer makes sense, then neither did the question.

A proposition is a truth function of elemental propositions.

Elemental propositions are the truth value arguments of a proposition. (An elemental proposition is a truth function of itself.) The structures of propositions relate to one another internally.

Propositions in the form of truth functions can be ordered as rows of a table. (That is the basis of probability theory.) All propositions can be expressed as the result of truth operators applied to the elemental propositions. Thus, 'logical objects' or 'logical constants' (in Frege's and Russell's sense) do not exist.

So every truth-function is a result of successive applications of the negation operator to elemental propositions. In this way, the limits of my speech mark the limits of my world.

A thought is a sentence that makes sense.

A sentence is an image of reality: for if I understand a sentence, I know the situation that it represents and I understand it without having had its sense explained to me. It shows its sense, it shows how things stand if it is true; and it says that they do so stand.

A proposition exhibits matters of fact which may be the case or not. The sense of a proposition consists of both correspondence and non-correspondence to matters of fact which themselves can be the case or not.

The truth values of elemental propositions denote the both the possibility that a matter of fact may be the case as well as not. A proposition expresses agreement or disagreement with the truth values of elemental propositions, so the truth values of the elemental propositions making it up are the conditions that determine whether it is true or not.

It now seems possible to give the most general propositional form: "As a matter of fact, this is so."

The logical image of facts is thought.

Thought expresses itself perceptibly in a sentence and that thought can be expressed in a sentence in such a way that the elements of the propositional sign correspond to the objects of consideration. Only a sentence makes sense; only in the context of a sentence does a word have meaning. The sentence determines a location in logical space so that the propositional sign, applied by thinking it, is a thought.

What is so, a fact, is that there are matters of fact.

We imagine the facts. What that image and what it depicts have in common is the logical form of representation.

The world is all that is so.

In logic, facts comprise the world; the world is an entirety of facts, not things. The facts determine the world, for they are all the facts and taken together determine whatever is the case or not. The world can be broken down into particular facts, so that one can be the case or not and all else remain the same.

Tractatus Logico-Philosophicus Title Page

The work is a monograph, so the modern version of the title of the Tractatus would simply be Philosophical Logic. The dedication to David Pinsent was heartfelt by all accounts as was the motto.

Comments on Method

A word of advice by René Descartes on how to read his work.

1. At first, go over the whole of it, as if it were a novel, without paying too much attention or spending time on difficult passages. Simply get to know in general what it is about.
2. Afterwards, if it merits more care, read it a second time, in order to get the reasonings. But there is no cause to give up just because the proof does not immediately convince or not all the reasonings seem understandable. Just mark the places where the difficulties occur, and continue to read without interruption to the end.
3. Then, if the book is worth taking up a third time, a fresh perusal will resolve of most of the difficulties that were marked before.
4. If any still remain, their solution will in the end be found in a fourth reading.

In the normal range of different minds, there are hardly any so dull or slow as to be incapable of following a valid argument, or even of learning science, with appropriate guidance. And this stands to reason; for when the principles are clearly stated, and only straightforward reasoning is asked for, anyone can comprehend the conclusions that flow from them. But no one is entirely exempt from prejudices, and those who are most committed to thinking that turns out to be wrong are most distracted by them.

It also happens that people of ordinary capacity neglect to study from lack of confidence, while others, who are more aggressive, go too fast. Both tend to jump to conclusions. For this reason, I assure those who doubt their ability that there is nothing in my writings which they may not entirely understand, if they only give themselves a chance. I also wish, at the same time, to warn those of an opposite tendency that even the most superior minds will have to take their time and work at it.

And now, I wish to explain the order one ought to follow in self instruction.
• In the first place, adopt a conventionally acceptable code of morals. This does not admit delay because it ought to be our first care to live well.
• Second, study Logic. But avoid the academic approach taught in school. That is only, properly speaking, a dialectic which teaches the mode of expounding to others what we already know, or even to speak much, without judgment, about what we do not know. That corrupts rather than increases good sense. Proper logic teaches valid reasoning so one can discover truths not known before.
• Because logic is a difficult skill, it is desirable to exercise for a length of time in practicing its rules on easy and simple questions, like those of mathematics.
• Then, when one has acquired some skill, start with philosophy in earnest.

René Descartes now outlines philosophy with a view toward agreeing with the Holy Office.
• The first part is Metaphysics, containing the principles of knowledge, among which is the explication of the principal attributes of God, of the immateriality of the soul, and of all the clear and simple notions that are in us.
• The second is Physics, in which, after finding the true principles of material things, we examine, in general, how the whole universe has been framed. In the next place it is necessary also to examine singly the nature of plants, of animals, and above all of man, in order that we may thereafter be able to discover the other sciences that are useful to us.
• Thus, all Philosophy is like a tree, of which Metaphysics is the root, Physics the trunk, and all the other sciences the branches that grow out of this trunk. By the science of Morals, I understand the highest and most perfect which, presupposing an entire knowledge of the other sciences, is the last degree of wisdom.

In the present day, one can divide the matters at issue in philosophy into three rough classes:
• matters of fact, which are studied by the natural sciences.
• matters of law, which are studied by the social sciences.
• matters of taste, the realm of art.

Foreword

This log is a record of a close reading of Wittgenstein's "Logisch-philosophische Abhandlung" in the original. A companion blog, "Wittgenstein's Pony" contains my English version of the text.

I decided to create a written record on the advice of Rene Des Cartes, whose "Principles of Philosophy" contains detailed instructions on how to carry on a conversation with the author by reading the work. A web log seemed the modern way to follow his advice.