This log was inspired by "How to Read Wittgenstein" and "Ludwig Wittgenstein: the duty of genius" by Ray Monk. It is based on reading Tractatus Logico-Philosophicus by Ludwig Wittgenstein translated by D. F. Pears & B. F. McGuinness (Routledge and Kegan Paul:1963)
Monday, March 31, 2008
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.
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.
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.
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.
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.
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.
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.
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.
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.
Sunday, March 30, 2008
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, 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.
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.
Saturday, March 29, 2008
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.
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.
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.
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.
Friday, March 28, 2008
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.
Thursday, March 27, 2008
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!
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.
Wednesday, March 26, 2008
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.
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 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."
Tuesday, March 25, 2008
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.
Monday, March 24, 2008
- Tractatus Logico-Philosophicus 1
- Tractatus Logico-Philosophicus 2
- Tractatus Logico-Philosophicus 2.01
- Tractatus Logico-Philosophicus 2.02
- Tractatus Logico-Philosophicus 2.03 to 2.063
- Tractatus Logico-Philosophicus 2.1
- Tractatus Logico-Philosophicus 2.2
- Tractatus Logico-Philosophicus 3
- Tractatus Logico-Philosophicus 3.0
- Tractatus Logico-Philosophicus 3.1
- Tractatus Logico-Philosophicus 3.2
- Tractatus Logico-Philosophicus 3.3
- Tractatus Logico-Philosophicus 3.32
- Tractatus Logico-Philosophicus 3.33
- Tractatus Logico-Philosophicus 3.34
- Tractatus Logico-Philosophicus 3.4 to 3.5
- Tractatus Logico-Philosophicus 4
- Tractatus Logico-Philosophicus 4.00
- Tractatus Logico-Philosophicus 4.01 to 4.022
- Tractatus Logico-Philosophicus 4.023 to 4.027
- Tractatus Logico-Philosophicus 4.03
- Tractatus Logico-Philosophicus 4.04
- Tractatus Logico-Philosophicus 4.05 to 4.0621
- Tractatus Logico-Philosophicus 4.1
- Tractatus Logico-Philosophicus 4.12 to 4.1213
- Tractatus Logico-Philosophicus 4.122 to 4.1252
- Tractatus Logico-Philosophicus 4.126 to 4.128
- Tractatus Logico-Philosophicus 4.2 to 4.28
- Tractatus Logico-Philosophicus 4.3 to 4.442
- Tractatus Logico-Philosophicus 4.45 TO 4.4661
- Tractatus Logico-Philosophicus 4.5 to 4.53
- Tractatus Logico-Philosophicus 5
- Tractatus Logico-Philosophicus 5 to 5.101
- Tractatus Logico-Philosophicus 5.05 to 5.156
- Tractatus Logico-Philosophicus 5.11 to 5.132
- Tractatus Logico-Philosophicus 5.133 to 5.143
- Tractatus Logico-Philosophicus 5.2 to 5.254
- Tractatus Logico-Philosophicus 5.3
- Tractatus Logico-Philosophicus 5.4 to 5.44
- Tractatus Logico-Philosophicus 5.45
- Tractatus Logico-Philosophicus 5.46 to 5.472
- Tractatus Logico-Philosophicus 5.473 to5.476
- Tractatus Logico-Philosophicus 5.5 to 5.503
- Tractatus Logico-Philosophicus 5.51
- Tractatus Logico-Philosophicus 5.52
- Tractatus Logico-Philosophicus 5.53 to 5.535
- Tractatus Logico-Philosophicus 5.5351 to 5.5352
- Tractatus Logico-Philosophicus 5.55 to 5.5571
- Tractatus Logico-Philosophicus 5.6 to 5.621
- Tractatus Logico-Philosophicus 5.63 to 5.641
- Tractatus Logico-Philosophicus 6
- Tractatus Logico-Philosophicus 6 to 6.01
- Tractatus Logico-Philosophicus 6.1 to 6.1202
- Tractatus Logico-Philosophicus 6.1203
- Tractatus Logico-Philosophicus 6.121 to 6.124
- Tractatus Logico-Philosophicus 6.125 to 6.1271
- Tractatus Logico-Philosophicus 6.13 to 6.2331
- Tractatus Logico-Philosophicus 6.234 to 6.3432
- Tractatus Logico-Philosophicus 6.342 to 6.372
- Tractatus Logico-Philosophicus 6.373 to 6.3751
- Tractatus Logico-Philosophicus 6.5
- Tractatus Logico-Philosophicus 7
- A proposition describes of a matter of fact.
- A sentence is an image of reality: it shows its se...
- A thought is a sentence that made sense.
- A propositional sign, applied by thinking it, is a...
- Any valid symbolic language must be translatable.
- Russell's Paradox
- The sign is that aspect of a symbol perceivable by...
- Only a sentence makes sense; only in the context o...
- What signs do not say, their application shows.
- Thought expresses itself perceptibly in a sentence...
- We cannot think anything illogical.
- An image depicts its sense.
- We imagine the facts.
- In a matter of fact, objects intertwine like links...
- An object is simple.
- A matter of fact is a compound of objects.
- There is no enigma.
- Wittgenstein's Preface
- Second Reading
- Whereof one cannot find the words to speak, thereo...
- All propositions result from successive applicatio...
- A proposition is a truth function of elemental pro...
- A thought is a sentence that makes sense.
- The logical image of facts is thought.
- What is so, a fact, is that there are matters of f...
- The world is all that is so.
- Tractatus Logico-Philosophicus Title Page
- Comments on Method
- ▼ March (29)