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Title page: Before reading the Philosophical Investigations: a Necessary Context


"He must so to speak throw away the ladder, after he has climbed up on it."[1]


This article provides the background needed prior to reading Philosophical Investgations (PI[2]). Philosophical Investigations was written with several hundred numbered sections. After having read this article, a reader will then be ready to make use of the section-by-section guides that will be in the series of articles called: "Aid and Commentary on Ludwig Wittgenstein's PHILOSOPHICAL INVESTIGATIONS". These section-by-section guides will provide some additional background and context not available to a reader who has not studied the earlier work of Wittgenstein.

Russell and his former teacher, Alfred North Whitehead collaborated in writing Principia Mathematica from 1910 to 1913. The book grew to three volumes and yet was left unfinished. Russell was left intellectually exhausted by the effort. He saw in Wittgenstein the man who could finish the work which he and Whitehead had left unfinished. But Wittgenstein went in his own direction and the result was Wittgenstein's Tractatus Logico-Philosphicus.

The common ground shared by Russell and Wittgenstein was the conviction that a complete system of mathematical logic (as first hinted at by Frege) or Symbolic logic could be used to analyze complex philosophical propositions into their simplest possible propositions about 'atomic' facts. In such a system of analysis of propositions, a device as simple as a truth table would be applied to the atomic propositions allowing one to determine if the complex proposition was true or false. Beyond these common assumptions Russell and Wittgenstein had many disagreements. Russell pursued the empirical approach with little or no empirical evidence. Wittgenstein saw that there was too little evidence to back this approach. So, his approach was a priori. Only if the World was logical, could our propositions be logical. Logic had to be 'in the world' to be in language. A logical proposition was a logical 'picture' of the World, the "picture theory" of language.

This first part of Reading the Philosophical Investigation: a Commentary Aid provides an introductory guide for Philosophical Investigations by reviewing key ideas from the only book by Wittgenstein published during his lifetime: Tractatus Logico-Philosophicus. It was written before and during the period of World War I, where he served with distinction in the Austrian Army. The book was published in 1918. Wittgenstein really thought he had answered all the legitimate questions of philosophy; only the propositions of the natural sciences could be stated in meaningful language.

From 1920 to 1926 Wittgenstein worked as a school teacher in a rural village school and then spent two years designing and supervising the building of his sister's house in Vienna. Although he had been out of philosophy, the Tractatus had developed a almost cult status with a minority of thinkers, most importantly with some of the Vienna Circle, a group of philosophers, scientists and mathematicians who met regularly from 1907 to 1938. It was in this group that logical positivism began. Wittgenstein was enticed into the group; the others in the group were quite upset when they discovered Wittgenstein's understanding of his own work was very different from theirs. During this time, he attended a lecture by the Intuitionist, L. E. J. Brouwer which opened up significant new lines of thought to him.

But when he went back to Cambridge on January 18, 1929 he had not given up on the Tractatus. There was a loose string in the fabric of the Tractatus, pointed out by his friend Frank Ramsey, the color exclusion problem. This was the loose string that when pulled out led to the complete unravelling of the fabric of the Tractatus. The string was pulled out sometime between the time he sent to the printer his speech, 'Some Remarks on Logical Form' which was to be his lecture to the 1929 Annual Joint Session of the Aristotlean Society and the Mind Association, to be held between July 12 to 15. That was the end of Wittgensein's early period.

From 1929 into 1931, often called his transitonal period, Wittigensein was thinking through the implications as one part after another of the Tractatus" was unraveled and the ideas inspired in part of the lecture of mathematician, L. E. J. Brouwer, were looking for a place in a new philosophy. The book he wrote for Russell as a review of his thinking during this time, Philosophical Remarks best represents his thinking between 1929 and 1931. Though Russell thought enough of Wittgenstien's work to recommend that he get the endowment he needed, he thought so little of the Philosohical Remarks that it was lost in a drawer and not found until after Wittgenstein's death in 1951.

Not all of the philosophy of the Tractatus was abandoned any more than all of Brouwer's Intitionism was accepted. Wittgenstein's thought was developing and changing quickly. By 1931 the basis of his "Later Philosophy" was in place. Moving away from the mistakes and illusions of the Tractatus in a matter of three or four years he developed a new method of doing philosophy: without theoretical foundations and the lofty generalizations of the Tractatus. He gave up the quest for the 'ideal' logical language that was the work of Frege and Russell and Whitehead. He looked to natural language as a place to look for logics that were not part of part of a monolithic perfect construction; instead, logic in language was the cultural traditions passed on to other generations, changed in past generations and always changing, however slowly in the present.


Too often the reader is faced with the temptation to blame Wittgenstein for our lack of understanding. One easy choice is to see a selection of Wittgenstein's work as just plain incomprehensible. We can also be tempted to look for hidden meanings in his writings, meanings that fit into the belief systems we have always taken for granted. Alternatively, the reader can make use of what Wittgenstein wrote as a way to jolt us out of a mental rut with words we know but that don’t seem to fit the context we see them in. The result from such different approaches to Wittgenstein's work is disagreement even among ‘experts’ about how to ‘interpret’ Wittgenstein. Such disagreements about his philosophy of language and, to a lesser extent his philosophy of psychology, also extend to his ideas about mathematics. Wittgenstein spent a good deal of time on his philosophy of the foundations of mathematics after his early exposure to symbolic logic (see below). The 'philosophy of the foundations of mathematics', the ‘philosophy of the foundations of language’ and the ‘philosophy of the foundations of psychology’ are three important parts of the philosophy of Wittgenstein about which there are differing interpretations.


This is why I think we should take Wittgenstein ‘at his word’. Wittgenstein should not be read in a way that substantially goes against the plain sense of the text until this first avenue of investigation have been exhausted. This wasn’t the way I approached Wittgenstein at first. I first heard of him in quotes in the work of other writers on language, often aphorisms. They were suggestive and intriguing as these quotes from The Book of Aphorisms by W. H. Auden and Louis Kronenberger show:

“Physiological life is of course not 'Life.' And neither is psychological life. Life is the world.”

“Ethics does not treat of the world. Ethics must be a condition of the world, like logic.”

“The work of art is the object seen sub specie aeternitatis. This is the connection between art and ethics."

“The usual way of looking at things sees objects as it were from the midst of them; the view sub specie aeternitatis from outside, in that they have the whole world as a background.”

“In my heart I have determined on it." And one is even inclined to point to one’s breast as one says it. Psychologically this way of speaking should be taken seriously. Why should it be taken less seriously than the assertion that belief is a state of mind?”

“If there were a verb meaning “to believe falsely,” it would not have any significant first person, present indicative.”

“There might actually occur a case where we should say, 'This man believes he is pretending'."

“To say ‘this combination of words makes no sense’ excludes it from the sphere of language and thereby bounds the domain of language. But when one draws a boundary, it may be for various kinds of reason. If I surround an area with a fence or a line or otherwise, the purpose may be to prevent someone from getting in or out; but it may also be a part of a game and the players supposed, say, to jump over the boundary; or it may show where the property of one man ends and that of another begins. So, if I draw a boundary line, that is not yet to say what I am drawing it for.”

“One often makes a remark and only later sees how true it is.”

Aphorisms are all that most people know of Wittgenstein. The only context that The Book of Aphorisms[3] gives is a category in which each aphorism of Wittergenstein is placed along with those of other writers.

My first acquaintance with quotes of Wittgenstein were in other books of other writers. The quotes were striking and suggestive, but since I had no background in the corpus of his works I had to rely on these authors to put Wittgenstein's ideas in an understandable context. I was to learn later that Wittgenstein's statements were understood by many commentators in many different ways. A quote frequently used by others, “If a lion could talk, we could not understand him,” is in the Philosophical Investigations [his central work of his later philosophy], p. 223. But I was not aware that the two books that are milesones in his philosophy were basically different. If the central work of his early period, the Tractatus, was all that I had read of Wittgenstein's work and if I assumed that the rest of his philosophy was a coherent extention of the first book, my understanding of the saying about the lion would be quite skewed. Just knowing that something was written by Wittgenstein is not enough; at the very least you need to know when he wrote it in order to place it in the context of his own changing thought. Luckily, upon reading the isolated aphorisms I could tell there were new insights and they were intriguing enough to get me started reading about, and much more importantly, reading Wittgenstein himself.

I dug into his texts over four years ago. I made all the mistakes I am now telling others to avoid, even working the ideas found in other books with his ideas. Doing it the wrong way is very long and tiring work, but it had its good points. I recall in June of 2000, while watching my mother dying of an unknown cancer and still being the person she always was, what saved my sanity was working with sticky notes and diagrammatic connections running for pages with lines and arrows between concepts. With such immersion for so long I did get a lot right. Eventually I put together a vague structure that usually led me to ‘good enough’ conclusions. Still there was too much that was puzzling. Then it all came together for me; it seems like it was just during the course of a day or two. I read the whole of the Philosophical Investigations in one day and then again the next day. Not every sentence was perfectly clear to me, but for the first time I was really reading Wittgenstein’s Philosophical Investigations - not putting together the pieces of an enigmatic puzzle. It was simple once I myself stopped complicating things. I gave up the “urge to misunderstand”.


But just as Einstein in his Theory of Special Relativity assumed that the speed of light was constant in a vacuum and the laws of physics were the same throughout the Universe, there are two assumptions in the way I read Wittgenstein. One is that this natural life is the only life we have; we are evolved animals, not a creation that is half animal and half spirit. The other is that there are only potential infinities in this finite universe. If someone disagrees with either of these, my reading will not ‘hang together’ for them.

These assumptions contradict deep roots---“bedrock” as Wittgenstein said---and I will not dispute those who do not accept my assumptions[4]. These two assumptions run contrary to strong undercurrents in our culture. I will not try to convert someone from their religious or humanistic-centered philosophies or their understanding of logic. Besides being impractical, it is very much the opposite of Wittgenstein's thought, brought out most explicitly in one of his last books, On Certainty". Also, Einstein, in a very perceptive review on Bertrand Russell's Theory of Knowledge#, compares the "more aristocratic" tradition with the belief "in the unlimited power of thought", such as Plato, to the "plebian" tradition, "according to which things 'are' as they are percieved by us through our senses. "But this conviction does not rest on the supposition that anyone has actually profed the imposibility of gaining knowledge of reality by means of pure speculation, but rather upon the fact that empirical (in the above mentioned sense) procedure alone has shown its capacity to be a source of knowledge."

The second assumption concerning the two types of infinity really have very simple mathematical explanations, But my experience in explaining them confuses people or people fail to see any significance in the distinction. I suppose that the long tradition of squeezing two concepts indiscriminately in the use of one word has led to a confusion that goes unnoticed in ordinary conversation. In recent decades some mathematicians know the distinction and think both are logical. I do not. They are happy with the dualistic worldview that result, even though it is filled with contradiction. "Let's imagine a man whose life goes back for an infinite time and who says to us: 'I'm just writing down the last digit to Pi and it's 2' Every day of his life he has written down a digit, without ever having begun; he has just finished. This seems utter nonsense, and a reductio ad absurdum of the concept of infinite totality. (Philosophical Remarks, p. 166)

I am, and have been, unhappening living in the shadow of that worldview. I am quite happy to reject the infinite totality, even if it means there is just this world, where contradictioins are just linguistic illusions and nothing more.

Philosophical Remarks[5] was the first of his books I read, an odd place to start. In spite of some confusion it may have been the best place for me to start. Most of the underlying support of the Tractatus had been left behind or was leaving. A lecture by the Dutch mathematician L. E. J. Brouwer, founder of the mathematical philosophy of Intuitionism, seemed to have inspired Wittgenstein to new and daring ideas of his own. When he came back to Cambridge after nine years or so away from philosophy, he wrote them down in a book to give to Russell and Moore a exposition of new ideas and questions. It wasn’t given much attention and was left in a drawer at Cambridge after his death. I was fascinated by the ideas about almost everything but the mathematical half. But in the mathematical half was a simpler understanding of one leg of Wittgenstein’s thinking----the need of things that might be described as infinite always to be actually finite.

Additional articles of this series of articles will serve as a guide to reading Philosophical Investigations. I want to demonstrate that Wittgenstein’s Philosophical Investigations can just be read and understood, though often a bit of background is needed. I expect the reader to have the Philosophical Investigations at hand and just read it until some confusion sets in. Then consult the commentary, from the beginning or wherever else is helpful. Do try to read his own words first. “Don’t think, look!”, Wittgenstein’s second of his three great ideas according to Avrum Stroll in his book "Wittgenstein", is appropriate advice.

The first part of the actual guide to Philosophical Investigations will be an article called "Aid and Commentary on Remarks 1 to 142 of the PHILOSOPHICAL INVESTIGATIONS". Sections §143 to §242 and §243 to §275 deal with the famous [or infamous, if you will] sections on rule following and the argument against private language. These parts of Philosophical Investigations will be given their own commentaries in articles later in this series. The importance of these two interrelated concepts is underscored by the fact that even in a survey course in philosophy that includes only brief discussion of Wittgenstein, these will be topics dealt with. The explanation of following a rule is a key concept which has been put off until after the commentary on §1-142 because before this he gives us the tools to deal with it----his method.

I will refer often to §81 in which Ramsey says that logic is a normative science and Wittgenstein later takes it to mean: "that, in philosophy we often compare the use of words with games and calculi which have fixed rules, but cannot say that someone who is using language must be playing such a game."

I would like to note that 'logic' is somewhat similar to 'time. St. Augustine said that everyone knows what time is until he is asked to explain it [§ 89 PI]. Logic is in some ways the same and in some ways different. Nearly everyone thinks they know what 'logic' is and most have a way of expressing what it means, although the meaning may be somewhat vague and not very coherent. These people are not necessarily wrong but they are only partially correct accounts of logic. The work of Frege, Russell and Wittgenstein was an investigation of a more complete and comprehension study of 'logic' that had not been done since Aristotle.

Although not well known in his lifetime for his work in mathematical logic, Gottlob Frege is seen by technical philosophers and many other traditional philosophers as the Father of Modern logic. He equated mathematics and logic and constructed an artificial language using math-like symbos. Because he was an avowed Platonist, believing that mathematiical entities had an eternal existence, his view was the coherent idea that he was revealing the logic of reality---eternal reality. Bertrand Russell was more well known and his work was with Alfred North Whtehead on a project very similar to Frege's in the Principia Mathematica turned out to be more pragmatlc, often solving problems in and as hoc fashion. He could be alternitively Idealist and Platonic, and then imperical and pragmatiac. After Ludwig Wittgenstein worked for a while studying with Russell, he struck out on his own. His approach to logic was not Platonic as Frege, nor as unsystematic as Russell. The study of logic of these three founders of Analytic Philosophy was an attempt to find the concept of logic, not in parts, but as a whole.

If the reader is unclear about what 'logic' means in the treatment of the Tractatus Logico-Philosophicus below, be patient. It will become clear when this first book is contrasted with the philosophy of his later philosophy in the Philosophic Investigations.

Tractatus Logico-Philosophicus[]

Wittgenstein considered himself to be primarily a logician. This is most evident in the first and only book published in his lifetime, Tractus Logico-Philosophicus. Initially, and briefly, he was a student of Bertrand Russell, and so he was focused on symbolic logic as exemplified in the unfinished work of Russell and Whitehead, Principia Mathematica. In symbolic logic there are logical propositions and logical forms[6] for deductive logic which looked like mathematical propositions. They are difficult whether or not symbolic logic and mathematics are essentially the same (the relationship between logic and mathematics was a key issue explored in Principia Mathematica) though there is no doubt that their form is similar. If one was accomplished at one he was likely to be accomplished to some degree in the other. Discussion of any mathematical details will be put off until it is the appropriate time to deal with mathematics in the context of Philosophical Investigations.

Mathematical Logic[]

Wittgenstein was introduced to Russell by Gottlob Frege, at the University of Jena, who was working on symbolic logic independently of Bertrand Russell. Principia Mathematica was really much more about language than about mathematics[7]. It was an attempt to find a second order or derived language in symbolism that would do away with the ambiguities and vagaries of natural languages--- language that seemed to hide and confuse the expressions of philosophy and logic. Relying on natural language could be seen as the reason philosophy seemed to have made little, if any, progress since the time of Plato.

Symbolic logic looked like mathematics with strange new symbols and a new syntax for their use. Some symbols used in symbolic logic:

Symbol Name description
Universal quantifier for all
Existential quantifier there exists
≡, ↔ material equivalence if and only if (iff)
conclusion therefore
~, ¬ negation not
∧, &, conjunction logical and
disjunction logical or
necessity could not possibly be false
possibility might be true
P, Q, x, y, z, φ, χ, ψ, ω variables place holders for expressions, names, statements

There is a short list of symbols and curt definitions in the back of The Oxford Companion to Philosophy and an online table.

A good example of the use of the symbols of formal logic is in the Philosophical Remarks, XII, §135: “Ramsey proposed to express the proposition that infinitely many objects satisfied a function by denying all propositions of the form:

~ (∃x) φx

  (∃x) φx ~ (∃x,y) φx φy

  (∃x,y) φx  φy ~ (∃x,y,z) φx φy φz, etc.

But let’s suppose there are only three objects, i.e., there only three names with a meaning. Then we can no longer write down the fourth proposition of the series since it makes no sense to write:
(∃x,y,z,u) φx φy φz φu

So I don’t arrive at the infinite by denying all the propositions in this series. ’We only know the infinite by description.’ Well then, there’s just description and nothing else.”

I, for one, am glad that Wittgenstein used ordinary language in the prose conclusion above. I agree with his conclusion but don’t understand why it is the logical conclusion of what preceded it. I gave a stab at translating by putting them together with this list and got nowhere. Evidently this is not enough for me to even to ‘translate’ into ordinary language the first proposition, much less the subsequent ‘operations’ on the propositions. More work to do if I ever want to learn Symbolic Logic. Only in quotes will symbolic logic appear in this work.

It is useful here to point out that whatever is plugged into the variables of the models of the propositions of symbolic logic, the, models of symbolic logic are concerned only with the most general logical forms and deductive arguments. The book Logical Forms: an Introduction to philosoophic logic, is an encyclopedic treatment of the forms of deductive logic. The author, Mark Sainsbury, makes clear from the beginning that only deductive logic will be dealt with. Inductive logic cannot be dealt with in symbolic logic.

Statements of symbolic logic are so general that they can neither be true nor false. The study of symbolic logic is the discriminations of valid and invalid forms of deductive logic. Whether a proposition formed from the deductive forms of symbolic logic are true or false is not an issue in the study of symbolic logic itself. The forms of symbolic logic are as completely general as possible and the content or meaning within the descriptions of certain kinds of variables are completely interchangeable. This high degree on generality in the propositions generated from symbolic means specificity of content in symbolic logic takes away attention from all but the most generic sort of meaning and content of words. The words themselves, taken from natural language, have a particular history, a number of related meanings in the natural language itself. These meanings in certain contexts may or may not be substitutable for each other. Paraphrase may or may not be possible. In Symbolic Logic, which may as well be called a language derived from natural language, symbols are not necessarily 'signs' for words of the natural language. I think they are 'signs' for concepts. Natural languages use words to express concepts; Symbolic logic seems to be an attempt to create an artificial language of concepts without the need for particular words---A universal philosophical language. In his 'later' philosophy, Wittgenstein abandoned the attempt to create such a language. He looked at words, propositions and other linguistic tools in the variety of meaning and contexts that would be essential in his later philosophy and philosophic method of language.

In reducing logic and language to mathematical logic their was a divorce between a separate monolithic concept of logic and the language as the media that logic was supposed to work with. Frege, Russel and Wittgenstein were attempting to create a perfect, an ideal language for , as Wittgenstein later called it int he Philosophical Investigations a subllime logic. For Wittgenstein in the Tractatus the fact that his theory was based on the assumption that the ideal language was attainable led logically to the conclusion that it must be based on atomic' facts expressed in simple propositions. It did not deter either him or Russell that they were without an example of either from creating the theories based on such assumptions.

The time between the meeting of Russell and Wittgenstein, and the publication of the Tractatus Logico-Philosophicus was time spent by Wittgenstein trying to solve the deepest problems of philosophy and in the trenches as a volunteer in the Austrian army. His book was published after the war ended.

The three volumes of Principia Mathematica came to an end when Russell and Whitehead just ran out of things to say in symbolic logic, even though central problems were left unfinished. Russell saw in Wittgenstein someone who was young, energetic enough to finish what he started; who was a genius and compulsive in his drive to find logical solutions. His personality made him very difficult for Russell to deal with on the human level. Wittgenstein had great prospects and great personal problems. The problems did not stop Wittgenstein from becoming the one "teaching" Russell.


The central problem. What is the connection between the world, thoughts and language?

The central problem he was trying to solve was how the world must be, how our minds must be, for there to be connection between the World and our thoughts that language was able to express with statements of fact, specifically, the language of logical propositions--- propositions that must be either true or false. There was no doubt that natural language, in spite of some problems, could express logical thought. At that time there seemed to be little doubt that the systems of symbolic logic (and predicate logic) would help clarify problematic areas of natural language. What needed explanation was how languages, natural and symbolic, could work at all.

Analytic Philosophy[]

Analytic philosophy is a dominating force in Western philosophy that started with heavy emphasis on logic and the philosophy of language. Frege, though not well known in his lifetime, is today considered the founder of Analytic philosophy, not Russell or Whitehead, the mathematician. Wittgenstein began with Frege and Russell connected to Analytic assumption[8]. His formal break with them came in 1929.

When philosophy and theology were intertwined in the West, no detailed explanation of just how language worked seemed needed: God was part of any explanation and it worked by his Grace. It was only when Humanism looked for purely human explanations that it took over the assumptions that kept the position of a universal human Nature which had formed as part of Christian theology and scholastic philosophy. A human being not only had reasons; he had the 'faculty of Reason. ' Humanistic Reason saw our inate intellect as capable of understanding the intelligible world of Nature without supernatural revaelation.

“In the seventeenth century these ideas were developed in the famous doctrine of the Two Books, Nature and Scripture. God has written the book of Scripture in words, and we copy it out in our lives. God has written the book of Nature in creatures and in numerical patterns and we copy it in our descriptions and mathematical equations that track his mind. Again we see how the rise of Modern science depended upon borrowing from the older worldview the belief that the world has been expressly made to be intelligible and describable by us, and in our language.”[9].

The assumption---never questioned until very recent centuries--- that was needed to make the shift from Authority of Church and State to Humanism and individualism, was part of our language and the explanation of language, Don Cuppit mentions this assumption:
"There is then something quite dazzling, namely, a pre-established harmony between thought and being, language and reality; between the questions we want to ask and the Answer that the nature of things is waiting to give us. (Notice that this most astonishing doctrine is also the one most profoundly taken for granted.)"[10]

Plato\'s allegory of the cave

Does human experience reveal reality or a shadow of reality?

The arguments about what exactly were the epistemological part of our Universal Human Nature resulted in the traditional arguments, that began with Plato and Aristotle, and continued after the Greek tradition and the Christian tradition merged in the Western thinking. The epistemology of Idealists was one polarllity and metaphysical Realism was the other. Idealism started out its life being called "Platonic Realism", meaning that the Ideas were real, with little reality left over for the day-to-day world we live in. For Plato it was as if we lived in a cave where we never saw real light, but only the shadows of reality. It creates less confusion to use the name "Idealism" as a replacement for "Platonic Realism" so as to contrast it with e.g., the metaphysical Realism of Aristotle and others who focused on on this world.

In the history of Western thought the philosophical popularity of Idealism and metaphysical realism has swung between extreme polarlities of each, and all comprise positions between . Both have their logical strengths and and logical weaknesses. No stable reconciliation has ever been established. Idealists have the edge in connecting thought and thing because they see reality as all, or mostly all, Mind already. Everything was ’inner’, so the problem of connecting the 'inner' with the 'outer' was finessed. Since the time of Aristotle metaphysical Realism and and similar variations of epistemology that believed in a the separate existence of what is 'outer',what is out there and the 'inner', thespace of thought reflects better our everyday experience of reality. But no matter how it was explained, there were always embarrassing logical flaws.

Wittgenstein in the Tractatus saw his work as showing how the “inner” and “outer” were connected by more than arbitrary sounds or marks on paper---signs. “Logic must take care of itself.” [Notebooks 1914~1916 p.2, Tractatus, § 5.473]. Logic must already be in the World in the form of atomic facts expressed by atomic propositions. Our language simply recognized the connection of the atomic facts with and their expression as simple propositions. Complex propositions would be analyzed down to the atomic propositions. Whether the simple propositions (called "simples") were true or false would be self evident. Explanation could go no further. The decision could then be made about the truth or falsity of the complex proposition. This explanation relied solely on natural processes of knowing. There was no appeal to anything supernatural. If appeal was made to metaphysical entities or supernatural intervention, it would simply be a reworking of the traditional explanation of language that had been just taken for granted for centuriees. Clarification of the last point will be one of the first objectives of the Philosophical Investigations. Again I beg your patience at holding in mind without premature judgement the last statement.

Did he succeed? In terms of the problem that was posed to him, yes, if success is seen as the creation of a theory that explained how the World must be for there to be logical propositions tractable to the treatment of universal symbolic logic. He had to have a theory without ‘metaphysics’, which was considered “meaningless” word. And he could not have anything of the supernatural in the explanation. The explanation must be natural.

The theory must be simple. The simplicity of what Wittgenstein did in the Tractatus was a result of just taking over the assumptions of Russell's symbolic linguistic analysis that only had one possible explanation: atomic facts, but he did not take on Russell's otherworldly platonic assumptions. He was left with part of traditional platonism (Logic pre-existed in a dualistic unchanging world) and a part of Aristotelian Realism: logic existed somehow in this world (not another world) and change was explained in dualisms such as mind and matter, body and soul. If the analysis is taken to its completion, all that will be left will be atomic facts expressed as simple propositions. It is a theory of mental representation which requires that a clear connection of the mental representation be made by an arbitrary sign to what is referred to in the “outer” world. In the case of the level of simple propositions in the Tractarian logic, the logic that maps the thought of complex propositions to all of the atomic facts will be self-evident. Platonism also finds self-evident facts, but only in transcending everyday life will the secret knowledge be attained.

However, in this material world, atomic facts are like 'snarks'; impossible to find. Neither he nor Russell could cite a single example. The lack of evidence and the lack of any knowledge of what kind of things these atomic facts were was not troubling as long as the theory was logical, coherent, and for the most part, complete.

Picture Theory[]

The center of the Tractatus solution to foundational philosophy of language was his “picture theory” of language. And this in turn rested on the existence of “atomic facts” and simple propositions that expressed the atomic facts and so could not be analyzed further. These were called “simples”. This was in line with an early remark in The Notebooks: 1914-1916; it (the explanation of how language must work) must be completely simple. And he succeeds in making his explanation of language simple. The troublesome problem left was the color exclusion problem[11] that contradicted the necessary independence of simples from each other.

David Pears in The False Prison thinks of the picture theory, based on atomic facts and simples, as a grid, where the intersections would represent the intersection of a point in time with a particular space where three dimensions are reduced to a point. This intersection would be represented by atomic propositions that could be either true or false. Each assertion would be a ‘simple’ that could not be analyzed into anything less complex. This is the point at which language would work to join the “inner” thought by means of an arbitrary symbol to the outer World. The symbol would be part of a system of symbols that could logically be put in the order that would make a complex proposition with many atomic assertions into a form that would be a “logical picture” ‘inside’ of the of the assertion or negation of what “is the case” in the world.

The ‘simples’ would be the possible assertions that could be made about a given space and time. The history of a given point or segment of time in a given three dimensional space would be whatever it was possible to assert, as either true or false about that point or cross-section of space and time. Of course there would be a seemingly infinite number of time lines for other points or segments in space. But the truth or falsity of one individual point or segment with other points or segments at the same time would be independent of those other points. If they were dependent on each other, by definition they could be further analyzed and would not, by definition, be atomic facts expressed by simples.

If you take the proposition, "This is red" is or is not true: a "simple" and so unable to be further analyzed, a dillemna arises. If it is true, all other colors must be false. If any other colors are true, then "This is red" must be false. But this contradicts a necessary component in the Tractatus of the "Theory of Atomic Facts and Simple propositions: ":1.21 Each item can be the case or not be the case while everything else remains the same. [The statement of the independence of ‘simples’ rp]

If it could be analyzed further, and would not be a simple proposition. The 'color exclusion problem' was, briefly, that any color you named as being true would necessitate all other colors being false. The theory of atomic facts and simple propositions had an obvious contradiction. Wittgenstein kept trying to solve the 'color exclusion problem when he returned to philosophy after leaving it for nine years.

The first sentence in the Tractatus is one of seven topic sentences that form seven sections of the Tractatus.

1. The world is all that is the case.


Language production. In propositions thoughts can be so expressed that the objects of the thoughts correspond the elements of the propositional sign.

The first section is brief, with only six more sentences representing two subheadings and four sub-subheadings. The next four sentences are:

1.1 The world is the totality of facts, not of things.
1.11 The world is determined by the facts, and by their being all the facts.
1.112 For the totality of facts determines what is the case, and also what is not the case.
1.13 The facts in logical space are the world.

This is simple as it is the direct implication of the picture theory and its basis, atomic facts and simples. But it is also unfamiliar and puzzling as to what he means by ‘the world’ without reference to ‘things’ and what is "logical space".

1.2 The world divides into facts.
1.21 Each item can be the case or not be the case while everything else remains the same. [The statement of the independence of ‘simples’ rp]

In the next three sentences of section 2, he defines, but gives no examples of atomic facts. Also in defining atomic facts, a place for 'things' is found in 'the World'.

2. What is the case---the fact--- is the existence of states of affairs.

2.01 A state of affairst (a state of things) is a combination of objects (things).
2.011 It is essential to things that they should be possible constituents of states of affairs.

Not until section 3 is the “simple proposition” explained, and that after the explanation of “proposition”.

3. The logical picture of facts is a thought.

3.1 In a proposition a thought finds and expression that can be perceived by the the senses.
3.12 I call the sign with which we express a thought a propositional sign.--- And a proposition is a proposition sign in its projective relation to the world.
3.2 In propositions thoughts can be so expressed in such a way that elements corresponding to the objects of the thought.
3.201 I call such elements“simple signs”, and such a proposition 'completely analyzed'.

The picture theory of language in terms of atomic facts and simple signs are all set out above in straightforward sentences. It seems straightforward to call this a theory of the analysis of philosophic language, i.e., symbolic logic. Other philosophers who see themselves, or are seen by others, as part of the Analytic school or tradition, must mean “analysis of language” as a much less clear cut concept.

The element left for Wittgenstein to explain is how the World must be for this theory of language to work. In The Notebooks: 1914 to 1916,this has already been simply expressed:
“A statement cannot be concerned with the logic of the world[12], for in order for a statement to be possible at all, in order for a proposition to be CAPABLE of making sense, the world must already have just the logical structure that it has. The logic of the world is prior to all that is truth and falsehood. (Notebooks: 1914-1916, p. 14)”. This is one good example of the saying/showing distilnction which we will briefly talk about a few paragraphs below.

This is how the World must be, [“our requirement” §107 PI], and how language must be explained for logic to be expressed in analytical propositional logic---logic in natural language and in symbolic logic. Frege, Wittgenstein, Russell and Whitehead never proved that all of logic could be expressed in propositions stated in Symbolic logic (or predicate logic). That was assumed. The way the world must be, as described above was not proved either---it was also assumed. We required the ideal of logic and ideal method of logical analysis to be a reality. Later, in the Philosophical Investigations, Wittgenstein repeatedly pointed out our misunderstanding of the role of the ideal. The ideal was not a reality, as in the Platonic view, nor was it something which we must strive for in hope of reaching. It was a standard, a measuring rod which we were to use to compare, among other things, the description of our own narural and human languages.


Language comprehension. Upon hearing the sentence, a thought comes from a logical picture of the facts.

Simple as the sentences of the theory as given are, there is nothing particular our minds can hold on to---no examples and no similes. Passing reference was made to the metaphor of a grid, but was left undeveloped. The horizontal lines would represent the time lines, with no end in sight. [Infinity in both directions makes time much too difficult to get a handle on. This is part of what we will see later in the Philosophical Investigations.] The vertical line would be the three dimensional space reduced to one dimension, a line, intersecting the time line representing the atomic fact expressed in a “simple’ proposition that would have to be true or false. So the intersection of a particular time line by the state of that particular place in space would represent the possibility of the relation of two or more ‘state of things’ that would constitute a fact---either a positive fact or a negative fact. That fact would be independent of the other intersections at that particular time at other locations of space; it would be independent of other facts at that time. In general these facts at a given time are located in “logical space”, not necessarily Euclidian space.

The reason it is called the ‘picture theory’ is not that every proposition would by its very form be descriptive of its content. Something like that might occasionally happen; but the important point would be that the proposition would be a logical picture of the World, the World built up by the smallest parts that added up to the complex propositions. The smallest parts would be the direct linguistic connection of thought to the World by means of language. The logic would have to be already present in the World for language to “show” it. Logic could not be expressed in language, it was transcendental. It could only be shown in the way language works. The complex propositions made of atomic facts would have to be true or false except for two exceptions that mark the limits of language--- the tautology and the contradiction. The tautology would be true in all cases and the contradiction would be false in all cases.


This idea that what cannot be said, can be shown, is used to briefly introduce solipson. solipsism. 5.61 paragraph 4: We cannot think what we cannot think; so what we cannot think we cannot say either.
5.62 This remark provides a key to the problem, how much truth there is in solipsism. For what the soliposist means is quite correct, only it cannot be said, but makes itself manifest.

Further development of the plight of the solipsist would not rely on the general saying/showing distinction meant to apply to the language theory specifically intended as part of the Tractatus in general. The particiular linguistic problems of the solipsist would lead in his later philosophy to an innovative philosophy of of psychology and one of the two key arguments of the Philosophical Investigations, the argument against private language. 'Solipsism' as used here is not the ontological assertion that I am the only entity that really exists. This would be the periennial problem of the existence of reality outside of oneself. To an extent it is the epistemological, but even more precisely, it is the consideration of the idea that a meaningful language must be formed using only knowledge the individual has from birth and what the individual perceives himself from of his own perceptons and experience. It is the beginning of what philosophers call "the problem of other minds". Wittgenstein later developed a philosophy of psychology and the argument against private language that began from a detailed examination of the plight of the solopsist. Like Decartes, Wittgenstein’s early philosophy was one which begins from scratch and attempted to explain how someone might attempt to formulate a language all of whose basic terms find their referents in the world of his own experience.

Answering why something can be shown and not said, would require a long aside on the saying/showing distinction, a distinction that Wittgenstein saw as necessary in the language theory of the Tractatus. It was needed because of the very narrow scope of the picture theory of language. Many of those sympathetic to the Tractatus saw it as unclear or even outright wrong. His good friend. Frank Ramsey, referring to Wittgenstein's remarkable ability to whistle long passages of classical music, makes the good point: if you can't say it, you can't show it, or whistle it either.. The saying /showing distinction is controversion and, in any case,does not play much of a role in his 'later philosophy'. [See A Wittgentsein Dictionary by Hans-Johann Glock under the heading "Saying/showing]

The saying/showing distinction was used to explain why logic itself was 'transcendental'. "Iogic must take care of itself." This is the first sentence in the Notebooks 1914-1916. Wittgenstein’s theory of language was not in need of anything transcendental, such as universals, that are characteristic of platonic epistemology; but it did share with platonism the imbedding of meaning as already in the World to be discovered by us and with our ability to see the logic in the world expressed as self-evident in the atomic facts that are stated in simple propositions. [When I use platonism with the lower case “p” I am referring to what the Jesuit historian of philosophy,Copleston, calls "vulgar Platonism". Vulgar here is not derogatory; it'simply means “common”. It would be the same as the sense of Nietzsche when he said, “Catholicism is the Platonism of the masses.”]

For Wittgenstein this is the only World, this was 'life', so it is not dualistic. He rejects this much of Platonism, and in doing so cuts a different path than Frege, totally a Platonist. Once we learned the atomic facts through empirical experience and baptized it with an arbitrary name, the inherent logic of the meaning takes control of the grammar [the logical syntax] of its use with little need of our cooperation, like a train on fixed wheels with tracks going on infinitely to the horizon. We have a magic talisman , as David Pears calls it,that tells us when the one, true meaning is applicable.The dividing line between what something is and what it is not at every time and circumstance, the clear and distinct definition. the ONE true meaning, the rule to be followed exactly in all circumstances and for all time---infinite time. The infinite is something we will have to handle with great care if we are not to get confused.

Empiricism is what Russell and Moore brought as a change from the Idealism of his first advisor, F. H. Bradley and the continental Idealism of Hegel. The tide had turned back to a type of “realism”. But Russell’s first love, even before Cambridge, was a retreat to the perfectionism of Plato. To some degree, it always stayed with him. His theory of knowledge was empirical, but when he got in a jam, he would fall back on knowledge that was not empirical, keeping the backdoor slightly open as an ad hoc platonic solution to a local problem.

Logicism and Scientism[]

The development of Symbolic language independently by Frege and the team of Russell and the mathematician Alfred North Whitehead had an ironic consequence. The result was a logicism that equated mathematics and logic. Since Plato saw geometry as the ideal of pure logic, equating logic and mathematics was an attempt to give philosophic logic the certainty that mathematics had brought to natural sciences such as physics.

Russell in the second to last paragraph of A History of Western Philosophy[13] makes clear the desire to be like science, in methods if not content.

. . . . . The philosophers who make logical analysis the main business of philosophy . . . . confess frankly that the human intellect is unable to find conclusive answers to many questions of profound importance to mankind, but they refuse to believe that there is some "higher" way of knowing, by which we can discover truths hidden from science and the intellect. For this renunciation they have been rewarded by the discovery that many questions, formerly obscured by the fog of metaphysics, can be answered with precision, and by objective methods which introduce nothing of the philosopher's temperament except the desire to understand. Take such questions as: What is number? What are space and time? What is mind, and what is matter" I do not say we can here and now give definitive answers to all these ancient questions, but I do say that a method has been discovered by which, as in science, we can make successive approximations to the truth, in which each new stage results from an improvement, not a rejection of what has gone before.” (pp. 835-6) [Notice the accent on progress now and a process of action and reaction in the past. But the action and reaction did not mean the total rejection of two opposing philosophies; both kept, in whole or in large part, the two main platonic assumptions: the ‘fit’ of creation and intellect and the dualisms needed to explain change, e.g., mind and body.]

In trying to establish a method as reliable and predictable as science, they tried to create a “perfect”, an ideal, language that didn’t retain touch with empirical reality. The result of this craving to be like science, ‘scientism’ [as distinct from 'scientific'] leads to the structure of the ideal language for deductive logic. It was an astonishing structure of logic, but little of the questions that people were really interested in, found solutions by means of deductive logic. One never got past arguments about the real meanings of statements and parts of statements.

Wittgenstein, though at first part of Analytic philosophy, never cared for the logicism and scientism. This is somewhat ironic in that his description was of a language limited to statements of the natural sciences. In part this may be explained by his respect for good, well-founded science and the narrow interest on the propositions of symbolic logic. He of course realized that there was more to life than the natural sciences and a language meant to express only propositions. The rest of life he described with a word from Schopenhauer meaning those things in life that are important but cannot be expressed in logical statements----the mystical. For Wittgenstein this applies to Ethics[14] and aesthetics. It would be a mistake to see this word, ‘mystical’, as being its logical, consistent and absurd conclusion.

Schopenhauer was one of the few obvious influences on Wittgenstein and it shows up in the Philosophical Remarks of the transition period.

For Wittgenstein the emphasis of the book, The World as Will and Idea[15], is not on Schopenhauer’s philosophy of “Will”. A better translation of the title of the book would be "The World of Will and Presentation" since it emphasizes Wittgenstein’s realism rather than what seems to be in the Philosophical Remarks statements of Idealism. The Phenomenal World is central to Wittgenstein’s thought.

For Wittgenstein, the nature of the ‘atomic facts’ in the Tractatus may or may not have been the same as Russell’s packet of sense data. Later Wittgenstein would be against the phenomenology dependent on the idea of sense data as all we know. Whether the atomic facts were points in space or sense data was left undetermined in the Tractatus. Russell was quite explicit in his platonism in his versions of the theory of atomic facts. Russell thinks we know mostly through empirical experience, but we also know, without experience, universals--- the necessary ingredient in traditional epistemology. Universals are considered the essential concept needed to explain how language works ever since Socrates asked how we could know a particular example of justice without already knowing the universal concept justice-in-itself.

This concept of Universals is alive and well today. For instance in the book of Stanley Cavell, The Claim of Reason:Wittgenstein, Skepticism, Morality, and Tragedy[16]. Cavell refuses to believe Wittgenstein does away with Universals and substitutes “family resemblances” of meanings. [From 1 to 66, he explicitly leads us to realize meaning is not singular but multiple 'meanings' with no one thing in common but having "family resenblance".] Cavell “interprets” and refuses to believe Wittgenstein really means it, even if all the context makes it clear he means what he wrote. Cavell’s teaching of Wittgenstein influenced others, such as Hanna Fenichel Pitkin who wrote Wittgenstein and Justice[17].

The fixed rails of platonism in language means that once the thought is expressed in a sign, the meaning or inner structure of this linguistic expression is a rule, and determines its use, now and for all time. Wittgenstein’s realism was more Aristotelian, seeing the object of knowledge and language only into this world, but with no further account of what kind of thing the atomic facts are. The theory is asserted as necessary for a theory of the connections of thought to language to world, but without abstractions or the “essences“ or Universals that seemed necessary to metaphysical realism.

In the beginnings of Analytical philosophy, Frege imported the whole of Platonism, Russell was inconsistent, and Wittgenstein, in the Tractatus, attempted to have a purely natural philosophy. There were elements left in his thought of the ‘fit' of mind and world especially the color exclusion problem, to left problems into his theory that made it unravel. Frank Ramsey pointed to the color exclusion problem in an article he wrote befoe Wittgenstein returned to Cambridge in 1929. Eventually recognized this was an Achilles heel to his Tractarian philosophy. In a rapid series of changes Wittgenstein walked away from Analysis and symbolic logic----and philosophical theories in general. Wittgenstein never liked Russell’s science-envy and scientism or his later logicism. This may help us understand his distancing himself from “theory” after the Tractatus.

The development of logic in which are mentioned Frege, Russell and Wittgenstein was called the ‘logicist’ school----equating logic and mathematics. Putting Wittgenstein in any ‘school’ is a reckless venture. Wittgenstein did not consider mathematic and logic as the same. Wittgenstein would agree on Russell’s statement of the relation of mathematics to logic in his earlier book, The Principles of Mathematics[18]:
"Symbolic logic is essentially concerned with inference in general, and is distinguished from various special branches of mathematics mainly by its generality. Neither mathematics nor symbolic logic will study such special relations as (say) possessing the formal properties of continuity . . . . . But symbolic logic , , , will not investigate what inferences are possible in continuous relations . . . . What symbolic logic does investigate is the general rules by which inferences are made, and it requires a classification of relations or propositions only in so far as these general rules introduce particular notions." (The Basic Writings of Bertrand Russell[19], pp. 145-6) Thus, Mathematics is logic, but logic isn’t necessarily mathematics.

In my mind, the Tractatus proved a great truth, the truth that has eluded philosophy since the pre-Socratics. The best example is contained in a paradox I learned from reading in high school The Portrait of the Artist as a Young Man. This book became a part of my living. The young artist in question is Stephen Dedalus, an Irish Catholic in Dublin, educated by the Jesuits. At the end of his education, he rejected it.

Then said Cranly, you do not intend to become a Protestant?

I said that I had lost the faith, Stephen answered, but not that I had lost my selfrespect. What kind of liberataion would that be to forsake an absurdity which is logical and coherent and to embrace an absurdity which is illogical and incoherent. [p.244]

The great feat of Wittgenstein, in my mind, was to doggedly follow the logic of the assumptions that Russell and he began with, the "atomic facts" theory of language and his picture theory of language to its logical, coherent and absurd conclusion.

[A paradox is not a contradiction; it is a seeming contradiction. The paradox must be able, at some level or from some viewpoint, be resolved to a noncontradictory understanding. Such was the case with Ptolemaic Astronomy. It was self-evident that the Earth was the unmoving center of the universe. Careful attention to the movements of Sun, Moon, planets and stars over centuries had revealed a recurring pattern to these movements. The explanataions of Ptolemaic Astronomy , thought complicated, fit the observed facts. It was a logical and coherent theory. But it was based on a false assumption, and thus, was absurd.]

By seeing the flaw, not only in content---the atomic theory---but in method---highly abstract and theoretical, he had learned much about how not to do philosophy. At the end of the Tractatus he seems to say that this was a learning experience he needed to go through, even though he recognized how his propositions were “elucidatory”, making things clearer, only when the reader recognized them as “senseless’. [6.54] He now could see things clearly and could “kick away the ladder”. When one reachs the top, the ladder must be kicked away. So what was left to do after you kicked down the ladder? He moved on.

At this time he didn't reject the Tractatus. He saw nothing left to do. after the War, when he returned to his family in Vienna, within a month he had given away the great inheriance that was waiting for him. For a while he worked to get his book, the Tractatus published but soon left this in the hands of Bertrand Russell to get it published. He quit philosophy. He studied in a teachers college and from 1920 to 1926 worked as village teacher. His father, Karl was one of the Richest men in Austria, very much in the category of Carnegie in the United States of America. He died while Ludwig was at Cambridge. When his mother died on June 3, 1926, he and the other surviving brothers and sisters, came into a great inheritance. Within a month Ludwig, against the advice of family and friends, gave it all away. For a time he worked as an architect on the new house of his favorite sister, Gretl. as architect on his sisters new home. The house still stands as an architectural monument.

The ‘failure’ of the Tractatus was the beginning of finding a method of close examination of ordinary language in the later philosophy, expressed, in particular, in the Philosophical Investigations.

The Beginning of the New as the Old Disappears[]

Moritz Schlick began the process that brought Wittgenstein back to philosophy. He gradually introduced Wittgenstein to the Vienna Circle: a group of philosophers and mathematicians that came to be the beginning of the logical positivist school of Philosophy. Some today still put Wittgenstein in this 'school'. The Vienna Circle generally highly regarded the Tractatus, but were disappointed to find their perception of the book was at great variance with the author’s. He was not a positivist nor did he share their interest in modeling philosophy on science. In the summer of l927, Wittgenstein was meeting regularly with the Vienna Circle. Wittgenstein's meetings with members of the Circle were, however, important in bringing him back to philosophy. He still held to the Tractatus, however different his view was from the Vienna Circle and logical positivism.

In March 1928, Wittgenstein attended, with Friedrich Waismann, Rudolf Carnap and Herbert Feigl, a talk entitled "Mathematics, Science and Logic", by L. E. J. Brouwer. Brouwer was considered a ‘Bolshevik Menace’ by Russell and by Frank Ramsey who had written a paper, “The Foundations of Mathematics”before Wjittgenstein returned to Cambbridge. Wittgenstein had read the paper in which Brouwer and the school of Mathematical Intuitionism was mentioned. That may have been all he knew about Brouwer and Intuitionism until attending the lecture. The lecture had a significant impact on him, not only in mathematics, but in his approach to language. Feigl reported:
". . . .it was fascinating to behold the change that had come over Wittgenstein that evening . . . he became extremely voluble and began sketching ideas that were the beginnings of his later writings . . . that evening marked the return of Wittgenstein to strong philosophical interests and activities."[20]

Wittgenstein did not become an Intuitionist, but his difference in the philosophy of the foundations of mathematics from the logicist view of mathematics, became much more apparent. Even before he gave up the picture theory, he saw in mathematics a new way of looking at things that sparked an overall reworking of his philosophy. It wasn’t as if he left everything in the Tractatus behind, but what he brought with him was to fit into a very different structure. He saw that the Tractatus did not say all that needed to be said in philosophy. “Wittgenstein appeared to accept Brouwer’s rejection of the notion of an infinite series in extension---[infinite totality, actual infinity rp]- It constituted "a philosophical attitude that is fundamentally at variance with the ‘bourgeois’ mentality of Russell and Ramsey.”[21]

Wittgenstein came back to Cambridge January 18, 1929 and went directly a friend and mentor, John Maynard Keynes, to announce he planned to come back permanently. “Well, God has arrived. I met him on the 5:15 train,” Keynes said after Wittgenstein's return to Cambridge. His Tractarian views lessened under his scrutiny and the conversation with his friend and 'advisor', Frank Ramsey. Though his work already had a devoted following, he had not received credit for a thesis because the Tractatus wasn’t written in the approved academic style. He needed a grant and a professorship. So, Russell would “oversee” Wittgenstein’s return to Cambridge, and Frank Ramsey, a friend and mathematician, would be his advisor.

Ramsey criticized the “picture theory” because it left the “color exclusion problem" unsolved. Wittgenstein put some work on this problem to save the “picture theory”. He did give up on it and we know when. He was to give a speech to the Joint Session of the Aristotelian and Mind Society in 1929 and to turn the speech into the printer in time for all to have the printed version. Sometime between turning the speech into the printer and the speech itself, he came to consider the speech as “quite worthless”. Instead he talked about infinity and generality in mathematics. I know of no record of that speech, but think it is fair to assume Brouwers inspiration was at work.

Unlike the picture theory, there were parts of the Tractatus which he did not have to reject, but could be seen as the beginning of subsequent development. Mathematics is such a case. Wittgenstein’s treatment of mathematics deserves a lengthy treatment, one that would show that from the Tractatus on he never equated logic with mathematics. But just a little from the Tractatus will make the point.

6.13 Logic is not a theory but a reflection of the world. Logic is transcendental.
6.2 Mathematics is a logical method. The propositions of mathematics are equations, and therefore pseudo-propositions

6.21 Mathematical propositions express no thoughts.
6.211 In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.

The Philosophical Remarks is a book put together by Wittgenstein to show Russell and Moore the kind of philosophy he was doing after he came back to Cambridge. It was put away in a drawer and forgotten about until after his death. It is probably the best representation of his what some call his transitional period. Half of the book has new thought that is heavy with the language of Schopenhauer; the other half deals with the topic of mathematics. The mathematics in The Philosophical Remarks is consistent with the later work, Remarks on the Philosophy of the Foundations of Mathematics. Philosophical Remarks extends what was said in the Tractatus and is simpler to grasp than much of what came later. The relationship of mathetics to the Philophical Investigations is limited to the long treatment of infinity and its use in the section on rule following.

A Bridge from the Tractatus[]

I’m certain people have heard stories about buying a new picture, then having to repaint the room to make it look right, and ending up with all new furniture and a new rug. This is the only place I’ve seen a similar description of how a change to solve the exclusion problem led to a series of necessary changes in the rest of Wittgenstein’s philosophy. It is from probably the best and hardest to obtain book on his mathematics: Wittgenstein and the Turning-Point in the Philosophy of Mathematics by S. G. Shankar.

As discussed above, in the Tractatus, the truth or falsity of each ‘simple’ and its ‘atomic fact’ had to be independent of the truth or falsity of any other simple and its atomic fact. The color exclusion problem, pointed out by Ramsey, was something Wittgenstein continued to work on until in 1929 when he wrote an article, “Some Remarks on Logical Form,” to be published before he was to give this speech to the Joint Session of the Aristotelian Society and the Mind Association. But before his talk, he had given up on the color exclusion problem as it was in the Tractatus. “Some Remarks on Logical Form” probably reflected the need prompted by Ramsey’s influence, to fix sections 6.375-6.3751 of the Tractatus. Wittgenstein decided that the material for the speech was useless. He then set out to resolve the color-exclusion by introducing two major innovations:

1. abandon the Tractatus’s sweeping model of a single amorphous calculus underlying language and shift to what he described as a ‘Satzsysteme’ (Sentence system) concept.
2. a radical shift from the Tractatus conception of inference, in which language was seen as comprising a complex network of interlocking calculi. The color exclusion problem is solved: to grasp the meaning of the linguistic unit, we must have grasped the meaning of the complete Satzsysteme [later called a game]. This meant he had to abandon the absolute logical atomism of the Tractatus.

The Satzsysteme also meant that a major theme of the Tractatus needed to be changed. In the Tractataus, contrary to the position of Frege, Wittgenstein's position was that names have meaning but not sense. So for meaning in general Wittgenstein abandoned the referential conception of meaning. “In its place Wittgenstein now argued was that a word only had meaning in the context of a propositional system, and that meaning of a word is the totality of rules governing its use in the system. This in turn led Wittgenstein to argue that 'unique source' of the profound 'ontological or episemological problems' result from the transgression of the rules, not of ordinary grammar, but rather, logical grammar.”[22].


Wittgenstien's Tractatus Logico-philosopicus was the last and most logical theory explaining how a centuries old idea of language would be able to work without appeal to anything outside "the World". When his best efforts could not make it work, he saw and admitted the failure. With the inspiration of some new mathematical concepts, he began with what was good in the old philosophy and saw an entirely new viewpoint on language.

The next article in this series is Aid and Commentary on Remarks 1 to 142 of the PHILOSOPHICAL INVESTIGATIONS, the first guide to the content of Philosophical Investigations.


To a good friend without whom I would never have been able to finish this project.


Because of late changes this will be incomplete
  1. ^  Wittgenstein famously wrote in section 6.54 of his book Tractatus Logico-Philosophicus: "My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.) He must surmount these propositions; then he sees the world rightly." Tractatus Logico-Philosophicus was published in German in 1921 (Logisch-Philosophische Abhandlung). Charles Kay Ogden translated the Tractatus into English (with help from Frank P. Ramsey) and an English version was published 1922. These two online hypertext versions (version1 and version2) are from Ogden's translation. D. F. Pears and B. F. McGuinness later produced another English translation: Publisher, Routledge. New edition (2001) ISBN: 0415254086. The printed edition translated by C. K. Ogden (Publisher, Dover Publications (1999) ISBN: 0486404455) is referred to in this article. The Project Gutenberg EBook of Tractatus Logico-Philosophicus may be the Pears/McGuinness translation.
  2. ^  The First 100 numbered sections of Wittgenstein's Philosophical Investigations are available online with commentary by Lois Shawver. Articles in this series will refer to the numbered remarks of Part I and the page numbers for Part II of the English text, Philosophical Investigations: 50th Anniversary Commemorative Edition by Ludwig Wittgenstein, G. E. M. Anscombe (Translator) and Elizabeth Anscombe (Translator). Publisher: Blackwell Publishers ISBN: 0631231277. Wittgenstein's book Philosophical Investigations was originally published in German as Philosophische Untersuchungen.
  3. ^  The Viking Book of Aphorisms: A Personal Selection by W. H. Auden and Louis Kronenberger. Published by Viking Press (1981) ISBN: 0140059660. First published in 1962, only four of Wittgenstein's books were then available in an English translation: Tractatus Logico-Philosophicus, The Blue and the Brown Books[23], Philosophical Investigations, Remarks on the Foundations of Mathematics[24]. Notebooks 1914-1916[25] had a copyright of 1961, close to any likely deadline for The Book of Aphorisms.
  4. ^  "If I have exhausted the justifications I have reached bedrock, and my spade is turned. Then I am inclined to say: 'This is simply what I do'." (PI, section 217) See the Appendix for a short description of "Natural life" and "actual infinity" in Wittgenstein's philosophy. The importance of these two topics in understanding Wittgenstein's Philosopical Investigations will be expanded upon later in this article and the entire series of articles that constitues the "Aid and Commentary on Ludwig Wittgenstein's PHILOSOPHICAL INVESTIGATIONS".
  5. ^  Philosophical Remarks by Ludwig Wittgenstein, Edited by Rush Rhees and Raymond Hargreaves. Translated by Maximilian A. E. Aue. (1975).
  6. ^  For a detailed discusion of logical forms, see the Stanford Encyclopedia of Philosophy entry for logical form. For a few quick examples of logical forms, see the Appendix.
  7. ^  Principia Mathematica by Alfred North Whitehead and Bertrand Russell. Published by Cambridge University Press (1997) ISBN: 0521626064. My description of the goal of Principia Mathematica has a different emphasis than traditional formulations. See the Appendix for a short description of the compatibility of my formulation with the traditional formulations.
  8. ^  Resources: an online introduction to the distinction between valid form and truth in the context of arguments and propositions and an online introduction to symbolic logic for a philosophy course.
  9. ^  The history and assumptions of Analytic Philosophy are discussed by Paul Newall in his online essay called Analytic Philosophy. See the Appendix for a short description of some key assumptions of analytic philosophy.
  10. ^  See page 138 of Mysticism After Modernity (Religion and Modernity) by Don Cupitt, Publisher: Blackwell Publishers (1998) ISBN: 0631207635.
  11. ^  After God: The Future of Religion by Don Cupitt, Publisher: Basic Books; 1st ed edition (1997) ISBN: 04650451461997.
  12. ^  The color-exclusion problem and its role in Wittgenstein's abandonment of logical atomism is described at the Stanford Encyclopedia of Philosophy.
  13. ^  Section 6.22 of the Tractatus Wittgenstein wrote, "The logic of the world which is shown in tautologies by the propositions of logic, is shown in equations by mathematics."
  14. ^  The History of Western Philosophy by Bertrand Russell. Published by Touchstone (first published 1945) ISBN: 0671201581.
  15. ^  Wittgenstein's 1929 Lecture on Ethics made the point that there is no way to use logic to establish absolute ethical standards. See the Appendix for relevant quotes.
  16. ^  Arthur Schopenhauer's The World as Will and Idea (original German title, Die Welt als Wille und Vorstellung) is sometimes translated as The World as Will and Representation. An English edition translated by E. F. J. Payne was published by Dover Publications (1966), ISBN: 0486217612 (volume 1).
  17. ^  The Claim of Reason: Wittgenstein, Skepticism, Morality and Tragedy by Stanley Cavell. Publisher: Oxford University Press (1982) ISBN: 0195031954.
  18. ^  Hanna Fenichel Pitkin's Wittgenstein and Justice: On the Significance of Ludwig Wittgenstein for Social and Political Thought Published by University of California Press (1993) ISBN: 0520023293.
  19. ^  The Principles of Mathematics by Bertrand Russell. Publisher: W. W. Norton & Company; Reissue edition (1996) ISBN: 0393314049.
  20. ^  Basic Writings of Bertrand Russell by Bertrand Russell and Lester E. Denonn (Editor). Publisher: Routledge (2001) ISBN: 041508301X.
  21. ^  See page 249 of Ludwig Wittgenstein: The Duty of Genius by Ray Monk. Published by Free Press; 1st American ed edition (1990) ISBN: 0029216702. The Duty of Genius is a good source of both general biographical information and insights into his philosophy.
  22. ^  See page 250, ibid.
  23. ^  See pages 6-8 of Wittgenstein and the Turning-Point in the Philosophy of Mathematics by S. G. Shankar. Publisher: State University of New York Press (1987) ISBN: 0887064825.
  24. ^  The Blue and Brown Books by Ludwig Wittgenstein. Publisher: Harper Perennial (1942) ISBN: 0061312118.
  25. ^  Remarks on the Foundations of Mathematics by Ludwig Wittgenstein. G. H. vonWright (Editor) and R. Rhees (Editor), G. E. M. Anscombe (Translator). Published by The MIT Press; Revised edition (1983) ISBN: 0262730677.
  26. ^  Notebooks, 1914-1916 by Ludwig Wittgenstein. G. H. von Wright (Editor) and G. E. M. Anscombe (Editor). Published by University Of Chicago Press; Second edition (1984) ISBN: 0226904474.

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