From the ALWS archives: A selection of papers from the International Wittgenstein Symposia in Kirchberg am Wechsel

Preamble

The [fantasy] Vienna School for Truth Exploration was founded by Ludwig Wittgenstein in 1918 [the Tractatus’s Preface date]. Its aim: Prepare students for exploring the world and its reality. Its textbook: The famous Tractatus. Its motto: ‘Argue or Agree!¹’ The School has a peculiar aura of back-to-the-future, since its students have already been to a mid-nineteen forties Ludwig Wittgenstein’s lectures at Cambridge. It may get confusing, as these ‘two’ philosophers happen to have exactly the same name. The students’ names are Greek letters, Alpha, Beta, Gamma, etc. [In this paper, all the characters, including Wittgenstein, are fictitious. Sometimes they are the Tractatus Wittgenstein, sometimes they are the Investigations one, and often they are I].

1. Students are all eager to learn

Wittgenstein: “Welcome to our school. Our aim is to prepare you for a career in truth exploration. The school will also conduct field trips in your training. I have prepared for you fill-in-the-blanks forms that list all possible states of affairs. In your field trips, all you have to do is to observe the world and indicate which state of affairs exists and which does not. This will provide you with all the facts. Indeed, the world is nothing but the totality of these facts. Now, does anyone have a question or a comment about our objectives or about our methodology?”

Alpha: "I would like, Sir, to start by indicating our reason for preferring your school over others. When your family asked you why did you want to do philosophy, you told them it was because you wanted to find the truth. Indeed, you have pursued that goal with the utmost of seriousness and with no ax to grind. Most other philosophers, for most of the time, carried out their investigations in order to support a religious belief, a political theory, or simply to maintain a livelihood. On the other, you have been ultra pure in seeking the truth for its own sake.”

Beta: "Just look at what you are planning to do, after you had written the book that embodied all the truth as you found it. You are now determined to give away all your immense wealth, and to prepare for a teaching position in an elementary school.”

Gamma: "I have a general comment, Sir, about your book. In introducing his article ‘On Certainty’², your Cambridge namesake raised the following question, ‘How does one know how to set about satisfying oneself on the existence of unicorns.’³ The mere raising of the question alerts us to the immense difficulty of finding the truth about even such a simple matter as to the existence of a myth. My question, Sir, is how on earth were you able to observe the whole world and decide that it is the totality of facts, and not of things [Tractatus 1.1]?”

Beta: "Not only what you are saying, Sir, but the utmost confidence in what you are saying. ‘ … the truth of the thoughts that are here communicated seems to me unassailable and definitive.’ [Tractatus’s Preface.]”

Alpha: "Also, Sir, the way you have expressed yourself in sentences that are as hard as nails and as knocks of destiny. Is the Tractatus a new Book of Genesis, or what?”

Beta: "We are wondering, Sir, whether you had utilized any equipment in your search for the truth. A telescope, a microscope, or, may be, a slide rule⁴.”

Wittgenstein: “Since I am the professor here, may be I’ll be permitted to put in a word edgewise!”

Alpha, Beta & Gamma: "Sir, Sir, Sir, all of this is because we are so frustrated while reading our textbook. We do not seem to have a handle on how to understand it. It has the tone of a scientific investigation, but it actually sounds so mystical!”

2. How to read the Tractatus: (i) in levels of logical importance & (ii) backwards!

Wittgenstein: “Now, I see your difficulty. I can give you two pieces of advice on how to read our text. My first advice is that you should not read it as a continuous stream. Begin with reading only seven sentences, the ones indicated by the numbers from 1 to 7, without decimals. Then read these sentences together with their first comments, e.g.,1.1, 1.2, …, 2.1, 2.2, … and so on. Then read all the above, together with second level comments that have a second decimal digit numbering, e.g., 2.35, and so on. This will keep you aware of the various levels of importance of the various statements.”

Alpha: "This is very interesting, Sir. What is your second advice?”

Wittgenstein: “My second advise is that you should read the book backwards! May be not completely backwards. Start with Section 5, then go to 4, etc., until you reach Section 1. In my student days, I started as an engineering student, then went on to the field of mathematical logic, while it was being created. I believe I did make a modest contribution to its creation. This led me to thinking about the nature of propositions, and how propositions are used to express the facts of the natural sciences. I asked myself, ‘How should the world be like in order to make it possible for propositions of natural science to be true or false, and to express facts when they are true?’ So, I began a journey of abstraction through successive suppression of dimensions: Abstracting from language, then abstracting from thought, then abstracting from us making to ourselves pictures of facts, until I reached the ultimate rock of states of affairs. I said to myself, ‘This is the rock on which I can build my system.’”

Alpha: “Wow! How fascinating! You make it all sound so simple and straightforward. Then, Sir, did you write the book backwoods?”

Wittgenstein: “Alpha, don’t be silly, you make me laugh! Of course not. Then I followed with an opposite journey of reconstruction: Adding dimension after dimension, in the opposite order in which they were suppressed.”

Beta: "In effect, Sir, you have touched upon all the branches of traditional philosophy: From ontology, to epistemology, to philosophy of mind, etc. Our text is a full-fledged traditional metaphysics!”

Wittgenstein: “Beta, I think I resent your remark. I believe my book solves all problems of traditional philosophy, rather than being one.”

Beta: “I am sorry, Sir. I beg you to postpone this issue until later. Gamma has been screaming for his turn to speak.”

3. Totality of facts exhibits Barber´s Paradox

Gamma: "Sir, I have a problem with your insistence that we should, in addition to knowing the facts, also know that this is the totality of all the facts. Shall we say, for argument's sake, that there are a hundred facts, f1, f2, .., f100. Further, let us agree that F = ‘There are exactly 100 facts’. Is F a fact? If F is a fact, then it is a fact that is outside the totality of facts, and therefore it is not a fact. If F is not a fact, then it is a fact has to be included in the totality of facts, and therefore it is a fact. This is analogous to the Barber paradox.”

Alpha: "In 2001 Wittgenstein Symposium, a paper⁵ was presented that showed how to resolve such paradoxes. I wonder if this paradox can be resolved in the same way.”

4. When is the Barber´s Paradox unresolvable?

Gamma: "No, the totality of facts paradox cannot be resolved similarly. Actually, if we take the barber’s definition to be: B1 = ‘The barber shaves all those who do not shave themselves throughout the universe’, then the B1 paradox is no longer resolvable. This is why: The new universe of discourse has no boundary, and the barber cannot be evicted outside it. That is why it is more suggestive to call the paradox ‘Barber of Seville’s’ rather than ‘Barber’s’. I trust you recall how this paradox was resolved. The barber was evicted out of Seville, and his definition was then restricted to be B2: The barber outside the new smaller universe of discourse. ‘Other than himself, the barber shaves all those who do not shave themselves.’ Now, if we are asked, ‘Does the barber shave himself?’ we can say, ‘We do not know; we have not been told!’ Clearly, the totality of facts paradox is similar to B1, as no boundary was established for the world, and is therefore unresolvable.”

Wittgenstein: “I must admit that you have made your point very clear. I will rebut it later. Now I’ll hand you your homework for the weekend. This form lists all the possible states of affairs, all 200 of them." You go forth and explore the truth: Find out which of these states of affairs exists, and which does not exist. The ones that exist are the facts. This way we get to know the totality of facts, which is obviously the world. Good hunting!”

[The students come to class after the weekend, but they are all excited and cannot settle down.]

Wittgenstein: “Now, what is the problem? Let us all sit down and begin collecting your homework.”

All the students: “Sir, Sir, Alfa discovered a new fact!”

Wittgenstein: “What you are saying is impossible!”

Alpha: "Sir, I saw the two hundred and one state of affairs, and it existed, So, that is a new fact, Sir!”

5. Gamma recalls his childhood chess

Gamma: "When I was a young boy, Sir, I used to love playing chess. After I grew up, I was shocked to find out that my childhood play was illegal! At the first move of each side, we used to permit ourselves to move two pawns, each one square forward. Later I came to realize that this was not permitted by the international chess rules committee. Now, Sir, I am wondering whether your world facts are rules of the game or moves in that game.”

Wittgenstein: “Now, Gamma, what is this sophistry. A fact is a fact!”

Beta: "May I, Sir, present a specific example. Say that Fischer in his game against Spassky moved his king one square to the right at his tenth move. This is a piece of chess news. If I say, ‘The king of chess moves one square at a time,’ this is a second piece of chess news for those engaged in learning the game. The first news could have been different, and; therefore it is a contingent fact. The second news could not have been different, therefore it is a necessary (tautological) fact.”

Alpha: "Sir, I do not want to be left out of this interesting discussion. Let us assume that I am a big shot in the world of chess, and I call for an open meeting of the chess rules committee to consider adopting Gamma’s childhood chess rule variation. In the committee’s meeting, chess rules are robbed their necessity status, and have become contingent facts, and subject to modification.”

Gamma: "Every game has two language levels: The object language level, and the metalanguage level. At the object level, those egged in using the language follow the rules of the game, as the Cambridge Wittgenstein would say, but never speak of them. If a reporter at a chess match says: ’The white king just now moved one square! (which happens to be a chess rule)’ he is liable to be fired on the spot. His remark is ridiculous and, at best, a silly an tasteless joke.”

Beta: "I presume this is, Sir, what the Tractatus 7 is meant to indicate, in your strikes of destiny style: ‘Whereof one cannot speak, thereof one must remain silent.⁶

Gamma: "In the metalanguage of chess, everyday language in this case, one may comment on the object language and speak about its rules.”

6. Third mistake: The dichotomy fallacy

Alpha: "May we consider, Sir, the genus/species distinction, which is usually associated with biological classification? I do think, Sir, that it also plays an important though role in abstraction. For example, the proposal ‘It is raining’, with no affirmation intended, is really a genus, and true and false are the differentia that generate the two statements: (i) ‘It is raining!’ and (ii) ‘It is not raining!’. The dichotomy fallacy is the unstable oscillation between the genus and between the positive species. I wonder, Sir, whether I presented this idea in a clear fashion.”

Figure 1. Dichotomy Fallacy: Oscillation between (1) & (2).

Beta: "Alpha, I think you did alright. It is a fine point, and probably no one can do any better.”

Wittgenstein: “Can anyone explain what Alpha is trying to say?”

Gamma: "I’ll try, Sir. Your state of affairs is really the possibility for a fact, and it becomes a fact when it exists. In your presentation, Sir, a fact is often confused with its corresponding state of affairs. Alpha is proposing the name of ‘dichotomy fallacy’ for this conceptual flaw.”

Alpha: "I believe, Sir, that flaw often appears in well-established contexts. However, in such contexts we can easily correct the situation, as there will morally be enough criteria to isolate the genus from its positive species.”

Alpha: "At the high level of abstraction in the Tractatus, we have no possibility of escaping this fallacy. We have no rudder to control our steering. We humbly submit to you, Sir, that this fallacy is a third grave mistake in section 1 of the Tractatus.

7. Is the vienna school closing down?

Gamma: "Don’t you agree, Sir, that the real problem is not having two choices in each of the three mistakes. It is rather the instability of the choosing. On Monday, we choose the first option, on Tuesday we choose the other option, and on Wednesday we go back to the first option!”

Beta: "Isn’t this what your Cambridge namesake described as the fly being at the top of an inverted bottle, trying desperately to escape by hitting the top upwards rather than retracing its direction downward to the exit?”

Alpha: "Sir, how can we escape these maddening situations, or should we just quit our truth exploration?”

Wittgenstein: “Now, you all make me feel sorry for myself: I wish I have never written this Tractatus! I am going to close down this school and look for a simple down-to-earth career, something like an elementary school teacher!”

All the students clamoring, “No, Sir! No, Sir! Never say that. Your Tractatus was the luckiest thing that ever happened to philosophy! With your beyond belief sincerity and with no ax to grind, you exhibited philosophic pitfalls in their purity. Thus, you paved the way for your Cambridge namesake to create his Socratic technique, explaining the nature of philosophic problems, how we get entrapped by them, how to scramble out of the entrapment, and how to recognize them and avoid them. Between the two of you, Sir, the world will one day credit you with curing human thought of a conceptual plague that lasted for more than two milleniums!

“Believe us, Sir! We are by no means condemning philosophy. What we are saying is this: There is bad philosophy, and there is good philosophy. Your Tractatus is an excellent illustration of the bad variety, and your Cambridge namesake’s Investigations is an excellent example of the good variety.”

Alpha: "I have one last thought, Sir. I would like to hear what everyone thinks of it. It seems to me, Sir, that the philosopher attempts to discover the rules of the language that he is using in order to discover those rules. Alas, this is an impossible quest. If, however, he or she should appear to succeed, then they will be inventing a new branch of mathematics, that one day may turn out to be useful for application in science or technology. If he or she should fail, then they are producing a new metaphysics. This, closing down your school is probably the only proper thing to do. ”