Tuesday, April 27, 2010

Logic Lecture April 28: Wittgenstein's Later Thought, The Philosophical Investigations, and Fallacies

BCC Logic
Eric Gerlach


Last time we talked about Wittgenstein’s early thought, the Tractatus, and proving axioms with Wittgenstein’s truth table method. Now we will look at how Wittgenstein’s thought changed in his later notebooks, the most famous being the Philosophical Investigations.

Because Wittgenstein went from believing logic is an airtight system in his early period to believing logic is a messy incomplete set of games in his later period, it is also the perfect time to study common fallacies or errors in human reasoning. These fallacies arise from using the moves of logic in a complex and imperfect world.

First we will consider how Wittgenstein’s thought changed since he formulated the truth table method in the Tractatus. Second we will read passages of the Philosophical Investigations. Third, we will consider the common set of fallacies and how they stem from logic itself.


In the Tractatus, Wittgenstein put forward a system of tautologies structured by truth tables, arguing that basic elements like ‘true’, ‘and’ and ‘or’ have a necessary structure but do not mean anything in themselves while propositions that have meaning are always contingent, dependent and possible. In this early period, Wittgenstein believed that ‘and’ always has exactly the same structure but no meaning in itself, while a proposition like ‘I have an apple and a pear’ has a meaning but is only true if I have both an apple and a pear. This is why Wittgenstein became upset with positivists, like his teacher and friend Russell, who tried to use his system to discover primary and necessary facts in the world.

At first Wittgenstein thought that he had solved all the problems of philosophy with the Tractatus truth table system (we do still use it today to teach formal logic), so he left philosophy and Cambridge behind, went to war, had many experiences, and then later decided that his earlier thinking contained horrible problems. He no longer believed that logic could be crystallized in the head as a truth table matrix, but rather it existed as a complex out in the world, as arrangements of people, thoughts, symbols, and objects. He continued to work on notebooks, progressing in his thought until his death, after which his notebooks were published.

In the early thought of his Tractatus tried to lay the ground for a complete system of logic, such that ‘and’ always has the same, perfectly defined meaning. In his later thought, Wittgenstein argued against this view. Just as he argued against positivists that there are no necessary facts in the world, he came to argue that no individual thing, not even ‘and’ or ‘true’ in logic, can have a single or necessary meaning. He came to see that, like the positivists, he had attempted to provide singular meanings for things that merely have common uses. Thus, there is no more a single necessary meaning of ‘and’ or ‘true’ in the head than there is a single correct scientific description or picture of the world. He came to argue that ‘and’ and ‘or’ are not exclusively in the head, but real things involved in the irreducibly complex games we play in the world.

Consider how we have seen that the IF>THEN operation in logic is capable of working in many different ways, and the truth table method chooses a regular way for it to work. Consider that OR can be inclusive or exclusive, and the truth table method chooses to use OR inclusively. Consider that AND can be used like OR as a general inclusion of several things, but we may agree that the AND is true even if every last thing is not present. Wittgenstein came to argue that any system of logic, like his truth tables, is a tool that is a thing in the world like any other. Because logic is a tool, it does not need to be perfectly defined or entirely consistent any more than an apple needs to be perfectly defined or entirely consistent.

There is an excellent passage from Lectures and Conversations that illustrates the turn nicely. This work was taken not from Wittgenstein’s notebooks but from the notes of his seminar students in the years leading up to his work on the notebooks which would be published after his death as the Philosophical Investigations. At this time Freud’s ideas had stormed onto the academic scene, infuriating Wittgenstein who now had come to hate the idea that things in the world, even logical operators and systems, can be boiled down to a single essential element or factor like sex, power or truth. It is this skepticism, which can be called the “problem of essences”, which marks the turn from his earlier thinking to his more influential later thought.

Wittgenstein attacked Freud’s psychoanalysis and dream interpretation of Freud for boiling everything down to sex. In the Lectures and Conversations (20-21), Wittgenstein proposes a thought experiment for consideration. If we cook a human being down to carbon ash in an oven, are we left with the essence of the human being? A human being is a “carbon-based” life form, so carbon is a dominant element. Consider that we could cook a human down to water in the same oven, and claim that because humans are 3/5ths water we have the essence of the person.

Would it be correct to say that humans are essentially ashy, or essentially wet? Why not? We would not say that a human is essentially ashy or wet because the human being is a complex situation that is not reducible to a single element. The properties of carbon or water do not in themselves explain how humans behave or what they mean to us. If we cooked people down to ashes or water, we have destroyed the situation and can no longer investigate how they work.

In the same way, Wittgenstein had come to believe that neither facts in the world nor logic in the head can be reduced to a single element or necessary structure. Facts and logic are not true in themselves, but true in real situations of the world which are irreducibly complex. Wittgenstein says in the Lectures and Conversations that we have to avoid the “lure of the secret cellar”, the urge to boil situations down to a single element like Freud had tried to boil human relations and the mind down to sex or he himself had tried to boil logic down to its necessary truths.

The task of philosophy, logic and science is not to fully or completely explain anything, but to investigate things. Thought never fully defines things but rather describes and re-describes things. If science is thinking about the world, then science has endless work to describing and re-describing things. Likewise, if philosophy and logic are ‘thinking about thinking’, and if thinking is merely a possibly description of things, philosophy and logic have endless work to do describing our descriptions, describing and re-describing the ways that we describe things.

One favorite way to approach this today is to describe how cultures of thought, perspectives, facts and models, are gathered together and lived in institutions. Thought ceases to be completely abstract, but is rather a culture and situation in the real world that involves people, buildings and money. The cryptanalysis of algebra worked so well as a modeling language that we came to believe that the mathematics was not in our practices and text books but rather sewn into the fabric of the world itself. As we look over the history of thought in the wake of Wittgenstein’s later work, it becomes evident that mathematics and logic are tools and lenses, not the hidden structures of things operating at secret levels out of our immediate sight.


In this monumental work, one of my favorites, Wittgenstein is arguing for a middle way between two extreme positions, between the objectivist position of positivism and the subjectivist position of skepticism. He argues against scientific positivism/realism (facts are in the world), and also psychological skepticism (meaning is in the head). He presents each position in quotes again and again, and then argues against each quote in a three stage process. First he states a position (either that there are facts given in the world or meaning is all in the head), then shows situations in which the position works, then shows situations in which the position does not work. He shows us that taking either position to extremes would be understandable given particular ways we think and act, but neither position explains all the ways in which we think and act.

In his earlier thought, the world and the head are separated by a Kantian gulf between objectivity and subjectivity. In his later thinking, the world and our heads work together seamlessly as a complex situation. One cannot remove either the head or the world to get the bedrock or anchor of meaning and truth without resulting in absurdities. The clean and ideal side of logic, math and grammar mislead us into thinking that meaning must be anchored entirely on one side, either in the head or (exclusively) in the world, but we gain much more ability to think and describe our heads and our world if we stop looking for meaning and truth to be entirely in one place.

Games and rules gather people together, but also individuals can always variously interpret rules and meanings. Both are only what they are together as a form of life. Notice that this thinking has much in common with Lao Zi’s thinking on the wheel as both empty and solid at the same time, and much like the Zen koans of a rock being not a rock and a rock and the sound of one hand clapping.

Let us turn to the text. In the preface to the Philosophical Investigations, Wittgenstein says that he now sees grave mistakes in his Tractatus. He says that this book is not to spare thinking, but to stimulate thinking. Notice that the Tractatus had the opposite goal: to put an end to the problems of logic and philosophy.

7- Language games (actions and language are interwoven as forms of life)
11- Language is like toolbox, a complex set of tools that have no absolute necessity
12- cabin in a locomotive, with crank wheel, pump, switch and brake
15- Naming is like attaching a label, and just this (hello my name is sticker).
17- Classification always is with purpose/point of view, like chessmen classes.
18- Language is like an old city, with side streets and squares (vs. logic matrix of Tractatus)
22- vs. Frege’s inner assumption of a sentence is rather the sentence in its place.
57-58- Red exists, yes, but not just in my head or in the world, but in my seeing, using and talking about red here and there with others, not apart from this.
65- no essence other than the family resemblance association.
66- use ‘games’ as example of family, a complicated network.
67- vs. Confucius, not one thread within (compassion as essence) but rather the twist of the chord is itself the only consistent thread that runs all the way through.
69- When we do draw rigid boundaries, it has a use and purpose in a game/culture we share with others. We do not draw boundaries because ‘that is what there is’, nor ‘simply how I see it’.
Read 80- example of disappearing chair
Read 83- Rules to aimless ball game of catch, but unwritten (who do you throw it to?)
Read 84- We don’t need to stop up all the cracks to live games.
85- a rule is like a signpost, not a guarantee in stone.
89- it seemed like the essence lay within the thing, waiting, but in fact we want to interconnect the thing with many other things, expanding it, getting more of its interrelations and possibilities interacting with other things.
90- It is investigating the possibilities of X, not penetrating X. Analysis is comparison and substitution, not getting to secret core. 91- Lang misleads.
99- Trying for definite sense other than sentence is like ‘locking’ man in room with the window open. We want a ‘must’, but too many openings to plug all (HD and Alice).
106- It would be like repairing a torn spider’s web with one’s fingers.
107- A Tractatus logic would be slippery ice, no friction, like ‘being’. Back to rough ground!
108- Need to remove crystalline by reversing investigation (Foucault and capillary)
109- do away with explanation, description takes its place (all we really were doing).
IN FACT, this means that our explanations are descriptions, sketches, not anchors or bedrock.
118- There is no need for final definitions or explanations, and saying this is not a nihilism that can mean nothing but rather CLEARING GROUND for meaning.
133- the real discovery is that we can start and stop philosophizing when we want to
478- fearing hand in flame, 1000 voices/reasons drown each other out together
498- towards nonsense and humor, like philosophy, showing us forms of life.
499- Calling something ‘nonsense’ or ‘no sense’ or ‘crazy’ is setting up a fence for a purpose, in a game/culture with others. It is not just that there is no meaning there.
500- ‘Senseless’ is like withdrawn from circulation (of library)
513- Consider, no sense unless trying to fit on a rollercoaster or something, a context could give it sense, but it sounds funny at first to everyone.
514-515- Rose in the Dark (Dada and Surrealism)
Book II- ‘Jastrow’ (Wittgenstein’s) Duck Rabbit, more towards art next time.


Fallacies, like Wittgenstein’s later thinking, go beyond formal logic equations as forms or arrangements of life, games of behavior. As everything is contingent on the world, institutions and cultures of human beings, including any formalized logic, there is no sure way to argue correctly but rather the correctness of an argument depends on how it is used or abused in the living situation.

We are going to talk about some of the famous fallacies that experts of logic discuss, even though there is not one set list of these fallacies nor a system of their structures.
(I found three different but overlapping lists in the three texts I reviewed for the class).

Appeal to Authority:
This has only become more and more complex with the passing of time.
Ex: ‘The police chief said that those people are evil’.
Ex: ‘If you brush with whatever toothpaste, 9 out of 10 scientists we gathered into a list to look just that way think you are awesome’.

Straw Man:
The ‘Straw Man’ refers to setting up a scarecrow as a fake person.
One essentializes the opponent’s position in a bad way, setting up their argument or position in a way that makes it easy to knock down. This is one of the most common fallacies that people accuse each other of doing: ‘My opponent is misrepresenting my position on the issues’.
If you pull particular details or properties out of an opponent’s argument to knock it down, it can lead to over-essentializing and simplifying the position to the degree that your opponent will claim that you are not adequately representing their position on the issue. It’s setting out a puppet of the opponent’s argument, like setting up a puppet governor of a country. The puppet is not going to resist you.

The slippery slope is an excellent way of setting up a straw man, drawing out a detail to absurdity, which is then easily dismissed. It is the easiest example to draw of a SM:

Slippery Slope:
One takes a consequence of the opponent’s position and blows it out of proportion.
Example: ‘Well, if you legalize drugs people will try them, see there is no consequences, and then everyone will be doing them and civilization will collapse’.
This person took the consequence of some new users and it slides all the way down the slippery slope of over-simplifying judgment to everyone becoming an addict.
Another Example: ‘If you want to legalize homosexuality, then you want to legalize all sexual conduct, including pedophilia. Thus you must be evil and wrong.’
The opponent would say, ‘I didn’t say legalize ALL sex…you are setting up my position as a straw man’ (OR, equally), ‘That’s a slippery slope’
A slippery slope focuses on one thing, while a straw man can have any complex of setting up an opponent’s position such that it is much easier to disprove when you say it rather than the opponent.

Appeal to Emotion:
Many types- one for every sort of emotion or desired goal
Advertising, of course, appeals to desires for success, for happiness, for respect and status, appealing to both the desire for the positive and fear of the negative.

Appeal to Force:
Ex: If you don’t believe me, Islamic extremists will eat your baby.
Ex: If you are wrong about this, everything will unravel and society will collapse.
Notice how this is a special kind of slippery slope, which assumes the worst consequences that threaten the opponent or audience.

Appeal to Pity:
Ex: ‘If we don’t do it like I say, small children will cry’.
Ex: ‘This particular country has been poor for hundreds of years, so we should totally sell them a bunch of weapons to make them feel better about themselves’.

Appeal to Ignorance:
There are things about X we don’t know, so my opponent isn’t sure that X is Y.
Notice that this is also ‘sharing the fault’ of the Nyaya Sutra.
Ex: Bush head of AAS on global warming as ‘just a theory’

Red Herring:
Also ‘Missing the point’, taking the argument after an issue that does not decide the original issue being argued.
Ex: ‘You keep talking about the time that Gandhi stole cookies as a four year old child, but this is really a red herring…Your side needs to stop bringing this up and thinking that it demonstrates that he was evil.’

One type of Red Herring, certainly the most popular-

Personal Attack:
When one attacks the opponent and not the opponent’s argument. This also applies to attacking the way the opponent always argues but not the argument itself.
Ex: ‘You cannot believe a word my opponent says, because she/he is a communist/Mormon/atheist/aquatic fowl etc.’
Ex: ‘You’re just crazy…I don’t listen to crazy talk from crazy people.’

Fallacy of Composition and Fallacy of Division:
Wrongly attributing property of part to whole, and whole to part.
These are interlaced with the fallacies so far.
Ex of Fallacy of Composition:
If water is wet, and water is 3/5ths the human, then the human being is essentially wet.
If San Francisco and LA are very liberal, then California is very liberal.
Ex of Fallacy of Division:
If water is wet, and water is H2O, then Hydrogen must be wet.
If California is very liberal, then Fresno must be rocking liberal.