Ludwig Wittgenstein is often considered one of the greatest philosophers of the 20th century and is certainly one of its most fascinating figures. Here are some facts to illustrate:

• Wittgenstein was the son of the second-wealthiest family in Austria-Hungry. He gave away his fortune soon after he inherited it, apocryphally, to his siblings because it would do them no harm as they were already wealthy.
• After finishing the Tractatus, he quit to become a school teacher, on the basis that he'd already dissolved all the problems of philosophy. Nearly ten years later he returned and frantically set about refuting his previous position. His positions changed so much that people are often advised to treat Early Wittgenstein and Latter Wittgenstein as two separate philosophers.
• Wittgenstein fought in WW1 and was decorated for his bravery, refusing to abandon his post amongst heavy shelling. He somehow managed to write Tractatus during this period.
• In another apocraphal story, Karl Popper was invited to give a talk at the Cambridge University Moral Sciences Club which Wittgenstein was chairing. Wittgenstein and Popper grew increasingly argumentative over time and Wittgenstein started gesturing with a poker to accentuate his points. Eventually Wittgestein demanded that Popper provided an example of a moral rule, which Popper countered, "Not to threaten visiting lecturers with pokers" leading Wittgenstein to storm out in frustration.

I enjoyed reading this book as Wittgenstein is eminently quotable and he writes with crystal clear language. However, the book is incredibly challenging due to the lack of structure, his preference to be implicit rather than explicit and the challenge of understanding how any particular sentence fits into to the overall picture.

Here are some reasons why I consider this book of relevance to this community:

• Wittgenstein introduced the notion of words capturing a family resemblance - which roughly corresponds to Eliezer's description of words as clusters in thingspace.
• Eliezer has written about the importance of dissolving the question, whilst Wittgenstein argued that most problems in philosophy were merely linguistic confusions and needed to be dissolved. I don't know if Wittgenstein was the originator of this concept, but he seems to have made it more prominent.
• Wittgenstein introduced the concept of language-games which I consider to be one of the best metaphors for understanding how language works.
• Wittgenstein argued for the importance of "meaning as use" which I see as effectively the linguistic equivalent of revealed preferences from economics and as prefiguring Conceptual Engineering.
• Wittgenstien helped me understand the extent to which we construct logic as opposed to it existing Platonically.

Please note that despite my best attempt to separate Wittgenstein's positions from my own interpretations, there will inevitably be areas where I end up reinterpreting without meaning to do so. I should emphasise that the sections on relevance lean strongly towards my own idiosyncratic interpretations.

Tractatus

Given that a large part of the Philosophical Investigations criticises the positions he defended in Tractatus, we'll begin with a brief overview of earlier book. He even notes in the preface of the latter work that it will be hard to understand The Investigations except by contrast with the Tractatus. I haven't read Tractatus, the following is based on secondary material. 

Wittgenstein attempts to give an account of what can and can't be said where Wittgenstein idiosyncratically uses said to mean things that can be said with real precision. He is trying to persuade us that there are certain things that we can't speak of, and therefore we are unable to philosophise about ("Whereof one cannot speak, thereof one must be silent").

Picture Theory

The Picture Theory of Meaning asserts that a proposition is true when the picture representing that proposition corresponds to reality. Pictures consist of elements standing in relations with the elements representing real-world objects which stand in a particular state of affairs. In particular, Wittgenstein claims that we can't sensibly speak of things that can't be represented by these kinds of pictures.

This is not to imply that everything that can't be spoken of is unimportant or non-existent. In fact, he even suggests that these might be the most important things of all:

There are, indeed, things that cannot be put into words. They make themselves manifest. They are what is mystical.

Picture theory is normally taken to be assuming a Correspondence Theory of Truth where Correspondence Theory claims that a proposition is true when it corresponds in some way to how the external world is. The easiest way to clarify the meaning of Correspondence Theory is to consider the most prominent alternative - Coherentism. Coherentism claims that insofar as there is such a thing truth to which we can aspire, it consists of ensuring that our propositions are coherent, rather than trying to make them correspond to some kind of external reality. Naturally, this tends to be heavily criticised for leading to a kind of relativism.

Logical Atomism

Wittgenstein's Picture Theory adopts a kind of logical atomism^[1] which Wikipedia describes as follows:

The world consists of ultimate logical "facts" (or "atoms") that cannot be broken down any further, each of which can be understood independently of other facts.

These atomic propositions assert the existence of atomic states of affairs which are combinations of simple objects. So far this seems fair enough, but instead of defining what these simple objects or states of affairs are, Wittgenstein just leaves a gaping hole.

A. C. Grayling explains this by suggesting that after having provided the general framework, Wittgenstein likely saw what was left as details to be filled in by others. Scientists seem better positioned than philosophers to fill in the gap by drawing on the latest scientific theories, but even these experts may have to defer to the future. For example, although we would have been tempted to use atoms as simple objects before the discovery of elections, these days quantum wavefunctions are a stronger candidate. 

The Wittgenstenian Ladder

Perhaps the biggest gap in the account so far is that Picture Theory, as Wittgenstein has characterised it, appears self-defeating due to an inability to represent itself. That is, the claim that Picture Theory is the correct account of language doesn't appear to be equivalent to asserting that particular atomic propositions correspond to the state of the world. Wittgenstein is aware of this and famously addresses this with the following metaphor:

My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.). He must transcend these propositions, and then he will see the world aright

The standard reading of this is to take him as having utilised nonsense to demonstrate an ineffable truth that nevertheless remains after the nonsense of the surface-level statements has been exposed^[2]. That is, the sentences are something to be worked through, rather than as literal assertions.

Here's an imperfect analogy. The Sokal Hoax involved Alan Sokal submitting nonsense to a journal of cultural studies in order to critique postmodernism. For many people, this constituted an effective critique of postmodernism, despite the fact that he didn't criticise postmodernism directly. The submission being utter nonsense didn't prevent his critique from being persuasive to at least some people.

Tractatus isn't the focus of this review, so I'll stop here. I finish by sharing my proposed solution to picture theory's inability to picture itself.

Philosophical Investigations

Augustine model of language

The Philosophical Investigations starts with a passage from Augustine:

"When they (my elders) named some object, and accordingly moved towards something, I saw this and I grasped that the thing was called by the sound they uttered when they meant to point it out. Their intention was shewn by their bodily movements, as it were the natural language of all peoples: the expression of the face, the play of the eyes, the movement of other parts of the body, and the tone of voice which expresses our state of mind in seeking, having, rejecting, or avoiding something. Thus, as I heard words repeatedly used in their proper places in various sentences, I gradually learnt to understand what objects they signified; and after I had trained my mouth to form these signs, I used them to express my own desires."

Wittgenstein summarises as providing a picture of language as follows:

The individual words in language name objects—sentences are combinations of such names. In this picture of language we find the roots of the following idea: Every word has a meaning.

Part of me wonders whether Wittgenstein is reading too much into this quote, however, I admit that it's a pretty common view of language.

Wittgenstein's Picture Theory adopted this kind of approach in that elementary propositions made claims about the relations of elementary objects. Wittgenstein explicitly rejects his previous theory with one of his main critiques being that Augustine doesn't "speak of their being any difference between kinds of word", explaining:

If you describe the learning of language in this way you are, I believe, thinking primarily of nouns like "table", "chair", "bread", and of people's names, and only secondarily of the names of certain actions and properties; and of the remaining kinds of word as something that will take care of itself.

Wittgenstein later suggests that we are fooled into believing words function homogeneously due to their "uniform appearance". He uses the analogy of a toolbox: even though we may class all the contents as tools, a measuring tape is nothing like a hammer. Another image he uses is that of handles on a locomotive which might all look identical but actually move in quite different ways depending on what they ultimately control.

He writes:

When we say: "Every word in language signifies something" we have so far said nothing whatever; unless we have explained exactly what distinction we wish to make.

I agree. If you haven't defined what it would mean for a word to not signify something, then asserting that they do doesn't really restrict what we should believe.

Wittgenstein introduces the term "Ostensive Teaching of Words" to describe teaching by saying a word whilst simultaneously pointing or otherwise directing the attention of the learner to the relevant object.

Wittgenstein criticises the claim that we learn language through ostensive teaching on the basis that it is only capable of teaching us to associate objects with words and that we need training in order to learn how we're actually supposed to respond to words. For example, imagine a parent shows a child a picture of someone striking another person and says the word "punch". If the child responds by punching the parent, not because they're malicious, but because they believe that's what they are supposed to do, the parent may very well respond with a timeout or a spanking to teach the child not to behave that way. Even if we insist that the naive child understood the word "punch", they misunderstood the meaning of the utterance in that context. In other words, competency in language goes beyond mere propositional understanding.

Another criticism he makes is that it is very difficult to teach words like "there" and "this" ostensively. Perhaps you could point to an object then take your other hand and alternate between pointing at your first finger and the object. However, this is kind of awkward and I doubt anyone teaches it this way.

Relevance: The Augustine model of language and obstensive teaching incline us towards a model where the meaning of words is represented by propositions since they focus on objects as the bearers of properties or as the subjects + agents of actions. Wittgenstein undermines these models of teaching/language in favour of the importance of training in learning and a model of language as use.

Explanation and Training

Wittgenstein doesn't believe that explanation is a sufficient tool for teaching people language. After all, we cannot understand an explanation unless we already understand its terms and how to interpret it. That is, explanation always seems to stand in need of further explanation:

Does the sign-post leave no doubt open about the way I have to go? ... But where is it said which way I am to follow it; whether in the direction of its ringer or (e.g.) in the opposite one?—And if there were, not a single sign-post, but a chain of adjacent ones or of chalk marks on the ground—is there only one way of interpreting them?

At this point, it's a wonder how we are able to talk at all. Wittgenstein's solution is to deny the need to explain everything:

Explanations come to an end somewhere

And then to assert, "So what?":

As though an explanation as it were hung in the air unless supported by another one.

At some level, we just do things because we've been trained to, not because it was explained to us. For example, a child might learn to say water whenever they are thirsty because this results in them recieving the water, leading their brain to send pleasure signals. This is probably instinctual at first and it is likely only later that we developed consciousness awareness of what it is that we are doing.

Relevance: If we learn language via training, then this will naturally incline us more towards his theory of language as use. This mirrors his epistemology: we can't provide a reason for everything, so at some level, we just do things.

Expressions

Wittgenstein considers an example where a builder shouts "Slab!" to get an assistant to bring them a slab. We might be tempted to say that "Slab!" is a shortening of "Get me a slab", but Wittgenstein points out that it makes equally as much sense to say "Get me a slab" is a lengthening of "Slab!". Which one is considered the default seems to be purely a matter of culture.

He acknowledges that it might make sense to say that "Slab!" means "Bring me a slab" in contrast to statements such as "Get him a slab" or "Find a slab!", but he rejects going so far as to claim that's the definition of "Slab!" is something along these lines. Part of his argument is to deny that when we say "Slab!" we necessarily form in our minds a full expression like "Bring me a slab"^[3]. Indeed, if we make regular use of this expression, I would expect "Slab!" to become a single unit of thought.

For Wittgenstein, this isn't just a curious fact about what goes through our heads when we invoke expressions like "Slab!". Rather, it is a point against any theory that claims that such expressions really represent something else, including the theory that the something else we're referring to is a proposition.

Here's another example. Suppose my girlfriend shouts "Leave!". Picture theory might reinterpret this as a logical proposition identifying the worlds where I leave. But surely, I'm not meant to only picture leaving, but to actually leave! One could respond the picture I form in my head should be of a world where my girlfriend wants me to leave. But this doesn't fully capture the meaning of "Leave!" as people can say things even when they don't desire them. Perhaps my girlfriend wants me to stay, but she knows it would be best for me to leave. Or perhaps, she doesn't know what she wants, and she tells me to leave in response to being overwhelmed.

Wittgenstein writes that people who are confused about language will be inclined to ask:

"What is a question?" —Is it the statement that I do not know such-and-such, or the statement that I wish the other person would tell me . . . .? Or is it the description of my mental state of uncertainty?"

Why do we have to pick one? Attempting to universally translate any particular question into a particular proposition seems reductive. Instead, these words seem more naturally represented as an attempt to achieve a result.

Relevance: These considerations further lay the ground for Wittgenstein's theory of language as use by demonstrating the limit of modeling language as propositions.

Language as Use

Reframing all language in terms of logical propositions is particularly tempting to those with rationalist inclinations, but we've already seen in the last section that it's more complex than it appears prima facie. 

We noted that if someone says "Leave!" they don't want you to just form a picture of yourself leaving in your head, but to actually leave. That is, we can conceive of an agent that has a mere propositional understanding in that they can form a picture where the action takes place, but without knowing what they are supposed to do with it. For example, are they supposed to leave, to consider leaving, to say whether they are thinking of leaving or perhaps even do the opposite and not leave?

Compare this with the following quote from The Investigations:

Imagine a picture representing a boxer in a particular stance. Now, this picture can be used to tell someone how he should stand, should hold himself; or how he should not hold himself; or how a particular man did stand in such-and-such a place; and so on

Perhaps the image of the boxer seems a little silly, but it illustrates a deeper point. Wittgenstein asks whether this kind of propositional understanding is the meaning of expressions and for him, it is not. While being able to bring to mind appropriate images undoubtedly assists in achieving our purposes, it seems that in the majority of cases we use words because we want to actually achieve something in the world and that merely picturing the image doesn't get us to the finish line. Further, this example illustrates one reason why we might want to follow Wittgenstein and conceive of learning language as training, rather than ostensive teaching.

It's worth noting that Wittgenstein doesn't ideologically insist that language is use in all cases, just that it is use in most cases. We haven't covered the concept of language-games yet, but I would argue that, contra Wittgenstein, the natural development of Wittgenstein's ideas would be to allow meaning as use to play a larger or a smaller role depending on the particular language-game in question.

I also think Wittgenstein wants to analyse meaning at the level of linguistic act rather than individual words, although I'm not confident in this interpretation.

Relevance: Rationalists have a tendency to insist on using words rather literally. This certainly has advantages: sticking to this rule reduces our ability to frame situations in accordance with our biases and can help train precise thought. However, if we accept Wittgenstein's argument that language is primarily about use, then this would seem to be attempting to use language in a way contrary to its nature. This isn't an essentialist claim. Rather, it's simply a claim that it's often easier to go with the flow, such as moving things downhill rather than uphill or driving the "right" way down a street. So this would be an argument for using language in a more "normie" way.

Additionally, I see language as use as broadly analogous to the economic concept of revealed preferences. When economists talk about revealed preferences, on the most part they aren't actually claiming that doing something necessarily means that there's a sense in which we prefer it. Rather the claim is that it is often better to look at what we do rather than we say, given our tendency to be unreflective and to deceive ourselves and others. Language as use seems to be making a similar move in terms of how we should understand language.

Indeed, I suspect that if we attempted to understand language by asking people what words mean, most people would just concoct some kind of hand-wavey explanation that would provide a misleading picture of how words are actually used. We can see this by noting the difficulty of defining words we use all the time. The language as use approach seems promising in light of these considerations.

Family Resemblances

Wittgenstein uses this term to describe phenomena that "have no
one thing in common... but that they are related to one another in many different ways". For example, we can imagine all members of a family appearing similar despite there being no one single feature that every member has. To be clear, most of the members of the family might have the same eyes, same hair and same facial structure, but for each such feature, there would be at least one person who is the exception.

This broadly corresponds to Eliezer's Yudkowsky's description of The Cluster Structure of Thingspace. Eliezer's definition is more amenable to mathematical formalisation, but there are slight differences between the kinds of sets that are defined by having N out of M attributes and those sets that are formed via some kind of distance metric.

You may be worried that the concept of family resemblances is overly vague, but Wittgenstein has a strong defence for not having specified them more precisely. This defence is that family resemblances are themselves family resemblances, which by their nature are not very amenable to precise definition.

Note that Wittgenstein doesn't claim concepts are always family resemblances, for example, he acknowledges that we can choose to provide "rigid limits" for what falls within a particular class. Instead, the point is that often our regular use of language typically does not draw boundaries nearly so cleanly.

Even though both Wittgenstein and rationalists embrace similar ideas here, there is a stark difference in behaviour. Rationalists understand that there is often no set of necessary and sufficient conditions that captures precisely what we mean by a word, yet often adopt such definitions anyway due to pragmatism. On the other hand, Wittgenstein responds by mostly eschewing explicit definitions and instead leans towards listing examples^[4].

Relevance: Understanding this concept helps avoid pointless linguistic disputes or falling into dysfunctional versions of conceptual analysis.

Language-Games

Language-games are another one of the most famous concepts that Wittgenstein introduced. Since Wittgenstein considers these to be a family resemblance, he doesn't provide an explicit definition, but instead explains by way of examples:

Review the multiplicity of language-games in the following examples, and in others:

• Giving orders, and obeying them
• Describing the appearance of an object, or giving its measurements
• Constructing an object from a description (a drawing)
• Reporting an event
• Speculating about an event
• Forming and testing a hypothesis
• Presenting the results of an experiment in tables and diagrams
• Making up a story; and reading it
• Play-acting
• Singing catches
• Guessing riddles
• Making a joke; telling it
• Solving a problem in practical arithmetic
• Translating from one language into another
• Asking, thanking, cursing, greeting, praying.

Roughly, I interpret language-games as referring to a particular activity or purpose for which language is used and which follows its own distinctive rules. I consider it valid to consider an utterance to belong to different language-games depending on how we want to frame it.

The Stanford Encyclopedia of Philosophy describes language-games as follows:

Language-games are, first, a part of a broader context termed by Wittgenstein a form of life. Secondly, the concept of language-games points at the rule-governed character of language. This does not entail strict and definite systems of rules for each and every language-game, but points to the conventional nature of this sort of human activity. Still, just as we cannot give a final, essential definition of ‘game’, so we cannot find “what is common to all these activities and what makes them into language or parts of language”

Regarding the first point, Wittgenstein seems to believe that it is impossible to understand a language-game outside of the context in which it is practised - "If a lion could speak, we could not understand him".

Consider the biblical injunction to "turn the other cheek". This is typically understood as suggesting that the most virtuous path is not fighting back against (perhaps figurative) violence, but instead allowing further injury.

On the other hand, Walter Wink has interpreted this as suggesting nonviolent resistance to attempts by their social superiors to humiliate them. One way to humiliate someone was to give them a backhand slap to their cheek. However, by turning their face, it would be impossible for them to be backhand slapped with their right hand as their nose would be blocking their cheek. Cultural tradition forbade the use of the left hand except for unclean tasks and a punch would be seen as a sign of equality.

This theory might turn out to be incorrect, nonetheless, it demonstrates the difficulty of understanding a statement outside of its cultural context and of severing certain expressions from the form of life in which they've arisen.

When he says that language-games have rules, he doesn't mean everything is precisely specified - indeed that would be contrary to his concept of family resemblances. Further, he allows these rules can have exceptions. He doesn't see this as contradictory, as often exceptions need rules in order to subvert them. His point seems to be that without rules, language wouldn't be usable for communication.

Another aspect of the metaphor of language-games that resonates with me is the idea that we can also create new language-games to handle new situations that arise. This perspective frames language as a realm of creativity. This may seem trivial, but sometimes it's useful to have a reminder that we can construct new ways of using language.

Relevance: We've covered a lot of different aspects of language-games, but the most important aspect of it for me is as an exhortation to take seriously the diversity of different ways that language can be used and to be very skeptical about any attempts at universal statements.

For example:

• If we say all language is an attempt to communicate, what about purposefully silly uses of language to make us laugh?
• If we emphasise the importance of connotations in language and make denotations secondary, what about circumstances where we are told what we already know? Saying "I am the leader" to someone who already knows that you are the leader could be used to remind them to show you respect.
• If we try to define questions in terms of an attempt to get someone to answer, then what about rhetorical questions?

Wittgenstein as Anti-Philosopher

In both the the Tractatus and Investigations, Wittgenstein was highly critical of philosophy. In Tractaus, his critique was that philosophers attempted to debate or argue for theses that didn't correspond to a picture of the world. In Philosophical Investigations, Wittgenstein's critique is words are used outside of the language-games in which they make sense - or that "language goes on holiday"^[5].

The results is abstract questions which aren't grounded in anything and which don't have any consequences outside of philosophical spectulation. Wittgenstein uses the following as examples of words abused by philosophy: "knowledge", "being", "object", "I", "proposition", "name".

For Wittgenstein, the consequence is that the vast majority of philosophical questions aren't real questions, but simply nonsense. These questions aren't resolved (ie. answered), but dissolved. He sees his task as "to show the fly the way out of the fly bottle"; that is to help philosophers escape problems that they created for themselves.

As an example, many philosophers have deeply pondered the question, "What is Being?". For Wittgenstein, this question wouldn't make sense, at least in the abstract sense meant by the philosopher. Wittgenstein suggests that what we mean by Being is "existence and non-existence of connexions between elements". For example, if we say that there happens to be a complete set of playing cards on my desk, I mean that there are elements representing one of each kind of card which are connected by all being located next to each other. And if I say that there happens to be a suitable candidate I may mean that there's a single person who has the skill, determination, and experience to handle the role; that is that these attributes are connected by all being contained in the one person.

For Wittgenstein, it doesn't really make sense to talk about individual elements existing in any non-trivial sense. He writes: "If this thing did not exist, we could not use it in our language-game". That is, saying that a simple element exists says nothing beyond the fact that this element is part of our language-game^[6], similar to saying that you're going to define a variable $x$ doesn't say much until you've defined it. In his mind, asking what it means for a simple element to exist is confused because the notion of existence doesn't have any non-trivial meaning outside of checking whether there is a thing for which the claimed connections hold.

This is further clarified by the following analogy: Wittgenstein suggests that it doesn't really make sense to say that the "standard meter in Paris" is either one meter long or not. The former is a tautology so isn't of any significance and the latter is false.

I'm not completely convinced by characterisation of Being as necessarily concerning connections between elements, but I still think he has a point. When we ask philosophical questions like, "What is Being?" we seem to be using this word differently from how we use it in everyday life. And this criticism seems compatible with multiple characterisations of what existence means in our everyday lives.

I'll demonstrate this with an alternate characterisation. If we ask "What does it mean for an animal to be an orangutan?" we probably don't actually care about whether the orangutan is ultimately built up from atoms or quantum wave-functions as opposed to wanting to know how to differentiate it from a gorilla.

Here the language-game consists of learning how to differentiate one kind of object from another. And if we try to extend this to differentiate objects that are from objects aren't, it may not make sense, as there might be nothing to compare to. Now, we could try extending the definition from another everyday definition of existence, but perhaps we'd just encounter the same issue.

Relevance: The general lesson I take from this is to be very careful about trying to use a term outside of the language-game or games that it originates from. Ignore this and our terms risk becoming ungrounded.

Take for example the Sleeping Beauty Problem. This has led to endless debate between the thirders and halvers, but perhaps the issue is that probability is a concept defined for situations where an event can only ever be counted exactly once. Once we leave that region of problem-space it's hardly surprising that the concept of probability starts to come apart. Merely asking, "What is probability?" in the abstract isn't very helpful. Instead, we have to pay attention to the language-games that people might want to play in these unusual situations.

Epistemology

Wittgenstein's concept of knowledge is deeply bound up with his concept of language. He thinks it was a mistake for philosophy to seek absolute knowledge and that we should only try to produce certainty in terms of what it means within our ordinary, everyday language-games. In particularly, he believes that the notion of certainty varies according to the language game:

I can be as certain of someone else's sensations as of any fact. But this does not make the propositions "He is much depressed", "25 x 25 = 625" and "I am sixty years old" into similar instruments. The explanation suggests itself that the certainty is of a different kind

Different language-games include different methods of either proving or attempting to disprove claims; and claims that pass muster according to these standards are classed as "certain". We might complain that this isn't true certainty as these methods will only reveal the truth under certain assumptions. Wittgenstein addresses these kinds of doubts when he writes "what we do in our language-game always rests on a tacit presupposition" and "doubting has an end". In other words, this is the best that we can do, and seeking absolute certainty, like Descartes, is the kind of foolishness only philosophers engage in.

Wittgenstein goes further and questions whether we really doubt:

But that is not to say that we are in doubt because it is possible for us to imagine a doubt. I can easily imagine someone always doubting before he opened his front door whether an abyss did not yawn behind it, and making sure about it before he went through the door (and he might on some occasion prove to be right)—but that does not make me doubt in the same case

And:

If I see someone writhing in pain with evident cause I do not think: all the same, his feelings are hidden from me

And also whether we can doubt:

But, if you are certain, isn't it that you are shutting your eyes in face of doubt?"—They are shut.

In other words, let's be honest here. Just because I can talk in the abstract about doubting something, doesn't mean that I'm really capable of it. Let's accept that there are things that we can't help to believe. And perhaps we should be open to the possibility that this might have consequences for how we should think about epistemology.

Elsewhere he writes: "What has to be accepted, the given, is—so one could say—forms of life." We can compare this to David Hume's injection to, "be a philosopher; but, amidst all your philosophy, be still a man.” Hume was a famous skeptic who doubted everything from causation to induction. Nonetheless, there was there was David Hume the Philosopher and David Hume the Billiard Player. When it was time to play billiards, he simply put aside his skepticism that we had any reason to believe that the balls would move the same way that they had in the past. Wittgenstein also emphasised being human, however for him, the only reason to be a philosopher is to avoid being fooled by philosophy.

We can also interpret Wittgenstein as making a similar move to Descartes' "I think therefore I am". Any question or statement can be seen as presupposing the existence of the language-game in which it makes sense. So perhaps being too skeptical ends up being self-defeating?

One of his key epistemological claims is that it only makes sense to talk about knowledge when there is some method of falsification or verification. For Wittgenstein, knowledge refers to beliefs that have passed some kind of test, with the appropriate kind of test depending on the language-game the belief comes from. If there is no test that we can apply, then we can't play any language-games related to knowledge, at least in any non-trivial sense. He uses this argument to try to demonstrate that we can't have knowledge of private sensations.

Wittgenstein presents these methods of falsification or verification as being intersubjective rather than objective. That is, the important element is that other people should be able to tell whether or not we are playing the language-game correctly. Without this ability, we wouldn't be able to inculcate people in this language-game.

My main objection to this definition of knowledge is that it carves the joints of the world in a strange way. The existence of some method of verification seems like a somewhat arbitrary criterion as it's not clear that we should put more belief in claims that are unlikely in our prior that have passed some weak level of verification vs. claims that seem extremely likely in our prior, but without any method of verification beyond it appearing as such. Perhaps Wittgenstein could respond that his notion of knowledge isn't supposed to always result in claims designated as knowledge having more certainty than those not so designated. This could be reasonable, but it would greatly undermine the importance of being classed as knowledge.

Relevance: Pragmatically, it makes a lot of sense to utilise different definitions of what does or doesn't count as knowledge depending on the use case and the level of certainty required. Naturally, these vary by language-game. On the other hand, if we adopt such a pragmatic definition, we need to be aware of the inconsistencies this introduces for what counts as knowledge.

His claim that we don't doubt certain things is a little black and white, but I think he is right to criticise the broadly Cartesian model^[7] where we doubt everything and refuse to adopt any belief unless it is proven.

Not only does is it unable to get us anywhere (we can't get anything from nothing), it fails to acknowledge that there are limitations to how much we can doubt. Yet this model is incredibly tempting because you might think that what we believe has no bearing on what we ought to believe.

However, Frank Ramsey demonstrates how an awareness of these limitations can aid our understanding of epistemology when he writes:

We are all convinced by inductive arguments and our conviction is reasonable because the world is so constituted that inductive arguments lead on the whole to true opinions. We are not, therefore, able to help trusting induction, nor if we could help it do we see any reason why we should.

Engaging with our inability to hold other beliefs makes his argument stronger. And this single counter-example is sufficient by itself to demonstrate that something is lost by never straying outside of the Cartesian model.

Reality

Throughout the book, Wittgenstein seems somewhat ambivalent on the existence of external reality. While reading this book, I spent a lot of time struggling to identify his position. I think a good entry point is to consider his position on internal feelings. Wittgenstein draws a parallel with an sealed and unopenable box:

The thing in the box has no place in the language-game at all; not even as a something: for the box might even be empty.—No, one can 'divide through' by the thing in the box; it cancels out, whatever it is.

That is, for the purpose of understanding language, it doesn't really matter whether there is anything outside of the language-game. He's not saying that there is nothing outside of it - just that it is irrelevant for this discussion. This is not the same as claiming that things outside the language-game are unimportant. In our summary of Tracatus, we already observed that he implied that these might be the most important things of all.

There are, indeed, things that cannot be put into words. They make themselves manifest. They are what is mystical.

On the other, this seems like it might be in tension with his suggestion that disputes between "Idealists, Sophists and Realists" are merely linguistic. The way I interpret this is that disputes between the schools are mostly about the language we use to describe the map rather than about the territory. That is, a realist might say "Bananas are very satisfying", an idealist may say, "The perception of eating a banana is accompanied by the perception of satisfaction" and the Sophist "My perception of eating a banana is satisfying for me".

And maybe the differences go deeper than this, but perhaps we've just expressed the same thought in three different ways. Someone can in fact hold that these differences are essentially linguistic even if they believe that there are different ways that the territory could be. One way this belief could make sense would be if you thought there was much less correlation between people's a) endorsed use of language + stated philosophy and b) their beliefs about the map. For example, both a sophist and a realist may assign 0.1% probability to nothing existing outside of themselves, but the sophist may wish to place a stronger emphasis on that probability. Similarly, both a realist and idealist may have the same level of doubt regarding our ability to know what exists outside of our experiences, but the idealistic may consider this a vital fact for understanding the world, while the realist is fine with just doing the best that they can and sees this as barely worth noting.

Adding to this, I've personally seen people who are allergic to any mention of "objective reality", yet make no objection as long as you avoid a specific list of keywords. In other words, we shouldn't assume that just because people use a different label that their object-level beliefs are actually fundamentally different.

Relevance: I also think it's quite reasonable to allow that there might be things that we can't know or observe that would nonetheless be important^[8]. Unlike Wittgenstein, I'd take this as a point against the notion that the differences between idealism and realism are merely linguistic. I don't think this is 100% about people's preferred use of language either.

Suppose I ask about how to grow coconuts. Someone who's an idealist may assert that there's no such thing as coconuts, only the perception of coconuts. Even if I consider this a plausible metaphysical theory, I'll be annoyed with the person for not answering my question. In this case, as far as I am concerned, the possibility of an external reality is irrelevant. I would even be tempted to describe it as a "nothing that just cancels out".

Internal Experiences

Just as Wittgenstein tends to be somewhat ambivalent about the existence of the external world, he tends to be ambivalent about the existence of internal experiences.

Nonetheless, in response to a demand to admit that there is a difference between "pain-behaviour accompanied by pain and pain-behaviour without any pain" he writes:

Admit it? What greater difference could there be?

To the claim that an inner process must take place:

What gives the impression that we want to deny anything?

Again, his position seems to be that the possible existence of inner processes has no impact on how the relevant language-games work.

Wittgestein famously considers the possibility that "only I can know whether I am really in pain" declaring that "in one way this is wrong and in another way it is nonsense". He argues that in the regular, everyday use of the term "know" others can know that we are in pain from how we are acting^[9]. And, he argues that on the contrary, if we take pain to be an internal experience, we can't know that we're in pain as there wouldn't be any criteria to distinguish between believing and knowing.

He boosts these arguments by reminding us of the inherent slipperiness of memory. Even if I think my experience of smelling lavender matches when I smelled it in the past, I might be misremembering. Further, I don't really have any criterion about whether two experiences match apart from the fact that they appear this way to me.

When reading The Investigations, I often struggled to try to figure out why he didn't consider himself a behaviorist. In response to, "Are you not really a behaviorist in disguise? Aren't you at bottom really saying that everything except human behavior is fiction", he responds, "If I do speak of a fiction, then it is of a grammatical fiction"

My interpretation is that rather than claiming internal sensations are a myth, he is claiming the talk of internal sensations is a myth, in terms of being a surface-level appearance. For example, he suggests that "There has just taken place in me the mental process of remembering" can be understood as just another way of saying, "I have just remembered". That is, he tends towards interpreting talk about internal processes as being figurative, whilst denying literal interpretations which involve "the yet uncomprehended process in the yet unexplored medium".

He makes a number of arguments for inner experiences not being a necessary component for a use of language to have a particular meaning or for us to have a particular understanding. One is that if he introspects, sometimes these experiences are there, but sometimes they are not. Another is that if we learned that someone had the same feeling when using "if" and "but" we might think it unusual, but we wouldn't claim they didn't understand how to use the words.

I see these as reasonable objections to attempts to ground meaning in emotions, however, he seems to assume that these processes must be conscious, which raises the obvious question of why can't we define meaning in terms of unconscious processes? I often felt that he was adopting positions that would be much less tenable today given the advance of neuroscience. However, he addresses this kind of argument by imagining that his blood pressure rises whenever he has a particular sensation:

So I shall be able to say that my blood-pressure is rising without using any apparatus. This is a useful result. And now it seems quite indifferent whether I have recognized the sensation right or not.

So maybe Wittgenstein would argue that neuroscience expands the scope of language insofar as language is understood as an intersubjective, error-correcting system of communication and coordination.

Relevance: Even though "He is in pain" nominally claims that someone is undergoing a particular experience, that need not be the intent. Someone may not, for example, believe that humans are nothing but machines and disbelieve the notion of subjective experience, yet they may make that statement so that the person is administered painkillers so that they shut up. Alternatively, we can imagine someone who isn't really sure about whether or not qualia exist, but who figures that they may as well proceed on the basis that there are qualia because that is the most natural thing to do.

As another example, suppose someone says, "I'm thirsty". Nominally, it asserts that they are experiencing a sensation (that of thirst). But perhaps they just want you to pour them a beer. Alternatively, maybe they are aware that they haven't drunk for a while even though they don't feel the sensation. In fact, the person themselves might not realise that they aren't feeling the sensation unless you prompt them.

Even if we shouldn't follow Wittgenstein by explaining "I'm thirsty" exclusively in terms of its role in the language-game, we shouldn't exclusively focus on subjective experience either. I'd suggest that we should take an intermediate position instead.

In this section, we discussed how The Investigations serves as a reminder not to take things too literally. This is a trap that rationalists often fall into, my past self included.

The Private Language Argument

The Stanford Encyclopedia of Philosophy (SEP) describes the private language argument as claiming the impossiblity of a language that is "in principle unintelligible to anyone but its originating user".

Attempting is discuss this argument is extraordinarily difficult. As SEP says, "Even among those who accept that there is a reasonably self-contained and straightforward private language argument to be discussed, there has been fundamental and widespread disagreement over its details, its significance and even its intended conclusion, let alone over its soundness. The result is that every reading of the argument (including that which follows) is controversial"

A significant part of the debate seems to concern whether Wittgenstein is claiming that there is something we cannot do (ie. produce a private language) or whether he is claiming that the concept of "private language" is nonsense. However, I don't see a need to focus too much on this distinction, so we'll move on. 

SEP also suggests that Wittgenstein might be responding to Bertrand Russell's ‘The Philosophy of Logical Atomism’:

A logically perfect language, if it could be constructed, would not only be intolerably prolix, but, as regards its vocabulary, would be very largely private to one speaker. That is to say, all the names that it would use would be private to that speaker and could not enter into the language of another speaker

… A name, in the narrow logical sense of a word whose meaning is a particular, can only be applied to a particular with which the speaker is acquainted, because you cannot name anything you are not acquainted with.

... We say ‘This is white’. … But if you try to apprehend the proposition that I am expressing when I say ‘This is white’, you cannot do it. If you mean this piece of chalk as a physical object, then you are not using a proper name. It is only when you use ‘this’ quite strictly, to stand for an actual object of sense [i.e., a sense-datum], that it is really a proper name. And in that it has a very odd property for a proper name, namely that it seldom means the same thing two moments running and does not mean the same thing to the speaker and to the hearer.

Bertrand Russell hoped that it might be possible to construct a logically perfect language. This would be built up from simple objects of sense-datum rather than external, physical objects presumably because of the inherent uncertainty in deriving what actually exists from sense data.

Note that Bertrand Russell conceded that his position meant other people wouldn't understand the proposition that he meant by "This is white" and that the meaning of that proposition would change from moment to moment.

Compare this to Wittgenstein's beetle-in-a-box thought experiment:

Now someone tells me that he knows what pain is only from his own case!——Suppose everyone had a box with something in it: we call it a "beetle". No one can look into anyone else's box, and everyone says he knows what a beetle is only by looking at his beetle.—Here it would be quite possible for everyone to have something different in his box. One might even imagine such a thing constantly changing.—But suppose the word "beetle" had a use in these people's language?—If so it would not be used as the name of a thing. The thing in the box has no place in the language-game at all; not even as a something: for the box might even be empty.—No, one can 'divide through' by the thing in the box; it cancels out, whatever it is.

There is a striking similarity between their positions. I suppose, as they say: one man's modus ponens is another man's modus tollens. However, perhaps Russell would dispute that the "thing-in the-box" has no role in the language-game. After all, even if we can't be sure that our sensations are the same as other people's, searching for a sensation similar to some other sensations seems to be part of how we understand when to use these terms.

Imagine I'm learning how to appreciate wine. I might miss a flavour upon my first sip because I'm distracted by other flavours, but notice it upon the second. If repeated attempts at tasting the flavour failed to detect it, I might wonder if there was something unusual about my taste receptors or whether I just wasn't paying close enough attention during the tasting. Wittgenstein would undoubtedly describe this process as a language-game and avoid any reference to private sensations, but I see this as a reductive account that leaves out a core part of the phenomenon.

Wittgenstein's definition of knowledge is key to his argument for private languages being impossible. If we accept his argument that we can't have knowledge of internal sensations, then anything that private language could communicate would be of dubious authenticity. I've already explained my skepticism of his epistemology which leads me to also be skeptical of the private language argument.

Relevance: His private language argument is probably the aspect of his philosophy that I am most critical of. Nonetheless, I think there is an important insight here. We shouldn't just take statements at face value, but rather we should always keep in mind the language-game that is being played and what function the particular use of language serves. In the section on Subjective Experiences, we discussed how apparent talk of internal feelings is sometimes just a surface-level appearance.

The episode of In Our Time that focused on Wittgenstein contained an interesting reframing of his private language argument. We often see language as something in which we dress our pre-existing thoughts in order to express them to others. However, participating in language-games with others is a key part of how we acquire the concepts and distinctions we make use of during thinking. Given this, we would expect that an individual who spent their whole life isolated from others would, at best, only be able to produce a severely impoverished form of thought and hence language.

Link to Linguistic Freedom

I've previously used the term linguistic freedom to describe the freedom that we have to define or redefine words to suit our purposes. This is related to the idea that the Map is Not the Territory as once we have realised that we construct the map, it is natural to assert the freedom to draw the map differently in order to better suit our purposes. At a number of points, Wittgenstein seems to argue for this kind of linguistic freedom:

What about the colour samples that A shews to B: are they part of the language? Well, it is as you please.

And

But how we group words into kinds will depend on the aim of the classification,—and on our own inclination

Logic and Maths

Wittgenstein criticises the idea that logical statements are true a priori:

We want to say that there can't be any vagueness in logic. The idea now absorbs us, that the ideal 'must' be found in reality. Meanwhile we do not as yet see how it occurs there, nor do we understand the nature of this "must". We think it must be in reality; for we think we already see it there.

In other words, someone can vigorously assert that logical statements "must" be true without realising that they lack any understanding why they believe that they must be true.

But: if anyone believes that certain concepts are absolutely the correct ones, and that having different ones would mean not realizing something that we realize—then let him imagine certain very general facts of nature to be different from what we are used to, and the formation of concepts different from the usual ones will become intelligible to him

Perhaps we lean towards classical logic because we exist at the macro scale, but if we were to exist at the quantum scale we'd feel drawn towards notions of logic that allow things to be both true and false.

Of course, in one sense mathematics is a branch of knowledge,— but still it is also an activity. And 'false moves' can only exist as the exception. For if what we now call by that name became the rule, the game in which they were false moves would have been abrogated.

We consider it a mistake to say that 2+2=5. However, let's suppose we ended up adopting this rule. Presumably, this would be because we've discovered facts about the world indicating that this system of maths is more applicable than ours. Then it wouldn't be completely accurate to say that 2+2=4 was wrong. It was correct within the language-game that we were playing. What happened instead is that we decided to play a different language-game - one where 2+2=5.

For the crystalline purity of logic was, of course, not a result of investigation: it was a requirement

We think logic must necessarily be true because we cannot think of any examples where it is false. But of course, if we could have thought of any counter-examples, then we would have constructed different rules instead.

I think the Liar's Paradox is instructive here. It's very common to think that statements that aren't nonsensical must be true or false. However, the Liar's paradox explodes this^[10]. Has this caused anyone to abandon logic?

Of course not! Everyone just updates their schema by excluding Liar sentences from this requirement. And then they make further adjustments in response to the extended Liar's paradox. This is much more what we'd expect from a system of ad-hoc patches than from a priori knowledge. And perhaps we can't think of any counter-examples to logic because if we could then logic would have already been adjusted to be compatible with this.

Mathematicians do not in general quarrel over the result of a calculation. (This is an important fact.)—If it were otherwise, if for instance one mathematician was convinced that a figure had altered unperceived, or that his or someone else's memory had been deceived, and so on—then our concept of 'mathematical certainty' would not exist.

Wittgenstein is claiming that mathematical "certainty" doesn't exist absolutely, but only under certain conditions.

Relevance: Wittgenstein has influenced me towards adopting a more grounded and embedded notion of what maths and logic are. I used to be quite tempted by Mathematical Platonism, but Wittgenstein argues rather persuasively against maths and logic consisting of a priori truths.

Link to Conceptual Engineering

Conceptual engineering is the idea that instead of asking what a word means, we should be constructing words that serve particular purposes. It is often contrasted to conceptual analysis to attempt to find necessary and sufficient conditions for being a part of a particular class and in particular, tries to avoid the existence of any counterexamples.

I suspect that if analytical philosophy had placed more emphasis on Wittgenstein they wouldn't have fallen into the trap of counter-example philosophy that arose from conceptual analysis. LukeProg describes the problem as follows:

The trouble is that philosophers often take this "what we mean by" question so seriously that thousands of pages of debate concern which definition to use rather than which facts are true and what to anticipate.

While as far as I know, Wittgenstein doesn't explicitly argue precisely for conceptual engineering, it seems to arise naturally from his philosophy. Firstly, his model of words as family resemblances suggests that it'll be impossible to find necessary and sufficient conditions that avoid all counterexamples. Secondly, his model of language as use seems to suggest that what is important about words is the purpose that they serve. Thirdly, his argument for language-games and a kind of linguistic freedom seems to suggest that we have the ability to collectively define and redefine conventions about how words are used in order to make them more convenient for us. Lastly, Wittgenstein even compares the different functions of words to the different tools in a toolbox.

Should you read this book?

I am a huge fan and would strongly recommend it, but be aware that the text is deceptively difficult to make your way through. It is best read slowly. My reasons for recommending this are as follows:

• Wittgenstein is eminently quotable so it is much better to hear him in his own words.
• This text is unlike almost any other philosophical text that you will ever read. Unlike analytical philosophy, tends to make arguments implicitly rather than explicitly. However, his thinking is much less fuzzy than that of Continental Philosophers. And, thank God, Wittgenstein actually writes in clear language!
• This text by its very nature resists summarisation. Wittgenstein goes off on countless tangents and it would be impossible to cover all of them. So many sentences can be interpreted in a multitude of different ways. And even when he repeats himself, he approaches things from a fresh perspective that adds new insight.
• Wittgenstein's focus on intersubjectivity means that he is coming from a perspective that is quite foreign. And I found engaging with this perspective surprisingly fruitful.

1. ^{^}

   See the Stanford Encylopedia of Philosophy for a more technical description.

2. ^{^}

   In contrast, the resolute reading asserts that when Wittgenstein asserts that his propositions are nonsense, he means precisely that. That is, the Tracatus is just plain nonsense, rather than some kind of elevated nonsense designed to reveal deep truths. And that end result is not some ineffable truth, but a realisation that Wittgenstein had embarked upon a fundamentally misguided project.

3. ^{^}

   Whether or not this is an issue depends on what properties we want the meanings we assign to an utterance to have. But it is at least plausible that we want our meanings to not provide a misleading picture of cognition.

4. ^{^}

   See Intension and Extension from logic and semantics.

5. ^{^}

   I like this expression because when we are traveling to other countries with different cultures, it's very easy for us to embarrass ourselves by doing things that don't make sense in our new context.

6. ^{^}

   He makes a comparison to chess. Putting the pieces on the board isn't making a move in chess, but someone who didn't know the rules might easily confuse the two. Similarly, take making a "linguistic move" to mean attempting to use language to do something. Then introducing an element x is merely preparatory to making an actual linguistic move. It doesn't do anything in and of itself.

7. ^{^}

    I would be surprised if this was an accurate model of Descartes' epistemology, as I understood him as merely proposing it as a useful thought experiment.

8. ^{^}

   I've argued as such in The Universe Doesn't Have to Play Nice.

9. ^{^}

   In other words, he defines "know" here to mean satisfying certain socially defined epistemic standards, rather than some kind of absolute standard.

10. ^{^}

    I concede that it might be reasonable to describe these sentences as nonsense. But I think it still suffices to make the point. Among the people who don't consider them, almost none of them have rejected logic as a result of the Liar's Paradox. And if I were to persuade someone who considers these sentences nonsense that they aren't actually nonsense, again, I'd expect them to merely update their model of logic rather than throw out logic itself.