I just finished David Stern's introduction to Wittgenstein's Philosophical Investigations, and my mind got blown in a non-minor way. I want to share some of the thoughts that went through my head while going through the book. I am not a philosopher, and I didn't read the original text (English or German), so I can't say I am representing Wittgenstein's views. But what I can do is to play both the role of what I think I read, and how I respond to that those particular ideas. This will be presented as a short dialog between a devil's advocate (indented) and a god's advocate, where the former takes a skeptical position. The devil's advocate should be taken as one would Zeno in proposing his paradoxes: he is trying to show how something that "obviously" happens as an impossibility. The god's advocate will then propose explanations as solutions.
It is impossible to learn a language. Consider how we understand a new word: we look it up in a dictionary, or ask someone for a definition. The definitions themselves are words, however, which means that the learner needs to already know some words in order to understand this new word. This is true of all words - all their definitions depend on knowledge of other words. In order to learn a language, at least one word must be learned first, but learning it already requires partially knowing the language. Thus it is impossible to learn a language.
Of course, words don't have to be learned by definition. The teacher may point to a car and say "car", or may wave a fork in front of the baby and say "fork"; nouns could be learned in this way. Similarly, the teacher can repeat a verb while performing a motion, or repeat an adjective while pointing to successive objects that the word describes. This method of teaching avoids words, and so avoids the need for a priori knowledge of the language.
The problem with this approach is that impossibility covers not only language, but all communication. When the teacher points to a car and says "car", how does the learner know that the word "car" is the object pointed to, and not the act of pointing? The act of pointing itself requires knowledge that it is only a reference, not the object itself - prior knowledge that the learner does not have. Repeating a word may be used to indicate subtle differences, that the learner believes they have not yet learned to distinguish. Even gestures of affirmation or of denial - nods and shakes of the head, for example - has meaning which can only be explained through additional communication.
Example-based learning - such as pointing to red objects for "red" - has an additional problem of induction. For any finite set of examples, there is an infinite number of patterns that can describe those examples. 1, 2, and 3 may describe the set of natural numbers, or the set of real numbers, or the set of all glyphs, or the set of all objects.
There is always the possibility of misinterpretation for any communication. This gets worse with interaction units that do not represent concrete objects or actions. The verbs "think", "feel", and "remember" has no demonstrable behavior, and one cannot point to "imaginary numbers". These concepts must be transmitted through existing common ground, and since that does not exist, communication is impossible.
Common ground is necessary, but it is a mistake to assume that common ground must be some form of communication. Any two strangers, in any culture in any period of history, already have a common ground: their shared evolutionary history.
Any two humans, when they communicate, already share 3.5 billion years of ancestral cohabitation on earth. Our physiology and psychology have been shaped by common forces, leading to similarities before even the first grunt. Our brains interpret - and misinterpret - perception in the same way; we process information through similar algorithms with similar biases. When a teacher waves a fork, the learner is biologically programmed to pay attention to the movement. In fact, this behavior is so primitive that it is a shared trait between a large portion of animals. We also associate and cluster stimuli that occur together, sufficiently so to mistake the ring of a bell for the presence food - and perhaps the audio signal "car" for a wheeled vehicle. Again, this is common ground with many other animals.
Other traits are more recent in evolutionary history. A number of vertebrates - cats, dogs, great apes, dolphins - are also social in nature, and our brains are also adapted for such an environment. We are biased to mimic other people's behavior, and project ourselves into their position to understand them. At least a partial understanding of facial expression is inborn, allowing infants to replicate certain expressions. There are theories which hypothesize the hard-wiring of stronger forms of communication structure, but it is clear regardless that common ground for communication exists. The information processing commonalities above, together with the correct assumption that the teacher operates in the same way, allows the listener to infer the meaning that the teacher intended.
It goes without saying that this shared evolutionary history does not rely on further prior common ground. It can therefore safely serve as the foundation for the building of communication and language.
This explanation of common-ground puts the burden of communication on the brain, and therefore leaves out one thing: precision in communication. For one, evolution does not account for everything in a particular brain; its structure is also determined by the specific genetic inheritance as well as the environment in which the brain matured. There is no guarantee that these differences will keep the biases for communication intact. Even if the neural machinery were all there, these differences make it impossible to recreate exactly what the speaker meant.
The more fundamental problem, though, is that brains are fuzzy. People not begin with definitions of words they want to communication, but general ideas that they themselves cannot define. All that exists in the brain are approximations and conglomerations of previous experiences. "Humans" are not "feather bipeds with broad nails", but some incoherent mixture of all humans the speaker has seen. This concept cannot be transmitted through any communication, language, gesture, or otherwise. What does gets communicated is itself misinterpreted by the listener for a different mixture of people. What two people call "human" may not in fact be the same thing at all.
All that occurs during communication is a double illusion of transparency, both sides thinking they understand the other, but neither getting the point across.
Brains are probabilistic, but so is the world! It is a fallacy to assume that communication needs to be precise exactly; it is sufficient for it to be precise enough. Precision is a double-edged sword: too little precision and there remains ambiguity, too much precision and the communication cannot be generalized. Language is learned and used in the real world, where nothing is clear cut. It is in fact a power of communication to capture these ambiguities.
That language is ambiguous doesn't mean that language is unlearnable. Language is not learned as a whole, but slowly, piecemeal, over a long time. The first word doesn't need to be precise - and as pointed out, it can't be. All it needs to be is a first approximation, and this approximation can be refined over time. The fuzzy concepts between the speaker and the listener do not need to match up exact, but just needs to have sufficient overlap. As long as this overlap is precise enough for the world, then communication is meaningful.
Most of the world may be ambiguous enough for communication, but not all of it is. That two speakers can get meaning overlap is not good enough. From whence does the logical calculus of mathematical symbols?
The first arguments from the devil's advocate is somewhat close to my understanding of Wittgenstein. Given that most of the counter-arguments are made decades after Wittgenstein's death, I don't know how much of it was known to Wittgenstein. The idea that human physiology and psychology has such unescapable influence on everything was a new thought to me. A smaller version of the idea, that no one sees an object/event in the same way, has been pushed on me before, but this is different. It suggests that even concepts we find "objective" - for example, the maxim of Ockham's razor - may be the result of our evolutionary history (although a Bayesian explanation exists). I have been occasionally interested in how cunning linguists propose we establish communication with aliens. Most schemes begin by establishing numbers, then showing mathematical concepts. But how does mathematics arise from probabilistic biology?