Commentary on PHILOSOPHICAL INVESTIGATIONS: Article Content

Title page:Aid and Commentary on Remarks 1 to 142 of the PHILOSOPHICAL INVESTIGATIONS
==Introduction==
This page contains the Commentary and Aid On § 1 to 142 to the PHILOSOPHICAL INVESTIGATIONS Of Ludwig Wittgenstein By Robert Parr.
[Please Note: When I am just paraphrasing, It is an aid to the reading of the text itself. Please read the text first. Paraphrase seldom says all an original text does; sometimes paraphrasing a text is just impossible. [From my high school years on, I thought ‘’Readers Digest’ was just a lazy mans way of saying he had read a book without really reading it. As years go by I have concluded that nothing of importance can really be paraphrased. Paraphrase is only an aid to understanding really good writing or correcting really bad writing.]
==Names and Games==
===§1 THE meaning of words===
This is an venerable example of a way language has been commonly explained from ancient times to the present. With various alterations it still could be the application of a theory of language taught and learned in Departments of Philosophy today. The theory of language in the Tractatus can easily be seen as an epitome of this kind of theory. The idea of language in the Philosophical Investigtions is entirely different. The difference is clear from the start. No ‘theory’ is being established. Just the opposite; the particular applications of this kind of theory theory will show it to be false and inadequate. 
Philosophical disputes usually come down to differing “meanings” of words---THE meaning of a word----the meaning of the word as we use it----the intension--what I mean (technical term, different from 'intention'). Why is there only one correct meaning? A close look at the actual usages of language begins a close examination by descriptions---not explanations---of ordinary language The theory most believed in, inadvertently or not, as to how language works is a collection of names----as a nomenclature. 
For most of Western history the predominant form of meaning was Essentialism: the ‘idea’ of language that ‘meaning ’requires the “essense”, the nature, the clear and distinct definition or abstraction, a single meaning for each word that applies in every use of that word. It is the ‘ideal’ conception of language. The real name of something was its essence. Learning language was learning names. That was the Graeco-Roman tradition. The same idea has also been called Adamic, another term used for linguistic essentialism, referring to the account in Genesis of Adam giving everything created its real name. The names that Adam gives in the Bible are not arbitrary names; they were names that gave the real meanings, the names were the nature of things in the world, in Paradise. After the Fall, with our benighted intellects, this gift of God was taken from us. #[I got this information from a Biblical scholar who became Master of Novices in the second year of my Jesuit training. He had just finished his postgraduate work in Biblical studies. I ran into the idea again in a book by Roy Harris, Language, Saussure and Wittgenstein: How to Play Games with Words: "The term Adamic emerges as describing a thesis, widely held in the eighteenth century and earlier, which assumes that originally in the Garden of Eden things were called by their correct names, which reflected their true essences and that recovery of the 'lost knowledge' was the Holy Grail of linguistic enquiry." (pp. 7-8)
"It is certainly interesting that both Saussure and Wittgenstein choose to introduce their own
views of language as views which are, or purport to be, anti-thetical to the nomenclaturist position."(p. 13)] 
"Nominalism" is another term that, while believing language is a collection of names---a nomenclature---emphasizes the arbitrary connection between the ‘inner’ idea to sign and the arbitrary sign to the ‘outer’ reference. Wittgenstein at one point calls it “Nominalism” [“Nominalists make the mistake of interpreting all words as names . . . . “ §383 PI] The actual 'name' that connects to its reference is arbitrary---conventional. The nature of the inner idea that is arbitrarily connected to the 'name' is, strictly speaking, left undetermined. It need not be essentialism, but that was the default conception for centuries.
Saint Augustine expresses the simplest form of the idea that every word in a language is at bottom a name. Saint Augustine is perhaps the best representative of the confluence of these notions, standing at juncture of the Graeco-Roman and the Biblical cultures. Ferdinand de Saussure has a just claim to being considered the father of linguistic science. In his Course in General Linguistics, he notes, “. . .the superficial notion of the general public: people see nothing more than name-giving.” [“nomenclature” as translated from the French by Roy Harris in Language, Saussure and Wittgenstein. The name that connects to the idea and to reference in the world is arbitrary. When Graeco-Roman and Hebraic tradition became one in the Third century CE, an essence in the “inner” and in the “outer” was required for language to work. Nomenclaturism and Adamic and simple “essentialism” are different words for the same idea.
The "Adamic" idea is expressed by Plato in Cratylus 383,A/B.<BR>
Cratylus: “Everything has a right name of its own, which comes by nature, and that name is not whatever people call a thing by agreement, just as a piece of their own voice applied to the thing, but that there is a kind of inherent correctness in names, which is the same for all men, both men and barbarians”<BR>
Cratylus defends ‘essentialism’ and nominalism, and Hermogenes represents belief in the conventionalism of language in this Platonic Dialogue.
Not all of this explanation of theory is needed to understand the text, nor is all of this general explanation expected to be in place for the reader to understand what he reads. It is understandable as it stands. This example is just the start of Wittgenstein's method. His method is very like the method he would have used when he was teaching simple village children. The child would not come to what Augustine says with an urge “to misunderstand”. So what I add is for those with more education and certain assumptions---and thus, the "urge to misunderstand".
===§2-4 Seeing language as a game===
In section 1, Wittgenstein introduced the idea of trying to account for human language in terms of each word having a well-defined, "natural" meaning. He now describes that approach to language as a primitive philosophical concept of meaning, but he also makes the point that it is an approach that could be successfully applied a language more primitive than ours. Looking at the same thing from different points of view is one important aspect of Wittgenstein’s method. As he said of the contents of Philosophical Investigations in his Preface, "The same or almost the same points were always being afresh from different directions". 
Another exmple of a commonly used method is also used in sections 2; the making up of simple “language games” to put in focus certain points that would be lost in the complex relations within a fully developed human language. This simple game makes the point that list of words do not in themselves make the simplest of languages. He wants us to see it as a complete primitive language. But that would be impossible if all we were given were 4 items, named by pointing to them. The very important thing that is present in §2 is that the words are given a job to do; they have a use in a human activity. The words of language mean something when they have a use.
The use of such “games” is introduced without explanation. It is the third of his method used so far: examples, looking at different points of view at something, and games. Wittgenstein will discuss this first use of the word ‘game’ in §7. This is just one example of how the word will be used. The appropriateness of calling a language an interconnected collection of different language games may not seem apparent until it is looked at from many different angles. 
Those who expect a clear and distinct definition of “language games”, "something they all have in common," will be asking a futile question. The right question would be if there is such an essential definition for game, a clear and distinct 'Cartesian definition possible. What Wittgenstein writes from §1-65 could be considered a review of all points of view that lead him to consider a language as an interconnected collection of different language games. If he were to answer, which he does not directly do, he would say that there are no such meanings or definitions for game or most words we use in language. 
§3 Wittgenstein wants us to see the limitations of Augustine’s description of language so he puts it into the context of a limited system of communication that can not encompass the whole of what we would want to call language. The metaphor of a board game such as chess that is only part of everything we call games makes his point clear. Good teaching. Chess is just one of many ways he tries to get you to look at alternatives. (see No. 140) Wittgenstein tries to get you to see language in a different way from the only way you habitually seen it. After viewing the alternatives, you may realize that the supposed logical force of an argument is actually only a psychological "force".
§4. The same point as in §3 is made again, but with a different example. 
Some may be old enough to remember the Danish pianist and comedian, Victor Borge. He would read a text having individual and comic sounds for all punctuation. If you took out the text, added many more written squiggles to represent many more sounds, you would have a good idea of what Wittgenstein intended. Here is another simile created to show the oversimplification in the theory of language represented by Augustine. The sounds and the squiggles on paper were related to each other and nothing else.
Wittgenstein's most direct criticism of the idea of language that Augustine wrote is his "conception of language is like such an over simple conception of the script.”
===§5 Primitive forms of Language===
The fog that surrounds our understanding of ‘meaning’ when we think of every word as a name, can be dispelled if we “study the phenomena of primitive kinds of application” of language. Two ways to approach "primitive kinds of application" of language are to consider the subsets of language that children first learn and to imagine how human language may have begun. Children naturally begin learning the primitive kinds of meaning; primitive compared to the more advanced developmental stage at which they can speak naturally and fluidly, according to their individual capacities and opportunities.
Does Wittgenstein also refer to historically primitive.? Would he theorize on the most primitive language----when first human speech began.?
The second question answers itself. No, he would not theorize. The answer to the first question is, maybe not, but the picture here is fuzzy---a little complicated. 
Overall the he best general answer would the conclusion Stephen Toulmin came to. 
I first noticed Toulmin as more than the co-writer of [italics]Wittgenstein’s Vienna[end] In a series video interviews of eminent thinkers I got at the library. He studied under Wittgenstein during his last series of lectures before leaving teaching and Cambridge. Toulmins read and was greatly influenced by R. G. Collingwood, the English historian and philosopher whose work provided a major 20th-century attempt to reconcile philosophy and history, [Footnote B]
Toulmin’s assessment was: 
“I began going to Wittgenstein’s classes more than fifty years ago, and I have three thoughts about him. First, it is a pity that he did not take a historical attitude to the changes he helped to start in philosophy. His blindness to the significance of history was for me a major lack; in order to make up for it in my own work, I had to hybridize what I god from Wittgenstein with what I found in Collingwood.” [Footnote. (Italics) Return to Reason(end), Stephen Toulmin, p.291, (2001) ISBN0-674-01235-6 (paper) #footnote for §5
§6. Here a language game is seen as a complete language, instead of a primitive part of complelex and complete language. The precise role of language games is described in § 130. The first paragraph is snapshot, using §2, of what Wittgenstein sees any language as being. The use of a name is part of its meaning in even this simple language. Key ideas: 1) children learn language by training, or what Wittgenstein calls ostensive teaching. In these situations, pointing and saying a word is not yet ostensive definition, because the child cannot yet ask what the name is. It is not necessary for the understanding of a word in this language game to produce a picture in the childs mind. although in other language games the same words may have that purpose. Pictures 'may be produced and it may help the ostensive teaching. The response in game §2 determines the understanding or lack of understanding. Different ostensive teaching in other circumstances will result in different understanding and actions. A rod and lever sets the brake. Connecting word and use gives meaning---but only if the rest of the structure of language is in place. (see §12)
§7. Wittgenstein is here pointing to what he means by language games at this early stage, using §2 as an example. The teacher points and says the word; the student repeats the word and then will repeat it often to make sure he remembers the connection to the action that shows he understands the word. The children play games that reinforce that understanding in the context of fun---games--- such as ring-around-rosey. So far a language game is the whole activity of “language and the actions into which it is woven”.
§8. The expansion of game §2 with numbers [using letters], color samples, and the words ‘there’ and ‘this’ makes possible orders that in our terminology: Put b slabs of this sample color there [where he points]. 
§9. New activities are now part of the language game: learning by heart the numbers a, b, c, and so on. Pointing can be used in different was to distinguish between the numbers. Learning ‘this’ and ‘there’ can’t be done just by pointing. Try to imagine some actions that would teach these words. 
§10 One answer to, “What do the words of this language signify?” will not be that every word stands for a name. Some words can be names when we see that a slab is different from a pillar. But ‘this’ is not a name, nor is the number ‘b’ a name. A color sample can be a ‘kind’ of name. What do each and every word in the sentence that are possibly made in this simple language game 'signify'? The of use they have.
The first example of the phrase so often associated with Wittgenstein, “meaning in use”, seems unproblematic here.
VARIETY OF USES OF WORDS
 
§11. The most quoted simile, the toolbox of language is portrayed in §11. Also the most frequent reason that people confuse the use of words but not the functions of he tools: tools look different but words look and sound too much alike. Usually the function of a tool can be understood just by looking at it. The similarity of sound and sight of words confuses us.
§12. Another simile with slightly different point: like words. the levers in an oldtime locomotive steam engine tend to look alike. But they move differently and accomplish different jobs.
#[Wittgenstein took on the repair of a steam engine when he was teaching the children of a rural village school between the time after World.War I and his tentative return to philosophy. The children of the village and the villagers as a whole were suspicious of this well-educated stranger yet he did one thing that earned him respect and attention.
The steam engine at the local factory stopped and could not be restarted. When he heard about it, he asked if he could come and look at it. After silently walking around it several times, he asked for four men with hammers. He gave each a number, one through four, and gave each a place to hit when he called out their number. After doing this awhile, the steam engine re-started. The people thought it was a miracle.]
§13. “T’was brillig and the slithy toves/Did gyre and gimble in the wabe , , , , , ," (Lewis Carroll)
Here we can say that some words signify nothing and some words signify something. Here is a distinction of words in the language signifying and nonsense words not signifying. "All the apples had worms," on the other hand has all words that signify, “Every word in language signifies something”, has a meaning. As applied to all well-formed it says nothing unless a particular distinction is intended; it overgeneralizes.
§14. It is comparalble to ‘’All’’ tools are a used to modify something.” It serves no purpose and there are important exceptions that make it a stretch, at best: a plumb line, glue, a ruler. 
§15. ‘Signifying is like labeling or branding with a name; such a label on a word does not make that word a name.The utility in philosophy of saying naming is like labeling a thing is said in §26 to be a preparation.
§16. In §8 color samples were part of that language game. A sample can perform the function of a word. It is natural to consider samples as instruments of language. In, “Pronounce the word ‘the’”, the second ‘the’ is a ‘’sample’’ of a word used in language.
1-16: CONCLUSION: Learning language is much more than learning names.
VARIETY IN CATEGORIZING
§17. Categorization , classification, putting similar things in one box and dissimilar things in another----this is what school grammar does. That is a different purpose than Noam Chomsky’s ‘Universal Grammar. In § 2 and §8 we have broken the spell of seeing all words as names. Here a deep philosophical spell is broken.
Wittgenstein’s view that categories are made by us for our own purposes---not out there for us to discover---is a complete break from the fundamental attitude of traditional metaphysical philosophy, whether Platonic or Aristotelian. Hilary Putman refers to “the metaphysical fantasy: “The metaphysical fantasy is that there is a totality of Forms, or Universals, or "properties," fixed once and for all, and that every possible meaning of a word corresponds to one of these Forms or Universals or properties. The structure of all possible thoughts is fixed in advance-fixed by the Forms.” [The Threefold Cord: Mind, Body, and World by Hilary Putnam]
Forms or Universals or properties are categories and classifica-tions, not of our making. Ever since Socrates said, according to Plato, “But the question you were asked, Theaetetus, was not, what are the objects of knowledge, nor yet how many sorts of knowledge there are. We did not want to count them, but to find out what the thing itself---knowledge---is.”, What the thing ‘’in itself---unrelated to knowers or to the rest of the language---has been the Holy Grail of Western thinkers. Particularly, traditional dualistic and metaphysical philosophy does not question whether such things exist; they begin with the assumption, often tacit, that they do.
A book by a linguist that points out the importance of viewing categorization as man-made is ‘’Women, Fire and Dangerous Things: What Categories Reveal about the Mind’’ By George Lakoff. He is an opponent of Noam Chomsky's "Universal Grammar". Saussure, Chomsky, Lakoff and others or linguistes, looking at language as a science, or at least hoping to make the study of language a science. This is not what Wittgenstein is about. He is studying the 'concept' of language and many of the main concepts found in our use of language. It is not a scientific quest not a metaphysical quest. It is an empirical examination of what we know "before all ____ and discoveries."
§18. When we compare the use we have today of different ‘’types’’ of categories, if we are unimpressed with the small and very limited language games Wittgenstein created in §2 and §8 and§15 with only the imperative form, we overlook the thousands of years humans have had to develop the very simple language that humans first used into the multiplicity of more complex languages used to-day. However it began it began simply. What we have now are the result of the histories of the evolution of many different languages over thousands of years. The present day languages may or may not have evolved from a common ancestor language. But they each have their own histories. 
Histories are contingent and filled with contradictions and dead ends. Scholars try to categorize the languages as they are now and categorize the elements and idioms as if they had an underlying logic. The purpose of grammars for high school have the purpose of simplify learning, to see a logical pattern---‘’as much as possible---in those languages, with list of “exceptions to the rule” ‘’Ideal’’, Ideal logical patterns will not be found when the ‘logic’ is historical and evolutionary. Those linguists who try to make language ideally logical would be like mapmakers of a very ancient city that was built according to the accidents of history: haphazardly, some very old parts, some parts destroyed and mixed with older homes, on the outer parts sometimes built with planning, and some areas of slums built with whatever materials were at hand. A map by which the maker tries to explain the city as built on a plan of founders by intelligent design is bound to fail. Extraordinary twists, convolution and contradictions of logic would be needed to present the map of such a city as planned and logical.
SAME WORDS USED IN DIFERENT POSSIBLE WAYS
§19. Sometimes a word is convertible; it can also be a sentence. 
§20. A one word sentence may have the same sense as a sentence of more that one word. The concluding paragraph elliptical as shorter that a paradigm used in that language game. 
§ 21 raise particular questions and give different answers about how we categorize and why we do so. The reader needs no help following the text to understand these examples and how Wittgenstein is using them. The only difficulty may be the readers' impatience at not satisfying his "craving for generalizations. As simple as the examples and questions are, they are worthy of attention. They are many of the common examples where we humans create and use categories.
 
§22. When the form of a sentence does not reveal the normal use of that form in the language, other forms can be used to achieve the same result, the same use. A question can be a command, e.g, "Will you please get out of my way?
§ 23, Here is demonstrated just how limited the view of Frege were about propositions, but also how limited a view Symbolic Logic has of language in general. When Wittgenstein looked beyond propositional, language used in logic, he lists a multiplicity of language games, a multiplicity “not something fixed” At the end of the list he says we should compare this treatment of language with the narrow focus he used in the Tractatus to explain language. It is obvious to him now that the former treatrment was inadequate when it was not false.
[A marginal note compares Frege’s ‘assumption’ to a ‘’radical’ in ‘’the language of chemistry’’. This is consistent with an unpublished letter in which Wittgenstein said of the ‘’Tractatus’’, “There was a deeper mistake — confusing logical analysis with chemical analysis.”
(Proops, Ian, "Wittgenstein's Logical Atomism ", The Stanford Encyclopedia of Philosophy (Winter 2004 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/win2004/entries/wittgenstein-atomism/>. 
§24. Wittgenstein would never ask, "What is a question?", any more than he would consider, "What is knowledge?" in Plato's Theaetetus a valid question. Each would require an essence. He has already shown those things are "grammatical illusiions" or the things that cause other grammatical illusions. Such illusions seem to point to philosophical problems, deep philosophical problems. Imagine yourself as a philosopher asking yourself again and again, "What is a question?". Of course you will find no philosophical answer because it is not a real philosophical problem or a question. gramatically a question could be thought of one way to transform a statement.
A more interesting transformation will be beginning statements with "I think" or "I believe. These change the statement into a description of "my inner life. Changing the form of a question by grammatical procedures into statements brings nothing new to bear on these topics. On the other hand adescription of my inner life" brings up important issues dealing with both the philosophy of language and the philosophy. The beginning is Wittgenstein's looking at the problems of the philosophical solipsist in the Tractatus (Tractatus 5.6-5.64 and David Pear's, The False Prison,vol. I, p35-60) , It will lead to an understanding of how the language of things we cannot point to are possible.. He develops his thought into a new-non metaphysical, non-physiological, non-psychologcal understanding of the mind that includes the necessity of a body. This was the kind of solipsism infected 
§25. The main point here seems to be that there is no necessary connection between 'thinking' and 'talking'. Both dogs and ourselves may 'think' in our own ways, but speaking is not a part of the natural history of dogs. Interesting that he that he does seem to believe that a dog may use the most primitive forms of language. Wittgenstein seems to have a broader concept of language than is published and taught in college classrooms. An even more inclusive concept of knowledge is in"§355: "The point here is not that our sense-impressions may lie, but that we understand their language. (And this language like any other is founded on convention.)
EVEN POINTING AT NOTHING IS IS NOT SIMPLE 
§26. The conclusion from much that has gone before is that naming is a preparation for use in language games. What uses?
§27. Talking about it! Too general and vague! Exclaiming, “Water!” isn’t a discussion of the properties of water; it imay be a cry for something to drink or as worning of a tsunami. The language games in §2 and §8 don’t name things in order to talk about them. Ostensive teaching is a language game that can lead to another language game---asking the name of something. We can also invent names for things---another language game. 
§28. The previous three numbers have zoomed us into a very particular topic that was in Augustine’s description of language---‘’pointing’’ used in naming. It may seem to the reader as so simple as to not require inspection. Defining by pointing is ‘’only’’ possible when the ‘label’, (name) has a place in a language game. Otherwise the bearer of the name has no meaning. You will know the bearer of the name, but not know it’s meaning in a language game.
In fact this inspection is fairly long and detailed. The "craving for generality" will tempt the reader to impatience. Up to now, however, everything we have dealt with begins with something ‘simple’. These are not the ‘’simples’’ dealt with in the ‘’Tractatus’’; Why Wittgenstein was unable to ever find a simple in that sense, begins at §39. This type of simplicity referred to here is “most important for us” because the things dealt with are “Hidden” because of their simplicity and familiarity. (One is unable to notice something---because it always before one’s own eyes.)” [§129 PI] In the end patience in resisting the "craving for generality" will pay dividends.
The reason to shine a spotlight on something normally taken for granted may be to show us we are in a rut and need to see some unnoticed problems connected with its use, to loosen the grip of habit. At first we ask, "What can go wrong with pointing to define a word?"
When you’re reading your four year old ‘’Horton hears a who’’ and he points to a picture and asks, “What is that?”, you say, “A Who”. This is not the time to explain how idiosyncratic the use of ‘who’ is. More importantly when a child’s attention instinctively drawn to a puppy in a friends house and you point and say, “Puppy.” does he learn a new word? Maybe, but his atten-tion was already on the canine and he may have learned something about the gesture of pointing (something that needs to be ‘’learned’’---not anything new about canines. Is a finger needed to point? If you are a teacher and have a laser pointer handy, you may want to show off to your friend and use it to point at the puppy. If you use the laser pointer all the time and you are the child’s only contact, will he know the purpose of the pointed finger?
In the first instance, the child may not know the normal use of ‘who‘ in the language game, and he is too young to discriminate the playful and humorous use of the word. That skill will be developed later. In the second case we have used a different, and more accurate method of pointing than is normally used. The point is that the meaning of the hand gesture is learned and, like all processes of learning, misunderstandings are possible. Wittgenstein’s conclusion::" . . an ostensive definition can be variously interpreted in ‘’every’’ case.”
§29. Ostensive definitions can be used to point to many things ‘’and’’ to the properties of things such as number, color, texture, etc Here typical problems are discussed. Of course misunderstanding of what property is pointed to can be avoided if naming the type of property is already understood, e.g., color. If however the word ‘color’ needs to be defined, other words are needed to explain ‘color’, and other words to define the last words used. Here is a “chain of explanations. 
[Is an "infinite regress of explanation possible"?Is there a last chain? Wittgenstein believes rightly, in my opintion, that the answer is a firm "No". Attempts to answer this question has, I think, been impossible because the word 'infinity' has been dealt with for centuries os one concept until recently. Very few people still seem to understand that there are two concepts that are dealt with in confusing and illogical ways. The parenthetical remark tell us what Wittgenstein means by infinity, and more importantly, that his understanding is the correct concept. More, he rejects the other concept because it is self-contradictory. Thrugh the centuries these concepts of infinity have not beeen made distinct and the result in contaminating Western logic has been widespread. In the Philosophical Remarks, §20. A wrong conception of the way language functions destroys, of course, the *whole* of logic and everything that goes with it, and doesn’t just create some local disturbance. This fundamental confusion on a word widely used in Theology and Philosophy explains the abundant contradictions in Western thought that are seen as "Perennial Problems" of Western thought or as deep mysteries. This will be dealt with in the section "On Rule-Following".]
The ostensive definition may or may not be properly understood” And that will depend on the circumstances . . ., and the person I give it too. His 'use of the word is the test of his understanding.”
§30. Pointing as a definition only works when the place of what is named is ‘’already known’’ in a language game. We need to know the meaning of, e.g., ‘color’ to know what is the meaning if the word ‘sepia’. There are requirements for being able to ask a name. One is knowledge. “Being able to do something” is also one; and this indicates a close connection of knowing and doing. 
Do not forget that all sort of problems attach to the word “to know” or “to be clear” along with “to understand” and “to mean”----used in the text bring together threads that will be in ‘’the Philosophical Investigations’’ at key points and to the very end of Part I [§81: “All this however, can only appearin the right light when one has attained greater clarity about concepts of understanding, meaning, and thinking.” §693. “’When I teach someone the formation of a series . . . I surely mean him to write . . . at the hundredth place.’----Quite right; you mean it. And evidently without necessarily even thinking of it. This shews you how different the grammar of the verb “to be” is from that of “to think”. . . . . .”] 
§31. Ostensive definitions in general is are made clearer by the concrete, particular example, “’This is the king’” and the possible ways it would be possible to make this an ostensive definition.
32. Clearly ostensive definition would be the first resource of, say, a missionary in a deep jungle of Brazil meeting a tribe that has [happily] had no contact with white men or other tribes that knew no languages of the white men. This is what Augustine describes at the beginning. One has a language, but doesn’t know the language of the place he is in. Wittgenstein gives another case: a child who could ‘’think’’ but couldn’t speak yet. The last sentence should be noted because thinking and talking to oneself are not the normal usage for Wittgenstein. But this usage is correct here. Normally he would say this “inner monologe”, not ‘’thinking’’ but ‘’’involuntary imagination". Understanding thinking will certtainly not be that easy.
§33. Naming by pointing is only obvious if you are pointing to an individual object, without any doubt that ‘’that ‘’ is what you are pointing to, and including all the properties that come with that object. You point to a toy six inches away and say “Teddy Beddy”. Wittgenstein here discusses and ask questions about all the other situation where you are ‘’trying’’ to point to a particular aspect or property of an object or to the type of object that is pointed to. In the end it is not the ‘pointing’ we do that draws another’s attention; it is the context, “the circumstances”.
§34. A schemata of Wittgenstein’s treatment of a topic could be: 1) description of a simple made-up language, 2) looking at it in one way 3) followed by an indefinite number of “suppose” and “now suppose. The conclusion of this is giving and hearing does not result in ‘intending’ or ‘interpreting’ a definition. Tthere is no process here that will clarify an ostensive definition.
§ 35. The ‘grammar of ‘to point’ to a book, is different than the grammar of ‘to point to an aspects like shape and color, even though by using consistent procedures misinterpretations will be less likely. At the end Wittgengtein lists the multiplicity of "mental activities" involved. Naming is not as simple as Augustine made it seem.
§36. Because we can’t really identify a particular body motion with ‘pointing’, it must not be an activity ‘’of’’ the body, we conclude. So we jump to the conclusion that it must me a ‘’spiritual” activity. The last sentence should give pause to those who want to see Wittgenstein as not firmly living in this world. When he talks of "life" he means this life.
§37. A brief review of ‘’some’’ of the relationships we have been shown of the relation of a name and the thing named.
SIMPLES: ARE THEY THE ONLY TRUES NAMES?
§38. ‘This’ and ‘that, words we use in ostensive definition of names, but are ‘’not’’ names, even though “”this” has been called the only ’’real’’ name". The “queer conception” of language grows out of the “subliming” of language, naming as an “occult process”, a philosopher “bringing out ‘”the’’ relation between name and thing” or staring at a thing and saying ‘’this’’ repeatedly hoping to find the deepest reality beneath the everyday use of the word. Language goes “on holiday” when thought of as Adamic, Nomencaturism, Nominalism, or more simply, Essentialism----a “remarkable act of mind, as it were a baptism of an object.”
[Bottom of page: a superstition: a factually or logically incorrect idea that is not a ‘mistake’ because it ‘expresses’ something important about humans wishes and thinking. The two examples illustrate the human tendency to take what is a proposition meant as a piece of information and seeing it as an ‘’explanation’.’ 
§39. Why call ‘this’ and ‘that’ as names. Because ‘"a name ought to signify a simple in atomic theory of language?" Wittgenstein begins this topic not to return to the explanation of language in the Tractatus. He is going to go into descriptions and a new language game to show why" neither Russell nor he could ever find even one satisfactory example.
The first example is the legenday sword of King Arhur, “Excalibur”, to try it out as an example of a ’simple’. If it is melted down to liquid metal and nothing now ‘’corresponds’’ to that proper name does the name cease meaning anything. Has Excaliber become a nonsense word with no use in a valid sentence. The study of logic often leads to this conclusion. Intuitively we know this isn't right, even if we can't put our finger on why. Excalibur is certainly not a simple constituent of the World. That much is certain.
§40. The first argument against the assertion in §39 of the correspondence theory of language: It is wrong to say a word has no meaning if nothing corresponds to it. This is the most basic [and overly-simple] conception of the correspondence theory of language. Yet it is taken very seriously in discussions of logic, especially Symbolic Logic. Great problems seem to face logic when this kind of correspondence is taken for granted. The basic error: here is confusing the ‘’bearer’’ of a name with the ‘’meaning’’ of a name. Wittgenstein gives a simple explanation of the error.
§41 Beginning with the made up language game §8, expanded to include proper names, Wittgenstein gives an example of a labled tool that is broken or stolen. It is clear and simple and needs no elaboration
§42. An extreme example of a sign with no reference but a possible meaning if it is inntroduced into a language game.
§43. An important distinction of two different uses of meaning: 
"For a ‘’large’’ class of cases----though not for all---in which we employ the word “meaning” it can be defined thus: the meaning of a word is its use in the language.
_____And the’’meaning’’ of a name is sometimes explained by pointing to its ‘’bearer’’." 
§44. What can be pointed to and named?
If the name of a sword is “Excalibur”, if it is broken ad spread across the whole world [ or even returned to its original metals by heat], does it exist? Nol Does the name Excalibur keep its meaning? Of Course. The bearer does not exist, but the “meaning” remains in different language games. This is true in our usual language game. Of couse we could imagine a language game demanding the actual presemce of the bearer of the name. Here the use of demonstrative pronouns and pointing would always be possible.
§45. ‘This’ must have an ostensive use in naming, but that does not make ‘this’ a name.
& 46 This quote from Plato’sTheatetus shows the Hellenic origin of the idea of atomic facts". That can only be named, not defined. If an example could be found, in theory an ostensive definition would be possible. Russell called them individuals; Wittgenstein called them ‘objects’.
A CLOSER LOOK AT 'SIMPLES': The Relativity of wholes and parts.
§ 47 here begins the question, “What are the simple constituent parts of which reality composed of? He is not going back to Pre-Socratic answers such as fire, water, unformed chaos. Nor is he talking about subatomic particles.Wittgenstein is putting to rest the Tractarian notion of atomic facts and “simple propositions” (names). 
§48. Mereology is the philosophic study the relation of whole to parts, and this is exactly what is dealt with, by many examples and a newly made-up language game. The relation of whole to part, of composite to elemental is as relative to the use that is intended for the distinction.. Wittgenstein here describes of another created game, based on a square composed of 3 squares on all 4 sides and one in the middle. Each small is labeled square with the name of a color. 
This is an easy way to describe it without a drawing it. It will be a tool to use in an investigattian mereology in language and questions that arise from it. This is not the only way to describe this setup. We could consider each small square a whole and 9 as the totality of all the wholes. We could consider each small square a letter that makes up a word to be used in a sentence. We could consider each small square with a label a word that we write one after the other. It would be an arbitrary decision to consider a small square as a simple. There is nothing in the nature of the small square that would keep it from considering it as a whole comprised of smaller parts: divisions into 2, 3, or 4 parts. Actually an area, like a line is infinitely divisible, but not infinitely divided.
§49. In this language game a where there are 'simples a small square can be used as a an a completely analyzed atomic fact word and so it could only be since it cannot be divided or analyzed further; it can only be part of a complex proposition: this depend on the context. It has no use yet in a language game so it is the bearer of a name but has no meaning Describing something with this word would make it a proposition.
The distinction of what is whole and what is part is completely dependent of the use we plan for its in a language game. In language names are for the preparation for use in language game. When Frege said that a word only has meaning in a sentence, this is what he means. Use in a language game is what normally gives a word its meaning. Sometimes it meaning is the bearer of a name. "For naming and describing do not stand on the same level; . . ."
§ 50. We can't say that an element exists or doesn't exist. If something didn't exist, it could not be named----except in one special case. Criteria, such as rulers and other standard of measuring and describing have a special place in language games. They can correctly be said to exist and not to exist. They are not representations that correspond anything, yet they exist as criteria, measuring rods. The meter kept in Paris under very specific conditions does not "correspond" as a metal bar a meter long. 
The fact that it is a metal bar is unnecessary to its role an ideal against which we measure other lines that do exist. In that regard meter does not exist. But meter does exist as a necessary paradigm to represent descriptions in a language game. Criteria are parts of the language. The are needed when we examine language games to see if something said is sense or non-sense.
§51. In setting up as a paradigm in a language game §48, learning it required pointing to a red square and say R corresponds to the red square, not the same as using the paradigm, e.g., standard color samples. The connection between R and a patch uses ostensive definition to set up the paradigm that is the standard. If one says R when seeing a black cube, what kind of mistake is it. Judging this needs 
focus on detail, from close in. 
§52. The well-known simile of spontaneous generation of a mouse from a pile ofgray rags and dust! The point is simple: if you’recertain that such a thing is impossible, you would take no time to examine the dust and rags that it came from. What if we think it possible, we should examine the rags and dust carefully.But why the resistance to a closeup examination of language in philosophy? Maybe a close inspection would be wise. 
Maybe the mouse doesn't represent anything in patricular. I doubt it. My own guess is the essences that miraculously seem to come into jump from the things in the World into the individual intellect.
The question left to be answered is, " . . .what is it that opposes such an examinatiaon of details in philosophy?
§ 53, The language game (&48) has variations, one of which is to make a table of elements and the sign used with it. The ‘table” can be thought ofa rule in a language game. Using such a table can be a guide in building a 'complex' statement. A rule in a language has many different roles 'in the game
§54. A definite rule has various uses in a language, some explicit and some learned by the actual use of the rule as it is seen in observing the play of others. In such a case, how does the learner distinguish a correct use from a mistake. By actions of the players characteristic of making and correcting a mistake.
§55, [Up to now, you probably noticed the sentences in parentheses and figured out that they were the thoughts of other than Wittgenstein, It is difficult to give these 'voices' a name that works whereever it is used. i've avoided facing the problem until now. I haven't found any other proposals I like, so I'll use a straightforward: Other Voice. If it can be identified further, it will look like this: Other Voice-Platonic.
Other Voice-Platonist: "The first paragraph proposes the Platonic idea that simple elements (meanings) must be indestructible. "Otherwise The words would have no meanings". This would be true if the truth of a statement depended on the actual existence at the time it is said. The confusion here: the bearer of the name is destructible, but the meaning is not. a meaning is a a paradigm in the language games. 
§56 This is a discussion of what it means to “bear in mind” the “indestructible” meanings in memory. Are there criteria to distinguish the correct and incorrect application of the rule by an appeal to memory. Samples of a color fade as does the memory of sample. There is no "court of last resort, criteria that assure us the precise reference to a color word. Here is the seed of the argument against private. language 
§57. 
Other Voice-Platonic---"Something red an be destroyed, but not red itself" Sure, one can't bent, stapled or mutilalted. But a world in which there is nothing red can be imagined. The word 'red would refer to nothing humans would use in their language, so red is destroyed in that world and that language. 'Red' is not eternal. It is a word created by humans for use in a language game. It is not an essential meaning in a language created by Nature or God.
§58 Other Voice-Platonic. "X could not be a name " in "X exists, e.g., 'Red is not a name in “Red exists”. It would be superfluoussuperfluous if ‘Red’ did not exist it, It could not be spoken of at all". 
Wittgenstein says “’Red’ exists” can’t yield a sense if it is supposed to say something about the ‘nature’ of ‘red’ or is a metaphysical statement about ‘red’----this would make it not only indestructible, but timeless. But we can say, that if “Red exists” could have a meaning at all, it would be a grammatical statement, or better, that “Red has no meaning” ‘in its own right". Two correct ways of saying what we want to say: 1) the proposition looks like it is about the color when actually it is supposed to say someting about the use of the word red, 2) Something exists that has the color red. Both are correct, expecially about what not a physical object that has the color.
§59. Above, "indestructable elements" were a last attempt to make an atomic fact an element of reality. We see how these 'indestrucable elements' fit into traditional metaphysics; they are the distinctive dualism of the accidential and the essential, body and soul, essence and existence. These and various other dualisms are there in our culture for a reason: the attempt to understand change. This seems to be the source of traditional philosophy: dualism (on many levels) to explain change.
When we try to use this kind of duality, in something as simple as a chair, we cannot pin anything down that is essential, that will remain unchanged through all changes.
LEAVING LINGUISTIC ANALYSIS BEHIND
 
§60. With an even simpler example, Wittgenstein takes aim at the idea of analysis that he had in the Tractatus, an idea he then shared with Frege and Russell. Asking for the wooden handle and the brush that fits with it, is a distinctly odd way to ask for the broom. Then he asks us to imagine a language game that can be expressed with the ordinary names of composite items (a). In the second mode of expression names are only given to the components of composite items and sentences put together that list all the components (b). 
§61. An order in (a) achieves the same as the order in (b). But we have no general agreement about the use of "having the same meaning" or "achieving the same".
§62. If the use of a table to translate an order in (b) were required, that would be an difference. Normally, (a) and (b) would have the same essential point, but the line between essential and inessential sometimes a blurry one.
§63. (b) is not more fundamental than (a). Each way can have a way of leading us to miss something.
 
§64. Wittgenstein changes §48 to demonstrate that there is no need or analysis may not be possible. It is just another language-game.
A NATURAL HUMAN IDEA OF MEANING
 
§65. "All these considerations": What is Wittgenstein referring to here? A more limited view could be taken, but I think he is talking about all thaat has been examined from §I on. There he described "This picture of language" where "we find the roots of the following idea: Every word has a meaning. This meaning is correlaated with a word. It is the object for which the word stands." There are not "different kind of words". The words "are primarily nouns like 'table'", and "people's names, and only secondarily the names of certain actions and properties; and of the remaining kinds of words" as something that will take care of themselves. All of the considerations after that have been a close examinations of the implications of this common view of language and alternative possibilities are mentioned along the way. Here he begins the first part of his alternative to what we see when we have looked up close" at language without our bringing with us "theories" and explanations.
There is a chorus of other voices criticizing him for not doing what is of primary importance to the idea of meaning in the 'standard view: he doesn't express what all language games have "in common", "and hence of language". In acknowledging the criticism he denies that there is something common to all langauge games that comprise language. Instead he says that all language games are related" in various ways and connections.
 
§66. This long paragraph gives alll sorts of examples of what comes undr the name 'game'; and we see "a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities sometimes similaraities of detail."
§67 The term “family resemblance” is introduced to take the place of essence to explain the varied uses of a term that give ‘meaning’ in different contexts. He compares the way these 'family' of meanings do not have any one thing in common to the way a thread is composed by spinning twisting fiber on fiber. No one fiber runs through the whole thread.
The idea of doing away with essences as the meaning of words was, and still is, unthinkable to the great majority of people who have been steeped in traditional Western thinking, Even outside of philosophy, in “the humanities” of literature and poetry, doing away with one clear and distinct meaning for a word is usually unthinkable. 
Stanley Cavell in his book The Claim of Reason: Wittgenstein, Skepticism, Morality and Tragedy 
says “. . . .and it looks as though is if he is here offeringthe notion of “family resemblances” as an alternative to the idea of essence. But if this is so, his idea is empty, it explains nothing. For a philosopher who feels the need of to explain meaning or naming will still feel their need to explain the notion of explaining “family resemblance”.” (p. i87) He denies the text, then “interprets” it into something more mainstream. 
A main aim in my writing is specifically to counteract this idea that the reader has the option of finding a strained “alternative interpretation”. The reader may say, “ I can’t agree.” The reader may put that part to one side for the time being and hope that further reading of the text ( and other writings of his) in which it is imbedded will clarify Wittgenstein’s.
[68] A significant comparison of ‘number’ to ‘game’that says more about interpretation. The Other Voice asserts that ‘number’ is “the logical sum” of interrelated concepts and sub-concepts and that ‘games’ is also the logical sums of sets of concepts and concepts, implicitly assuming that both have ‘rigid boundaries. Wittgenstein says not necessarily. for specific purposes a boundary may be drawn but in general they are not needed. Wittgenstein admits that he can't tell where games end and something else begins, except for particular uses. Tennis is an example of game with rules---but not for everything, 
The fact that he sees both ‘number’ (mathematics)and ‘game’ (language, as open ended is an indication that for Wittgenstein, his philosophy of Language, the philosophy of psychology and the Foundations of Mathematics were not in separate departments, but part of a whole that support one another. 
THE VIRTUE OF BEING SOMEWHAT, BUT NOT TOO, VAGUE
§69. If we are asked the meaning of a word, most likely we give examples, samples, words that could be used to paraphrase the new word, situations in whichwe would use and things like it. In other words we will tell what we know about the word. In very many cases, we do not know any distinct limits or boundaries. Even so,we have mastered our language and use the word with condidence.
This will be the the usual case. But look back to §43. Sometimes we need only say one name or point to an example and we will call that meaning exact. But whether we call the meaning of a
word either exact or inexact,can we define exactly the meaning of 'exact?.
§70 Other Voice: "An uncircumscribed ‘game’, game with blurred edges, is a word you don't really know the meaning of." We imderstand the example Wittgenstein gives. It is a description, but not a description that would allow us to paint a picture of. But it lis useful and conveys a definite meaning. 
Frege thinks of a meaning as a field, and a field with indistinct boundaries is no boundary at all. But Frege is looking for meanings that can be used in his Symbolic Logic where certain mathematical-like operations can be used for different kinds of truth preventing deductions. Meaning for him is the hardest problem of this idealiized Symbolic Logic, set up to solve abstract philosophical problems. 
Having fuzzy borders is not a fault of ordinary language, it is a virtue. Ordinary language is meant to be used. It can be used in many was that the more exact term can. Specialied vocabularies , such as us used in organic chemistry, has limited uses and for good reason. It may appear, at first blush, that without everyone having the same clear and distinst meaning communication would not be possible. In fact,we do the immpossible all the time. 
§71. Having fuzzy borders is not a fault of ordinary language, it is a virtue. Ordinary language is meant to be used. It can be used in many was that the more exact term can. Specialied vocabularies , such as us used in organic chemistry or differential calculus, have limited uses and for good reason. It may appear, at first blush, that without everyone having the same clear and distinct meaning communication would not be possible. In fact,we do the immpossible all the time.
Frege thinks of a meaning as a field, and a field with indistinct boundaries is no boundary at all. But Frege is looking for meanings that can be used in his Symbolic Logic where certain mathematical-like operations can be used for different kinds of transformation rules to preserve truth in logical deductions. Meaning for him is the hardest problem of this idealiized Symbolic language, set up to solve abstract philosophical problems with exactly defined symbols. Frege cannot use blurred concepts in his special language. 'Professional' philosophers spend a great deal of their time looking for these (perhaps mythical) defining lines. Where they draw the lines determines the model of 'reality' they profess.
I really do not think the kind of exactness is in the world we live in. Ironically, exact does not have an absolute meaning, even if you are talking about the standard of measurement. (This is no commmentary on things like atomic clocks and the like.) Exact is always relative to the purpose for which it will be used.
We, in ordinary language and everyday use, do quite well, most of the time. And if there is a possible misinterpretation. we give examples to be used as we intend. These examples are not poor relatives of clear and distinct definitions. Our examples serve the purpose quite as well and we tell what we know. "Any general interpretation may be misunderstood,too"
§72. Not seeing what is common was the charge against Wittgenstein in §65 about 'games and lalnguage games. "Seeing what is common" may, in other cases, be a definition or a way of naming. Exmple (1) is a definition. One can show understanding of this definition by pointing to the yellow ochre in each picture. The second example may be the naming of of yellow ochre. The third example would be a more precise naming of a color by representing the possble range.
§73. A sample of a color on a table: red, green, blue. This is what Wittgenstein means by ‘’calculi’’. How about a table with a leaf, a limb, a branch, a trunk, a root? Since there is no general shape of a leaf (general scientific description of the parts and functions of leaves ‘’is’’ possible), the shape could not be ‘’defined’’, but the meaning could be given be a representative group of pictures or list of illustrations. 
§74. The “leaf shape in general” will not be seen as such on its own. If it is the ‘’custom’’ (rule) to see a particular example as a general leaf shape, usually that shape will be recognized as such; but someone may not "see it as" the typical shape of a leaf. This "seeing-as" is different from seeing ‘’aspects’’ of certain visually ambiguous visual stimuli, such as “duck-rabbit” (§2-4) SEEING LANGUAGE AS A GAME)
§75. In §73 we see that seeing a shape as the typical leaf-shape is not as simple as we had imagined. Here he returns the the example of defining a game. Definition---abstracting, finding an essence or nature---is found to be impossible. Even if we cannot SAY what 'game' is in a definition, we KNOW what a 'game' is!!! We SAY what we know by telling what we know by examples, illustrations, etc.
§76. If one draws a sharp boundary around a concept , others would draw different boundaries or no boundary. The different versions of the concept would be akin to each other----they would have “family resemblances” (See §67)
§77. How vague a conceptual boundary is determines if a "sharper image" is possible or if the vague boundary must remain vague. Such is the case in ethics and aesthetics, concepts so vague they can be made to resemble any concept. And this is an answer to those who fault Wittgenstein for not dealing with
aesthetics and ethics. “’Anything----and nothing----is right.----.’
The meaning we have of words like "good" and "beauty" will come from understanding how we learned to use such words and under what circumstances. We each have a loose network of beliefs, beliefs we just "took in" while growing up, that we need to make judgements. We fall back on these when judging good or bad, beautiful or ugly.
§78. The discussion in §75 of knowing and being unable to 'say' (define) 'game' is clarified by 3 other examples. If you can't say how high Mount Blanc is, you don't consciously KNOW the answer now. That knowledge may still be in your mind, hidden from memory; or it may no longer exist in your memory. The vocabulary of sounds is so impoverished that even a professional musician cannot SAY how a clarinet sounds,even though he definitely KNOWS it. He may attempt to communicate to someone who has never heard a clarinet by comparison with other musical instruments, metaphors and creative description. The clarinet example could be related to the "argument against private language' (§243-§275)
The point of examples 1 and 3 is to show the place of example 2 about the use of 'game', already touched on in §73 and §75. The uncertainty inherent in a language game, though in some ways similar to the other examples, is basically different. 
§79 Wittgenstein here changes to words with many meanings, instead of with vague meanings; he also subverts the idea that is the basis of many kinds of “Symbolic” logics, that for a word to have meaning, what is meant must actually exist either outside the ‘mind’ or as an independent identity inside the mind. Both are wrong and Wittgenstein shows how they are. Instead of ‘Moses’ substitute ‘Santa Clause’. Does “Santa Clause is coming” have no meaning because there is no Santa clause; or is it a meaningless sentence because Santa Clause in fact does not exist. This should make the meaning of [79] clear enough, even the aside about scientific explanations. 
§80 A word can have meaning, even if used in the most outlandish and even impossible contexts in a sentence, e.g., “The king of France is bald.” Russell made abig deal trying to make it fit with Symbolic logic. The core of Wittgenstein’s philosophy of language and how it hints at the need to better understand rule following and the argument against private language. 
CALCULI, RULES, AND GAMES'
§81 “Logic is a normative science.” This is a one part of a hinge concept that helps our understanding of a great deal of the PI. I will be coming back often to this part. F.P. Ramsey was a close friend and a scholar with great prospects who worked with Wittgenstein when he came back to Cambridge on January 18th 1929.
 
Officially Wittgenstein at Cambridge was an “Advanced Student” studying for a Ph.D in Philosophy under Ramsey. In fact they were close friends and spent the time talking about philosophy. Wittgenstein’s Doctorate was to be the Tractatus. Only a year later, January 19th 1930, Ramsey died at the age of 26. The importance of the first sentence is, I believe. was a sort of tribute to his friend.
"Moreover, for any game there are countless bizarre possibilities which cannot be budgeted for in advance. . . . .
___This insight transforms the Tractatus'insistence that 'all propositions of our everyday language, just as they stand, are in perefct logical order' (TLP 5.5563). Ramsey had condemned this as a piece of 'scholasticism'. Wittgenstein concurred by referring approvingly to Ramseys' remark that logic is a normative science. (Mathematics 269; PI §89)		
	 		
The other part of the hinge is that logic is not like a natural (empirical) science that finds what it studies; instead it constructs ideal languages, e.g. the Tractaraian picture theory based on atomic facts with atomic statements. These do not exist nor are they a goal to strive for, but as a ruler that we can use to understand natural languages. We don’t require a supposedly 'ideal' Symbolic Logic to form a valid sentence. This is an echo of the mathematical Platonist who believe that mathematics is “out there” even before there were human minds to “discover them”. The Platonic notion of language and math is opposed to the idea that mathematics, like language and logic, is a cooperative creation of human thought. So when we say, "Logic is a normative science," it is set apart from other human creations such as the natural sciences. The notion that Logic, like Mathematic,---'ideal' logic, "Sublime" logic (refer to §38 and §89ff)---in a 'pure state' even without the existence of any human minds is pure Platonism as advocated by Gottleib Frege, Wittgenstein's first contact with Analytical philosophy. And Frege, in fact, is the "Father" of modern 'Analytical' philosophers.		
In A Wittgenstein Dictionary, By Hans- Johann Glock, the author gives a different meaning than I had to: “if anyone utters a sentence and means or understands it he is operating a calculus according to definite rules.” He says that it says Wittgenstein did believe it but no longer does when he wrothe the Philosophical Investigations. He may be right, especially if 'calculus' is seen solely as a strict calculus with clear and distinct rules. 'Calculus' here is not part of higher mathematics, but simply an aid to calculation such as as the table of the value of ‘sine ’in trigonometry, or the addition or multiplication tables. Construction of the Addition tables will be useful, now and later in the discussion on "Rule Following". [§138-§242]		
Across the of a piece of paper, leave a space then write horizontally the numbers 0 through 12. Then along the left side of the paper, beneath the space left before, write vertically the numbers 0 through 12. Then draw parallel vertical lines from the top numbers and horrizontal lines from the numbers on the left side. Every intersection of a vertical line and a horizontal line is where you write the sum of the top number and he left side number. At the intersection of 3 across and 2 down, 6 would be written. If it helps, circle the answer. Fill in all the intersections and you have an Addition Calculus. Since this calculus leaves no doubt about the answers to be inserted, I'll call it a "strict calculus".
So, addition is a rule-governed human activity and the Addition Calculus is a set of rules to guide that activity. So is language a rule governed activity but when we compare it to a 'calculus' it is also a social activity. We say the language calculus has fixed rules, "but cannot say that someone who is using them is using language must be playing such a game". The necessary element of uncertainty in language must be part of what makes it a game. Neither the outcome of the game, nor the application of the rule in a particular instance is certain. The comparison to a strict calculus will be just that---a comparison, a made up yardstick to hold up to the realities of our language, an ideal that is not realized nor an ideal whose realization is sought after. The ideal languages we try to construct are not "better, more perfect" than everyday language. An 'ideal' logic is not needed beore we can recognize a proper sentence. 
[‘Game’ is not only the exemplar of the notion of ‘family resemblance of meanings. All sorts of language games rely on family resemblances of meanings to keep the uncertainty of outcome and meanings and yet make it a rule-governed human social activity, instead of the Strict Calculus model of language with strict rules and predetermined outcome. This is also a rule-governed model of language where meanings and outcomes are the result of the strict application of a set of rules---a calculus.
An example of the Strict Calculus model of language would be the Essentialist representational model. When meaning is an essence there is only one correct meaning [mental] for what is outside the mind [physical or spiritual]. There will be exact agreement between two minds on the one and only correct meaning of that essence because both minds will have received identical essences---either a priori or through experience. The rules of correct sentence construction (the grammatical and syntactical calculus) must be used correctly or the meaning of he sentence will not be clear and distinct---it will be ambiguous. e.g.; another important example of a Strict Calculus model of language would be the ‘picture’ theory based on atomic facts and atomic statements in the Tractatus. RP] 
		
We will have to wait for “greater clarity” untill we thoroughly examine ‘understanding’, ‘meaning’ and ‘thinking’ [the philosophy of psychology]. 
 An early and brief discussion about identifying "the rule by which he proceeds" begins with §82. 		
I believe the work here evolved from Wittgenstein's insights that change strict “calculus” into satzsystem and then into language games. Logic is more than syllogisms and the forms of Symbolic Logic. The fact that this idea of logic is so widely accepted shows, to Wittgenstein, a lack of understanding of both language and logic. “ A wrong conception of the way language functions destroys, of course, the whole of logic and everything that goes with it, and doesn’t justcreate some local disturbance.” [§20 Philosophical Remarks] Are language and logic the same? “§501 Am I not getting closer and closer to saying language cannot be described. You must look at the practice of language, then you will see it." [On Certainty] The first statement is early, around 1928. The second was shortly before he died. [82] Above, Wittgenstein has said “definite rules”, Now he asks “what do we call the rule by which he proceeds”. The person himself of
§82 Above, Wittgenstein has said “definite rules”, Now he asks “what do we call the rule by which he proceeds”. The person himself offers answers that he himself is not satisfied with. Wittgenstien asks at the end, ‘What meaning is the expression: ”therule by which he proceeds” supposed to have left here?”’ [Since he said before “definite rules”, why is there a question? Since he has said that linguistic terms are generally multiple and vague; only the exceptions are clear and distinct, we need to find out where a rule about ‘rules’
stands.]
§83 The analogy of games to rules of language. Here there is a gamut of multiplicities and and degrees of vagueness. At this point ‘’game’as a simile has for language has little left of it’s metaphoric quality. Earlier we
saw that the meanings of ‘game’ have too great a diversity of family resemblances for the simile to apply to all of them. Yet probably more than one type of game like language. Perhaps The Games People Play by Eric Berne is a collection of similar games. Or perhaps they are examples of language games themselves.
§84 A game completely bounded by rules still leave open the possibility of a doubt requiring another rule which can raise doubt . . . . But we are not skeptics looking for every imaginable doubt. [A striking simile about skepticism, or maybe, paranoia: of the man standing before the door, afraid he will open the door and
step into a deep chasm.]
§85 A rule is like a signpost. Normally it leaves no room for doubt, occasionally it does. This an empirical question, not philosophical one.
§86 If the Game in §2 could used a table, would it make it seem so obvious that there is no room for
doubt? But the diagrams are shown to have other possible ways of reading the diagram, so we then need an abstract 'picture' of which way of reading the diagram is meant here! Then will some other sort of explanation be needed to assure the 'picture' doesn't mislead.
§87 Assertion-doubt-explanationdoubt-more explanation-new doubts, more explanations, and none are final. “Without a final explanation, I don’tknow what the assertion means!!”. No explanation needs another unless WE need it to prevent a misunderstanding. A doubt does not reveal a gap in the foundation of our understanding requiring us to doubt everything, as it were to plug up all the holes in advance. Even if you test a 55 gallon drum by putting it under high pressure to see when it will spring a leak, you don't take it to the extremest pressure to make sure it is perfect. All you will find out is that at some point it will explode violently.
This is symptomatic of Platonic mathematics: that mathematicians _discover eternal Truth, rather than mathematics being the fruit of human thinking and imagination. Wittgenstein’s sums it up in an aphorism; “The signpost is in order----if, under normal circumstances, it fulfills it purpose.”
§88 Refer back to the last of §68…. “Very well, it was an inexact one.----Though you still owe me a definition of exactness.” The concept of the essentialist might give as the definition of exactness, would be Descartes Ideal definition----clear and distinct (what something is and what it isn’t).
Wittgenstein uses many examples are showing that such definitions are the are the exceptions (indeed unabtainable!), not the rule. “No single ideal of exactness has been laid down; we do not know what we are
supposed to imagine under this head----unless you yourself lay down what is to be so called. But you will find if difficult to hit upon such a convention; at least any that satisfies you." Descarates Ideal Definition is just that----an ideal.
IS LOGIC SUBLIME
§89. How does what has gone before §89 lead to the question, “In what sense is logic something sublime?” Everything from [81] and [§88] hinges on, 1) “in philosophy we often compare the use of words with games and calculi which has fixed rules but cannot say that someone that is using must be playing such a game” and that 2) this led Wittgenstein “to think that if anyone utters such a sentence and means or understands it is operating a calculus according to definite rules. ”The tension is between rules that are definite, yet with the
uncertainty of both the speaker and the listener of not knowing what the rule is, or if it is actually being used.
“In what way is logic something sublime?” The answer we should expect having seen the way language can be vague and having many possible and related meanings is that logic is not sublime. The description that is
given of sublime logic begins with “For there seemed . .” Wittgenstein looking back on his thinking in the Tractatus, 6.13 “Logic is transcendental.” 
§90. The second and third paragraph of no. 89 and the first of no. 90 are how we usually to think of logic.
There is confusion if they are taken as his position at the time of writing the PI. The second paragraphs is
Wittgenstein’ current voice and it takes the investigation as “grammatical” investigation, not a metaphysical one. He speaks of “analysis” that is far more simple than the the Tractatus analysis---clearing up misunderstandingss “by substituting one form of expression for another [a good way to understand useful paraphrase].
§91. The term analysis presents the temptation to look back on Tractarian “analysis” and expect the same results as and purposes as Tractarian ‘analysis’. 
§92 We expect the ‘essence’ of language, expect it to be below surface appearances; so we ask questions like, “What is language” and “What is a proposition”. “And the answer to these questions is to be given once for all; and independently of all future experience.” 
§93 A proposition is an ordinary thing but the forms of the way we explain a proposition confuse us and we see the proposition as unusual, mysterious. [94] That is the beginning of “the subliming of our whole account of logic”, “sending us in the pursuit of chimeras.”
§95 Some background from the Philosophical Grammar for the first part, and referring back to no. 40 of the PI is helpful.
§ 21 . . . .“That its to say that form
there are only two things involved
in the fact that a thought is true,
i.e.the thought and the fact:
whereas for Russell, there are
three, i.e., thought, fact and a third
event which, if it occurs, is just
recognition. This third event , a
sort of satisfaction of hunger ( the
other two being hunger and eating
a particular kind of food), could,
for example , be feeling of
pleasure . It’s a matter of
complete indifference here how
we describe this third even; that is
irrelevant to the essence of the
theory.The causal connection
between speech and action is
external relation, whereas we
need and internal one.
§22 believe Russell’s theory
amounts to the following: if a give
someone an order
and I am happy with what the then
does, he then he has carried out
my order.(If I wanted to eat an
apple, and someone punched me
in the stomach, taking away
my appetite, then it was this
punch that I originally
wanted.)”[Philosophical Grammar,
[pp. 63-64]
The first sentence of [95]
means that for Wittgenstein,
nothing stands between the
thought and the fact. It helps to
understand the meaning of the
second sentence by referring
back to &40 in the PI. Formal
Symbolic Logic often, but not
always, that for a proposition to be
true every element must signify
something and that something
must actually exist now when the
propositions is stated. This
requirement is one of the reasons
the Formal and Symbolic Logic
often ties itself up in knots and
also why the idea of an infinity of
alternate worlds is dragged in to
explain conditional clauses,
references to historical figures,
mythic figures, and things like it.
Trying to force natural language
into the arbitrary demand of
Formal and Symbolic Logic is
what produces unnecessary
contradictions and so-called
‘paradoxes’. A paradox is a
seeming contradiction that further
examination show to be noncontradictory.
The paradox here
would be that every thought would
have to have a fact. This seeming
contradiction is explained by the
fact that “Thought can be of what
is not the case.
§ 96 The above “paradox”
was an illusion and related to a
number of related illusions.
Thought and language now
appear as something special, a
queer picture of the world.
Proposition, language, thought
and world, because of their
“specialness” all seem to be
equivalent. But no use for these
terms as ‘sublime’ can be found.
They have become
“metaphysical”.
§97 Here it becomes clear that,
although there are general
arguments against the “subliming”
of language, the particular focus
here is on what he wrote in the
Tractatus.
Wittgenstein is saying that
his own earlier concept of
language and logic is wrong. If the
words proposition, language,
thought and world, their meaning
must be down-to-earth as “table”,
“lamp”, “door’. We are not looking
in our quest to understand
language anything “what is
peculiar, profound, essential.
[refer back to §65ff]
§98 Look back to §81 where we
are standing in the very brink of a
misunderstanding: that we are
seeking an ideal language and “a
logic for a vacuum, rather than on
object of comparison to our
natural languages. A logic for
vacuum would be one that
extracts the “essence” if language
that can stand on its own, using a
notation that would be so general
that any ‘meaning’ could be
plugged into the formulae and, if
the formulae is the correct one,
the result would be a correct
answer, a true answer. If this
sounds a lot like Symbolic Logic, it
is no accident. It would also apply
to the many syllogisms began by
Aristotle and continued in
Scholastic philosophy.
§99 Sinn und Bedeutung: Sense
and Reference. This a distinction
of meaning created by Frege to
solve the problem of identity in
Symbolic Logic. Frege’s example
is that of the “Morning star” and
the “Evening star”. They used to
be considered different in
reference. Now we know that
they are the same under different
names----in fact it is not a star at
all. It is the planet, Venus.
Wittgenstein has said that a good
way to understand a linguistic
term is to look at the language
game in which it arose. . For
example: “NaClis “’salt’” gives
information, whereas “NaCl is
NaCl” Is tautology and gives no
information. The references in
both sentences are the same. .
However, the ‘senses’ ofeach
sentence are different.
Since ‘sense’, arose in the
context of Frege’s Symbolic Logic,
how does it apply in natural
languages. The simile of the
prisoner retained in a room with
locks on all but one door, raises
the question of whether the sense
of a sentence, however vague,
needs to be complete.
The Phrases “one would like
to say” and “But is it true” seem to
leave the question of whether or
not a sentence must have or need
not have a definite sense up in the
air. A rather long discussion is
needed to explain my conclusion
to this question.
"For a large class of cases--
--though not all----in which we
employ the word "meaning" it can
be defined thus: the meaning of a
word is its use in the language.
And the meaning of a name
is sometimes explained by
pointing to its bearer."
Sense (Sinn) in Frege’s
example refers to components
whose meanings refer to
something else. The picture
theory of the Tractatus allows a
reference by a proposition to
something else and that is it’s
meaning. The same does not
seem to apply to the proposition in
the Philosophical Investigations.
The proposition will not have a
reference as it it’s meaning as it
did have as a logical picture in the
picture theory of the Tractatus.
The meaning of the proposition
(sentence) well be the sense of
the sentence. Wittgensein gave
up a representational theory of
meaning.
I think a good way to look at
sense (Sinn) is to consider all of
the multiple and vague meanings
that are possible in the language
game as distinct from the
particular meaning in the present
use in a sentence. Meaning is the
particular use we make of the
‘sense’ in the language game.
The questsion then is, no
matter how vague the
components of the sentence are,
must the meaning of the
sentenced be complete.
Since language has many
other uses than declarative
sentences, I don’t think
incomplete meaning in all of the
language games need to be ruled
out. But in declarative sentences
(propositions), I believe a
complete sense (meaning) Is
needed. In the context of this
discussion of “vagueness”, the
point seems to be that a vague
sentence will have a complete,
even if vague sense.
§100 An interesting short dialogue
of the interlocutor and
Wittgenstein: ‘I’’ (it can’t be a
game with vagueness in the rules.
W) Yes, it can. ‘I’) Well, not a
perfect game.)
Language is vague but still
is numbers of interconnected
games. Language works as a
game. Ideal language is just a
ruler to hold up to the natural
language to better understand
natural language, not to seek to
reach an ideal language. [see
§81] “. . .on the brink of a
misunderstanding. . . “ in §98 and
§99 and here, the message that
“misunderstanding of the role of
the ideal language . .“ is
reiterated.
[If the reader thinks all of
this repetition is unnecessary and
confusing, Wittgenstein has told
us earlier that is part of his
method. [18] “Our language may
be seen as an ancient city: a
maze of little streets and squares,
of old and new houses, and of
houses with additions from
various periods; and this
surrounded by a multitude of
boroughs of straight regular
streets and uniform houses.” He
could also look at the Preface,
paragraphs 1 and 2. He repeats
but each time from a different
perspective. London, Paris, even
a relatively new city as St. Louis
or New Orleans would be good
examples. A newcomer would
say, “I don’t know my way about”.
When you park your car in a huge
parking lot, one trip to the mall will
not allow you to know your “way
about.
§101 There follows a series of
comments on this misunderstanding
of the role of the
ideal in language [logic]. We don’t
want logic vague. We seem to see
the ideal because that is the way
“it must be”. 
§102. We think we _
see_ the monolithic structure of
ideal logic in the background as in
a ‘dark mirror’.
§103 Perfection----the ideal----
traps us into uncertainty, inaction,
or fanaticism. 
§104 If we use, say
a metaphor to explain, we
become trapped by our
explanation into a hardening of
the categories. The metaphor
becomes a ‘system’.
§105
Because we want logic to be pure
and clear-cut, we are dissatisfied
with our own natural language.
Here Wittgenstein warns to resist
the temptation to overreach,
looking for depth and subtleties.
These are beyond our abilities
and beyond the reach of human
language. Metaphysics is a
mirage. The image of repairing a
spider’s netwith our fingers is
worth noting.
§107 We require the crystalline
purity of logic because we want to
transcend this world for a perfect
world. We don’t really get
anywhere [except the
expectations that accompany it].
This is our world and we need its
resistance to accomplish
anything. The investigation so far
has shown how differently reality
is from the ideal. The ‘ideal’
serves its purpose by being a
measuring rod. In all we have
done so far the reality of language
and logic, that is useful for us, is
much different from the ideal
model of language and logic that
we accept without giving it hardly
a thought.
§108 When we give up the formal
unity, for instance in the Tractus,
for the structure of ‘family
resemblances doesn’t logic
disappear? It doesn’t but we have
to give up the quest for the ‘ideal’
in language and logic: generalities
and abstractions----turn our back
on it, and use different methods to
determine how language works
much differently in practice than in
the various traditional
epistemologies. Wittgenstein will
not develop a new epistemology;
he will treat of logical grammar,
the philosophy of the
foundations of language. Words
and sentences are not mysterious
“chimeras”, they are everyday
things we use for everyday work.
§109 This looks back to the
purposes of Wittgenstein’s
investigation: not scientific,
theoretical, hypothetical or
explanatory. The investigation
uses description to arrange what
we already know in a way that
throws light on philosophical
problems. Multiplicity of example
is not mentioned here, but it is a
main method of description.
Philosophical problems are
illusion of grammar and disappear
when we understand the way our
language works. The obstacle to
this investigation is “an urge to
misunderstand”. Because of this
urge, language “bewitches our
intelligence unless we rethink our
assumptions about language. We
may not even be aware we have
such assumptions. Not only must
we learn new viewpoints, we must
unlearn old ones. 
§110 These old
assumptions are based on
grammatical illusions. Seeing
through these illusions brings us
to see philosophical problems in
perspective. We are not then so
intimidated by the perennial
problems of traditional philosophy,
a list of problems that never find a
conclusion.
§111 Puns are a good example of
grammatical jokes. Often they are
becomes a ‘system’.[105]
Because we want logic to be pure
and clear-cut, we are dissatisfied
with our own natural language.
Here Wittgenstein warns to resist
the temptation to overreach,
looking for depth and subtleties.
These are beyond our abilities
and beyond the reach of human
language. Metaphysics is a
mirage. The image of repairing a
spider’s netwith our fingers is
worth noting.
§112 I wish I could be sure what
simile Wittgenstein had it mind.
My best guess is the form/matter
the main simile behind the
mind/body duality. Of course there
other candidates, but I think they
would be of the same sort. We
see this dualism everywhere, but
often it is so familiar that we see
through it and aren’ aware that it
is there. We ourselves as the
source of the “urge to
misunderstand”.
So we arrange our linguistic
rules according to this
simile; that is the way it is
supposed to be. But the rules lead
us astray. The results don’t turn
out as we expected. The way they
are is not the way they are
supposed to be.
§113 We think we must be
missing something, something
deep and mysterious. We keep
looking inside for this deep
essence, a form of contemplation.
We see nothing. 
§114 Here is a
specific error of Wittgenstein from
the Tractatus and a good simile of
that error.
§115 Here again may be a
reference to his error in the
Tractatus, the picture theory of
language, which misled him
because it was in the language
itself.
§116 This is a clear and direct
opposition to “essences”and
metaphysics. He also gives a
check to see if a metaphysical
word has any meaning.
§117 Here he expands on the
phrase used in §[?]---the gaseous
meaning of thought.
§1l8 In effect Wittgenstein is
reflecting the reverence people
have for metaphysics and the
essential idea of language. Many
people, people that are intelligent
and well-read think of these
concepts a the glory of Western
thinking, the very things they think
are superior to the concepts of
other cultures. Wittgenstein
admits it is an imposing front, but
weak from the inside out---a
house of cards.
{I have to admit in prior
thinking about this that a better
realism could be built on cleared
area that would not be a “house of
cards”. People want realism, but
none the many models of
metaphysical realism are
unworkable. A new kind of
realism is needed. But I have
come to be unsure if Wittgenstein
would see it that way. Would he
be unhappy that any theory, no
matter how convincing, should be
built on the ground he clears.
I think a better realism could
be asserted based on Darwinian
principles. My candidate would
be Millikans’s Thought, Language,
and Other Biological Categories. Wittgenstein was very
strict in the science he accepted
and Darwinism was not proven
before he died, or at least he
didn’t have access to the
information on the discovery of
DNA, the tool that tells how basic
evolution works. I believe he
would have welcomed the present
evolutionary theory and see how
well it fit his idea of ‘nature’. On
the other hand there is nothing in
the text of the PI, that I know of
that would prove it.}
§119 Running up our heads
against the limits of language?
This he seems to say is the
negative purpose of this
examination of language. The
idea of “the limits of language”
played an important role in the
Tractatus. The limits in the
Tractatus gave room only for
statements of natural science.
Beyond this was the ‘unsayable’—
something “mystical”,
Schopenhauer’s word for the
unexplained: important but
beyond language. In the PI the
limits depend on which language
game you are using. If you are in
the wrong language game and go
beyond its limits, you will come up
with “plain nonsense” and learn
the hard way.
§120 A clear statement of the
argument for the use of ordinary
language only. The last paragraph
is intriguing. The interlocutor says
the point is not words but
meanings, as if meaning was
something like the immortal soul
that exists free of the body. The
reader should think: not the
money and the cow to be bought,
rather money and its use.
§121 This fits in with what has
come before: the defense of
natural language against a metalanguage.
The reference I believe
is to Frege, Russell and Symbolic
Logic.
§122 An important statement of
his methods, a perspicuous
overview and ordering of things
we already know. It may seem
repetitious but there are a number
of intermediate examples.
In §123 is an aphorism of the type
of problems philosophy deals
with.
§124 Wittgenstein gives us
a perspicuous overview of the
philosophy of language. It implies
language is a natural
phenomenon, not a logical edifice.
It is very important to see that
philosophy gives no foundation,
either to language or
mathematics. There is also a
perspicuous overview of the
philosophy of the foundations of
mathematics. In this respect they
are alike. The difference is the
distinction between a proposition
and an equation. [Propositions
have meaning, equations have no
meaning. They are rules in the
mathematical games that we have
created. The “meaning of a
mathematical system or ‘game’is
it application, such as those in
physics.
§125 Mathematical
contradictions are not resolved,
but a perspicuous overview of the
problem keeps the contradiction
from developing. After that he
deals with rules and our getting
tangled up in them so that we
don’t, for example, express
successfully what we meant, even
though the rules were followed.
The exact following of rules leads
not to the promised land of
successful communication of what
we mean.
“This entanglement in our
rules is what we want to
understand (i.e. get a clear
view of).”