1. The Private Language Argument

2. Rule Following
(Sec. 201) “This was our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule.”

3. Rule-Following
What makes it true that you are following one rule, rather than a different one that is also compatible with what you’ve done so far?

4. Rule-Following
Furthermore, how can we tell if you’ve made a mistake and are not following the rule you intended to?

5. Plus and Quus

6. Features of the Case I use the word ‘+’ to mean addition.
I have in my life computed finitely many sums.
There is a largest number that has ever been part of my past computations: suppose for example it is 57.
Although the sums I’ve computed are finite in number, the rule that I ‘grasp’ determines the sums of infinitely many pairs of numbers.

7. A New Problem
Now I am asked to add 57 and 68. Naturally, I respond ‘125.’ I think (a) the answer is correct and (b) the answer is in accord with my past use of ‘+’ and the rule I learned in school.

8. The Skeptic’s Challenge
The skeptic comes along and asks: How do you know that in the past, your uses of ‘+’ meant plus, rather than quus? x quus y = x plus y, if x, y < 57 = 5 otherwise

9. The Skeptic’s Challenge
NOTE: while the skeptic’s challenge is bizarre, the skeptic is not a skeptic about everything, just this. It would suffice to provide one fact about your past behavior/ mental states that justified you in now believing ‘+’ means plus and not quus.

10. The Skeptic’s Challenge
Of course, if there is no fact about your past usage that justifies you in one response over another, then the same would be true of your present usage.

11. All of Language
The worry here is a general one about rule following and hence all of language, not simply mathematics.

12. Definition of ‘Grue’
An object x is grue =df x is examined before t0 and green; otherwise x is blue

13. t0

14. The Algorithm Solution

15. Counting
Adding isn’t one of our “primitive functions”: usually we add by doing more basic procedures, like counting.

16. Quounting
But the skeptic can just push the problem further. How do you know that by ‘count’ you meant count and not quount? Quount: like count up to 57, always returns 5 thereafter.

17. Quum A similar response goes for abstract definitions of addition.
x + 0 = x x + s(y) = s(x + y)

18. The Dispositional Solution

19. Dispositions
The vase is fragile, the safe is not. But this isn’t a matter of how they are: neither IS broken. To be fragile is to be disposed to break, if struck.

20. Dispositions to Add
Clearly in the past, I have only computed the values of ‘x + y’ for finitely many numbers. But perhaps I had a disposition to give an infinite number of responses, for arbitrary x and y.

21. The Disposition Theory
Theory: the function I mean by ‘+’ is the one consisting of the answers I am disposed to give when queried with ‘x + y’.

22. The Problem of Finitude
“[S]ome pairs of numbers are simply too large for my mind… to grasp. When given such sums, I may shrug my shoulders for lack of comprehension; I may even… die of old age before the questioner completes his question.”

23. Ceteris Paribus?
Suppose we say: the answer to ‘x + y’ is the answer I am disposed to give, all things being equal.

24. If I did have the memory, and the time…
“How in the world can I tell what would happen if my brain were stuffed with extra brain matter or my life were prolonged by some magic elixir? … We have no idea what the results of such an experiment would be. They might lead me to go insane, even to behave according to a quus-like- rule.”

25. The Problem of Error
Some individuals commit systematic errors of addition. According to the disposition theory, these aren’t “errors,” rather, these individuals denote nonstandard arithmetic functions by ‘+’.

26. Lesson: dispositions might (
Lesson: dispositions might (!) solve the problem of finitude, but they don’t capture the normative force of meaning: uses of words are correct or incorrect.

27. CTM
One popular view among philosophers is the Computational Theory of Mind: the brain is a computer and the mind is its software.

28. Adding Machines
On this view, the brain when it adds is an adding machine. So if Kripkenstein’s argument works, it should work for adding machines too. But can the skeptic maintain that the calculator means ‘quus’?

29. Adding Machines
Problem of Finitude: calculators can only process numbers of a certain size. What fact determines how they add/ quadd after? Problem of Error: gears break, wires melt. What fact determines when the output of the calculator is wrong?

30. The “Special Quale” Solution

31. Qualia
Is there as special ‘what it’s like’ to mean addition?

32. The Skeptical Solution

33. The Main Problem
‘The main problem is not, “How can we show private language– or some other special form of language– to be impossible?”; Rather it is, “How can we show any language at all (public, private, or what-have-you) to be possible?”’

34. “The skeptical paradox is the fundamental problem of Philosophical Investigations.” (p. 78)

35. Skeptical Solutions
Straight solution: deny the skeptic’s claims. Show that there is an error in the skeptic’s argument. Skeptical solution: accept the skeptic’s claims BUT claim that our ordinary way of talking is justifiable, because it never required the justification the skeptic asked for.

36. Wittgenstein’s Skeptical Solution
“The skeptical solution does not allow us to speak of a single individual, considered by himself and in isolation, as ever meaning anything” (pp )

37. Accept the Skeptic’s Claims
“Wittgenstein holds, with the skeptic, that there is no fact of the matter whether I mean plus or quus.” (pp )

38. “Don’t Think, Look!”
The solution: my meaning addition by ‘+’ is NOT a matter of my mental states or my past actions (skeptical solution). Rather, it is an accordance of my responses to those of others in my community. To give the ‘right’ answer is to give the answer others’ would give.

39. “Don’t Think, Look!”
“An individual who claims to have mastered the concept of addition will be judged by the community to have done so if his particular responses agree with those of the community in enough cases, especially the simple ones (and if his 'wrong’ answers are not often bizarrely wrong…)…”

40. “Don’t Think, Look!”
“…An individual who passes such tests is admitted into the community as an adder; an individual who passes such tests in enough other cases is admitted as a normal speaker of the language and member of the community.”

41. “Don’t Think, Look!”
“…Those who deviate are corrected and told (usually as children) that they have not grasped the concept of addition. One who is an incorrigible deviant in enough respects simply cannot participate in the life of the community and in communication.”

42. PI 87: “The sign post is in order if, in normal circumstances, it serves its purpose.”

43. Private Language

44. On Private Languages
“But could we also imagine a language in which a person could write down or give vocal expression to his inner experiences – his feeling, moods, and the rest – for his private use? – Well, can’t we do so in our ordinary language?”

45. On Private Languages
“But that is not what I mean. The individual words of this language are to refer to what can only be known to the person speaking; to his immediate private sensations. So another person cannot understand the language”

46. The Question
As we saw, Wittgenstein believes that there are public criteria for uses of mental state expressions, like “he has a toothache”: for example, clutching one’s cheek and moaning. The question here is: can there be a language (game) which has only private criteria? A language where only one person in principle has access to the criteria?

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

48. The Diary Case
Wittgenstein approaches the question of whether a private language is possible by imagining a speaker who wants to privately name some sensation S, and then keep a diary about when he feels S. Can we make sense of what this person is doing?

49. The Diary Case
Suppose that I have what I think is the same sensation on multiple occasions. Now I want a name for it (?). Wittgenstein points out that if I use a definition, then the name won’t be “private” in the relevant sense: others can learn it by learning the definition.

50. The Diary Case
So he claims what I have to do is to inwardly point to the sensation (concentrate on it) and say “Let this sensation be called ‘S’!” This is called an “ostensive” definition. Wittgenstein now wants to know whether this can establish a criterion for the use of the word “S.”

51. Issues with Ostensive Definitions
(From Sec. 33) “Suppose, however, someone were to object: ‘It is not true that you must already be a master of a language in order to understand an ostensive definition: all you need– of course!– is to know or guess what the person giving the explanation is pointing to. That is, whether for example to the shape of the object, or to its color, or to its number, and so on.’ “–And what does ‘pointing to the shape’, ‘pointing to the color’ consist in? Point to a piece of paper. –And now point to its shape– now its color– now its number (that sounds queer). –How did you do it?”

52. Issues with Ostensive Definitions
Here, Wittgenstein is suggesting that a lot of appropriate context has to be in place for ostensive definitions to succeed. It’s one thing to ask: Which of these two different objects is being pointed at? It’s another entirely to ask: Which aspect of this one object is being pointed at?

53. Issues with Ostensive Definitions
“When one says ‘He gave a name to his sensation’ one forgets that a great deal of stage-setting in the language is presupposed if the mere act of naming is to make sense…”

54. Issues with Ostensive Definitions
“And when we speak of someone’s having given a name to pain, what is presupposed is the existence of the grammar of the word pain; it shows the post where the new word is stationed.”

55. Issues with Ostensive Definitions
“‘I can (inwardly) undertake to call THIS “pain” in the future’ –‘But is it certain that you have undertaken it? Are you sure that it was enough for this purpose to concentrate your attention on your feeling?’ –A queer question.”

56. On the Need for a Criterion
If you’re Saul Kripke or Hilary Putnam, objects and natural kinds have ‘essences’ that themselves provide external ‘criteria.’ An application of a name or a natural kind term might be wrong or right, regardless of how the community used the words in question.

57. On the Need for a Criterion
For example, on the question whether whales are ‘fish’, it might not matter that everyone in the community thought they were and applied ‘fish’ to whales. The kind named ‘whale’ happens to not be of the same kind as that named ‘fish’, regardless of whether anyone knows it.

58. On the Need for a Criterion
Wittgenstein, however, thought that there weren’t these objective essences. You can’t latch on to these objective ‘essences’, you had to be taught to “follow along” with a rule for calling things ‘fish’ and your ability to do so was largely dependent on the type of creature you were.

59. The Issue
OK, but what’s exactly the problem with an ostensively defined term for a private state?

60. Criteria vs. Symptoms
There are different ways of telling that a field goal has been scored in basketball:
Watching the scoreboard
Listening to the crowd
Hearing the announcer say “a field goal has been scored”
Seeing the ball go through the hoop.

61. “If a philosopher asks, ‘Why does the fact that the ball went through the basket show that a field goal has been scored?” a natural reply would be, “That is what the rules of the game say; that is the way the game is played

62. Criteria
“Once we understand the rules for playing chess, the question whether a player has won when he has achieved checkmate cannot arise.”

63. Criteria
The ball going through the hoop is criterial of a goal being scored. There is a logical or conceptual connection between the two.

64. The Diary Case
What could NOW be the criterion by which you were able to judge that a certain sensation was the same one you named “S” to begin with? Thus far we’ve been worried that you can’t succeed in naming anything and maybe that’s supposed to be the objection.

65. The Diary Case
But put that to the side: it seems the answer is: I remember the sensation I named before, and this is the same one.

66. Private Rule Following
(Sec 202) “And hence also ‘obeying a rule’ is a practice. And to think one is obeying a rule is not to obey a rule. Hence it is not possible to obey a rule ‘privately’: otherwise thinking one was obeying a rule would be the same thing as obeying it.”

67. The Diary Case
How is remembering what you did before (seeming to remember!) any different from just believing it? You remember the sensation being like this and you use that criterion to apply “S”– but there is no further standard of correctness!

68. “As if someone were to buy several copies of the morning paper to assure himself that what it said was true.”