Abstract
I want to go on now to a chapter by itself.
This chapter title does not head the original manuscript, though the two expressions have been chosen because of their uses in the manuscript.
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Notes
- 1.
The references to ‘chapter’ are absent from Ambrose and MacDonald , whilst present in Skinner’s version.
- 2.
‘is in’ added by Eds.
- 3.
Such a question requires many undeveloped researches. A case of deep progress from one angle is Ganesalingam (2013), which shows the way forward.
- 4.
In MacDonald’s (11.2.35.) version the lecture notes begin as follows: “What [sic] the criterion for a proposition being a proposition of logic? Criterion used to be self-evidence, a word taken from psychology .” (There is no use of “Russell, and Frege said” in MacDonald’s version, though she mentions Frege in a related connection.)
- 5.
The abbreviation ‘exam.’ (example) is written after ‘extraordinary’, then deleted presumably in favour of ‘theory’.
- 6.
This sentence is absent from MacDonald (1935) Lecture SEVEN, p.4. It is typical of those that are absent from her typescript and present in Skinner: i.e., an evaluative overview by Wittgenstein of a position or philosopher . This appears to indicate that MacDonald was listening for, or only wished to note, a narrower scope of data than Wittgenstein offers.
- 7.
Depending on how we compute the re-ordering from this above equation back to the beginning of the manuscript, there are 831 or 377 words before this equation to the opening of the manuscript. This contrasts with MacDonald’s 200 words back the beginning of the chapter. The difference between 831 and 377 is because Skinner’s manuscript re-orders the chapter and adds new chunks of discussion.
- 8.
This line, which commences with ‘=’ is parallel with the table and its first line in the MS.
- 9.
An obvious but important point: the pronoun “I” presumably identifies Wittgenstein, as elsewhere in this chapter, not least since Skinner would hardly pitch his authority against Russell’s.
- 10.
The letters in this column are written very lightly, in contrast with the bold emphasis of the letters in the other columns.
- 11.
‘with’ is added here.
- 12.
‘the’ is written after ‘Now’ and crossed out.
- 13.
Written in MS as ‘find’.
- 14.
Written ‘different’ in MS.
- 15.
The symbols are: “W p F W q F W.” Note the vertical mark contiguous to F, drawn on the lower connecting line.
- 16.
First written in the plural, then changed to singular.
- 17.
The word ‘taught ’ is written before the term ‘tautology ’, then crossed out.
- 18.
After the end of this sentence, ‘If you’ is written then deleted.
- 19.
‘on’ is written as ‘one’.
- 20.
The following incomplete sentence is written, broken off, then crossed out: “(The use will have nothing to do with giving us inf)”.
- 21.
This equation is an example of those that are not present in MacDonald’s notes.
- 22.
‘p ⊃ q’ is written after ‘into’, then heavily deleted in favour of ‘p ⊃ p’.
- 23.
‘To that’ begins the next line, yet is deleted.
- 24.
The next sentence was commenced by ‘This seems to’, but has been deleted.
- 25.
‘Is’ is spelled ‘If’ in MS. (Also, as with mathematicians of the period, Wittgenstein and his amanuensis sometimes end a conditional antecedent with a full stop, and (presumably for emphasis) commence the consequent with a capital letter.)
- 26.
Note that the original word order has been retained here, rather than the more usual ‘twice had’.
- 27.
This sentence originally commences with a phrase, now crossed out; the first word is ‘The’, while it is possible that the second term is ‘same’.
- 28.
These italics correspond to broken underlining under these words, which is not matched word for word; so it may indicate a pause for the reader and or the author to reflect on the phrasing.
- 29.
A symbol was written after the ‘=’ and before ‘p ⊃ q’, then deleted; it seems to be ‘q’.
- 30.
Notice how the right-hand side of the equation has a parallel with “├ p ⊃ q. p” in Wittgenstein’s MS 222, p.151 remark §212, which manuscript is drawn upon for the earlier part of his Remarks on the Foundations of Mathematics.
- 31.
This underlining is reproduced from the MS.
- 32.
‘as’ is written then deleted in favour of ‘in this way’.
- 33.
‘What’ commences this sentence, but is deleted.
- 34.
Most of this lecture is absent from Ambrose’s account, and MacDonald’s (1935, pp. 5–7) typed copy is very different from Ambrose’s. MacDonald’s opening ‘sentence’ is: “Inference and implication ”, which among other things misses off ‘tautology ’.
- 35.
The word ‘is’, which is inserted over the line, could be inserted by Wittgenstein’s hand since he sometimes (but not typically) writes a looped ‘s’ such as is the case in the manuscript here. Skinner typically writes ‘s’ very much like the printed ‘s’ (as with Skinner’s writing in the present manuscript, for example VII, pp.4–5, VIII, p.4, etc.). So the attribution is uncertain here.
- 36.
Wittgenstein’s pencil hand (which is a different pencil line style and width from Skinner’s) adds the word ‘further’, with his parentheses around ‘(other)’, and he placed square brackets around ‘[From these he sets out]’ with an arrow to indicate that he re-orders and adds to Skinner’s hand to indicate, as far as one can see, the result above.
- 37.
The word ‘to’ is inserted above ‘and’; the word ‘between’ is added above ‘application ’ in Wittgenstein’s hand; also, there is an underline.
- 38.
The phrase ‘as given by’ is inserted in ink over the line in Skinner’s hand, together with new ink parentheses (those which open a parenthesis after Russell’s name, and close after the first use of ‘application’, as well as the final two parentheses for the last phrase of the sentence). A pencil parenthesis around ‘or Newton’s Laws ’ has been deleted. Wittgenstein’s hand lightly adds a final phrase that appears to be ‘of law’.
- 39.
Behind this reference to Newton lies the possibility that Newton’s 2nd Law may have a family of subsets within it (cf. J. C. Baez (2011)).
- 40.
‘itself’ is first written then deleted in favour of ‘it’.
- 41.
“like” appears to be in Wittgenstein’s hand.
- 42.
The word ‘always’ is diagonally crossed through in pencil with one long stroke, which seems to be in Wittgenstein’s hand as elsewhere on the same page.
- 43.
These three lines are in Wittgenstein’s handwriting , though written on the reverse of the sheet for this context. The last line is encircled in the same pencil as the symbols , whereas the main text is in ink in Skinner’s hand. These details are not present in MacDonald (1935); nor in Ambrose (1979: 138–39).
- 44.
Changed from “I.E.” to “e.g.”. This detail is mentioned because Wittgenstein’s hand alters Skinner’s handwriting , for which see Chap. 2.
- 45.
Before ‘You’ there is a vertical oblong, which may be there to indicate a new paragraph, since it is towards the end of a continuous line and after a full stop.
- 46.
The words ‘embodied in’ are added above ‘given’.
- 47.
Here in the MS the incomplete expression ‘anothe’ is written, then deleted.
- 48.
‘you’ seems to have been written first, then deleted, with ‘I’ (presumably Wittgenstein’s first person) is squeezed into the available space.
- 49.
This italicized expression is underlined.
- 50.
‘at the view’ is added by Eds.
- 51.
‘way’ is not in MS.
- 52.
‘are’ is written first then deleted.
- 53.
‘there’ is written then deleted.
- 54.
Note above in VIII.2. that Wittgenstein has changed I.e. to e.g. in line with present context.
- 55.
What appears to be Wittgenstein’s hand draws a line from ‘axioms back to ‘ordinary propositions’ above.
- 56.
MacDonald (1935, p.5) has a different attribution: “Russell was inclined”. Prior to this sentence she has two schematically sketched points not present in Skinner: “You do not explain the connection with pns. By calling them the prim. Pns. Axioms . It is a pure game.”
- 57.
‘is’ is inserted by Eds.
- 58.
‘not’ is inserted above line.
- 59.
The word ‘which’ is written in Wittgenstein’s hand, over the line with an instruction to insert it.
- 60.
‘Therefore’ is written on a separate line, deleted.
- 61.
‘in his use of’ is added by Eds.
- 62.
‘grou[p]’ is written and deleted.
- 63.
‘one’ is inserted by Eds.
- 64.
The manuscript reads oddly: “has seemed where they/seem/paradoxical and interesting is a tiny point”. The word “/seem/” is marked for insertion, and it is retained above. This squares oddly with “has seemed”, which we delete, and judge that Skinner intended this. We add ‘– it’ to mark the proposition here deemed “tiny”.
- 65.
Skinner starts writing ‘sh’, deletes it, then writes ‘could’.
- 66.
‘it’ is first written and then deleted it in favour of ‘I’.
- 67.
Written ‘Frs’ in text.
- 68.
Written in MS as ‘tempted’.
- 69.
Skinner wrote ‘p follows from p v q’. Wittgenstein revises and reverses this order – as above, having encircled the original “v q”, so that only ‘p’ is left, and he wrote ‘v q’ to follow after Skinner’s writing of ‘p’.
- 70.
‘were’ is inserted here by Eds.
- 71.
‘did’ is written and deleted.
- 72.
A word is written, perhaps it is ‘become’, and is deleted and ‘be’ written over the deletion in Skinner’s hand.
- 73.
MacDonald (1935, p.7) does not have this sentence, while she does have: “Logic is a calculus and you can make inventions in it but not discoveries. But I am not taking the view of Lewis and the Warsaw school that there are many different ‘logics’.”
- 74.
‘do’ is squeezed in space after ‘what’ and ‘you’ written.
- 75.
‘for’ is inserted by Eds.
- 76.
‘it’ is written after ‘that’ and deleted; restored here by Eds.
- 77.
Note that Goodstein refers to Brouwer in his letter, reproduced in Appendix [J]. Also, from 1929, Wittgenstein’s mathematical colleague Max Newman , as early as 1923 (p.6, footnote 1), had taken on board a similar use of Brouwer to the above, which is reflected in Newman’s teaching of undergraduates such as Goodstein and Skinner. Newman (1926) combined the foundations of mathematics with theoretical physics .
- 78.
After ‘the’ ‘sta’ is written and deleted.
- 79.
‘point’ is written over the line in Skinner’s hand.
- 80.
‘down’ is inserted by Eds.
- 81.
See Wittgenstein’s small notebook MS 157b, f.28r for the ‘T’ negation sign, and f.26r for ‘Apfel’.
- 82.
Quotation marks for ‘~’ and ‘apple’ are supplied by Eds.
- 83.
‘it’ is supplied by Eds.
- 84.
‘be’ is supplied by Eds.
- 85.
‘make’ is supplied by Eds.
- 86.
‘remark’ is supplied by Eds.
- 87.
The varying uses of single and double, and no quotation marks, in direct speech is worthy of attention here; they do not seem ad hoc – i.e. not a result of arbitrary transcription by Skinner. Re. the latter, note that the sentence that commences ‘Is the word for “not”, was initially opened with a double quotation mark, which was then changed to a single. See Heal’s (1995) analysis of dialogue and argument and its use of punctuation in the Investigations .
- 88.
‘with’ is added by Eds.
- 89.
‘an’ is added by Eds.
- 90.
‘who’ is written, then crossed out.
- 91.
MS has ‘an’ not ‘a’.
- 92.
It is instructive to compare and contrast this graph , and reference to “lab”, etc., with Ambrose 1979: 142. MacDonald’s lecture notes have no diagrams at all for this lecture in contrast with Skinner’s; this not untypical.
- 93.
See an earlier, brief, use of a similar point in Wittgenstein (2005: 384).
- 94.
It is worth comparing and contrasting this form of expression and its context with Ambrose (1979: 142).
- 95.
‘in’ is supplied by Eds.
- 96.
‘with’ is written first, deleted and ‘in’ placed over it.
- 97.
It looks as if ‘as’ was first written, and then changed to ‘our’.
- 98.
‘These are’ is written before ‘We’ and deleted.
- 99.
We have moved back this occurrence of ‘I.E’ to this point from its position in the MS immediately after ‘useful’, since it appears to have been intended to mark the clause that it introduces.
- 100.
Term in singular in MS.
- 101.
Lower case opening in MS, here capitalized to match (2).
- 102.
The original manuscript is written in black including the sample patch. Wittgenstein could have instructed a blue colour to make up the patch but did not. He is inviting us to think of the notion of the colour blue rather than a patch of a particular shade of blue.
- 103.
‘as’ in the MS is written ‘a’.
- 104.
‘in’ is written after ‘putting’ then deleted.
- 105.
This shape is the same as that in Wittgenstein’s 1935 C Notebook (MS 148), p.39.
- 106.
‘it meant’ is written twice, second occurrence deleted.
- 107.
‘We’ is written before ‘It’ then deleted.
- 108.
The word written is ‘hear’, a mistake for ‘here’.
- 109.
After ‘apple’ the pronoun ‘I’ is written and part of another word, which are crossed out.
- 110.
Notice that while Skinner’s notes for Lecture 10 are replete with illustrations, MacDonald (1935: 10–13) has none.
- 111.
This shape and its complementary form are the same as that used in Wittgenstein’s unpublished 1935 Notebook MS 148 (pp.37 and 39). The discussion is different, though some underlying concerns aim at the same end.
- 112.
‘The word ‘its’ is written in the MS; changed to ‘is’. The first ‘it’s’ is written with the apostrophe in it; ‘not’ is inserted above the line.
- 113.
- 114.
He states the negation of this in the Tractatus §5.4732: “we cannot give a sign the wrong sense”.
- 115.
‘to’ is added by Eds.
- 116.
The numerals ‘1’ and ‘2’ are written in each ‘body’ respectively.
- 117.
After ‘I.E.’ ‘to’ is written and crossed out.
- 118.
Note that ‘Apple’ is spelled with a capital A in the MS.
- 119.
‘the’ written before ‘chalk’ is crossed out.
- 120.
‘down’ is inserted by Eds.
- 121.
‘it’ is first written and then deleted with ‘to’ replacing it.
- 122.
‘app’ written after ‘takes’, then deleted.
- 123.
Before ‘One’ ‘There’ is written then deleted.
- 124.
The MS reads ‘have’, changed here to ‘has’.
- 125.
Above the equation retained in the main text, the following draft equation has been written, and then crossed out: “∃(x y). (f(x). f(y)) : f (z). ⊃ z = x v. z = y”. Written above this equation is: “∃ (x) y z”. All this is deleted; and below it the above equation in the main text is written and retained.
- 126.
‘different’ is written after ‘two’ and crossed out.
- 127.
In a typical variation and in a shortened form, (MacDonald 1935, p.13), this sentence reads differently as: “Russell leaves open the question whether x = y but I say we do not want to leave this open but only if they are not equal will we use two letters.” There is no text in MacDonald for the rest of the lecture, whilst here Skinner has some fourteen lines of extra detail.
- 128.
‘as’ is written after this equation, then crossed out.
- 129.
The word ‘in’ is written twice here – last word of the line and first word of the next line.
- 130.
Although the full stop is raised and lighter than others, it seems certain that this is the meaning of the mark.
- 131.
Insofar as there is a parallel between Skinner and MacDonald (1935, p.13) here – and the latter’s notes are much shorter and lack Skinner’s technical detail, it is plausible to suppose that her use of ‘to involve’ is the missing expression that Skinner has omitted here. A sentence later MacDonald has the statement: “Russell’s notation is about the thing referred to. But I never say, this chair is identical to itself.”
- 132.
‘exampl’ is written before ‘expression’, then crossed out.
- 133.
This equation is mentioned in MacDonald’s (1935: 25) unpublished “Lectures on Logic, etc.”, though the contexts are very different.
- 134.
‘with’ written, crossed out, and ‘by’ inserted over it.
- 135.
‘Russell’s’ written before ‘this’ and crossed out.
- 136.
Quotation marks are added by Eds.
- 137.
Opening parenthesis is written and crossed out before the negation sign.
- 138.
Closing parenthesis is written and crossed out after ‘x’.
- 139.
⊃ written twice contiguously – once at the end of the line and once at the beginning of the next line.
- 140.
‘This’ is written twice, one crossed out, with extra space between – perhaps to enable indenting the sentence.
- 141.
This sentence is crossed out.
- 142.
‘3’ is written underneath and changed to ‘5’.
- 143.
‘3’ is written oddly.
- 144.
This symbolism reads:
$$ {\displaystyle \begin{array}{l}\left(\mathrm{E}\ 11\;x\right)\upphi x.\left(\mathrm{E}\ 111\;x\right)\uppsi x.\mathrm{Ind}.\supset .\\ {}\kern2.52em .\supset .\left(\mathrm{E}\ 11111x\right)\upphi x\ v\psi x.\end{array}} $$Skinner’s drawing of the lines is much more informative and technically communicative than MacDonald’s (1935: 14) Lecture Eleven.
- 145.
‘we’ is written then crossed out.
- 146.
‘to’ is added by Eds.
- 147.
Word order reversed; it is written: ‘by unnecessarily’.
- 148.
The MS reads ‘which with’ and ‘with’ is deleted. I suggest the above reverse order, rather than deletion, was intended by Wittgenstein.
- 149.
As with the previous use of the form four lines above, to the far right of this ‘=’ and what might be ‘Tau’ is written, and then crossed out.
- 150.
‘the’ is written and crossed out.
- 151.
May be Frege and Russell, or Russell and Whitehead in relation to their Principia Mathematica .
- 152.
‘to say’ is written above the sentence.
- 153.
‘in’ is written twice.
- 154.
‘On the other’ opens the sentence and is crossed out.
- 155.
‘the same’ is written and crossed out.
- 156.
‘didn’t appear’ is written, and two dots undeleted on line as if the remaining expression was intended as another instance.
- 157.
The word ‘be’ is inserted by Eds.
- 158.
‘were’ has a thick double underline in the manuscript.
- 159.
The five lines below in this footnote are written in the main text above after “this”, and indented in the following manner; yet they are deleted in favour of the equation above in the main text:
$$ {\displaystyle \begin{array}{l}\left(\mathrm{E}\;x\right)x=a\\ {}\kern1.68em \left(\mathrm{E}\;\upxi \right)\upxi =x\ v\ \upxi\;y\end{array}} $$This proposition is a relation between x and y:
$$ {\displaystyle \begin{array}{l}\;x=a\ v\ x=c:\\ {}:y=b\ v\ y=d\end{array}} $$ - 160.
A capital ‘W’ is written before “It” and deleted.
- 161.
The letters ‘ur’ are written in pen over the pencil writing of “four”, and ‘s’ is added in ink to “letter”.
- 162.
‘test’ is written first, and then crossed out.
- 163.
These lines are crossed through.
- 164.
‘f’ is missing from this series.
- 165.
‘d’ is missing from this series.
- 166.
‘the’ is inserted by Eds.
- 167.
“if” written and crossed out.
- 168.
‘A tribes’ is written, altered to ‘tribe’ above. The expression “They can” precedes this term and is crossed out.
- 169.
‘of’ appears before “a”, which is crossed out.
- 170.
‘talk’ is inserted by Eds.
- 171.
‘tackled’ is inserted by Eds.
- 172.
The MS reads ‘meaning’.
- 173.
I.e. Abraham Gans, an American student attending Wittgenstein’s class in 1935, along with Skinner, Goodstein and others. (Cf. McGuiness (2008: 283) notes that Gans was with Moore on occasions when Wittgenstein was in dialogue with both; sometimes spelled ‘Ganz’ – cf. as noticed here by McGuinness ; also, Ground and Flowers (2015: 565); Klagge and Nordmann , (2003: 346).)
- 174.
‘formulate’ is inserted by Eds.
- 175.
After the question mark, the following sentence is written and crossed out: “The number 3 is class of all collections of nuts which can be put on A B C.” “collection of” is also written above the line over ‘nuts’.
- 176.
‘able’ has had ‘cap’ squeezed in to as prefix to ‘able’. Since ‘to be’ has not been changed to ‘of being’, I have left the above first version.
- 177.
‘W’ starts the sentence and is crossed out.
- 178.
‘People’ is written after the end of this sentence and crossed out.
- 179.
‘I give’ is written and crossed out on the next line, after this line of dots.
- 180.
‘There’ is written twice, and the first crossed out, which perhaps indicates that the beginning of the sentence is to be indented, as above.
- 181.
‘you’ is written before ‘I’, and crossed out in favour of ‘I’.
- 182.
‘have’ is inserted by Eds.
- 183.
Dash is inserted by Eds.
- 184.
This US spelling of ‘theater’ is in the manuscript.
- 185.
MS says ‘mean’, which is possibly short for meanings but more likely ‘men’.
- 186.
The comma interprets a very light dot in the manuscript.
- 187.
‘word’ is first written, then deleted, with ‘sign’ written over it.
- 188.
The word ‘four’ is written, then crossed out in favour of the numeral.
- 189.
‘the words’ is written, then crossed out.
- 190.
‘who’ is written after ‘man’ and crossed out.
- 191.
‘Df.’ for ‘Definition’.
- 192.
‘questions’ written first, then it is overwritten as ‘sentences’.
- 193.
‘They’ is the form in the manuscript, taken to be an error for ‘There’.
- 194.
‘They’ is written before ‘Compare’ and crossed out.
- 195.
‘One’ is written first and crossed out in favour of ‘A’.
- 196.
It seems that ‘it’ is written first, then overwritten as ‘is’.
- 197.
Perhaps ‘white’ because Wittgenstein drew the negation sign in chalk on a blackboard.
- 198.
‘you’ is inserted over the line.
- 199.
Opening quotation mark is supplied by Eds.
- 200.
There follows the sentence, which is crossed out:
‘If you say it is about the scratch 4, then I say, “Be careful, it is about the use of 4.”’
- 201.
‘that is,’ is added by Eds.
- 202.
‘common’ written first; then overwritten as ‘command’ with ‘you’ added over line. The word ‘gave’ is preceded by ‘can’ and crossed out.
- 203.
‘it’ is added by Eds.
- 204.
‘made’ written first; then crossed out and ‘did’ written over it and crossed out. Furthermore, ‘made’ then written over the line, to restore the original choice. ‘certain’ written over the line and inserted in main text.
- 205.
Margaret MacDonald’s lecture notes for Wittgenstein’s lecture on 4.3.1935 (MacDonald 1934–35: 18) ascribe third person speech to Wisdom (“Mr. Wisdom asks”), whereas here we have Skinner’s preservation of Wisdom speaking in his own first person – which if accurate, is the work of the amanuensis taking down actual speech, rather than MacDonald’s and Ambrose’s transposition and reduction to handy notes. Ambrose and MacDonald’s notes sometimes switch or disagree about first and third person ascriptions of theirs and Wittgenstein’s 1st person. A.J.T.D. (John) Wisdom was appointed as a lecturer at Cambridge in 1934, which led to a Fellowship at Trinity. Wittgenstein comments on his engagement with him in his letter to W.H. Watson (cf. McGuinness 2008: Letter 180).
- 206.
‘by putting’ is inserted above line.
- 207.
MacDonald’s LECTURE THIRTEEN (given on 4.3.1935), presenting notes that are roughly similar to the above sentence, prefaces them with “Wittgenstein replies that”.
- 208.
‘be’ is missed out here.
- 209.
A word is deleted after ‘This’.
- 210.
Here ‘;’ is oddly written: it might be a comma.
- 211.
Three words are written, then crossed out, and placed before the start of this sentence. The first word is ‘Wisdom ’; the other two cannot be read.
- 212.
On the next line a sentence commences and is crossed out. It reads: “Or it may be”.
- 213.
A word is written and heavily deleted here.
- 214.
‘had’ is written over the sentence, marked for insertion – as is the first indefinite article in the next sentence.
- 215.
A word is heavily crossed out after ‘is’.
- 216.
The parallel sentence by MacDonald (4.3.1935), p.19, varies from the above, as follows: “If I use the word rule it will always be in a particular case where I wish to oppose a rule to something else.”
- 217.
Inadvertent indefinite article after ‘be’ was removed by Eds.
- 218.
Note a similar chart, and parallels in discussion, in the manuscript MS 116 (Philosophische Bemerkungen, XIII), pp.143–44, but with a, b, c, d; but matched with arrow order →, ←, ↑, ↓ respectively.
- 219.
‘this’ is ‘his’ in MS.
- 220.
After ‘the’, ‘other’ is written and crossed out.
- 221.
Presumably Wittgenstein has resumed speaking, and this ‘he’ indicates John Wisdom .
- 222.
Wittgenstein resumes speaking here.
- 223.
It seems that four words have been written and crossed out; only the first can be read – ‘of’.
- 224.
After the comma, ‘then’ is written and crossed out.
- 225.
Two words are written and heavily crossed out, with ‘moving’ added over the line.
- 226.
‘line’ is added here by Eds.
- 227.
Written ‘numeral’ in the manuscript.
- 228.
Close quotation mark is added by Eds.
- 229.
After the question mark, the next line commences with ‘In order”; yet is crossed out.
- 230.
After ‘correlation’, ‘of’ is written and crossed out.
- 231.
‘Suppose’ introduces the box and is crossed out.
- 232.
Although this lecture in Skinner’s manuscript has very many diagrams , yet MacDonald’s has none.
- 233.
‘given’ is squeezed into a small space at the edge of the page, though legible.
- 234.
This opening and the term ‘Remark” do not occur in MacDonald’s (1935) notes, nor in Ambrose’s (1979: 159).
- 235.
This underline is in pencil, while the text is ink. It is possible that this term ‘Remark’, with its underlining, is a custom deriving from the currency in German and the formal style of 1930s Cambridge mathematics lecturing – the latter which are laid out in the style of numbered “Chapters”, typically with divisions into axioms , lemmas, premises, proofs, theorems, with numbered “Remarks” in such a sequence. This also obtains for contemporary Cambridge research publications (see H. Baker 1937: 259).
- 236.
Wittgenstein appears to be mentioning Russell’s use in his Principles of Mathematics (1903: 267–69, §256).
- 237.
The opening remarks up to this point are absent from MacDonald’s (1935, p.23); nor are they in Ambrose’s 1979: 159 publication).
- 238.
The spelling in the manuscript is ‘apply’.
- 239.
See Russell’s use in the latter’s Principles of Mathematics (1903: 260–67, §251–55).
- 240.
‘If these’ commences this sentence, and the expression is crossed out.
- 241.
This form of ‘corresponding’ also appears in Wittgenstein’s MS151 (1936, p.2) where a geometrical source for the term is explored.
- 242.
‘one 0’ is inserted over the line after ‘puts’.
- 243.
‘by’ is inserted by Eds.
- 244.
‘because’ is written above the line with signs for insertion.
- 245.
‘take’ is written above the line with marks to insert.
- 246.
Since Hardy was a founding father of early twentieth century pure mathematics in Cambridge, and was averse to recognising the relevance of pure to applied mathematics , then this use of his name about ‘experiment ’ may well be ironic.
- 247.
Stick’ is written over the line.
- 248.
Quotation marks are added by Eds.
- 249.
‘Go back’ commences the sentence, then is crossed out.
- 250.
‘with’ is written over the line with instructions to insert.
- 251.
The following expression and punctuation is written after the above sentence, then crossed out:
‘If I say: “With normal chalk 275 x 899 gives so-and-so’.
- 252.
‘property’ is written over the line with marks for insertion.
- 253.
This illustration, and some others like it, are absent from MacDonald’s MS 1935 (pp.23–24); also absent in Ambrose’s (1979: 159–61) partial copies of this lecture.
- 254.
It is typical here of Skinner that he takes down dictation from Wittgenstein in the first person, whereas MacDonald (1935) LECTURE SIXTEEN, p. 24, typically has fewer or no first-person narratives.
- 255.
This sentence is similar to MacDonald’s Lecture Sixteen, p.26.
- 256.
The manuscript has: ‘not’.
- 257.
The manuscript has: ‘line’.
- 258.
Dash is inserted by Eds.
- 259.
The text has ‘manyfold’.
- 260.
‘theory’ is written over line with instruction for insertion.
- 261.
‘since’ is written above ‘though’ with the latter crossed out.
- 262.
After ‘that’, the expression ‘to say theory’ is written and crossed out.
- 263.
‘sets of’ is written over the line.
- 264.
This illustration is similar to mapping from one domain to another in graph theory, which the author perhaps had in mind.
- 265.
Dash is inserted by Eds.
- 266.
‘the’ is inserted by Eds.
- 267.
‘be able to’ is written over the line.
- 268.
‘You’ written, deleted; then ‘When’ is written.
- 269.
‘I have chalk’ is written over the line and marked for insertion.
- 270.
‘be’ is inserted by Eds
- 271.
‘with’ is supplied by Eds.
- 272.
After ‘Each’, ‘other’ is written and crossed out.
- 273.
‘exist’ is written in manuscript.
- 274.
‘One might sa’ is written and crossed out before ‘Suppose’.
- 275.
‘determine’ is written and crossed out after ‘is’.
- 276.
‘has’ is replaced by ‘is’ in MS by Eds.
- 277.
‘more’ is written and crossed after ‘is’.
- 278.
‘was’ is written over the line.
- 279.
Indefinite article is inserted by Eds.
- 280.
‘it’ is written, then deleted after ‘means’.
- 281.
After ‘for’, ‘your’ is written and crossed out in favour of ‘this’ written above the line.
- 282.
‘correlated’ in the manuscript is changed to correlation’.
- 283.
‘Russell’s’ in the manuscript, changed to ‘Russell’.
- 284.
In the manuscript ‘great’ occurs, changed here to ‘greater’.
- 285.
‘with lines’ written over the line; also ‘line’ is written and crossed out after ‘was’.
- 286.
‘have’ is missing in the manuscript and supplied by Eds.
- 287.
‘(Miss Macdonald)’ is squeezed into the margin, and on the next full line, is written: “If you say ‘must’” is written, and crossed out.
- 288.
‘Who’ occurs and is crossed out after ‘asked’.
- 289.
‘Suppose’ is written and crossed out before (1).
- 290.
‘as to’ is added by Eds.
- 291.
Close quotation marks are added by Eds.
- 292.
‘that’ is added by Eds.
- 293.
The italics indicate a line of dashes under these italicized words.
- 294.
The last two words are crossed out.
- 295.
This was the last lecture of the Lent Term. Lectures continued in the next – Easter – Term. We do not know why Skinner’s manuscript of Wittgenstein’s lectures does not include the other Terms. Even so, the manuscript here is self-contained, with a few detailed signs of Wittgenstein tuning it. It may be that Wittgenstein did not view the other Terms as something he wanted to place alongside this manuscript and wished this manuscript to be a composite member of the Archive that he sent to Goodstein .
Some unpublished lecture notes of the Easter Term Lecture, 1, p.1, typed by Margaret MacDonald (1935) commences with: “Recapitulation of Russell’s theory of number. There is certainly something tempting in Russell’s idea. But the whole idea of trying to define Number springs from a misunderstanding. We do not need a definition of Number. A definition of Number can only ‘reduce’ the idea of number to a set of indefinables. If this had been Russell’s intention , this would have been very unimportant. But it was not his intention. The reason for giving a definition was an attempt to answer the question. What is a Number? It was an attempt to get rid of this puzzlement by getting clear about the grammar of the word ‘Number’ and of the numerals. We do not define Number any more than we define the King of Chess apart from the actions of the various kings of the sets. Any definition of number loses its meaning when we cease to ask the questions ‘What is Number?’ We try to get clear about how we use the word Number and do not think that here is the digit ‘3’ and somewhere else intangible which is the number ‘3’.”
- 296.
This is April 1935.
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Gibson, A., O’Mahony, N. (2020). Self-Evidence and Logic. In: Gibson, A., O'Mahony, N. (eds) Ludwig Wittgenstein: Dictating Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-030-36087-0_8
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