14 ;;Quote: a philosopher can talk about mathematics by dealing with words that have a natural meaning; e.g., "proof", "number"

20 ;;Quote: you understand an expression when you know how to use it, although it may conjure up a picture

24 ;;Quote: two strokes is as good a definition of "two" as any others

24+;;Quote: any definition can be misinterpreted

26 ;;Quote: suppose someone says "I know what series '1 4 9 16'" is but then writes 20,000 for the 100'th element; may still be following a rule

26 ;;Quote: saying two pieces of chalk are the same could mean different things; but saying everything is the same as itself seems utterly unambiguous

30 ;;Quote: 1+1=2 is not know by calculation or intuition, but because we all were taught it and know it

33 ;;Quote: a definition is a transition between one technique into another, e.g., from mathematics to logic; not an abbreviation

33+;;Quote: is p|q an abbreviation for ~p.~q or is it vice versa; i.e., definition is not abbreviation

43 ;;Quote: the calculi of mathematics was invented to suit experience and then made independent of experience

69 ;;Quote: when you philosophize, don't leave your commonsense outside like an umbrella, bring it in with you

70 ;;Quote: some propositions are true and some are false; same as asserting and denying or nodding and shaking the head; this is done often

83 ;;Quote: we fix our technique that 13 follows 12; the only discovery is that this is a valuable thing to do

102 ;;Quote: it is absurd to say that "12*12=144 may be wrong" because agreement is the justification for this technique; calculation is based on agreement

104 ;;Quote: can always affix "by definition" to a mathematical proposition; this refers to a picture, e.g., "12*12=144", in a standards archive

112 ;;Quote: if math is about numerals instead of definitions, math is about scratches on the blackboard; absurd; math is not about how symbols are used

156 ;;Quote: saying that number is a one-one correlation between classes is just substituting another expression for number

161 ;;Quote: if numbers correlate two classes, need to know when you repeat the same name so that one thing has one name; e.g., shadows

167 ;;Quote: nothing in English provides for "There is an x which is a man"; no way to identify "a man" or even "being a pair of trousers"

190 ;;Quote: can represent the meaning of a word by a picture that corresponds to the word, or by the use of the word (again a picture)

194 ;;Quote: there is no such thing as a logical machinery behind our symbols; where logical machinery is like a clock plus necessity

206 ;;Quote: the Liar's paradox is just a language game that behaves differently than others

206+;;Quote: normally a contradiction is a criterion for having done something wrong; not for the Liar's paradox

223 ;;Quote: what is important is not meaning as something in the mind, but whether something has a use; "'Wolf' is a wolf" seldom has a use

247 ;;Quote: consider the reality corresponding to a sentence; this means either that the sentence is true or that the sentence has a meaning; e.g., "There's nothing red in this room" vs. "red"

248 ;;Quote: words such as "two" and "and", and rules such as "2+2=4" have many uses but not much of a meaning

250 ;;Quote: mathematics and logic are part of the apparatus of language, not part of its application; allows us to use "900" in our daily life

252 ;;Quote: for most words a picture represents the meaning of the word, e.g., "chair"; for others, pictures are misleading, e.g., "particle"

252+;;Quote: if you want to understand a word, you have to know its use

262 ;;Quote: mathematics does not rest on logic; instead arithmetic and logic are the same

271 ;;Quote: even though Russell has translated mathematical procedures into logic does not mean that this explains mathematics

271 ;;Quote: a child has got to the bottom of arithmetic by learning to use it; that's all there is to it