## Philosophical Grammar, Parts 1-2Wittgenstein wrote this book during 1932-1934 - the period just before he began to dictate the Blue Book. In Part I he discusses the notions of "proposition," "sense," "language," "grammar"; what "saying something" is, what distinguishes signs form random marks or noises. Must we start with "primary" signs which need no explanation? In what sense have we a general concept of proposition or of language? The phrases "family of cases" and "family similarities," which the Investigations use, are here; and comparison brings out what is special in the later development. But although it is close to the Investigations at some points, and to the Philosophische Bemerkungen at others, the Philosophical Grammar is an independent work and discusses much that is not in either of them. It is Wittgenstein's fullest treatment of logic and mathematics in their connection with his later understanding of "proposition," "sign," and "system." In Part II he writes on logical inference and generality - criticizing views of Frege and Russell and earlier views of his own, developing his conception of "law of a series" and of " ... and so on"--Leading to his discussion of mathematics, which fills two fifths of the volume: the ideas of "foundations of mathematics," of cardinal numbers, of mathematical proof, and especially of inductive or recursive proofs (with reference to Skolem), which he treats to a depth and extent beyond anything he said of them elsewhere. |

### Contents

How can one talk about understanding and not under | 39 |

Infinity in Mathematics 39 Generality in arithmetic | 451 |

On set theory | 460 |

The extensional conception of the real numbers | 471 |

Kinds of irrational number π PF | 475 |

Irregular infinite decimals | 483 |

Note in Editing | 487 |

Translators note | 491 |

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### Common terms and phrases

accordance answer apples application arithmetic calculus cardinal numbers chess circle colour connection consists construction contains corresponds course criterion cube decimal describe disjunction equation essential Euclidean space example existence expectation experience explanation expression fact feel finite follows Frege G. E. M. Anscombe geometry give grammar hand happens hypothesis imagine induction inductive proof infinite irrational numbers justify kind language length look mathematical proof mathematics mean meant method negation notation object occur ostensive definition particular patch perhaps Philosophical picture possible prime numbers problem proposition proved question rational numbers reality rectangle Recurring decimals recursive proof rules rules of chess say Thinking schema sense senseless sentence set theory sition someone speak square Suppose symbolism tautology thing thought tion translation trisection truth-functions understand the word want to say wish word red word-language write