By L. Mirsky

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**Extra resources for An Introduction to Linear Algebra **

**Sample text**

Page 43 "Laws" like the law of sufficient reason, etc. deal with the network not with what the network describes. 15. Page 43 It must be through generality that ordinary propositions get their stamp of simplicity. Page 43 We must recognize how language takes care of itself. Page 43 The proposition that is about a complex stands in internal relation to the proposition about its component part. 15. Page 43 The freedom of the will consists in the fact that future events cannot be KNOWN now. --The connexion between knowledge and thing known is the connexion of logical necessity.

For the generality notation contains a proto-picture. [Cf. ] Page 69 All invisible masses, etc. etc. must come under the generality notation. Page 69 What is it for propositions to approximate to the truth? , from "All men are mortal" and "Socrates is a man" there follows according to this logic "Socrates is mortal" which is obviously correct although I equally obviously do not know what structure is possessed by the thing Socrates or the property of mortality. Here they just function as simple objects.

Page 61 Every proposition that has a sense has a COMPLETE sense, and it is a picture of reality in such a way that what is not yet said in it simply cannot belong to its sense. Page 61 If the proposition "this watch is shiny" has a sense, it must be explicable HOW THIS proposition has THIS sense. ----There will, of course, also be something that it does not say--but what it does say it says completely and it must be susceptible of SHARP definition. Page 61 So a proposition may indeed be an incomplete picture of a certain fact, but it is ALWAYS a complete picture.