(Remarks on the Foundations of Mathematics) PDF DOWNLOAD Ê Ludwig Wittgenstein
Ted correctly and are not empirical statements or statements giving knowledge Wittgenstein is directly against Russell in that he did not believe mathematics reuired a rigorous foundation and takes aim at the idea that the real proof of an arithmetical statement is the one found
in a system such as Russell s PM One of the reasons for this is that PM or a system such as Russell s PM One of the reasons for this is that PM or foundational calculus cannot be considered the ground of 224 as one of the criteria someone would look for in a potential foundation is that it would have to prove statements like 224 Russell s PM would have been rejected if it had proved statements like 225 There are some interesting discussions
about Godel Cantor and Dedekind Wittgenstein tends to be attacked for comments Godel Cantor and Dedekind tends to be attacked for his comments these mathematicians although Wittgenstein isn t disputing the proofs themselves it s the interpretation they re given and the significance they hold and the nusual statements that people make in connection with them There is some interesting discussion on whether or not you nderstand mathematical propositio. Rise discovery invention; Russell's logic Godel's theorem cantor's diagonal procedure Dedekind's cuts; the nature of proof.
read Remarks on the Foundations of MathematicsRe reading material great for public communication each point a
Different Riddle This Is Where Nassim Taleb Took Wittgenstein Sriddle this is where Nassim Taleb took Wittgenstein s from points 94 and 93 This book contains comments written over a decade of work of Wittgenstein A large part of the text was originally supposed to be the second half of the Philosophical Investigations and there are lots of themes in common what it means to follow a
for example would only recommend reading it if you are already familiar with the later Wittgenstein s philosophy in general as parts of this book are difficult to interpret if you were to read it without nderstanding Wittgenstein s broader aims The collection of remarks was never formulated into a fully cohesive book and much of the comments were just Wittgenstein s comments to himself so some parts were repetitive and other parts without development That said there are plenty of interesting ideas For example Wittgenstein that basic arithmetical statements such as 32 5rule for example
Are Used As Rules Or Criteria To Determine Whether Someoneused as rules or criteria to determine whether someone calcula. This analyzes in depth such topics logical compulsion mathematical conviction; calculation as experiment; mathematical surp. ,
Ns without knowing a proof eg Fermat s theorem before the
proof and to what a proof is There are also interestingand to what a proof is There are also interesting around nonconstructive existence proofs and "how starkly less clear they are in their meaning than constructive ones Wittgenstein considers as an example "starkly less clear they are in their meaning than constructive ones Wittgenstein considers as an example about whether or not the string 777 occurs in particular irrational numbers and what it means to say that 777 does not occur in the infinite decimal expansion of an irrational number I can t give a rating to a book in which I don t Les Altaens : Peuple turc des montagnes de Sibrie understand most of the content There s definitely food for thought I ll have to come back to it when I can betternderstand the topics and engage to a respectable level still in progress I gave this five stars even though I m pretty sure I don t The Possible Police understand it I m reasonably sure that nobodynderstand Wittgenstein but that s another story Nonetheless the book provides a wealth of brain food for thinking about issues in the philosophy of math and logic and gives obscure but invaluable insights into Wittgenstein s takes on such matter. Contradiction; the role of mathematical propositions in the forming of conceptsTranslator's NoteEditors' PrefaceThe TextInd.