Questions tagged [principia-mathematica]

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Why can Goedel's Incompleteness Theorem be proven?

Preliminaries: The way I understand it, Gödel took Russel's and Whitehead's Principia Mathematica (PM) and mapped strings of symbols from PM onto the integers, their Gödel numbers. He then constructed,...
Johannes Bauer's user avatar
2 votes
1 answer
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Source of a Russell quote about difficulties in his work

Some years ago I read somewhere a memoir by Bertrand Russell. He wrote about the difficulties he encountered in writing Principia Mathematica (or trying to solve the paradox that bears his name). He ...
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Validity of physical laws and observation

I am placing this question on philosophy stack exchange because a mathematician wouldn't care, and a physicist would be extremely insulted. Consider Newton's Law F=ma. First, I am observing this as ...
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2 votes
1 answer
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Why is ZFC not as susceptible to Gödel's incompleteness as was the Principia Mathematica?

So, from what little I have read (such as this answer), it appears to be that one reason why the program of Logicism, as laid out in the Principia Mathematica, failed was that its goals (of finding a ...
J.M.W Turner's user avatar
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4 answers
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In the construction of the Theory of Types, by what principle is "Socrates is a man is a man" judged nonsense?

While explaining why a function cannot take itself as an argument, I realize that the vicious-circle principle says nothing about why a function cannot take one of its values as argument. The ...
George Chen's user avatar
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6 votes
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What do logicists mean when they try to "reduce mathematics to logic"?

I've read a lot about Russell and other Logicism advocates and their trial to reduce math to logic. But what does that mean? We know that all known mathematics can be reduced to Set theory, is that ...
FNH's user avatar
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5 votes
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What is the “intended project” in Appendix B of Principia Mathematica?

In Linsky's The Evolution of Principia Mathematica it is written, Chapter 6 studies in detail the content of Appendix B, On induction. The appendix consists of a technical proof that even without ...
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