Questions tagged [principia-mathematica]
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11 questions
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Does Russell’s notion of typical ambiguity involve equivocation?
Does Russell’s notion of typical ambiguity involve equivocation?
I ask because Solomon Feferman notes the following: “The first place that the issue of ambiguity comes up is on pg. 251 or pg.174. For ...
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Are properties and sets of the same type in Russell’s theory of types?
Are properties and sets of the same type in Russell’s theory of types?
I ask because of the following, if properties and sets were of different types then the following would hold: For all properties ...
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Can you hold the axiom of unrestricted comprehension under Russell's theory of types? [closed]
Can you hold the axiom of unrestricted comprehension under Russell's theory of types?
I ask because of the following: Assume Russell’s theory of types. Then consider the following: For all X if X is a ...
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What do the symbols 1, 2, 3, 4, … mean in Russell’s theory of types?
What do the symbols 1, 2, 3, 4, … mean in Russell’s theory of types? I ask because of the following. Consider the symbol 1. It can signify the object 1 of type zero. It can signify the set with only ...
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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,...
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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 ...
user46399
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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 ...
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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 ...
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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 ...
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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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