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When does a formal system cease to be able to be complete and consistent?

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#incompleteness #formal-systems
43
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Help interpreting a logical formula

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#logic #formal-systems
152
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Proof of *2.38 in Principia Mathematica (Russell/Whitehead)

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#logic #propositional-calculus #foundations #formal-systems
112
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Are there in mathematics some non-logical axioms which are not obviously true but we accept them as true?

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#axioms #formal-systems
96
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What motivated people like Euclid to create such a general axiomatic systems like the one in the book Elements so early in history?

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#euclidean-geometry #math-history #axioms #formal-systems #axiomatic-geometry
68
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How weak can a formal system be that codifies most formal systems?

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#logic #formal-systems
73
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Is there a point at which you can no longer formally define something in math?

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#meta-math #formal-systems
77
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Question about MU puzzle from GEB

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#logic #propositional-calculus #formal-languages #formal-systems
110
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Are Real Numbers a Formal System?

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#real-numbers #axioms #meta-math #formal-systems
79
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Does a formal system that proves everything that is provable exists?

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#logic #computability #formal-systems
146
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Is linear algebra a formal system?

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#linear-algebra #formal-systems
34
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Is the semantics of a first order logic system defined as part of the first order logic system?

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#computer-science #first-order-logic #formal-systems
300
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Defining functions in second-order arithmetic

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#logic #formal-systems #higher-order-logic
223
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equality – just a relation between *two* objects?

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#logic #philosophy #foundations #formal-systems
145
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Can Left Conjunction Elimination Get Proven in M in Less Than 30 lines?

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#logic #propositional-calculus #formal-languages #axioms #formal-systems

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