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How do I find out effectively what particular formal system I'm using in any particular moment when doing math in school?

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#formal-systems
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What is the reason we usually don't use formal proofs in mathematics?

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#formal-proofs #formal-systems
33
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Could formal systems be viewed as a short version of saying what I believe in without necessary listing all theorems which flow from that system?

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#formal-systems
67
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Are theorems (not axioms) listed as a part of a formal system?

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#formal-systems
29
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How to imagine a process of generating theorems from a formal system in a computer?

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#computer-science #formal-systems
175
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Contradictory vacuous truths in consistent formal system

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#logic #formal-systems
138
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Gödel's Second Theorem and the Consistency of Robinson's System

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#incompleteness #meta-math #formal-systems
265
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What is some easy illustrative example of an non-recursive formal system and recursive formal system?

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#recursion #formal-systems
922
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Is there any easy example of a formal proof in mathematics and an equivalent informal proof to illustrate a difference between those two?

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#proof-writing #soft-question #formal-proofs #formal-systems
403
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If $T$ proves any incorrect $\forall$-rudimentary sentence, then $T$ is inconsistent

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#logic #first-order-logic #incompleteness #formal-systems
1.1k
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Precisely, what is a primitive recursive definition?

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#logic #recursion #formal-systems
183
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How do definitions work in Martin-Lof type theory?

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#foundations #type-theory #formal-systems
72
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Are there any formal theories that are not axiomatic?

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#axioms #formal-systems
528
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What are the differences between a collation and a rule of formation?

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#definition #formal-languages #formal-systems
115
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What do "completely described" and "complete formalisation" mean?

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#logic #foundations #formal-systems

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