Assumptions and axioms [closed]

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By Godel, if mathematics is consistent it must be incomplete. Given that mathematics is essentially believed to be a tautology it must be incomplete.



Can we assume mathematics itself as an axiom? What are the limits on scaling up axioms? Do they have to be bare bones axioms or can we take something as large as mathematics as an entire axiom?



Thanks.




logic soft-question axioms




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closed as unclear what you're asking by Carl Mummert, Simply Beautiful Art, Xander Henderson, amWhy, Leucippus Aug 7 at 1:09


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.










  • 10




    Uh, what???????
    – Asaf Karagila♦
    Aug 6 at 19:04






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    I guess in your question there is a huge confusion about crucial notions of logic and in particular about Gödel's incompleteness theorem. I suggest to start reading Wikipedia's page on incompleteness theorem, then reading Nagel's and Newman's Godel's proof.
    – Taroccoesbrocco
    Aug 6 at 19:11















up vote
-5
down vote

favorite












By Godel, if mathematics is consistent it must be incomplete. Given that mathematics is essentially believed to be a tautology it must be incomplete.



Can we assume mathematics itself as an axiom? What are the limits on scaling up axioms? Do they have to be bare bones axioms or can we take something as large as mathematics as an entire axiom?



Thanks.




logic soft-question axioms




share|cite|improve this question











closed as unclear what you're asking by Carl Mummert, Simply Beautiful Art, Xander Henderson, amWhy, Leucippus Aug 7 at 1:09


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.










  • 10




    Uh, what???????
    – Asaf Karagila♦
    Aug 6 at 19:04






  • 1




    I guess in your question there is a huge confusion about crucial notions of logic and in particular about Gödel's incompleteness theorem. I suggest to start reading Wikipedia's page on incompleteness theorem, then reading Nagel's and Newman's Godel's proof.
    – Taroccoesbrocco
    Aug 6 at 19:11













up vote
-5
down vote

favorite









up vote
-5
down vote

favorite











By Godel, if mathematics is consistent it must be incomplete. Given that mathematics is essentially believed to be a tautology it must be incomplete.



Can we assume mathematics itself as an axiom? What are the limits on scaling up axioms? Do they have to be bare bones axioms or can we take something as large as mathematics as an entire axiom?



Thanks.




logic soft-question axioms




share|cite|improve this question











By Godel, if mathematics is consistent it must be incomplete. Given that mathematics is essentially believed to be a tautology it must be incomplete.



Can we assume mathematics itself as an axiom? What are the limits on scaling up axioms? Do they have to be bare bones axioms or can we take something as large as mathematics as an entire axiom?



Thanks.





logic soft-question axioms





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Aug 6 at 19:02









George Thomas

51416




51416




closed as unclear what you're asking by Carl Mummert, Simply Beautiful Art, Xander Henderson, amWhy, Leucippus Aug 7 at 1:09


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.






closed as unclear what you're asking by Carl Mummert, Simply Beautiful Art, Xander Henderson, amWhy, Leucippus Aug 7 at 1:09


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.









  • 10




    Uh, what???????
    – Asaf Karagila♦
    Aug 6 at 19:04






  • 1




    I guess in your question there is a huge confusion about crucial notions of logic and in particular about Gödel's incompleteness theorem. I suggest to start reading Wikipedia's page on incompleteness theorem, then reading Nagel's and Newman's Godel's proof.
    – Taroccoesbrocco
    Aug 6 at 19:11













  • 10




    Uh, what???????
    – Asaf Karagila♦
    Aug 6 at 19:04






  • 1




    I guess in your question there is a huge confusion about crucial notions of logic and in particular about Gödel's incompleteness theorem. I suggest to start reading Wikipedia's page on incompleteness theorem, then reading Nagel's and Newman's Godel's proof.
    – Taroccoesbrocco
    Aug 6 at 19:11








10




10




Uh, what???????
– Asaf Karagila♦
Aug 6 at 19:04




Uh, what???????
– Asaf Karagila♦
Aug 6 at 19:04




1




1




I guess in your question there is a huge confusion about crucial notions of logic and in particular about Gödel's incompleteness theorem. I suggest to start reading Wikipedia's page on incompleteness theorem, then reading Nagel's and Newman's Godel's proof.
– Taroccoesbrocco
Aug 6 at 19:11





I guess in your question there is a huge confusion about crucial notions of logic and in particular about Gödel's incompleteness theorem. I suggest to start reading Wikipedia's page on incompleteness theorem, then reading Nagel's and Newman's Godel's proof.
– Taroccoesbrocco
Aug 6 at 19:11











1 Answer
1






active

oldest

votes

















up vote
1
down vote



accepted










Mathematics is not generally believed to be a tautology. There are some who regard any given mathematical theorem as being "true by definition" but this is not the same as saying mathematics itself is a tautology, whatever that might mean. On another note something has to be a statement before it can or cannot be a tautology and "mathematics" does not qualify as a statement.






share|cite|improve this answer





















  • excellent answer thank you!
    – George Thomas
    Aug 6 at 19:11

















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote



accepted










Mathematics is not generally believed to be a tautology. There are some who regard any given mathematical theorem as being "true by definition" but this is not the same as saying mathematics itself is a tautology, whatever that might mean. On another note something has to be a statement before it can or cannot be a tautology and "mathematics" does not qualify as a statement.






share|cite|improve this answer





















  • excellent answer thank you!
    – George Thomas
    Aug 6 at 19:11














up vote
1
down vote



accepted










Mathematics is not generally believed to be a tautology. There are some who regard any given mathematical theorem as being "true by definition" but this is not the same as saying mathematics itself is a tautology, whatever that might mean. On another note something has to be a statement before it can or cannot be a tautology and "mathematics" does not qualify as a statement.






share|cite|improve this answer





















  • excellent answer thank you!
    – George Thomas
    Aug 6 at 19:11












up vote
1
down vote



accepted







up vote
1
down vote



accepted






Mathematics is not generally believed to be a tautology. There are some who regard any given mathematical theorem as being "true by definition" but this is not the same as saying mathematics itself is a tautology, whatever that might mean. On another note something has to be a statement before it can or cannot be a tautology and "mathematics" does not qualify as a statement.






share|cite|improve this answer













Mathematics is not generally believed to be a tautology. There are some who regard any given mathematical theorem as being "true by definition" but this is not the same as saying mathematics itself is a tautology, whatever that might mean. On another note something has to be a statement before it can or cannot be a tautology and "mathematics" does not qualify as a statement.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Aug 6 at 19:10









Daron

4,3581923




4,3581923











  • excellent answer thank you!
    – George Thomas
    Aug 6 at 19:11
















  • excellent answer thank you!
    – George Thomas
    Aug 6 at 19:11















excellent answer thank you!
– George Thomas
Aug 6 at 19:11




excellent answer thank you!
– George Thomas
Aug 6 at 19:11


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