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 5 orthography edit approved Dec 28 '13 at 0:58 RegDwight 12155 bronze badges Mathematics is not based on assumptions. Most of commonly used mathematics is yes, but not as a whole. If you look at the whole mathematical subject you find that every possible set of assumption is explored, which amounts to no assumption. Mathematics is not narrowed down to one set of axioms that everyone follows, people are infact exploring almost every conceivable axiomatic system and deduction rules possible. What has been observed, however, is that many of these systems are not interesting or provide no fruitful structures, and that alota lot of the mathematics we need or are interested in is possible to do with some small common set of assumptions. To prove the point that we dontdon't use any assumtions -, try to write down a deterministic system of any kind - unless. Unless you have just disproved the Church-Turing thesis -, your system is already describable by our mathematical system, and probably isomorphic to some already discovered model. How would that be possible that we can model and describe any system you make on any assumptions at all, if our system is based on narrow assumptions and believes? Mathematics is not based on assumptions. Most of commonly used mathematics is yes, but not as a whole. If you look at the whole mathematical subject you find that every possible set of assumption is explored, which amounts to no assumption. Mathematics is not narrowed down to one set of axioms that everyone follows, people are infact exploring almost every conceivable axiomatic system and deduction rules possible. What has been observed, however, is that many of these systems are not interesting or provide no fruitful structures, and that alot of the mathematics we need or are interested in is possible to do with some small common set of assumptions. To prove the point that we dont use any assumtions - try to write down a deterministic system of any kind - unless you have just disproved the Church-Turing thesis - your system is already describable by our mathematical system, and probably isomorphic to some already discovered model. How would that be possible that we can model and describe any system you make on any assumptions at all, if our system is based on narrow assumptions and believes? Mathematics is not based on assumptions. Most of commonly used mathematics is yes, but not as a whole. If you look at the whole mathematical subject you find that every possible set of assumption is explored, which amounts to no assumption. Mathematics is not narrowed down to one set of axioms that everyone follows, people are infact exploring almost every conceivable axiomatic system and deduction rules possible. What has been observed, however, is that many of these systems are not interesting or provide no fruitful structures, and that a lot of the mathematics we need or are interested in is possible to do with some small common set of assumptions. To prove the point that we don't use any assumtions, try to write down a deterministic system of any kind. Unless you have just disproved the Church-Turing thesis, your system is already describable by our mathematical system, and probably isomorphic to some already discovered model. How would that be possible that we can model and describe any system you make on any assumptions at all, if our system is based on narrow assumptions and believes? 4 deleted 43 characters in body edited Dec 10 '11 at 17:55 TROLLHUNTER 13155 bronze badges Let me offer a different point of view: MathematicsMathematics is not based on assumptions. Most of commonly used mathematics is yes, but not as a whole. If you look at the whole mathematical subject you find that every possible set of assumption is explored, which amounts to no assumption. Mathematics is not narrowed down to one set of axioms that everyone follows, people are infact exploring almost every conceivable axiomatic system and deduction rules possible. What has been observed, however, is that many of these systems are not interesting or provide no fruitful structures, and that alot of the mathematics we need or are interested in is possible to do with some small common set of assumptions. To prove the point that we dont use any assumtions - try to write down a deterministic system of any kind - unless you have just disproved the Church-Turing thesis - your system is already describable by our mathematical system, and probably isomorphic to some already discovered model. How would that be possible that we can model and describe any system you make on any assumptions at all, if our system is based on narrow assumptions and believes? Let me offer a different point of view: Mathematics is not based on assumptions. Most of commonly used mathematics is yes, but not as a whole. If you look at the whole mathematical subject you find that every possible set of assumption is explored, which amounts to no assumption. Mathematics is not narrowed down to one set of axioms that everyone follows, people are infact exploring almost every conceivable axiomatic system and deduction rules possible. What has been observed, however, is that many of these systems are not interesting or provide no fruitful structures, and that alot of the mathematics we need or are interested in is possible to do with some small common set of assumptions. To prove the point that we dont use any assumtions - try to write down a deterministic system of any kind - unless you have just disproved the Church-Turing thesis - your system is already describable by our mathematical system, and probably isomorphic to some already discovered model. How would that be possible that we can model and describe any system you make on any assumptions at all, if our system is based on narrow assumptions and believes? Mathematics is not based on assumptions. Most of commonly used mathematics is yes, but not as a whole. If you look at the whole mathematical subject you find that every possible set of assumption is explored, which amounts to no assumption. Mathematics is not narrowed down to one set of axioms that everyone follows, people are infact exploring almost every conceivable axiomatic system and deduction rules possible. What has been observed, however, is that many of these systems are not interesting or provide no fruitful structures, and that alot of the mathematics we need or are interested in is possible to do with some small common set of assumptions. To prove the point that we dont use any assumtions - try to write down a deterministic system of any kind - unless you have just disproved the Church-Turing thesis - your system is already describable by our mathematical system, and probably isomorphic to some already discovered model. How would that be possible that we can model and describe any system you make on any assumptions at all, if our system is based on narrow assumptions and believes? 3 added 9 characters in body edited Dec 10 '11 at 16:36 TROLLHUNTER 13155 bronze badges Let me offer a different point of view: Mathematics is not based on assumptions. Most of commonly used mathematics is yes, but not as a whole. If you look at the whole mathematical subject you find that every possible set of assumption is explored, which amounts to no assumption. Mathematics is not narrowed down to one set of axioms that everyone follows, people are infact exploring almost every conceivable axiomatic system and deduction rules possible. What has been observed, however, is that many of these systems are not interesting or provide no fruitful structures, and that alot of the mathematics we need or are interested in is possible to do with some small common set of assumptions. To prove the point that we dont use any assumtions - try to write down a deterministic system of any kind - unless you have just disproved the Church-Turing thesis - your system is already describable by our mathematical system, and probably isomorphic to some already discovered model. How would that be possible that we can model and describe any system you make on any assumptions at all, if our system is based on narrow assumptions and believes? Let me offer a different point of view: Mathematics is not based on assumptions. Most of commonly used mathematics is yes, but not as a whole. If you look at the whole mathematical subject you find that every possible set of assumption is explored, which amounts to no assumption. Mathematics is not narrowed down to one set of axioms that everyone follows, people are infact exploring almost every conceivable axiomatic system and deduction rules. What has been observed, however, is that many of these systems are not interesting or provide no fruitful structures, and that alot of the mathematics we need or are interested in is possible to do with some small common set of assumptions. To prove the point that we dont use any assumtions - try to write down a deterministic system of any kind - unless you have just disproved the Church-Turing thesis - your system is already describable by our mathematical system, and probably isomorphic to some already discovered model. How would that be possible that we can model and describe any system you make on any assumptions at all, if our system is based on narrow assumptions and believes? Let me offer a different point of view: Mathematics is not based on assumptions. Most of commonly used mathematics is yes, but not as a whole. If you look at the whole mathematical subject you find that every possible set of assumption is explored, which amounts to no assumption. Mathematics is not narrowed down to one set of axioms that everyone follows, people are infact exploring almost every conceivable axiomatic system and deduction rules possible. What has been observed, however, is that many of these systems are not interesting or provide no fruitful structures, and that alot of the mathematics we need or are interested in is possible to do with some small common set of assumptions. To prove the point that we dont use any assumtions - try to write down a deterministic system of any kind - unless you have just disproved the Church-Turing thesis - your system is already describable by our mathematical system, and probably isomorphic to some already discovered model. How would that be possible that we can model and describe any system you make on any assumptions at all, if our system is based on narrow assumptions and believes? 2 added 36 characters in body edited Dec 10 '11 at 16:25 TROLLHUNTER 13155 bronze badges 1 answered Dec 10 '11 at 16:15 TROLLHUNTER 13155 bronze badges