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SheldonEinstein

  • 2 years ago

Can postulates be proved?

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  1. tkhunny
    • 2 years ago
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    Please provide the definition of "a postulate".

  2. lgbasallote
    • 2 years ago
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    it can...but people prefer not to....mathematicians love to do it though....they are somewhat masochistic.....

  3. tkhunny
    • 2 years ago
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    Here's a definition I found. Definition of Postulate Postulate is a true statement, which does not require to be proved. A little odd with the grammar, but it does answer your question.

  4. SheldonEinstein
    • 2 years ago
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    a proposition that requires no proof, being self-evident, or that is for a specific purpose assumed true, and that is used in the proof of other propositions; axiom. @tkhunny http://dictionary.reference.com/browse/postulate

  5. SheldonEinstein
    • 2 years ago
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    @tkhunny your statement says that " postulates does not require to be proved" but can they be proved, is my doubt ...

  6. CliffSedge
    • 2 years ago
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    Modern mathematician usage has 'axiom' and 'postulate' be interchangeable, but their original meanings are quite different.

  7. SheldonEinstein
    • 2 years ago
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    How sir?

  8. tkhunny
    • 2 years ago
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    There is some variation, depending on which author you read. This is why I ask SheldonEinstein to provide a working definition for this discussion.

  9. CliffSedge
    • 2 years ago
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    Axioms cannot be proven because they are "self-evident" or "obviously true" which strict mathematicians and logicians don't like because they don't like to assume that anything is true. They don't allow things like a-priori knowledge or empirical evidence to influence their strictly formal logical sequences.

  10. CliffSedge
    • 2 years ago
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    A 'postulate' is something that one requests to be accepted as true without proof, so that the discussion can move along to prove something of greater consequence.

  11. CliffSedge
    • 2 years ago
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    Postulates are often axioms, but they can also be previously proven theorems that have already been accepted, and are being used as bases for additional proofs.

  12. SheldonEinstein
    • 2 years ago
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    Oh OK got it now!

  13. SheldonEinstein
    • 2 years ago
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    So : either they CAN BE proven or CAN NOT BE?

  14. lgbasallote
    • 2 years ago
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    heh mathematicians love proving imaginary things

  15. lgbasallote
    • 2 years ago
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    i think it's a psychological problem......i don't know.....

  16. tkhunny
    • 2 years ago
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    Definitive and final answer? Maybe. It is possible that some postulates can be "Proven", however, this is absolutely not the point of a postulate. Postulates are to be assumed so that we can observe the implications of the assumption. It would be entirely inappropriate to attempt to DISPROVE a postulate.

  17. CliffSedge
    • 2 years ago
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    As an example, let's say I want to prove the statement, "The base angles of an isosceles triangle are congruent." First, you have to accept the definition of what an isosceles triangle is as a postulate, and also accept the axioms of things being equal to themselves, and that of equals added to or subtracted from equals leaves their sums or differences equal, and so on. A previously proven theorem, such as certain triangles having corresponding congruent elements being congruent can be used as a postulate to further along the proof of the current statement - without having to go back and re-prove the prior theorem.

  18. SheldonEinstein
    • 2 years ago
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    ^Nice example sir, agreed.

  19. SheldonEinstein
    • 2 years ago
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    Thanks a lot guys, I think my doubt is clear now, Thanks @CliffSedge @tkhunny @lgbasallote

  20. CliffSedge
    • 2 years ago
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    @lgbasallote 's notion of 'psychological problem' raises a good point. It depends on what you mean by "prove." This gets into philosophy of epistemology, etc. which shouldn't be allowed to bog down the work of mathematics.

  21. CliffSedge
    • 2 years ago
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    In mathematics / logic / etc. One can "prove" *anything* as long as the postulates are accepted and the logical train of argument stays consistent and valid.

  22. SheldonEinstein
    • 2 years ago
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    Right sir...

  23. CliffSedge
    • 2 years ago
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    If you want "prove" to mean that a proposition necessarily corresponds to objective reality, then you have to take into account sensory perception, fallibility, empirical bases of conjecture, reach of explanation, difficulty to vary an explanation, the process of experimental testing and peer criticism. . . .

  24. CliffSedge
    • 2 years ago
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    Me, though? I'd rather just lay out the rules of the game ahead of time and just play by the rules. As long as everybody stays consistent and all the explanations still work, I'm cool with it.

  25. SheldonEinstein
    • 2 years ago
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    Thanks for your reply sir, I got it now!

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