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Unfortunately, this write-up is a load of irresponsible crap, because it can be proven that it can't be proven that two plus two equals five. This is a load of

• batista 14y ago
  >because it can be proven that it can't be proven that two plus two equals five Really? What does that even mean? In what number system it can it be proven? Does it hold for all? >This is a load of ivory-tower hogwash, precisely why people get turned away from math and philosophy. If people get "turned away from math and philosophy" then it's the peoples' problem, not math and philosophy's problem.
• chris_wot 14y ago
  Can you supply us the proof that it can't be proven that two plus two equals five? Even a citation would be fine. Thanks!
  • debacle 14y ago
    The Math 101 'proof': Assume it can be proven that 2 + 2 = 5. Then 2 + 2 = 5. It can be proven that 2 + 2 = 4. The closure axiom of addition states that the expression 2 + 2 is a unique number. 4 != 5. Therefore it can't be proven that 2 + 2 = 5. ----- I'm sure it can't be that simple, but logically I can't see a reason why not.
    • sklipo 14y ago
      You haven't proven that it can't be proven that 2 + 2 = 5. All you have proven is that if 2 + 2 = 5, then mathematics are inconsistent. Which they could be; you can't just assume math and logic are consistent.
      • debacle 14y ago
        > you can't just assume math and logic are consistent. What a bunch of bollocks.
        • javert 14y ago
          Precisely my point. Wow, that guy really stepped in it. Claiming that logic isn't valid is worse than a logical contradiction, because if logic isn't valid, you can't claim anything.
          • chris_wot 14y ago
            Nobody ever said logic isn't valid. We're talking about consistency.
            • javert 14y ago
              If logic isn't consistent, then logic isn't valid. I'm not assuming specialized definitions of "consistency" and "validity" here, just your normal everyday layman's usage.
              • chris_wot 14y ago
                Well, you were responding to someone who was using the correct formal terms. You, after all, don't dispute the second theorem - but given it uses the term "consistent" you can hardly complain when someone makes their argument using the same terminology as the theorem you agree with! Interested in what you define "consistent" and "valid" as in laymans terms though.
                • deleted 14y ago
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                • javert 14y ago
                  I'd rather continue the other thread of discussion we have going, than this one. Anyway, you can look up "consistent" and "valid" in any dictionary to find out what I mean.
  • javert 14y ago
    Take two objects. Take two more objects. How many do you have? Four. Could you ever have five? No. Thus, two plus two does equal four, and it does not equal five. Can you ever prove something to be true, that is not true? No; your proof would simply be incorrect. By definition of "proof" and "truth." Thus, it can't be proven that two plus two equals five. I would like to hear your response to this. I don't understand how mathematicians can justify referencing some kind of mathematical formalism and just skipping reality altogether, and then not mentioning that they had done so. To be clear, I am not contesting Godel's Second Incompleteness Theorem; I'm criticizing the writeup posted here, which uses everyday language to blatantly contradict what is obvious in reality.
    • chris_wot 14y ago
      For someone who said that someone who pointed out that you can't assume math and logic are consistent "really stepped in it", you have a funny way of proving you don't contest Godel's second incompleteness theorem, which is: For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.
      • javert 14y ago
        A formalism (layman's definition of "formalism") need not include a statement of its own consistency in order to be valid (including, in order to be consistent). For example, I know that basic addition and subtraction are valid by observing individual concrete objects in reality, rather than because of some kind of formalism stating that. I am not very familiar with the kind of "math and philosophy" that went into Godel's theorems, but what I'm saying is that either (a) actual math and logic as such (as opposed to something made up, like a false math where 2 + 2 can equal 5) are ruled out by the giant disclaimer that takes up most of the 2nd theorem (i.e., they are not "formally effectively generated theories..."), or (b) they are, but simply "do not include a statement of their own consistency."
        • chris_wot 14y ago