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When does '1 + 1 = 2' become false?

  1. Sep 22, 2014 #1
    when does a truth like '1 + 1 = 2' become false?

    I ask because how can truth be eternal when the universe is finite
  2. jcsd
  3. Sep 22, 2014 #2
    A "truth" in mathematics is never false. A statement which is true given a certain interpretation of the symbols used may be false under a different interpretation. In order for "1+1=2" to be considered false, you would need to interpret one or more of the symbols 1,2,+, and = to mean something different than is standard.

    Questions/comments like these aren't really appropriate for this forum.
  4. Sep 22, 2014 #3
    Thanks for the reply but its too bad you cant answer my underlying question

    I know mathematics is abstract but I guess we cant talk about it too much since this is a physics forum

    Anyways never mind thanks
    Last edited: Sep 22, 2014
  5. Sep 22, 2014 #4
    Philosophy - even philosophy of mathematics - is basically off-limits on this subforum. They sometimes allow discussions like this to continue on the general discussion forum, but I reckon it'd need to be firmly rooted in "real" philosophy of math. I'm not a student of philosophy, but I'm guessing your questions don't fit the bill.
    Last edited: Sep 22, 2014
  6. Sep 23, 2014 #5


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    You can see this in terms of model theory. You can look for an interpretation/possible world where this sentence is mapped into the truth value false.
    1+1=2 lives in a syntactic world where truth does not apply. You need to map this into
    a semantic world where concepts like truth and validity apply. This is precisely what model theory is about. Look up
    model theory, interpretation , follow the links and get back to us with follow-ups.
  7. Sep 23, 2014 #6


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    As has already been said, it becomes false once you change the interpretation of the symbols. At the moment, we're adding two equivalent quantities of size 1 and finding that the result is one equivalent quantity of size 2.

    If I instead chose to equate water droplets however, then when I add 2 water droplets, I get 1 water droplet. 1+1=1 in this instance. Of course this is useless however. In the usual system of maths we wouldn't equate the water droplet entity as being 1 quantity but rather the mass or volume of the water droplets.
    Last edited: Sep 23, 2014
  8. Sep 23, 2014 #7

    Simon Bridge

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    ... another example:
    1 cup of popcorn added 1 cup of water does not get you 2-cups of soggy popcorn
    but 1lb of water added to 1lb of popcorn does get you 2lbs of soggy popcorn.
    ... oh look: mapped the statement onto different syntactical whatsits ;)
  9. Sep 23, 2014 #8


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    If you drop the water droplet fast enough it might fracture into many water droplets! In which case 1+1=14 might be possible.
  10. Sep 23, 2014 #9
    On the computer I use, it internally interprets 1 + 1 = 1, and then again at another time it might interpret it as 1+1 = 0.
  11. Sep 23, 2014 #10


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    O.K, my answer was unnecessarily formal, and it was unclear. Basically, an expression like 1+1=2 has no intrinsic meaning; it is just a string of symbols together with "connectives" and rules for acceptable strings in your system (wffs) . This formula acquires meaning when you describe what each of the symbols means and what each connective does.
    Other posters gave good examples of this; of how different meanings assigned to the symbols and connective give rise to different ways of interpreting the string. The formalities of this process of assigning meaning are treated in Model Theory. Hope I was more clear this time.
  12. Sep 23, 2014 #11


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    If you mix 1 volume of hydrogen and 1 volume of oxygen, ignite them and let them cool down to the initial temperature, you will either get a 1.5 volume of gases (1+1=1.5), or half a volume of gas and some liquid (something like 1+1=0.5008).
  13. Sep 23, 2014 #12


    Staff: Mentor

    In the spirit in which I believe the question was asked, in which the symbols 1, 2, +, and = have their usual meanings - the answer is never. The equation above is true, period.
    Likewise, the equation 1 + 1 = 3 is false, always.
    These questions have nothing to do with what you asked before. In a sense, you're comparing apples and oranges, with eternal referring to time, and finite referring to size. In any case, as far as the mathematics is concerned, they are irrelevant.
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