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Non-Logical Logic

  1. Mar 16, 2004 #1
    Logic is a great concept, having proven data support ideas. Can't there be a "logical logic"? Yes, because [our] "logic" is "logical" itself. 1=1. That's logical, because we say that 1 is existing, and then we say it equals one. Which is true, so its logical!

    Now what about nonlogical logic? Such as saying " 1 = 3". Before, I said "1=1". We call that logical because we have "1" as "1" in our minds....which is where I've come up with this. Can't we all be wrong, and have "1 thing" actually be "3 things"? It's nonlogical to our understanding of logic, but it is still logical because we can not prove that our language is correct.

    Err..right? Is there other examples of "nonlogical logic"? [Edit] Chaos? (just trying to spark some ideas)

    1=3. It's wrong by our mathematical system, but that doesn't mean its not logical, does it?
    Last edited: Mar 16, 2004
  2. jcsd
  3. Mar 18, 2004 #2
    Logic is just one aspect of our minds, just one particular way of thinking among many. You can't think logically in most situations of your life, because in reality you're never sure what you're dealing with. There are many cases when what you think is "1" also appears to be "3" and logic will take you nowhere.
  4. Mar 18, 2004 #3
    Kanzure, I think the problem lies in the definition of "logic" that you seem to be working from. There is nothing "illogical" about 1=3, it is perfectly logical, it just doesn't necessarily make sense. Common sense does not equal "logic".
  5. Mar 19, 2004 #4
    1=3 is not logical. Hold one rock in one hand and three rocks in the other. Count them.

    First hand : "tet" (arbitrary counting sound)
    Second hand: "tet" "tet" "tet"

    Nope. Not the same.

    When people think about making statements such as "1=3", they think about it linguistically. But you can't just think about it linguistically. 1 and 3 are symbols for actual things ("this many" and "that many").
  6. Mar 23, 2004 #5
    1+1 = 10, 10+1 = 11, 11+1 = 100

    hows this for logic?
  7. Mar 25, 2004 #6
    There's nothing illogical about 1+1=10, or 1+1=3, or 1+1=sausage. The point of logic is that all different ways of writing the same thing must be perfectly equivalent. Thus 2=1+1=5-3=8/4=...

    10=1+1=101-11=1000/100... perfectly logical.
  8. Mar 25, 2004 #7
    I believe that logic has to follow a certain structure or semantic structure of events and thus 'logic' becomes the 'logical'. When you try to put something in illogical format, it no longer follows the notion of logical form. It has to be played at a significant role in theories of meaning for natural languages. That's logic.
  9. Mar 25, 2004 #8
    All I want to say is: Crap.

    I learnt a new thing today everybody!

    Now I can argue with my friends. >=)
  10. Mar 26, 2004 #9
    We cannot be correct in saying that 1=3 unless we change the rules by which we make our statement (which we can't). Logic is based around rules and any statement which breaks the rules is logical, but it is simply a false staement.
    Last edited: Mar 26, 2004
  11. Mar 26, 2004 #10


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    Saying that '1 = 3' is to say a false statement. The truth value of that statement is 'false'. We can judge it using logic, because we know what '1' represents and what '3' represents and what '=' represents. Using logic, we can make a judgement about that statement, that it is false. The statement itself isn't logic, but what we use to judge it is.
  12. Mar 26, 2004 #11
    Verigo: Yes, that is the best way to put it. I agree, but isn't a "logical statement" a statement which can be evaluated via logic? I know the statement itself is not logic, but it could be described as a "logical statement" becuase we use logic to evaluate it. Maybe this is a matter of opinion.
  13. Mar 27, 2004 #12


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    darkmage, we can evaluate anything using logic. I would say that a statement is logical if we can logically evaluate it to be true. If it is unspecific, or lacking in information, I wouldn't call it logical.

    We wouldn't normally talk of logical statements, but rather logical arguments, where we go from some initial premises and, though the use of logic, come to some conclusion. If the logic used in formulating that argument was correct, I would call the argument logical.
  14. Mar 28, 2004 #13
    1+1 = 10, 10+1 = 11, 11+1 = 100 is binary. :)
  15. Apr 2, 2004 #14


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    I think you have effectively shown that you must specify both the language and the number system you are operating with, then we can evaluate your statement. If, in order to be considered true, it must defy logic, then it is illogical. It is also untrue. If it is true in accordance with logic, then it is logical.
  16. Apr 6, 2004 #15


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    Sure, 1=3 is logical if there is no definition of what these numbers represent. Numbers are just a shortcut. Without further explanation, they are an abstract concept, not a concrete amount. 1 coin = 3 coins (1 quarter = 2 dimes + 1 nickel). 1 rock = 3 rocks (1 30-kg rock = 3 10-kg rocks).
  17. Apr 7, 2004 #16
    in the old DOS days there were commands a=c or c=b which were logical. without parameters any equation is logical. once we establish the subject and ground rules, an otherwise logical statement maybe false and illogical.

    olde drunk
  18. Apr 7, 2004 #17
    It depends on what the definiton of "1" is. "1" could represent 5 things in one case to make 1+1=10.
    "1 thing" is made up of millions of counterparts (i.e. atoms etc.) so by saying "1 thing", your are referring to millions of counterparts which make up this "one thing". Therefore, 1 may = billions .
    But I don't understand how your aforementioned examples (quoted from Gara) could be logical by our concept of logic.
  19. May 29, 2004 #18
    Words only have demonstrable meaning according to their function in a given context. In other words, you can have nonlogic logic if you so choose, but if you want it to have any meaning to anyone else you must demonstrate it's meaning in a specific context.
  20. Jun 24, 2004 #19
    Just to chip in,In every illogical,impossible solution,will have a logical interior that is hidden within a question's process.Whether inter-affecting or related to the subject,or a piece of the question that isnt shown.Btw nice picture gara XD XD
  21. Jun 24, 2004 #20
    From the start there is clearly a confusion based on the use of the word logical for rational. All this about 1 rock + 1 rock = 2 rocks is rock logic. There are very defined boundaries. A sheep is or is not a sheep. It can't be sort of a sheep.
    How about lateral thinking and WATER LOGIC?
    If removal of tonsils is a tonsilectomy and removal of an appendix is an appendectomy, what do you call removal of a growth from your head?
    There is also a view of logic in which it is generalized with a bayesian probability viewpoint by Professor Edwin Jaynes in PROBABILITY: THE LOGIC OF SCIENCE. In this view, deductive logic follows from probabiloity rules and involves statements with a probability of 1 while inductive logic involves the same rules but probabilities between 0 and 1.

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