Instigator / Pro

2+2=4: Change my Mind


The debate is finished. The distribution of the voting points and the winner are presented below.

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After 11 votes and with 22 points ahead, the winner is...

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Contender / Con

It is my position that when the number "2", as used in standard american math, is added with another "2", you get the number "4". No semantics allowed. These numbers are used in American math, primarily school. I will waive, first round, con will waive last. Failure is loss of argument and conduct point.

Round 1
2+2=4 in every school system in America.  This is my position.  Con tries to change my mind.  No semantics.  I waive.
Well in sex-ed if you take 2 in relationship with people you get 1 child. So 2 people plus another 2 people equals 2 kids.

Mic drop
Round 2
Notice I said "math," not "health."  If we were talking about reproduction, then that would be true.  But we are not.  We are talking about public school math.  I also said the number "2," not 2 people.  I used the "+" and "=" as in math.  If I were talking about health, I wouldn't have used math terms.  This is also a semantic argument.  I made clear that it was math and felt everyone knew I was talking about math.  I applaud the effort by con tho XD
You want math, I got you dawg

There is a field named abstract algebra (wiki) which defines and allows you to create pretty much any mathematical context you wish.E.g. let’s create a thing, called group where 2+2=4, WILL NOT hold, but 2+2=2, actually WILL be true. The definition of group states (wiki) that in order for algebraic structure to be called a group we have to do the following:
  • Define a set of elements (which may or may not be finite). We define a set of 2 elements 2,2,4
  • Define a single operation. Let’s define a single operation ‘plus’ which we will denote as ++ for simplicity (Although, we can use any sign we wish, e.g. $$ or ∗∗ if you think it suites you)
  • Make sure our group satisfy some group axioms. We will first list and explain then and then define our elements accordingly. The axioms are the following:
    • Closure. The result of operation between any 2 elements of the group should still be part of the group. (In our case it means that regardless of what you do with 4 and 2 and in what order the result should always be either 4 or 2)
    • Associativity. For any 𝑎,𝑏,𝑐a,b,c the following should hold true: 𝑎+(𝑏+𝑐)a+(b+c) =(𝑎+𝑏)+𝑐(a+b)+c where ()() shows which operation should take precedence
    • Identity elements. There should be a unique element (let’s call it ‘𝑒e’) which is part of the group and for any element 𝑎a (including 𝑒e. Any means naturally ANY element of group) the following equation should hold true 𝑒+𝑎=𝑎+𝑒=𝑎.e+a=a+e=a.
    • Inverse elements. For any element 𝑏b from group there exists and element 𝑎a from group, such that following equation holds true 𝑎+𝑏=𝑏+𝑎=𝑒a+b=b+a=e (where e is and identity element)Not we have to suffice this 4 axioms in order for set of elements {2,4} and operation + to be called a group.
Let’s define our identity element as 2. And then list all of possible equations in this group. They are the following:
  • 4+4=2. Why? Because any element in group should have an inverse element. What is an inverse element for 4? Well. it’s 4. Nobody have stated that the inverse element can not be the same element!
  • 2+4=4. Because 2 in an identity element. This also defines 4 at inverse element for 2. So now 4 is inverse element for itself AND for 2. (Again nobody have stated that the same element can not be inverse element for more then one element)
  • 4+2=4. Because 2 in an identity element.
  • 2+2=2. Finally. We are here! Why is this correct? The short answer is because we said so.
The long answer is because we can prove, that the group defined in such a way suffice all axioms for groups. And we can prove it!
  • Closure axiom is trivial. We can clearly see that there is no other element apart from 2 and 4 which is produced by all 4 possible combinations of 2 and 4 and + operation between them
  • Associativity maybe harder to prove. One of the ways is to check whatever ALL possible equations such as 𝑎+(𝑏+𝑐)=(𝑎+𝑏)+𝑐.a+(b+c)=(a+b)+c.Hold true.In our case it's rather easy, because we only have 2 elements in group, thus only 8 possible equations.
  • Our Identity element is 2 and the equation defined in axiom holds true (2 + 4 = 4 + 2 = 2)
  • Each element has an inverse element. Inverse element is 4 for element 4. Inverse element for 2 is also 4.
As you can clearly see, abstract mathematics is not about ‘logic’. It’s more about defining whatever you want however you want and then proving (this is the most important part) that your definitions suffice axioms of algebraic structure you are trying to create.
So... back to question. Is 2 plus 2 always 4? The correct answer is: It depends. Depends on what algebraic structure we are dealing with. What are the elements of this structure and what exactly does ‘plus’ mean.

REAL Mic Drop
Round 3
I was never talking about this weird math concept.  This is semantics, which is against the rules.  In the public school system, 2+2=4.  They teach basic math skills for later classes like algebra, calculus, and almost any math program.  Abstract algebra is not taught and not a standard in public schools.  Nice try, but you lose.  Good debate.  You waive last round, per the rules.
waive, though evidence for connection of abstract math and real algebra tough in schools are in comments