The Laws of Mathematics are Unchangeable

A quick opening: as long a new symbol or concept is added to "math", we have a change in the laws in terms of the addition of new laws. That is, the moment a new branch of mathematics is developed or an old branch is modified, the laws change. For example, let us examine the United States' Constitution. Every time an amendment is added, the Constitution changes. Therefore, the Constitution is not unchangeable. Therefore, Con should immediately win this debate. As you will see further on in my case, math is dynamic and constantly changing. I will take the resolution as: "Resolved: The laws of mathematics are unchangeable" Definitions: Mathematics - accepted (with the note that applied math is mathematics - physics for example is applied math) Unchangeable - not changing or to be changed . http://www.merriam-webster.com... Change - to make different in some particular . http://www.merriam-webster.com... Laws of Mathematics - basic principles upon which mathematics is founded (my own definition, I hope it is rigorous) Basically, I will prove that the laws of mathematics have been changed (ergo, are changeable) and can still be changed (again). First, we must look at our definition of unchangeable. For something to be unchangeable, it must not be altered or able to be altered (not to be changed). The laws of mathematics are always changing. The history of mathematics shows us that concepts are always changing. To list a few areas where the laws have changed: 1) Zero; introduction of, use of 2) Calculus; introduction of, definition of, specifics of 3) Limits; definition of 4) Infinity; rules defining 5) Space; Euclidean and Non-Euclidean I will touch on infinity in this round. Contention One: Infinity is an example of changing mathematical laws Sources -. http://www.mathacademy.com... Infinity began as a concept of the unending. Aristotle laid down basic ideas of infinity. He stated that actual infinities could never exist, which we now know to be false, infinities do exist within mathematics. Here we have one example of a change in mathematical laws (the resolution now goes Con). Nevertheless, I will continue. When Newton and Leibnitz developed calculus, the need for infinity became apparent. They dropped the issue, believing it to be impossible, but the laws of calculus depend on infinity. Side Note: The development of calculus, and its laws, gives an example of how the laws of mathematics are changeable. Calculus added laws to math, therefore a change. Back to infinity. Georg Cantor finally laid down some laws defining infinity, which is called Cantor's Set Theory. My source provides a good explanation of this, so I will not explain it here. Thanks to Cantor's work, we have defined several aspects of infinity. Infinite sets can have parts removed from them without getting any smaller. Another important result of his work is the proof that infinities can be larger than each other. They are denoted by the Hebrew letter Aleph, with Aleph-null being the smallest infinity, Aleph-one being larger, Aleph-two larger etc. Here we see a drastic change in the laws of mathematics. Previously, the concept of infinity was completely undefined and thought to be nonexistent. With the advent of Georg Cantor, the Laws of Mathematics had to be modified to fit these new findings. My opponent's argument: "My argument is that as long as the symbols and functions of math do not have their meanings changes, the laws of mathematics are unchangeable, no matter what you try to prove. " -What mongeese is saying is that as long as symbols and functions are not redefined, the laws of math do not change. Here are a few points to think about. Math is constantly evolving, with new fields emerging and old fields being redefined. There is still much work to be done concerning infinity, and even more in other fields. -Also, mongeese's argument is inherently flawed. It assumes that math is unchanging and concrete. Math is not like this, however. It is by definition constantly changing. Like a set of laws that a country lays down, what may be permissible at one moment may not be allowed the next. This whole argument is based on a false assumption. -Here's an interesting thing to note, the phrase "no matter what you try to prove". What if I were to prove something radical, like "2x2 is not equal to 4" (coincidentally this can be proved in a system that is not ten-based. In ternary, for example, the correct notation is 2x2=11)? If I prove something which is not included in the laws of mathematics, they change to accept this new fact. When it was proved that there are more real numbers than rationals, the laws of mathematics changed to accompany this. When infinities were accepted as existent, math modified. And a final note. Technically, everything which I have proved above can be considered false. In pure mathematics, statements like 2x2=5 can be proved to be true. The only reason we accept that 2x2=4 is true is because we have assumed the basic properties of math. Math, truly, has no foundation. It is based on assumption at its most basic level. To explore this more: . http://en.wikipedia.org.... On the most basic level, all that is necessary for a mathematical change is a change in assumption. I think mongeese was trying to block this, but saying that you cannot change symbols and functions is not allowing math to be math. Quite simply, math changes, the laws change, and the resolution is negated.