The Instigator
Pro (for)
The Contender
Con (against)

The square of any even integer is always even

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Debate Round Forfeited
ConservativePolitico has forfeited round #3.
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Voting Style: Open Point System: 7 Point
Started: 12/20/2016 Category: Miscellaneous
Updated: 2 years ago Status: Debating Period
Viewed: 1,023 times Debate No: 98294
Debate Rounds (3)
Comments (7)
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I will most likely not use sources because the arguments that I will most likely use do not require sources, for this reason unless both me and my opponent use sources do not give the mark for the most reliable sources to either of us.


The square- The product of an integer multiplied by itself
An even integer- A number that when divided by 2 produces an integer

My opening argument:
An even integer can be represented as 2x where x is an integer
(2x)^2 = 4x^2
(4x^2)/2 = 2x^2
2x^2 is an integer because any integer multiplied by itself produces an integer and 2 multiplied by any integer is always an integer.



I would like to start off by saying a couple of things about the nature of debate and the nature of truisms. What my opponent has put forth to debate is something that most in the rational world today consider to be a mathematical law. Such a thing is considered to be undeniably true beyond any doubt and can thus be trusted to hold as such during any type of discussion. Laws are the basis of our rational way of thinking. We must hold things to be undeniably true in order to build upon said foundation to understand the world around us.

The definition of debate is as follows:
a formal discussion on a particular topic in a public meeting or legislative assembly, in which opposing arguments are put forward

Note the final part of the sentence. If something is undeniably true, there cannot be opposing arguments, at least no valid ones. Then why bring up such a thing as a topic for debate?

What my opponent has inexplicably done, either in hopes of an easy victory or some other mundane motivation, in opening this topic for debate is just that... he has opened it. What was once considered something to be undeniably true has now been called into question, willingly so.

My opponent and I ask you, dear reader to open your minds while reading this debate and consider the possibility that my opponent has put out that this statement could in fact not be true. And I will explain why.

The Nature of Always

always: at all times; on all occasions

My opponent has stated that at all times and in all occasions the square of any even integer is always even. While that sounds fine and dandy to our ears today I wish to put forth that my opponent has taken a very narrow view and has perhaps overlooked this very important word: always.

By its very definition always means that no matter what, from now until the end of time, in all occasions this thing is true. Yet my opponent has no way of a) judging the full extent of possible time and the full future of the universe and b) cannot know all occasions this universe could face during this potentially infinite timespan. Therefore, my opponent has assumed that what we experience today and know to be true in our limited experience (~10,000 years) must be and will always be true. Forever. That is an extremely bold assumption for anyone to make, no matter what sort of rational foundation they think they might be standing on.

Possible Disqualifiers

Next I would like to lay out, in conjunction with the assumption that my opponent has made regarding the word always, some possibilities that could disqualify his law to be always true.

1. Eradication of All Sentience

Imagine for a moment an event that eradicates all sentient life in the whole universe, forever. For example, the heat death of the universe. With no sentience left in the universe we would be left with mere matter and no energy. This universe is devoid of life, devoid of light, devoid of motion. It is simply matter sitting in a void. Is the statement put forth still true? With no one to perceive it, think about it or believe it can it be true? In this universe there is no language, no math, no higher thinking, no concepts beyond what exists because there is nothing to bring those things into being through thought. The idea of an integer would not exist because there is nothing to conceptualise it into being. With no rational actors to conceptualise non-physical ideas do such things exist? I would argue no.

Just as there are no pink flying dragons that live on the surface of the sun because no being has created them and made them so. Without sentience I argue there cannot be non-physical conceptions. They cannot be created and with nothing to remember or reconceptualize a past creation for all intents and purposes they do not exist. Without the ideas of numbers, integers and squaring this statement cannot be true because it is simply gibberish in the heat dead universe.

2. The Complete Destruction of the Universe

Take the previous idea one step further. Instead of the heat death of the universe the universe ceases to exist all together. Still a possibility in the time span of infinity. Perhaps the Big Crunch happens and everything collapses back into a spec and disappears in reverse of what it did when we suddenly appeared 14 billion years ago. Again, these are possibilities in the timeframe of always. Now there is nothing. Nothing exists. It is complete and utter emptiness. Is this still true? I would again argue no. With nothing in existence there is nothing even to begin to build a foundation for the idea of numbers on. In fact, we have come up with these laws and ideas through observation of our universe. With nothing to observe there can be no observations and following conclusions about them. What is a mathematical law but an observation of the universe repeated to the point where we agree it will always be so if the observation is repeated forever? But with nothing to observe we cannot make such a claim.

With nothing to count, nothing to do the counting, nothing to conceptualize numerical categories for objects that you have counted then there is no law and thus it is no longer true.


While my opponent's statement is true NOW in this moment and the moments leading up to this one since humans came up with the idea of integers there is no guarantee that such a thing will stay true ad infinitum due to a whole host of unknown circumstances that could happen in the course of eternity. If my opponents argument was that "The square of any even integer is even if done right now" it would have been unarguable. However, my opponent put this topic up for debate knowing there must be some sort of argument against it and I have presented it.

There are more situations which could render this statement untrue in the future, again hinging on that powerful word of always, that I will withold for future rounds.

Debate Round No. 1


The Nature of Laws
In his post my opponent said on multiple occasions that the components of maths; numbers/integers and squaring are merely Ideas which in a universe without sentience to perceive them would become "gibberish". That is the main downfall of his rebuttal because mathematics is not merely a construct of our imagination, it is a universal law that is constant throughout the entirety of time and space inside of this universe. For that reason it is arbitrary whether I know how long the universe will exist or not. By definition Mathematical laws will exist whether they are perceived or not because laws are principles that must be obeyed at all times. Also, the fact that you said if there was no sentience then it would become gibberish, to me it begs the question, gibberish to what exactly?

I would have written more however I am short on time.



My opponent seems to have missed the points of my arguments in which I stated that there could be extraneous circumstances that could happen to the universe that could change what we today perceive as "laws". Here merely repeated his point in that the statement is always true without any real backup of such a statement.

He did nothing to refute my points about the changing nature of the universe, which I will elaborate on shortly.

1. The Universe Has Changed In the Past and Could Change In the Future

The universe started out as a tiny hot ball in which, we believe, everything in existence was contained inside of it in a singularity. Singularities are points of extreme gravity and microscopic proportions and the laws of gravity, general relativity and quantum mechanics break down when exposed to a phenomenon like a singularity [1].

What this tells us is that the universe once existed in a state where things that we today consider law did not apply. Therefore, perhaps at this time this law of square integers also did not apply. The universe changed from a point, evolved, expanded and became the universe we see today but we still cannot, and my opponent has not fulfilled his burden of proof, in proving that this law of square integers is and has been and will ALWAYS be true.

2. Speed of Light

We used to believe that the speed of light was a universal constant sort of like your law of squares. It is a pillar of modern physics and thought to have been true always. However, now it seems as though it has come to light that the speed of light could be variable and subject to change by changing conditions of the universe [2]. Just because we think things to be constants because in our limited history of viewing them they haven't changed yet this is not always the case.


My opponent did nothing to effectively refute my previous arguments and points and merely claimed that his statement is a law. A simple repetition of his opening argument and main assertion. I have laid out multiple ways that this law is not always necessarily true ALWAYS and cannot be proven as such which is a main point for his starting assertion. He has the burden of proof to show that this statement is always true on all occasions which he has not done. There are many occasions we have discovered in which rational laws and ways of thinking simply don't work when exposed to extreme forces of galactic nature and we could be subjected to universe-wide conditions such as these in the future and have had some instances (black holes, singularities, Big Bang) in our universe's past, present and future which have bent the laws of reason and science into things that don't work with our conventional way of thinking.

Therefore, my points stand and the square of any even integer is not necessarily ALWAYS even.

Thank you.

[1] Zebrowski, Ernest (2000). A History of the Circle: Mathematical Reasoning and the Physical Universe. Piscataway NJ: Rutgers University Press. p. 180.

Debate Round No. 2


I withdraw my case because I do not know that an event will happen that changes the laws of physics and causes the total number of objects in 2 groups of 2 objects to not equal four.
This round has not been posted yet.
Debate Round No. 3
7 comments have been posted on this debate. Showing 1 through 7 records.
Posted by Into_The_Jaws_Of_Hell 2 years ago
I must admit that this was not at all the sort of debate that I expected, when I said always I meant it to mean with every even number not with every even number on every occasion. However I will roll with it and stick up for my case.
Posted by Smithereens 2 years ago
Patterns in the universe tend to exist when humans aren't there to assign words to them, but y'know. I see you're trying to deny an easy win which is great imo :)
Posted by ConservativePolitico 2 years ago
Never ye fear. Everything is debatable in my opinion.
Posted by Capitalistslave 2 years ago
This isn't a debatable topic, it's mathematical fact. It's like debating what 2+2 equals.
Posted by PowerPikachu21 2 years ago
Oh. I did cube. Still a truism, though.
Posted by PowerPikachu21 2 years ago
2x2x2= 8
4x4x4= 64
6x6x6= 216
8x8x8= 512
10x10x10= 1,000

Any more even integers are double, triple, etc. of these problems.
Even x Even = Even, Even x Odd = Even.
Posted by sboss18 2 years ago
This is a truism, not a debatable topic.
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