All human beings belong to a same race.
Voting Style:  Open  Point System:  7 Point  
Started:  11/1/2012  Category:  Science  
Updated:  5 years ago  Status:  Post Voting Period  
Viewed:  2,976 times  Debate No:  26817 
== Structure of Debate == R1 is for acceptence. In R2 I will present a proof that all human beings belong to same race under certain assumptions. (The assumptions are listed below). In R2, my opponent must explain the flaw in my arguments. If my opponent is successful in doing so, I will concede the debate in R3. Alternatively I will explain the flaw in R3. Con does not have to do anything in R3. Please note that the resolution is not true (Under my assumptions). Voters will vote Pro if Con is not able to spot the mistake in my arguments in R2. In either case, the flaw will be obvious by the end of debate. == Assumptions == We assume that there is a well defined set of possible races. We also assume that there exists a well defined method to assign a race to each human being. It doesn't matter how the method breaks the tie, as long as the method is deterministic. A perticular human being will be allowed to be part of a single race. In simple terms, my opponent will not be able to point out persons who may belong to no race or more than one races. We will assume that we are allowed to use some genetic feature to break the tie and assign a unique race to everyone. == Disclaimer == 1. This debate has nothing to do with racism. The resolution could have been  'All mobile phones belong to same brand'. This would have caused no significant change in my arguments. 2. Personally I recognise that races exists. The world would be boring if we were all alike. Our races should not matter in our daily life  except as an identity. However my opinions are irrelevant to this debate. The Holy Quran  49:13 O mankind! We created you from a single (pair) of a male and a female, and made you into nations and tribes, that ye may know each other (not that ye may despise (each other). Verily the most honoured of you in the sight of Allah is (he who is) the most righteous of you. And Allah has full knowledge and is well acquainted (with all things).
Thank you for your debate challenge. I am looking forward to your next post. 

Let us use proof by mathematical induction. == Inductive Hypothesis == P(n) ≡ In any set of n human beings, each of the member belong to a common race. Proving P(n) for arbitrary n, would be sufficient to affirm the resolution. == Base Case == P(1) is true. This is trivially true as there is only one person in any such set. The person can only belong to one race. == Inductive Assumption == Let us assume P(K) is true == Inductive Increment == If P(K) is true, then P(K+1) must be true. Proof: Consider a set ‘X’ of human beings of size K+1, as shown in figure. Also consider two members of set – ‘a’ and ‘b’. Let us define set A = X – {a}. Size of A is K since it is formed by removing one element from a set of size K+1. As per our inductive assumption (P(K) is true), all members of set A must share a common race. Without any loss in generality we can assume that this race is ‘p’. This means all members of set ‘X’, except ‘a’, belong to the race ‘p’. Let us define set B = X – {b}. As in case of ‘A’, size of ‘B’ is also K. Thus all members of this set too must share a common race. However all members of ‘B’, apart from ‘a’, belong to the race ‘p’. This means that ‘a’ too must belong to race ‘p’. The natural observation is that all the members of set ‘X’ now belong to race ‘p’. Thus all the members of set ‘X’ share a common race. The preceding analysis can be applied to any set of size K+1. This means all sets of human beings of size K+1 share a common race under inductive assumption. This proves P(K+1) under inductive assumption and confirms the inductive increment. == Inductive Argument == We have already established that if P(k) is true, then P(k+1) must be true. We also know that P(1) is true. This means that P(2) must be true. But if P(2) is true, then P(3) is true. That makes P(4) true. Usual inductive argument establishes that P(n) is true for any arbitrary natural number n. This completes the proof and affirms the resolution.
Hello. Thanks for this fun debate. The size of A and B is K, which means they have the same number of elements as K, but it doesn't follow that all the elements of A and B belong to p. They have K1 units of p and one extra unit that could belong to any race. So you haven't proven that P(K+1) is true if P(K) is true. 

== Flaw == The proof of inductive increment breaks down for K=1 (or K+1=2). When the size of set is 2, there are only two elements in the set. The situation looks as shown in the following figure. The arguments is correct for K>=2. An alternative way to look at the proof is that the base case should have been K=2 rather than K=1. It is does not appear feasible to prove P(2), breaking down this approach as well. (By common observation, P(2) is false) == Opponent’s response == After looking at the flaw, it should be apparent that my esteemed opponent has failed to spot the problem in my argument. She has made a blatant assertion that my ‘argument does not follow’ without any explanation. In fact, she has failed to demonstrate that she even understands my arguments. == Conclusion == This proof a modified version of the ‘All horses are of same color’ proof presented by Polya[1]. Should be an easy win for me. VOTE PRO.
Thank you for your comments. I've read it all through again and I still think my reasoning is sound. Granted, I did not use the same proof as you and I have used general rather than formal language. It's true, as you claim, that I may not have understood anything you say (certainly, I don't understand what you mean by "blatant assertion". It sounds like a criticism, but how can an assertion be too obvious and at the same time wrong?), but in that case wouldn't it have been more courteous to explain the flaws in my argument? 
baggins  rross  Tied  

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Total points awarded:  5  0 
baggins  rross  Tied  

Agreed with before the debate:      0 points  
Agreed with after the debate:      0 points  
Who had better conduct:      1 point  
Had better spelling and grammar:      1 point  
Made more convincing arguments:      3 points  
Used the most reliable sources:      2 points  
Total points awarded:  5  1 
baggins  rross  Tied  

Agreed with before the debate:      0 points  
Agreed with after the debate:      0 points  
Who had better conduct:      1 point  
Had better spelling and grammar:      1 point  
Made more convincing arguments:      3 points  
Used the most reliable sources:      2 points  
Total points awarded:  3  1 
However, Con did not see the hole in the modal argument so he effectively bit the bullet.
I will grant Con conduct for maintaining his dignity. I laughed after reading his closing remarks. Quite clever:
"It's true, as you claim, that I may not have understood anything you say (certainly, I don't understand what you mean by "blatant assertion". It sounds like a criticism, but how can an assertion be too obvious and at the same time wrong?), but in that case wouldn't it have been more courteous to explain the flaws in my argument?"
So if all humans are of then same origin then there would not be any biological differences.
If they are all of the same origin then this debate would not be happening. Since this debate is happening it is proof that they are not of the same race.
Besides anyone who has looked at even the basic biological differences in the races would agree that they are all different.
Like a horse is to a donkey or zebra.