Point: Presuppositional Apologetics as taught by Cornelius Van Til, Greg Bahnsen and John Frame states that Christianity as a worldview is the precondition for human experience and therefore should be for the Christian one of the least negotiable presuppositions to be reconsidered. In the same way, from the illustration of the world of Mathematics, one would also be of skeptical rather than give in, to disproof of Mathematics or alleged proofs that 0=2, etc., because they are essential in interpreting the world intelligibly.
Picture 1: Supposed that someone who do not believe in mathematics comes up to you with the following “proof”against Mathematics. His “disproof” of math is derived from the “proof” that 2=0:
“Proof” that 1 + 1 = 1
a = 1
b = 1
a = b
a2 = b2
a2 – b2 = 0
(a-b)(a+b) = 0
(a-b)(a+b)/(a-b) = 0/(a-b)
1(a+b) = 0
(a+b) = 0
1 + 1 = 0
2 = 0
Question for the listener: Even if you cannot find what is wrong with the argument, would you still say it is warranted to still hold that Mathematics is valid and that 2 does not equal 0?
Follow up Answer: Even if one is unable to demonstrate the specifics of which step in the proof has gone wrong, one is still warranted to believe that 2 does not equal 0. The premise that 2 not equaling 0 is foundational for human experience such as commerce, shopping, banking, etc. Imagine a world where you owe 0 dollars to the bank, only to have them send a letter that you owe them two dollars since 0=2! Or if 1+1=0, you put a dollar in with the dollar that’s already in your bank account and your bank statement then reads 0! In the same way, even if one does not have the skill or unable at the moment to identify what is wrong with the alleged disproof, one is still warranted to believe 2 does not equal 0, or that Christianity is still true, given that they are the foundation for the intelligibility and meaningfulness of various human experiences.
Picture 2: The following is another alleged “disproof” of math, with the argument that 1=2. This is from a math website, and click on the link of which step you believe is where the mistake has occured!
- Step 1: Let a=b.
- Step 2: Then
, - Step 3:
, - Step 4:
, - Step 5:
, - Step 6: and
. - Step 7: This can be written as
, - Step 8: and cancelling the
from both sides gives 1=2.
Question 1 for the listener: Even before a careful analysis of the proof given, what leads one to be prejudicial against the conclusion 1=2, and thereby lead one to evaluate the form and premises in the following proof?
Follow up Answer: Because 1 not equaling 2 is important for everyday human experiences (see the above). In the same way, Christians also has a similar prejudice towards arguments against Christianity.
Question 2 for the listener : Is the prejudice against the conclusion 1=2 warranted to lead one to suspect something wrong with the proof given?
Follow up Answer: Yes, due to the fact that 1 not equaling 2 is important foundation for the intelligibility and meaningfulness of human experiences. Likewise, since the Christian worldview is the precondition for human experiences (morality, epistemology, etc), any prejudice towards argument against Christianity is similarly warranted.
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I know your post is not about where the proof went wrong but I just feel so tempted to point it out.
Picture 1:
Step 5: Dividing by zero is undefined. (a-b) =(1-1) =0
So (a-b)(a+b)/(a-b) = 0/(a-b)
(0)(a+b)/0 = 0/0
0/0 =0/0
undefined= undefined
Dividing by zero are special cases.
Yay, math still works.
My point exactly! I just assumed that people would figure it out eventually
Good point though. If before analyzing the picture, I already know that the proof is wrong because I don’t believe the conclusion of the proof that 2=0. So, is the proof an valid argument with false premises? Or is it an invalid argument with false premises?
I think the form of the argument is invalid.
Picture 2: Same mistake as Picture 1
So, can there be valid arguments, with faulty premises, against Christianity?
Yes there can be a form of an argument thats logically valid but false premises
Sorry, Completely beyond me and I’m left wondering what Evangelistic value it has. Maybe an explanation for idiots like myself.
Hey Mike,
I’ve used this analogy at time when I’m evangelizing at the Universities or Community Colleges to illustrate the point why it’s not altogether irrational that I do no suspend by Christian worldview even as I critique objections to the Gospel. I’ve never had the situation nor felt the need to use this math puzzle to illustrate my point outside of the confines of campus ministries. It’s only been engaging it seems to some who are students. I do have people in the past say they got the point of what I was trying to say. How are you doing Mike?
Hi Jim,
Yes I see that. I couldn’t see myself using it but then I’m a bit dim.
Not been blogging much of late but I am trying to prepare a couple of posts and trying to get a local Church Evangelistic magazine off the ground.
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