Rise of atheism: 100,000 Brits seek 'de-baptism'

[Sqrl]

appolose said:

Sqrl said:

appolose said:

I do not know if I have eyes; I could be a brain floating in a vat recieving electrical stimuli, for all I know, or even less.  But, I do agree with the idea of the existence of sensory data; whatever "this" is, it can't be nothing (what else could I be referring to?).  It's what we do with it that I have issue with (making statements about other parts of reality, or proposing other parts of reality). 

 

 

So you have a problem with anything proved using mathematical induction, or its basic concept at least, as a basis?

No; math is (I think) a system of definition and logic (on the other hand, what was Russell trying to prove?).

 

The concept is used outside of math as well, but math is the best way to explain it:

The basic premise of mathematical induction is that if you prove, or in this case accept, the base case as true you don't have to prove every case.  Instead of trying to prove every related case you simply prove that, in general terms, the next case is also true. 

A good example is helpful, but math is the best way to express it:

Problem: Prove that the sum of the first 'n' odd numbers is equal to n squared.

Let S(n) = the sum of the first n odd numbers greater than 0.

We need to show that S(n) = 1 + 3 + … + (2n – 1) = n² 
 
Base Case (n = 1):  S(1) = 1 = 1²

         The result holds for n = 1.
 
Induction Hypothesis:  Assume that S(k.) = k²
 
We must show that S(k+1) = (k + 1)²
 
S(k+1)  = 1 + 3 + … + (2k - 1) + (2(k + 1) - 1)

           = S(k.) + 2(k + 1) - 1      (by definition of S(n))

           = k2 + 2(k + 1) - 1      (by the induction hypothesis)
           = k2 + 2k + 1
           = (k + 1)(k + 1)      (factoring)
           = (k + 1)²
 
Therefore, we can conclude that since S(1) = 1 and that S(k.) logical implies S(k+1) then S(n) is
equal to the sum of the first n odd numbers for all n > 0.

The idea is that you can prove an infinite number of cases by proving a basic case and then proving a generalized case.  I think you can do something similar in the example I quoted as well.  Once you have decided to accept sensory data, even if reluctantly, it logically follows (logic being a result of our experience with our sensory input) that you can expound on this.  Even to the point of proposing other parts of reality.