Best Religious/Nonreligious Debate Ever

[_Tarski]

Look at this:



This is an inductive proof for a binomial theorem.

Actually, no it is not. It is merely the binomial theorem itself in the case of the power n+1.
The proof involves quite a few more lines where the proof of the inductive step from n to n+1 would end with the displayed equation or at least its right hand side.

Here is one version:
http://planetmath.org/encyclopedia/Indu ... eorem.html

I would like to add that mathematical induction as used in the proof of the binomial theorem is not the same thing as what is generally called inductive reasoning. It isn't even an instance of the latter.
In fact, mathematical induction is really a form of deductive argument implicitly based on the so called "axiom of induction".

Wiki puts it this way:

Mathematical induction should not be misconstrued as a form of inductive reasoning, which is considered non-rigorous in mathematics (see Problem of induction for more information). In fact, mathematical induction is a form of rigorous deductive reasoning.

I am thinking about some other things mentioned in this thread.
At first blush, I don't see that an argument that is intended to make the conclusion more probable must necessarily have the form of a probabilistic analogue of a deductive argument. I don't think that rational argumentation is exhausted by what that we have formalized --no? I know I have been convinced by arguments that I could never formalize. Sometimes just laying things out in the right way makes things more or less obvious.

It seems relevant to note that while modern probability theory proceeds without any logical problems as essentially a subset of measure theory once the usual axioms are accepted, the very notion of what probability actually means and how at the most fundamental level do probabilistic notions figure into warrant for beliefs is still a philosophical problem with room for disagreement. There are, as most of you know, several approaches to this (I am not happy with letting any one of them dominate to the exclusion the others since no one of them seems sufficient for all purposes).

If we take a subjectivist view on probability, then what would an argument designed to "prove" that something is likely or unlikely amount to when we are faced with anything but an artificially unrealistic toy problem?

[_Bond James Bond]

From the same youtube creator:

ttp://www.youtube.com/watch?v=RB3g6mXLE ... ure=relmfu

[_Bond James Bond]

Also for the global floodists:

Part 1
Part 2

[_Hoops]

steeped in pretentious douchebaggery like this was.

Hilarious!!

[_Tarski]

Stak, Marg etc.
Don't miss the post (above) that I made late last night concerning mathematical induction etc.

[_Some Schmo]

For those that wanted "one or two" things that I found wrong with the The God Delusion, below is a list:

1. Sweeping generalizations of religious groups, conflicts, and culture at large.
2. Same old posivitist argumentation
3. Secular anger
4. Self serving and an absolutely condescending attitude
5. Talking out of place, for example giving out psychological diagnoses on mass groups
6. Complete rambling and senseless words
7. Dawkins lacks even basic theological knowledge. He does not even care to research the context of when religious texts or acts had taken place, displaying a lack of care to do the research.
8. Mischaracterizations of Jesus Christ's life, again a flawed understanding of history which he could gain greater understanding by taken a few theology courses. This exposes his ignorance (not as bad as Some Schmos)
9. The work starts as radical atheist diatribe reflecting much cultural and religious bigotry which he attempts to cover up, in a weak fashion, the same way a racist would by downplaying.
10. His use of probability arguments is the same type of argumentation he often criticizes in lectures when he speaks against creationism.
11. Can he actually be serious when he discusses the origin of religion?
12. by the way, where the hell are his sources? How did he even get through grad school, this makes me question his writing immediately, much like any person who spent descent time in academia should
13. Along with 12, Dawkins fails to take Jefferson's and Einstein's views as a whole and instead disregards easy access to history and chooses to throw them on his side of the fence.
14. Along with 12 and 13, it appears that Dawkins has no interest in displaying the truth but rather winning an argument which he fails to do when he applies his logic mid way through his book.

There really is so much wrong with this book, but likely SomeSchmo and his Dawfags will continue to buy his drivel and spout it off much like seminary scripture and Dawkins will not face extinction. Dawkins has raised a semi-sizable religion and that's the credit he deserves.

Wow, I forgot all about your propensity to put on full display how much of a moron you are.

This list mostly consists of "I don't like Dawkins 'cause he's a big meany and doesn't understand me! Wah! Wah!" Not a single thing in here that actually rebuts any of his arguments. Oh, the shock of it all!

...

Thanks for resurrecting this thread, Tarski. Nice trip down memory lane. I forgot what a rebel atheist Stak is.

[_MrStakhanovite]

Actually, no it is not.

Noted, and corrected, thank you.

I would like to add that mathematical induction as used in the proof of the binomial theorem is not the same thing as what is generally called inductive reasoning. It isn't even an instance of the latter.

In fact, mathematical induction is really a form of deductive argument implicitly based on the so called "axiom of induction".

I would argue otherwise, the presence of an axiom doesn’t turn the reasoning into deduction, since you are still making statements about an infinite set of numbers from an example.

I think there is hesitance from Math types to call that “Induction” because there is significant baggage with that word, and they don’t want people thinking that someday we are going to discover some even number that isn’t divisible by 2.

What makes mathematical induction so strong, is that anything that can be systematically defined, can be described by mathematics, which is a luxury the Natural sciences don’t have.

At first blush, I don't see that an argument that is intended to make the conclusion more probable must necessarily have the form of a probabilistic analogue of a deductive argument.

I don’t understand, if I want to assert that X is more probable than Y, don’t I need to show why and at least attempt to quantify that?

I don't think that rational argumentation is exhausted by what that we have formalized --no?

If you are going to write a book that calls billions of people deluded because they have a differing metaphysical belief, your arguments better be crap hot, and a formalized validity is just the start of that. Hence, my criticism of Dawkins.

[_Tarski]

I think there is hesitance from Math types to call that “Induction” because there is significant baggage with that word, and they don’t want people thinking that someday we are going to discover some even number that isn’t divisible by 2..

I still don't think you have got this right. First, it is a relatively simple matter the set up an argument by mathematical induction in the form of a deductive argument by simply including the axiom of induction explicitly.

It is also not a matter of drawing conclusions about an infinite set of things from a number of examples.

The axiom of induction is nothing like saying that if a large number of cases C1, C2,.....,C100 are true then CN is true for all N. Far from being self evident, this is just silly of course. This is not the axiom of induction.

But let us look at the axiom of induction and compare with induction in the sense of inductive reasoning.

Suppose that I have a set of objects hidden from view and I uncover and check a large number of them and it turns out that each one of them has property X. I will have been applying inductive reasoning if I conclude that it is likely that they are all have property X. This could be overturned at any point. This is not math induction.

Now suppose I don't check any of them but the first one and it has property X. But now suppose that I can actually prove deductively that whenever one of them has property X, then the next one will also. Then all of them have the property (obviously).

Such things are hard to apply to anything but abstract objects but just for the spirit of it, suppose I know rock number one is red and I also know that consecutive rocks must be the same color. Then it follows that all the rocks are red. That this conclusion is obvious is just the "moral content" of the axiom of induction. It is a formalization of this bit of obviousness.

This is a far cry from merely seeing that the first 100 rocks are red and then concluding that all 1000 (or all infinite number of them) must be red.

Induction in science and everyday reasoning is more like the latter (the reason we wouldn't actually draw the conclusion suggested in this toy example, is simply that we already have a lot of experience with rocks and they aren't all red). It would be different if all rocks in history were so far found to be red. In that case we might reason that they are all red but we would be conscious that this was not a logically necessary conclusion.

Consider the conclusion that all rocks obey Newton's laws of motion (now this is more like real scientific inductive reasoning). No one has checked all rocks. However, if, counterfactually, we knew that we could order and label all rocks by the natural numbers and if we knew that the first rock obeyed F=ma, and if we knew that consecutively numbered rocks either both obeyed F=ma or both did not then we could deduce that Newtons law is obeyed by all rocks. This kind of thing can't be done for rocks obviously but we still draw inductive conclusions about rock (in the other sense).

But it (mathematical induction) can be done for analytically defined abstracta in mathematics. There is even a transfinite version of induction which is also an entirely deductive procedure once the set theoretic axioms are set out. The results follow deductively from those axioms and the hypotheses specific to the theorem being proved.

Inductive reasoning in science is just not a proof of anything in the mathematical sense. On the other hand, mathematical "induction" used to prove the binomial theorem is a full fledged proof.

Another example: There are formulas that will give the first 100 or so primes but then fail. If we just checked the formula on those first 100, inductive reasoning might lead us to conclude that all primes were given by the formula. However, if a formula for primes could be found that succumbed to an inductive proof like the binomial theorem then all doubt would be removed.

Maybe you would find this guy more convincing:
http://www.earlham.edu/~peters/courses/ ... th-ind.htm

[_MrStakhanovite]

Tarski, I have to run to class, but before I go:

I still don't think you have got this right. First, it is a relatively simple matter the set up an argument by mathematical induction in the form of a deductive argument by simply including the axiom of induction explicitly.

I'm thinking of Peano's 5th axiom here...how does this eliminate more information in the conclusion (the conclusion about an infinite set) than what is contained in the premises?

[_Tarski]

Tarski, I have to run to class, but before I go:

I still don't think you have got this right. First, it is a relatively simple matter the set up an argument by mathematical induction in the form of a deductive argument by simply including the axiom of induction explicitly.

I'm thinking of Peano's 5th axiom here...how does this eliminate more information in the conclusion (the conclusion about an infinite set) than what is contained in the premises?

They are not always numbered the same way so you must specify. Are you talking about the axiom of induction?

If a set S of numbers contains zero and also the successor of every number in S, then every number is in S.