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On Chickens, Eggs and Proof by Naive Paradox

April 21, 2012

This is inspired in part by what I affectionately know as Dawkins‘ Super-Dooper-Upside-Down-Jumbo-Jet-From-Hell argument, as he believes he expounds in chapter 4 of the God Delusion.

Consider birds.
All birds are born from eggs.
All eggs are laid by birds.
Which came first?
Either produces a contradiction.
Thus birds and eggs cannot exist.  QED.
(And, of course, those eggs you see stacked in Sainsbury’s near the chicken in the meat counter are just pure delusion… they can’t logically exist after all.)

Now look at Dawkins’ summary of his Jumbo Jet argument.

There is a challenge in explaining where everything came from.
The natural temptation is to attribute this to powers beyond our understanding.
This is false due to the ‘who designed the designer problem’.
The most ingenious mechanism (aka crane) discovered so far is Darwinian selection.
We don’t yet have such a ‘crane’ for physics.
We should not give up hope.

Now to an aside, results famous in the foundations of Mathematics known as Godel’s undecidability theorems.  The basics can be summarised as:

Consider the statement: ‘This statement has no proof’
If it has a proof, it contradicts itself, hence inconsistency.
If not, it has no proof.
Thus the possibility of proving all true statements is incompatible with consistency.

(Consistency is the notion that a system, in this case arithmetic, will not prove absurdities such as 1+1=3.)

If the argument above takes only four lines, why does Godel take many pages to spell it out?  To keep things brief what I shall say is that one must carefully lay foundations such that one cannot escape the argument through clever interpretation of its meaning.  (For example, having a logic that denies the possibility of such statements as ‘this statement has no proof’ may provide a way around.)

Now lets look at Dawkins’ six points in turn.

1. There is a challenge in explaining where everything came from.

True, and much can be made of taking on this challenge.  But for those who do, out of choice or necessity, other things in life such as provide food and shelter, there is a need for something to believe in in the absence of an answer to that challenge.  This is very much as true today as it was two millennia ago.  Science hasn’t, and probably can’t provide all the answers, so we still need faith in something, and religions exist to satisfy this need, amongst other things.

2. The natural temptation is to attribute this to powers beyond our understanding.

And the millions of pages of closely worded argument that makes up the current scientific literature is beyond the understanding of most scientists.  Thus we still need to attribute reality to things beyond our understanding even if we follow the Science-is-all line in a Dawkinsish way, so rejecting explanations such as some kind of unknown and ununderstood divine origin, or even just Genesis 1, still doesn’t get us to the answers to these philosophical questions that some of us seek.

3. This is false due to the ‘who designed the designer problem’.

This is where Dawkins needs to follow Godels lead by spending a great deal of time producing incontestible arguments that mean that this isn’t just another naive chicken-and-egg paradox to which there must be a solution that we don’t know about yet (chickens exist, so the chicken and egg paradox can’t prove they don’t, it only shows the lack of foundations of such an argument.)

4. The most ingenious mechanism (aka crane) discovered so far is Darwinian selection.

And so far we know that this ‘crane’ can explain much of how nature, at present, changes.  It can suggest a coherent framework for understanding nature’s distant past.  But it cannot of itself rule out alternatives.  I like to point out the big difference between ‘it’s 99% due to Darwinian selection’ and ‘it’s totally due to Darwinian selection’: current scientific understanding makes the former likely, but is nowhere near proving the latter.  For practical reasons most scientists must assume, and take on faith, that our origins are totally due to Darwinian selection, but this is an unproven, untested, untestable assumption.  We can’t do more than show that it’s a plausible explanation based on what we currently know and what we can currently test experimentally.

5. We don’t yet have such a ‘crane’ for physics.

And the who-designed-the-designer paradox can easily be turned around so that, even if we find such a crane, we can then ask what was the crane that was used to make it.  Such paradoxes are easy to come out with.

6. We should not give up hope.

 Maybe, but there are other things that need sorting out in the current world like the environment and the economy.  For now we need some kind of faith.  I choose a rather eclectic source of spiritual inspiration spanning Taoism, Buddhism and to a certain extend ideas from Hinduism and Yoga, but ultimately grounded in a humanistic Christian belief system that has its roots in my childhood and best fits my experience of life.
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