If for each system there is an element that does not belong to the system but at the same time the system does not exist without that element, then the hope for reductionism is void. There are many other ways to interpret Gödel’s incompleteness theorems, but they all draw same conclusion and what is even more important, they are widely accepted. Why then majority of acclaimed scientists, physicists, evolutionary biologists (but not mathematicians) still believe they will scientifically prove final cause (final cause being at the same time prime cause).
Trouble with Gödel
Richard Dawkins, Dan Dennett and other Neo-Darwinists are perhaps best examples of this “conflict with Gödel” in explaining origins of life as being result of physics and chemistry. They claim that all that exists, including mind, consciousness and other apparently non-material phenomena can be reduced to material cause. Consciousness emerges from matter in brains, neurons, dendrites, chemistry and electricity.
Intelligent design supporters criticize Dawkins and others exactly from this point. There should be an element within material system of physics and chemistry that does not belong to that system and that constitutes that system. They call it God. And since God is then immediately understood as a fairytale creature from Bollywood like Gospels (at least in Western world), such claim is the easily rebuked for the thesis of such God cannot be falsified and can thus according to valid scientific method not be true.
But God is not necessary to fill the gap opened by Gödel. There are but few other ways, but all at the cost of reductionism.
Emergent property production
One way is to make a bridge between emergence that produces non-material phenomena and material substrate. Emergent property production can be called the process in which a complex system produces phenomena that are not part of that system. Saltiness is emergent property of salt. In this case it is quite clear that it only when my perception interacts with salt, saltiness emerges. Measurement produces saltiness. Emergence is a result of measurement in this case. Sounds are produced by mouth, tongue, lungs … but the meaning of sounds (words) is emergent property that does not belong to the system that produced sounds. But could all emergencies be understood as products of measurement?
Consciousness and memes emerged from a brain activity, but are as such not part of a brain structure. If emergence is a result of measurement, interaction of stuff and measurement tool, what interacts with brains so that consciousness emerges? Our own mental activity (and sometimes consciousness)? But then we come nowhere if we say that consciousness measures consciousness for we stumble around the question of how the first consciousness emerged.
This apparent paradox is similar to the one of innovation. Innovation is something that comes from the system but trespass its boundaries. Evolution for example is nothing but one such emergent property (innovation) after another. Each innovation producing an element that does not belong to the previous system but immediately a part of a new system … producing new emergent properties… And it seems that we stumble around same basic question: what is the origin of the first innovation?
Taking Dawkins seriously brings his own theory in dead end. Taking reductionism seriously disapproves reductionism. Such conclusion is in full accordance with Gödel’s incompleteness theorems. We did not solve the question of the origin, but as already explained, origins are much overrated.
Religion of materialistic reductionism
If Dawkins and Dennett are right in explaining evolution as an infinite set of emergent properties, then they are not only wrong with reductionism but also with God. God namely is an emergent property of human evolution. Its memetic presence is ubiquitous. Its memetic existence is as “necessary” for our existence as language or music. God in fact saturates (makes sense of) science and our life regardless the fact that it is not a first cause of everything. That God as memetic entity created universe does not contradict the non-reductivist claim that God or anything else cannot be the first cause in principle. Contrary to what Dawkins fight for from 2000 on, it is his own reductionism that opens options for a God as prime mover. Only if you exit materialistic reductionism you can free yourself from a God as prime mover and relax with memetic existence of God.
This also explains why materialism as a foundation for communism is a religion as much as Christian orthodoxy. Both believe in a kind of prime mover. That they find different prime movers does not differentiate them as religious.