Let’s reconceive proof in terms of what we now know about human beliefs systems, justification, and the progress of the human knowledge enterprise. Coherentists maintain that we can and should work to achieve a high degree of coherence within our belief structures. What that means is that the propositions we believe should be logically consistent, they must be probabilistically consistent, the system is improved in virtue of having more and stronger inferential connections between beliefs, it is less coherent in proportion to how many unrelated, and unconnected subsystems of beliefs there are, the system is less coherent by to the extent it has unexplained anomalies, and the system, above all, must be responsive to the evidence provided by experience.
It’s naïve and antique to think that a proof for a belief is a contained, modular entity, as if once we have a finished proof in hand, a person can stop gathering more justification and stop incorporating new information into their view of the world. Beliefs are not modular, autonomous entities. We only have them and they only become justified in virtue of being embedded in a larger framework that guides us with regard to principles of evidence, rules of inquiry, and standards of justification. Proof for a proposition that gives us perfect, deductive certainty and final justification is a myth from a simpler age. We do not simply accrete new pieces of knowledge that are then finished and laid down for the next layer. Euclid could prove propositions in geometry in the naïve sense until we discovered non-Euclidean geometries. Newton could prove the force of an accelerating object until quantum indeterminacy. Paley could prove the existence of God until Darwin’s natural selection.
What happens inside the head of a reasonable person should mimic the growth of science. As we leave childish beliefs and the over-simplified world of our youth, we incorporate more and more of the new experiences.
We do our best to catch up to the 21st century, which is considerably harder and more complicated than mastering the worldview of a 11th century goat farmer. We have to build and rebuild the raft of beliefs that are keeping us afloat. Sometimes our worldview is shaken deeply and we abandon many planks of our feeble vessels. But with time, patience, and honest inquiry, we can make it more robust and expand its boundaries. Various propositions, sometimes contradictory ones, appear to have been proven, and in a sense they are. But what constitutes proof is a function of the other things a person believes, and the principles of inference that they deem valid, and the contents of both of those categories change dramatically for a person. So what constitutes proof, and what a person takes to be proven change dramatically as they mature intellectually. Forward progress is possible, and more inclusive, coherent system of belief can be constructed as we ask and answer more questions. But this progress may not be acquiring more and more “proven” propositions as knowledge. In fact, progress may amount to abandoning much of what we thought before as we become more discriminating and struggle to achieve greater coherence.What constitutes proof for us shifts with experience and the expansion of our ideas about the world. When we are young and understand little, we may be easily satisfied with simple answers to simple questions. When we grow intellectually, we become more discriminating. We make finer distinctions, see more subtle problems, and can foresee more distant implications and problems. If we are growing intellectually, what constitutes proof will become more careful too. If our belief structures are increasing in coherence along all the vectors listed above (logical and probabilistic consistency, fewer anomalies, more and stronger connections) incorporating a new belief into the system will require meeting more rigorous standards.
I submit that for a well-educated, reasonable person in the 21st century who can see the expansion of naturalistic explanations of the world into every corner of our lives—genetics, disease, physics, biology, psychology, sociology, and so on—atheism is a more coherent belief (and belief structure) than theism. This is so not because there is a single, definitive geometric style proof of the proposition, but because an atheistic, naturalistic, non-magical, non-supernatural worldview has more potential to achieve a higher degree of logical and probabilistic consistency, better internal connections, fewer anomalous beliefs, and a better incorporation of empirical experience. And that amounts to the most important and substantial sort of proof that humanity has ever had in its long, slow process of maturation.