I'm beginning to realize that the former more closely matches most people's experiences with formal reasoning
many don't even know the latter is an option in terms of "how to think"; forget being able to do it
that ideas are possible to treat in this way doesn't occur to them
this took me a very long time to understand, as I've treated reasoning in this way for as long as I can remember; as a deterministic process with distinct objects and transformation rules between them
now I'm no longer sure which came first; programming skill or reasoning skill