It seems to be hard to say in what sense a truth can exist apart from a context, even one so seemingly clear as “1 + 1 = 2” or “Two contradictory statements cannot both be true.” Think of it in terms of works such as Whitehead and Russell’s “Principia Mathematica” which attempted to ground our ‘intuitions’ about arithmetic upon an elaborate formal apparatus. In order to build that apparatus a large amount of sophisticated mathematical thought is already assumed. This doesn’t mean that such works are useless — they can be at least consistency checks — but it does mean such works don’t provide a foundation for our belief that “1 + 1 = 2.” One way to see this is to think about a point raised by, I believe, Wittgenstein — The logical structures that was first believed to justify our beliefs in arithmetic are indexed by numbers and the indexing process assumes the very truths meant to be justified.
It seems more likely that our mathematical systems are the result of bootstrapping operations which have sometimes moved slowly and have sometimes involved jumps to new plateaus especially during the explosion of mathematical thought which began with Leibniz and Newton and, maybe, hasn’t yet ended. After some digestion of the these major jumps, and perhaps at times when smaller jumps have accumulated, mathematicians have reformulated human understanding of what mathematics is and what formal truths are. This is not to deny the large amount of exploration which can be done on each plateau once a formal understanding has been accepted, but I’m not setting out to produce a serious work of the history of mathematical thought. I’m raising a very large claim:
Individual truths, as creatures can know them, are true only in context of the entirety of Creation, though our view of that entirety is necessarily time-bound and contingent.
Or at least: those individual truths need a context, but the context has to be greater the greater or more abstract the individual truth. Absolute truths have to be a plausible part of a narrative understanding of Creation. Plato and Aristotle produced a narrative of sorts for higher pagan thought but they didn’t do it in a self-conscious manner as did Augustine when he produced, in The Confessions and The City of God, a well-organized narrative for a system combining Christian theological beliefs and Neoplatonic metaphysics. St. Thomas Aquinas also produced such a narrative in which the metaphysical aspects were dogmatically deformed by his alleged followers despite his clear teaching of the need to shape our minds in response to our environments. This will force us into intellectual developmental processes which involve bootstrapping.
I’m trying to produce a very explicit, but very sketchy, narrative of Creation. I’m a child of an age of some substantial historical awareness, an awareness that cuts across true (human) history, our understandings of the evolution of life, our understandings of the development of this expansionary phase of our universe, etc.
As our understanding of all these narratives has become more sophisticated, we’ve found ourselves facing a conundrum of sorts. Under my claim that truths are contextual, we can say the ancient Greeks could understand the elementary truths of arithmetic in light of arithmetic itself along with their understanding of geometry, physics, and some sort of Platonic-Aristotelian understanding of the human mind. Now arithmetic can only be truly understood as part of a whole that includes transfinite set theory, modern logic, quantum physics and all that, more modern understandings of the human mind, etc. We can now see the world as a far more complex story, more complex in its plot but also in its material stuff and its characters. Even simple truths are part of a not so simple whole.
I believe that Wittgenstein said something of this sort: the search for the foundations of our universe may well reveal that the foundations are supported by the superstructure. This is in the same spirit as my claim.