What is a firm foundation?
Being human, one is very limited in the time and space available to test hypotheses.
In logic, that demands that we accept than we can only ever submit a very tiny fraction of the observable reality to testing, and it seems that observable reality is a very tiny fraction of reality.
Isn’t it logical to accept that a degree of uncertainty must accompany all knowledge?
Isn’t a search for hard Truth little more than an addiction to the first and simplest form of logic we are each most likely to encounter as children – simple binary logic?
Isn’t the more mature response to accept that our reality is sufficiently complex to encompass instances from an infinite class of possible logics, from the simple binary to the fully stochastic?
It seems clear to me that the evidence from Quantum Mechanics points clear to our reality containing stochastic elements at the quantum level.
It seems clear to me that freedom demands such a complex mix.
I don’t advise abandoning anything, except absolute certainty. And reality is rather insistent, instant by instant, about us making choices, so even the lack of choice is a choice of sorts; so we all need heuristics we can use with confidence.
I don’t say abandon axioms. Axioms have their place in the realm of logic.
I am saying quite explicitly that when dealing with the realm of reality (which includes all other humans), it pays to keep quite a spread of uncertainty – and not get over confident.
Just that humility thing in the title of this.
For me, paradox is simply an indication that the paradigm in use has reach the limits of its utility and needs to be replaced with a more general paradigm set.
I don’t see any end to that process, should I be fortunate enough to live the rest of eternity.