It's actually logically necessary. This is known in philosophy as the problem of the criterion. Every syllogism starts with premises, and at some point the premises have to be a fundamental given that cannot be further dissected. All of our fields of knowledge have this characteristic. They all have a set of foundational concepts.
It is also related to Godel's incompleteness theorem. There are an infinite number of truths that cannot be derived from any finite axiomatic system. These truths are "beyond rational comprehension." If we are able to access these truths then we must have some meta-rational cognitive capability. This is an aspect of what Christianity calls 'faith', i.e. belief in that which cannot be seen, yet which is not an irrational made up belief.
One obvious area this shows up in is the concept of infinity. There is no way to derive such a concept from any finite axiom. Since everything we experience in the physical world is finite, yet the concept of infinity is extremely useful in STEM, this leaves us with a dilemma. Either STEM is based on a fundamentally false concept, which is absurd, or we have access to truth beyond the finite realm.
This observation was made by Eugene Wigner in his article "The Unreasonable Effectiveness of Mathematics in the Natural Sciences".
> It is also related to Godel's incompleteness theorem. There are an infinite number of truths that cannot be derived from any finite axiomatic system. These truths are "beyond rational comprehension."
This isn't what it means. It simply means that all axiom systems of a certain form have that limit, not that human knowledge itself does.
> One obvious area this shows up in is the concept of infinity. There is no way to derive such a concept from any finite axiom.
Obviously false, given even Peano arithmetic.
> Every syllogism starts with premises, and at some point the premises have to be a fundamental given that cannot be further dissected. All of our fields of knowledge have this characteristic. They all have a set of foundational concepts.
Except we can interrogate reality and build from there. We're not reasoning in a vacuum.
"However, the other axioms are insufficient to prove the existence of the set of all natural numbers. Therefore, its existence is taken as an axiom—the axiom of infinity."
The human mind could be meta-rational so it can generate new consistent axioms that cannot be derived from the existing known axioms. The history of mathematical progress seems to be pretty good evidence our minds can do this.
As a semi-related aside, Cornelius Van Til developed a lot of similar ideas about the logical necessity of the supernatural in the area of theological apologetics.
> It is also related to Godel's incompleteness theorem. There are an infinite number of truths that cannot be derived from any finite axiomatic system. These truths are "beyond rational comprehension."
No, not rational comprehension. They are beyond reach of logical reasoning, not rational comprehension. They are different things. I can use AI or some complex statistical methods which I do not understand to find something I cannot see. It wouldn't make my findings to be a faith.
> If we are able to access these truths then we must have some meta-rational cognitive capability. This is an aspect of what Christianity calls 'faith', i.e. belief in that which cannot be seen, yet which is not an irrational made up belief.
Rationality is a belief in something that cannot be seen. For example a Newton laws of gravity. Have you seen any gravity? Maybe you smelled it, or touched? Have you seem an atom? Electron? Did you see entropy? Energy? Momentum? Or lets look at social sciences, for example psychology. Have you seen any subconscious thoughts? Or cognitive dissonance? We have not seen any of those, what we seen (or felt) was some companion feelings, and we believe that that feelings are explained by underlying principle which no one have seen. Or we can look at rationality itself, have you seen any principles of rationality? Belief, for example. It is a fundamental idea behind rationality, have you seen any belief? I felt some ideas as a belief, I have seen people who claimed that they have some beliefs. But the whole idea stinks of being not real but imagination.
So rationalist also believes in a lot of things he/she cannot see. Is it faith? I think not. The main difference between a religious faith and a rational belief, that rational belief can be rejected with ease if proven wrong or even not wrong but irrational (unfalsifiable for example). While it is almost amoral from point of view of religion to loose faith and to stop believing in God. It is highly moral to keep religious faith despite of heaps of counter evidence.
The behaviour of people dealing with failing faith or beliefs is the best to decide what is faith and what is belief. Behaviour allow us to demarcate them.
> One obvious area this shows up in is the concept of infinity. [...] Either STEM is based on a fundamentally false concept, which is absurd, or we have access to truth beyond the finite realm.
The math itself is a fundamentally false concept in your terms. Have you seen a point with size of 0? Or number? Homomorphism? Math is based on concepts that are pure imagination and they does not exist in reality. Math deals exclusively with concepts that are pure imagination. The link between math and reality is being made each time by a practitioner, who knows math and use it to solve a real problem. But it is not nessesary for her to have a faith in math or in her ways to use math, she can double check that her way to apply math to a problem is a good one. To make an experiment for example.
It is not a faith I think. It is a doubt. A constant doubt in myself and mental tools I use. A rational disbelief.
From other side, you are free to use such a definition of a faith as you like. So if you like to think of faith as of belief in something unseen, then it is ok for me. I just wanted to point, that if you follow this definition to a logical end, you'll end with the idea that every person is a religious person. So what the point to have special word for a religion? If any person is the religious person, than it is truism, it is the identity, the sameness, we can omit "religious" and we would loose not the tiniest part of bit of information.
We agree, you are just using the word 'faith' differently than myself and arguably most of Christian history.
If you read the epistles the sort of faith you describe is not commended. Paul specifically calls out people who are zealous without knowledge, and on the other hand tells everyone to test everything they are told. He also rests all of Christianity on whether Jesus actually rose from the dead or not. He believed that Jesus actually did based on his own vision and the accounts of the others he met that had been with Jesus while Jesus was alive. So, none of Paul's beliefs were based on the blind faith you describe.
