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(This article started as a response to the post about Ayn Rand and Objectivism, and the original version has been moved to Reason Alone - hence the confusing comments.)
Reason is a big subject. Here are the main articles touching on the subject.
Perhaps our understanding is convergent, but not able to completely align.
You say to me: “I think that you, like me, believe that human connection and compassion should shape our beliefs, as well as Reason. But, in that case, you don't believe in 'reason alone' any more than I do”. Yes, I think you are right about what I believe. Perhaps the distinction is that Reason should be the underpinning of things that matter in terms of our and humanity’s well-being, and for determining Absolute Truth (whether mathematical or philosophical or theological), whereas emotion provides colour and makes the whole thing worthwhile. I don’t use Reason when I am in an art gallery, or looking at a country landscape. I don’t use Reason as the basis for deciding to indulge in gliding and other aviation-related hobbies; I love the open spaces and there is a human desire to soar: but I do use Reason to assess the risks involved. I didn’t use Reason when deciding who to marry: perhaps I should have done, things might have been smoother subsequently, but I think I would have regretted it if I had never had the experience of a romantic relationship, even if those feelings don’t last for ever. I would use Reason for arguing with a flat-earther: they have become the cliché for the obviously faulty use of reason in the same way that the Nazis are the cliché for evil.
It doesn’t help that the English language can be ambivalent, especially with words such as “believe” or “I’m sure”. You say that you wouldn’t say that you [only] “believe” that two plus two equals four [because you know it]. I do use the word “believe” in that way, meaning that I am satisfied that it is provable logically and mathematically and is an Absolute truth at least in the Newtonian universe, but I also use the word in the other sense, meaning: “I believe the kebab shop is open until 11pm (but I’m not sure)”.
The elephant in the room in all this is the implications for religious faith. To me, belief in any kind of supernatural can at best follow from belief in the second sense that I defined above (because we can’t see or measure the supernatural). Your first example is valid: I have faith that if I get on the bus, the driver will take me to where Google Maps says they will, because this has almost always worked in the past. But can that be applied to religion? Does prayer get answered? I cannot be sure that if I trust in God I will not die of cancer or get killed in a car crash, because this has happened to some Christians that I know. So what use is a belief in God here on earth, and can this be extrapolated to certainty about an afterlife? Maybe religion is not about our needs but about making the world a better place (the bible pretty much says that), but do we need formal religion for that? I will admit that sometimes situations which might have become a problem for me have turned out very well in a way that I could interpret as miraculous. Maybe I am merely detecting a pattern and ascribing meaning to it, but there is something in me which doesn’t want to be ungrateful to God if he is looking after me. (I could tell a story illustrating this at one of our meetings). But if he is looking after me, why are some other people’s lives so disastrous?
This brings us back to the Sovereignty question and I will think more about that last bit when I reply to your last post on God’s Sovereignty. I would agree that Christianity is more Rational and less weird than most other religions, but questions remain. Christians have worked very hard at providing logical reasons why the Resurrection “must be” true, and done a good job, but questions remain, quite apart from theological disputes about the meaning of the Cross and Resurrection (Propitiatory Substitutionary Atonement vs “God showing His Love”).
Okay, you may have a point about the Incompleteness Theorem. Although, in my defence, I only suggested it is 'surprisingly easy' to understand. I suppose it depends on how easy it is to surprise you...
I think we are all trying to make sense of the world around us - it is often a confusing place.
I'm not sure how to understand your claim that Reason is only the “least worst” option for determining Truth and Belief, when you tell us this is not what you actually do in practice, and it doesn't even seem to be what you want to do. I think that you, like me, believe that human connection and compassion should shape our beliefs, as well as reason. But, in that case, you don't believe in 'reason alone' any more than I do.
You talk about believing in something provable - isn't that a contradiction? For me it is - I would not say that I believe two plus two equals four. But perhaps we are using language differently here?
And you talk about believing in things that do not need to be accepted by faith - again, I think we have a very different understanding of the nature and role of faith in human life. When you get onto a bus, you don't know where it will go, but you have faith the driver will take you along the expected route. When you get married, you do not know if the relationship will work out, but you have faith that you will each keep the promises you make. All the important decisions in our lives are fundamentally questions of faith - what do you believe is the right thing to do, or the best thing for you and those you love? Which is not to say that reason has nothing to do with these choices, but reason is (as I am arguing here) only one part of a larger picture. Maybe an important part - but certainly not the whole picture.
I need to keep this short, so just one other brief comment: over the years, I have put quite a lot of work into Christian apologetics, and (while it is not impossible) you would find it hard to find a Christian who is trying to prove their religion. I certainly was not trying to prove that Christianity is true. What I was trying to prove is that some forms of Christianity are reasonable - and they appear very reasonable when you compare them against the blind faith required by other belief systems. I invite people to consider questions of evidence, and compare the various alternatives. And I have never claimed that other holy books - or other books of any kind - are not inspired at all. But the question of what we mean by 'inspiration' is probably getting too far off topic...
I think I am right in remembering that your degree was in Mathematics and Philosphy, which explains why you suggest that Godel’s Incompleteness Theorem is easy to understand! I am afraid that I am more of an amateur in these things, and much of what I am saying in these discussions represents my own attempts to make sense of it all and work out what I do think and what I can justify believing, or not believing.
Perversely, my attraction to Reason and Rationalism, of the Enlightenment and of Ayn Rand’s Objectivism, is probably not entirely driven by Reason, but by my desire to be able to believe in something provable rather than something that needs to be accepted by faith or by my feelings: so a psychological or even spiritual need. On the other hand, I do like Art, which exercises my spiritual side and/or the right side of my brain: primarily Modernist Art but also Romantic Art, which as you say was a reaction against pure Reason. But then, Rand was not against Art, though she saw Abstract Art as decadent (I quite like it), and so championed something called Romantic Realism: I have been unable to work out from her writings a precise definition of this. Many of the decisions that I make in life are down to what I happen to like: whenever I spend money on something that I don’t actually need, I am not applying reason.
So again I come back to the conclusion of Reason being only the “least worst” option for determining Truth and Belief. Faith, whether in a Religion or in believing what you want to believe such as Trump winning the 2020 election, depends on even more axioms. People of faith tend to take as axiomatic that their God exists and that their Holy Book is inspired by God and other religions’ aren’t. A very small proportion of people of faith think much about apologetics, trying to prove their religion, and at least they should be respected for trying. Even Richard Dawkins has said that the Argument from Design is a strong one. I don’t particularly want to get into knocking Religion, except that it seems an obvious example. But Reason can lead us into conclusions that we do not like. As I write this, the Conservative Party is choosing a new leader. Not being a party member and never likely to be, I won’t be voting for any of them. But I lean toward Richi Sunak because he is not promising tax cuts straight away. I would like there to be tax cuts, and for wages to increase: but Reason says the country cannot afford it. The national debt is into the trillions, largely due to Covid spending which Sunak concluded was justifiable at the time and some Conservative Libertarians called him a socialist for trying to help people: but now there is no more money. Likewise. I don’t like the implications of the need to tackle climate change, but it will be unreasonable not to.