Good question. I think this is really a matter of prioritising the number of lines of enquiry that you pursue, at any one time, as the means of limiting the exploration of doubts. Once you commit to a line of enquiry, you have no real option but to follow the thinking where it takes you.
In terms of processing, a doubt presents us with two options: suppress it, or explore it. If we suppress it, it remains unresolved for now. So the problem is knowing which doubts will trip up your research, and invalidate your end result.
I like Elon Musk’s way of approaching this, which he calls “thinking from first principles” or axiomatic thinking. An axiom is a self-evident, unquestionable truth - the most fundamental principles on which you must proceed, or your solution will fail.
It was explored most clearly in his interview on Lex Fridman’s podcast (a recent interview in the last couple of months; he’s had Musk on the show a few times). Axiomatic thinking is a way to approach a problem or question by sticking to the smallest possible well-defined number of focus areas: or simply put, knowing what you MUST think clearly about.
Musk used the example of building the best rocket engine ever. His team at Space-X had to solve this problem at three levels: designing maximum thrust, making the lightest engine possible (which clearly impacts power to weight ratio and thus thrust) and making it as cheaply as possible. So his production example of axiomatic thinking, was that the minimum cost of production is always the cost of raw materials plus the cost of intellectual property rights. It’s not possible to make something like a rocket engine any cheaper than that, and you seldom reach that minimum cost unless you can reach production volumes that yield economies of scale.
Thinking within these parameters, therefore, if you arrive at a minimum possible design weight of the combustion chamber using available alloys/construction materials, in such a way that it still meets your design axioms (based on laws of physics, ie relating to thermodynamic behaviour of gases), then the only way to make it cheaper or lighter (or both) will be to innovate to find new alloys or materials or new methods of construction. So your ways forward, in pursuing solutions, are very clear when the axioms are clear.
I’ve tested this way of thinking recently on a project I’m working on. It’s not rocket science in my case! But I’ve been working on a set of problem solving tools that are designed to facilitate people facing specific types of problems. The research for the project could have been so open-ended that I’d never finish. But by thinking about the axioms the project should be based on, I was able to contain the research to the key success factors for the project. I started with more “candidate” axioms than I ended up with finally, so I had to do some initial research to decide where to place my focus, based on my desired end product’s features and benefits.
A final thought. If you haven’t read Henri Bergson’s booklet “An Introduction to Metaphysics” I’d thorough recommend it for an exploration of intuition versus analysis. In short he concludes that intuition can inform analysis, but analysis can never lead to intuition. In other words, he contends that the scientific method itself - usually portrayed as analytical and evidence-based “truth” - is itself, in reality, always the product first of intuition: ie the testing of a hypothesis, which is never arrived at via analysis.
By extension, every hypothesis is riddled with doubt. Most hypotheses turn out to be wrong. Therefore, we tend to “imagine” that our best thinking is analytical, when in truth it starts with intuition.
Bergson’s paper on metaphysics was written after all his famous books on things like the duration of time. He referred many times to “intuition” in his earlier writing, but never explained his working method. Until the metaphysics paper, that is, which unpacks his thinking approach to intuition.
He’s probably best known for his writings about time as “duration” - that is, we never experience clock time, since all measurement is by definition backward-looking (ie measurement of past events). If someone asks you what time it is, you can only answer what time it was a moment ago! You could only experience clock time by freezing time at a “point” in time. Therefore, our REAL experience of time is the experience of the “flow of time” or in other words we experience “the present” as as a flow of time through the present. He called this duration.
Intuition, Bergson argued, is a durational phenomenon. Whilst analysis is a reductionist activity, comprising the breaking-down of problems into component parts, just as we might break time into chunks of seconds and minutes that in reality don’t exist other than as duration. Intuition is not fragmentary, but a sort of understanding of the whole. When we have an insight, it comes from intuition. That intuition has access to the whole of our past experience and knowledge.
What I’m suggesting, is that we explore our doubts guided by intuition not analysis. Intuition is how we navigate connections.
Another neuroscientist, Hofstadter refers to the way the brain thinks as “analogical thinking” - ie we think by analogy. Our analogies exist in nested sets of entailed analogies, that ultimately add up to everything we’ve experienced and known in our personal history. Analogical thinking is based on likeness, which itself is recognised in perception as familiarity. Familiarity, if you reflect on your own experience, is an intuitive sense of knowing (cognitive scientists might use the term “schema” as in your intuitive grasp of “up” or “down” can apply to anything, irrespective of subject matter).
All this is to say, that resolving doubts is experienced as “not knowing” or having no clear “analogy”. Analogical thinking is some of the fastest, least conscious thinking we do… the basis of intuition, possibly? Anyway, how far you take your doubts is really a matter of how certain you need to feel about what you know. In Musk’s rocket case, lives are at stake, so certainty needs to be as high as is possible. And even then, doubts will remain due to the complexity of the projects and impossibility of testing for all scenarios and conditions.
In summary, the formulation of the question or problem drives the lines of enquiry. The doubts then demand to be pursued until they are all satisfied, or judged inconsequential.
