I would also protest against
"the assertion that if science cannot measure something, then it isn't knowable or worth knowing"
However, I wonder why we would turn to science to explain everything?
Science generalises our experience of life or consciousness or the colour blue, to use Ken’s examples. So, we can recognise these things, well, rather more concepts in those cases. What science cannot do is explain our individual experience of it. But why turn to science for that? Why demand such a thing from science in the first place?
Wouldn't literature and art be more suitable for these questions? At the end of the day an artist might be inspired by academic research (not only by science= natural science) and an academic might get ideas for their research from art and literature. Paula Metallo gave a presentation of this mutual inspiration at the conference called: Give and Take: science and the humanities.
She also made me aware of the original meaning of religion: "The word religion comes from reverence, and before institutionalized religions, based on power and money and manipulation of the masses came to be, there were many cultures that funnelled their (nature) informed reverence into a set of rules for non-exploitation of man and planet. This has room for reflection in Big History."
This is a far cry from religion as a set of beliefs that are not to be questioned, and that are the base of monotheistic religions. I wonder whether we could go back to that original meaning, because that would certainly inspire academic research. It would not, however, compete with academic research.
Now, about the limitations of science and the scientific method. I came across a very interesting article by Rebecca Newberger Goldstein proposing "The scientists and the philosophers should be friends." She explains science as a tool to find out what is, that the term scientific method is somewhat misleading because it does not capture very well, the "creatively freewheeling character of science, the ways in which it utilises intuitions and even aesthetic judgements; nor the widely differing types of cognitive activities, and thus talents, that are required by the scientific enterprise, with variations depending on the kind of problem being pursued."
She furthermore makes clear why science is based on naturalism: "Science is, per definition, the methodology that enlists reality itself as collaborator..."
Then she makes it clear that philosophy is not to compete with science in that department. Philosophy brings other qualities to the toolset.
For her, "the point of philosophy is to maximise coherence among the multiplicity of propositions and propositional attitudes that we generate in the course of trying to get our bearings." Essential techniques are "thought experiment, counterexamples, conceptual analysis, and formal arguments trying to force all suppressed premises out into the open... These are all techniques not designed to prod reality into answering us back but rather to probe our internal consistencies."
So, science as a tool to find out what is, and philosophy as a tool to find out what matters. And finally she also shows, how those two questions are "thoroughly enmeshed with each other."
The longer I think about it, the more it looks like the collaboration between science and philosophy as sketched out by Goldstein could serve as kind of checks and balances only with respect to the project of mapping reality and making sense of it. That is to integrate a shared „meaning“ into our world view. There would still be ample room to add some personal meaning. After all, we are individuals - that basically means we cannot ever share the whole of our experience with others. I guess that is the point of being an individual.
What I really loved about this article beside its informational value for our project of big history, is that I learnt this phrase "one's bearings." The dictionary gave me the explanation: awareness of one's position relative to one's surroundings.