Considering that nearly everything that exists cannot be even imagined by humans (or would it be reasonable to assume the contrary?), what is the chance of finding a scientifically coherent explanation of the perceivable or imaginable or thinkable (is there a difference?) Universe? Can interactions between unthinkable and thinkable things be ruled out?
Reason provides us of a biased model of nature: knowledge, which helps survival. The model is biased because it is adapted to the purpose of the subject. So, eating bones is not healthy for me because it is healthy for hyenas.
Scientific knowledge is just some kind of knowledge (obtained by the scientific method, etc.), which means it is still biased by the goal of our survival. Scientific knowledge does not provide a final truth, only an empirical truth. For example, relativity explains the universe using time and space, representations that, according to most mature philosophical branches, are just a product of our mind. In spite of that, scientific knowledge is still capable to describe our biased perceptions with extremely high accuracy.
The branch of knowledge which aims for final truths is philosophy, not science, which aims for empiric truths. But final truths seem quite far of our reach. Aiming for a complete scientific description of the perceivable would imply removing the perceiving entity --us-- from the problem. That is the only way to remove all possible biases. Such act would imply the complete negation of the subject, so only the knowable object would exist, which is in essence, illogical. That was the form of knowledge in medieval times: no notion of a subjective bias; given that man was the supreme creature, it was assumed that perception absolutely corresponded to the perceived object. The Copernical approach was one of the first examples of how the subject determines the object. Before him, only the object held the truth, and the subject was excluded, necessarily forcing a bias.
So, aiming for a complete scientific description of nature is a naive idea. The more we know, the more we are conscious of how knowledge --including scientific knowledge-- cannot be purified of the bias of subjectivity.
"A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do. He may as well concern himself with his shadow on the wall. Speak what you think now in hard words, and to-morrow speak what to-morrow thinks in hard words again, though it contradict every thing you said to-day. — 'Ah, so you shall be sure to be misunderstood.' — Is it so bad, then, to be misunderstood? Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh. To be great is to be misunderstood." -Ralph Waldo Emerson
"The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. He to whom the emotion is a stranger, who can no longer pause to wonder and stand wrapped in awe, is as good as dead —his eyes are closed. The insight into the mystery of life, coupled though it be with fear, has also given rise to religion. To know what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty, which our dull faculties can comprehend only in their most primitive forms—this knowledge, this feeling is at the center of true religiousness." -Albert Einstein
"There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory mentioned, which states that this has already happened." - Douglas Adams
What is 'making sense'? Why and how do we do it? Is it something we can expect to progress to an ultimate limit?
What are explanations? Can we expect them to progress to an ultimate one, and if so what would that be like?
What does thinkable mean? Can we engage with unthinkable things, or find evidence they exist?
You need a big set of tools to be able to approach questions like these. A cosmology, both of structure and regarding what meaning is. An idea of what consciousness is or might be, how thinking works and makes progress. These questions are not free-floating abstract universals, but occur relationally between specific questioners or subjectivities, and their specific experiences (these will include sharing experiences & interacting, so also intersubjectivity).
Thinkable vs unthinkable: Turing-completeness or computational universalisability, points to there being something about algorithmically progressive structures, which is universal. With the exception of Turing oracles. This has been extended to quantum Turing machines, though as quibits increase the issue of difference by degree may be too great to be waived away by 'in principle', as with approaching being a Turing oracle by degree. The hypothesis of digital physics is that the universe can be thought of as a Turing machine.
I would relate this to issues of translation. Can any statement be translated? Arguably yes, with accuracy arbitrarily limited by how closely the translator can approach the speakers experiences and the role the quote had for them. A dog will not understand a talk about relativity. We know dolphins have complex language, but we don't have enough shared experiences yet to translate between us. Integrated Information Theory points to a way of thinking about being 'more conscious' that can account for these examples, with a better translator able to integrate more experiences to relate different sets of abstracts to (languages).
The 'ultimate' extent that can develop to would be to integrate all experiences, and all possible experiences, into a structure that can translate between them. That is I think the mission of science, it is notable that scientific knowledge is always tentative, is based on evidence so far. Reductionism seeks to find the simplest phenomena, exactly because they are the most 'translatable'. The particle physics/QFT picture can then be used to build up conceptual groups like chemistry, and information theory, which we know will be inter-operable, translatable between, because they share a mapping to the same layer of constituents. The layers of other explanations exist like particular languages, exactly because they refer in a tractable efficient way to a communities experiences; so we might expect translations between languages efficient for specific contexts to be laborious. Languages as embodying salience landscapes helps us see why.
The way to picture consciousness for me, is as a strange loop. Different from simply a computation, by not being purely an algorithm that progresses. As in Buddhist thought, there is a fundamental quality of awareness, ability to return from the 'world of ideas' and abstractions, to presence in the moment, reconstructing a cosmology of meaning from there. This is what allows minds to avoid the halting problem, and go beyond the foundationalist picture of meaning that gets caught on Munchausen's trilemna. You can see 'strange loop' thought processes in action doing this here.
I would describe consciousness as having this quality of 'just begin where you are', but also the quality of making a picture of the world, a meaning-cosmology, from there, out of experiences, ideas, methods - to make what Hofstadter calls a tangled hierarchy, that includes self-reference and so feedback loops and emergent phenomena. When experiences are shared and methods progressively improved these cosmologies will often converge, or sets will prove in practice more effective, especially by supporting a more positive cohesive and capable society of people that share meaning-cosmologies. But there might always be a better set, especially as challenges change.
David Deutsch's book The Fabric Of Reality gives I think a nice example of someone using what is available to build such a cosmology and check it for consistency and coherence, where he identifies, quantum mechanics, information theory, epistemology, and evolution, as pillars of his meaning-cosmology, establishing how they can be shown to be inter-operable or can be translated between, at least in principle. Sean Carroll is another person with the kind of breadth of interests to be trying to do this kind of work.
An individuals capacity to do this kind of thing, while fundamentally relating to their own experiences, also crucially uses the sets of efficient abstractions created by communities, eg. language. Making sense and explaining things, occurs in this shared context. Insights help make language better, able to articulate more, be clearer, and relate individuals not only to a physical cosmology but a social one. Durkheim identifies social cohesion as resulting from sharing attitudes to sacred things - these can be habeus corpus, free speech, or scientific method, as much as commandments or catechisms. Challenge the values, challenge the basis of coherence of a community. Durkheim talks about anomie as the experience or manifestation of the decohering of community, and loss of meaning it embodied or was drawn together or structured by. James C Scott has this idea of legibility of values, that to transfer or propagate values in the face of change, they have to be continuously valuable, in making the world tractable. But this need often involves ignoring complexity, oversimplifying. We have to balance making sense, with encountering mysteries and unknowns, towards better understandings that can integrate more experiences.
So. We have reason to think the universe is intelligible. Consciousness and intelligence are able to be open to new experiences in a way that is different to computation. We can see a kind of gradient toward more integrated, but we can't expect that to be complete as long as new experiences continue. Unknowable things could be out there, in relation to experiences we haven't had, or can't yet translate into our experiences. When we make sense of and explain things, we relate ourselves to them, in a tangled-hierarchy of ways of knowing, which embodies salience landscapes about how to act and ask new questions in efficient ways. We inherit the processes involved in doing that, languages, methodologies like science. And when we develop insights they can contribute to these, and be passed on. This is fundamentally a cultural practice, and relates to successful living and cooperation, including whether or not progress is cumulative.
Phenomena, through tactics like consilience and scientific methodology, should generally be able to be agreed on. But what patterns we find, how we group them, involve choices, that express implicitly ideas about how to live. But much -most- of how we live is not similarly fixed, we are more free than we realise, or typically even wish to realise, to live differently.
To say an ultimate stance had been reached, would be to close to new experiences. Death, or close to it. Emerson & Einstein describe this. And we can think of Adams' comment as saying, whatever we find we will demand more. That is living, that is being a strange-loop, elaborating it's world with each recursion.