I'd take an angle on the question. My intention is to focus on the key role the notion of Lebenswelt (viz. lifeworld) in approaching certain deep quandaries of philosophy and discuss how it can serve the solution of (philosophically) concrete problems and leave detailed accounts to more specific questions, if raised.
Beforehand, I shall briefly dwell on an intermediary step concerning how we stipulate our axioms (and/or postulates) in our activity of theorising.
The choice of axioms sets up the foundation upon which a theoretical framework is built, influencing the structure, coherence, and implications of the ensuing theory. A crucial point is that the axioms do not reveal themselves as pre-existing truths, we choose them to build our best theory ("best" to be assessed in consideration of various values) as an outcome of a decision-process during our arduous engagement with the relevant area of inquiry. In the introduction to his Foundations of Geometry*, David Hilbert states this as follows:
Geometry, like arithmetic, requires for its logical development only a
small number of simple, fundamental principles [Grundthatsachen in
1899 edition, Grundsätze in 1903 edition]. These fundamental
principles are called the axioms of geometry. The choice of the axioms
and the investigation of their relations to one another is a problem
which, since the time of Euclid, has been discussed in numerous
excellent memoirs to be found in the mathematical literature. This
problem is tantamount to the logical analysis of our intuition of
space.
The quest of axioms, or better to use the broader term, premisses, bears the same import to philosophy. On the way, we dispel some issues as barren and inconsequential in the problem space we have engaged with, whereas we concentrate on some others as seminal and useful. In this regard, phenomenology provides Lebenswelt as a constituent of the latter class of premisses.
I deem phenomenology as a discipline of philosophy that explores the subjective experience of consciousness and the structures of experience. Hence, its focus is on the essence of human perception and interpretation of the world. As such, it incorporates the movement whose representative figures are Edmund Husserl, Martin Heidegger and Maurice Merleau-Ponty, to cite a few, but not limited to it.
The conception of Lebenswelt is mostly associated with Husserl's views, however, it is a central notion of phenomenology in general. Lebenswelt is the world as it is experienced and directly engaged with by individuals. It comprises immediate experiences, practical engagements, and taken-for-granted assumptions that form the pre-theoretical backdrop for our understanding of reality.
It should be noted that Lebenswelt does not involve solely our lived experiences that are articulated through language (i.e., categorisation and breaking down to linguistic components); it embraces non-discursive aspects of them, without appealing to abstract concepts and complex reasoning of "theories."
Metaphorically speaking, we interlock with Lebenswelt like a robust mechanism of gears and shafts. We are already immersed in Lebenswelt, actively participating in it, as opposed to passively standing apart and analysing it and the lines between subject and object are blurred. Lebenswelt occurs within holistic experience; we directly apprehend the world.
Lebenswelt aligns with the conception of Weltbild (viz. worldpicture), the epistemic bedrock that Wittgenstein sets forth in his posthumously published work Über Gewißheit (On Certainty). Weltbild thrives in Lebenswelt and could be seen as the obverse of Lebenswelt. A succinct account of Weltbild is given by Henry Finch in his Wittgenstein - The Later Philosophy - An Exposition of the 'Philosophical Investigations' (pp. 221-222) as follows:
On Certainty concerns the role of facts which serve as frameworks for world views. They might be called framework facts because in
some ways they are like other facts, though in other ways they are not
like other facts at all. They are facts which, Wittgenstein says, are
the basis for our thoughts, our language, our judgments, and our
actions. Such world view facts (to give them still another name)
include also the various strata we call common sense. They include the
vast numbers of things which we take for granted and which provide the
settings for all our questions and investigations, as well as for our
language activities. They are facts which we do not doubt because,
among other things, they define what doubting is or what it makes
sense to doubt. They establish what is accepted or agreed-upon in
ways of talking and acting.
By delving deeper into the relationship between Lebenswelt and Weltbild, we gain a richer appreciation for the complexities of human knowledge and the crucial role of our lived experiences in shaping our sense of reality.
A deeper look at Lebenswelt in connection with Weltbild reveals us the sought-out premisses that could relieves us of the subject-object dichotomy, the notion of a separate thinker observing an external world, and by the same token, mind and body duality in a furthering capacity.
