Where does science begin ?

Haven't you seen a lot of scientific work built on fundamental assumptions? A problem I have is in accepting unintuitive assumptions in a lot of research. Especially in a nascent field like Natural Language Processing, you find a lot of these. These are not like Euclidean axioms which seem pretty reasonable. Yet, research without such asssumptions seems to be an impossibility. The problem is then to determine the right set of axioms which serve as a basis to build the theory. Some insights I found in a Phd thesis:

Any philosophical system, any science has to start with assumptions, axioms which cannot be really proved or disproved, which are fundamentally arbitrary but hopefully convincing. In his Tractatus Logico-Philosophicus, Wittgenstein [1918] writes that the only true philosophy would be to utter proven scientific facts, to use nothing but defined symbols of a defined formalism – i.e. to renounce on metaphysics and thus on philosophy:

Die richtige Methode der Philosophie wäre eigentlich die: Nichts zu sagen, als was sich sagen lässt, also Sätze der Naturwissenschaft – also etwas, was mit Philosophie nichts zu tun hat–, und dann immer, wenn ein anderer etwas Metaphysisches sagen wollte, ihm nachzuweisen, dass er gewissen Zeichen in seinen Sätzen keine Bedeutung gegeben hat. ... (Wittgenstein 1918: 85, § 6.53)

Wittgenstein is aware that the problems with this suggestion are, however, that every definition necessitates a definition of the defining terms until we reach the unprovable maxims. If we refuse to accept these fundamental maxims, the cornerstones of meaning, we cannot state anything and are condemned to remain silent.

Wovon man nicht sprechen kann, darüber muss man schweigen. (Wittgenstein 1918: 85, § 7)

These maxims have transcendental, metaphysical quality, only they make any meaning possible and can thus instantiate our questions and answers in life.

Wir fühlen, dass, selbst wenn alle möglichen wissenschaftlichen Fragen beantwortet sind, unsere Lebensprobleme noch gar nicht berührt sind. Freilich bleibt dann eben keine Frage mehr; und eben dies ist die Antwort. (Wittgenstein 1918: 85, § 6.52)
Only the transcendental character of metaphysical philosophy can really give answers and assert meaning. If we only utter scientific proven facts we can only replace meaningless utterances with one another. E.g. in semantics we can step from language to metalanguage to meta-meta-etc.-langauge, but this does not bring us an inch closer to real meaning. On the other hand, because we cannot define the maxims we use, we remain incompetent about them nevertheless. Again, Wittgenstein’s famous quote applies:

Wovon man nicht sprechen kann, darüber muss man schweigen. (Wittgenstein 1918: 85, § 7)

We are therefore in principle disqualified from speaking, from stating anything meaningful or even “scientific”. If we accept a minimal set of maxims on which everybody agrees science seems to be possible nevertheless, as long as we can base everything on these maxims.