Presuppositions are a priori suppositions, usually unstated. They are not inevitable. Presuppositions may be replaced with suppositions. That is, presuppositions may be made explicit.
For example, someone might say, “I will flip a coin. If it is heads, I will adopt presupposition A; if it is tails, I will adopt presupposition B.” In that case, neither A nor B are presuppositions; they are suppositions that are chosen a posteriori.
Mathematics is the discipline that is based entirely on suppositions. It is purely conditional. “If X is supposed (or given), then Y follows necessarily.” If X is rejected, then something else may follow.
The existence of mathematics shows it is possible to have knowledge that is truly universal. Science is the attempt to mathematize all knowledge and remove all subjectivity. That is the “view from nowhere”. See here for how induction works through formal definitions and conditions.
But is it wise to remove all subjectivity? No, for the simple reason that it would turn us into mere objects. The person in us cries out, “I am not a number; I am a free man” (The Prisoner). We are subjects and so want a “view from somewhere”.
Yet we should not swing to the opposite extreme of relativism and subjectivity. Rather we should seek a pluralism that avoids both extremes. We should recognize that we’re always subjects without being completely subjective. How can this be done?
First, keep a subject in the model at all times. Even if it is a simple model of a subject, that is far better than eliminating subjects altogether.
Second, keep an object in the model at all times. Even if it is a simple model of an object, that is far better than eliminating objects altogether.
Third, accept that knowledge will vary by culture (or subculture). There is flexibility about where to draw distinctions. Different people will draw distinctions in different ways. Don’t try to force everyone to accept the same distinctions, except for a specific purpose such as a particular exam.
Fourth, always keep the purpose of knowledge in mind. Whether the purpose is wonderful (as wonder is the beginning of philosophy/knowledge – Socrates) or practical (as knowledge can help people), let that purpose guide the definitions and conditions that are adopted.
In short, be wise about knowledge.