Science&Society

The request in the OP is insufficiently clear, despite its attempt to speak plainly: ‘Can anyone put into words or at most, concepts that humans can understand and grasp, what it means to "exist".’ Firstly, "it” in the request needs to be clarified or at least explained. Currently, “it” is meaningless, or fails to signify what it refers too. If the OP title "Existence" is taken as an indication, then perhaps the OP is asking for an answer to 'what [existence] means to "exist",' which is, secondly, a self-referential question, and perhaps is better formulated as the absurd question: "what does existence's existence mean?" In addition, the OP has failed to live up to its own criteria ('to put into words, or at least concepts, that humans can understand and grasp') in proposing the request. Or perhaps the OP is simply asking "What does existence mean?"

The “two main approaches” to the fundamental reality of what science does, as asserted in the OP, depends very much upon an initial assumption about Scientific Realism in relation to all other metaphysical positions in the philosophy of science. Although Scientific Realism is a popular view of science, it is not the only philosophical approach that explains what science does. Other positions such as Instrumentalism, Epistemological Anarchism, Constructivism, Empirical Falsificationism and more explain scientific activity or elements of scientific activity through different analytical techniques and metaphysics. What stands Scientific Realism apart is the focus on “truth” as an empirical qualifier in the relationship between scientific theory and physical phenomena. It is on the basis of this metaphysical difference that any philosophy not appealing to a doctrine of truth, and instead focuses on development of scientific theory in different ways, is classified as “anti-realist”. The distinction between realism and anti-realism is really a political distinction, rather than a rational or scientific distinction. By classifying other metaphysical positions as “anti”, Scientific Realism is normalized as something positive against which other positions must be considered. But as often the case, non-realist positions are based, and developed, on other metaphysical prerogatives in their attempts to explain scientific activity. Any comparison between realist and anti-realist position is inappropriate because the doctrine of truth has no metaphysical significance in "anti-realist" theory. (It could even be argued that Scientific Realism’s adherence and demand to view knowledge in terms of truth is essentialist and anti-scientific. But that is a topic for a different debate.) The assumption that I alluded to which the OP makes is that Scientific Realism is normal, standard, or natural; and incorrectly assumes other positions as hostile, challenging, and adverse, and therefore inherently opposed to realism. For example, the OP states: “Most of the versions of Anti-Realism make the distinction between believing a theory is true and accepting that it is empirically adequate.” But if you read the “anti-realists” such as Feyerabend or Kuhn, they make no such distinction, nor explore the difference between realism or anti-realism. Only through a Scientific Realist interpretation of the issues in their work do their respective theses appear to be anti-realist. The perception that numerous alternate positions are anti-realist ultimately requires reading and translating “anti-realist” ideas within the interests of realist metaphysics, especially truth evaluation (e.g. "Is antirealism true?" is a realist, not an anti-realist question). "Anti-realist" positions are respectively based on different metaphysical groundings.

Context is never a simple matter of a relationship between outside and inside. Often “inside” contains the conceptual elements of various contexts that may be attributed. For example, the totality of a solitary geometric point that only has itself for reference, intuitively suggests no context; the point is simply an undefined reference. However, the conceptual basis of its referential totality includes what it means to be a “non-point” in achieving its identity as a point. Otherwise, without this difference - between point and non-point – the point could not have been distinguished as a geometric point in the first instance. The very notion of its geometric significance entails its corollary non-point context. If, as you have suggested, there is no context for a closed system or its totality, then how can the system or totality be identified as such in the first instance?