On logic and the assertions of “a true tree of life” and “Higgs particle”

In logic, there are universal assertions (conjectures, claims, theorems, etcetera), ie, concerning all elements in a set, existential assertions, ie, concerning only some elements in a set, and uniqueness assertions, ie, concerning single elements in a set, but there aren’t existential uniqueness assertions concerning sets, like the cladistic assertion that there is a single “true tree of life” (ie, a single true set). This assertion is thus not possible to either prove or falsify logically.

The reason for this impossibility is that set theory in terms of ZFC contains the axiom of regularity (also known as the axiom of foundation), which states that every non-empty set A contains an element that is disjoint from A. It means that the axiom implies that no set is an element of itself, and that there is no infinite sequence (a_n) such that a_i+1 is an element of a_i for all i. Using the axiom of dependent choice (which is a weakened form of the axiom of choice), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true. Hence, the axiom of regularity is equivalent, given the axiom of dependent choice, to the alternative axiom that there are no downward infinite membership chains. The axiom of regularity thus effectively excludes the cladistic assertion that there is a single “true tree of life”. There simply isn’t any such set axiomatically.

The same reasoning applies on particle physics’ assertion that there is a ”Higgs particle”. Neither it is possible to either prove or falsify logically, because it isn’t consistent with the axiom of regularity, ie, is excluded by this axiom, and is thus false per axiom. However, the problem with this assertion is that particle physicists recently asserted that they have found this “particle” empirically. If this is a fact, then this finding actually falsifies logic (at least ZFC). Not only that, it thereby also asserts that functioning computer programs actually do not function, and moreover that computers do not work at all. Even if this assertion is in line with what Peter Higgs think about computers and today’s internet society, it is, to say the least, surprising that a clearly fake empirical confirmation of his false assertion could render him the Nobel Prize. How can the Nobel committee miss this clear contradiction? And, why don’t other scientists react? Is this a conspiracy in science? Do scientists think that a God particle is advantageous for science? Do they think that turning science into a religion is advantageous for science?