In recent philosophy of physics the role of mathematics has been questioned. It is no longer the case that mathematics is simply “applied” to physical theories, but development of mathematical languages has to some degree taken over the articulation of theories in physics, and physics also contributes to new areas of mathematics. Some theories claim that reality itself is directly mathematical (cf. Galileo), and other theories in foundational physics like string theory and some “interpretations” of Quantum Mechanics (QM) are problematic since they cannot be tested empirically (such as the “many world” interpretation of the collapse of the wave function).Peirce’s late sign theory contains an analysis of measurement which can be investigated in relation to recent criticism of the “Copenhagen interpretation” of QM and its “measurement problem”. Bohr’s idea that measurements of quantum systems had to be understood through classical physics lead to paradoxes and inconsistencies. One of these is that it is human intervention that causes the collapse of the wave function responsible for probabilistic measurement outcomes, but human actions and consciousness are not the kind of things that foundational physics should be about. It should describe reality as we understand it independent of human observers. In Relational Quantum Mechanics these problems are resolved by proposing a relational conception of reality, where all facts about the world are relative to interacting objects as “observers” (including humans and instruments), and this seems to be supported by Peircean semiotics (even if he did not have a fully articulated cosmology).