Michael Redhead's recent argument aiming to show that humanly certifiable truth outruns provability is critically evaluated. It is argued that the argument is at odds with logical facts and fails.

This review is a critical discussion of three main claims in Debs and Redhead’s thought-provoking book Objectivity, Invariance, and Convention. These claims are: (i) Social acts impinge upon formal aspects of scientific representation; (ii) symmetries introduce the need for conventional choice; (iii) perspectival symmetry is a necessary and sufficient condition for objectivity, while symmetry simpliciter fails to be necessary.

I analyse three most interesting and extensive approaches to theoretical models: classical ones—proposed by Peter Achinstein and Michael Redhead, and the rela-tively rareanalysed approach of Ryszard Wójcicki, belonging to a later phase of his research where he gave up applyingthe conceptual apparatus of logical semantics. I take into consideration the approaches to theoretical models in which they are qualified as models representing the reality. That is why I omit Max Black’s and Mary Hesse’s concepts of such models, as those (...) two concepts belong to the analogue model group if we consider the main function of the model of a given class as its classification criterion. My main focus is on theoretical models with representative functions as these very models and, in a broader context, the question of representation. (shrink)

The aim of this paper is to argue that the (alleged) indeterminism of quantum mechanics, claimed by adherents of the Copenhagen interpretation since Born (1926), can be proved from Chaitin's follow-up to Goedel's (first) incompleteness theorem. In comparison, Bell's (1964) theorem as well as the so-called free will theorem-originally due to Heywood and Redhead (1983)-left two loopholes for deterministic hidden variable theories, namely giving up either locality (more precisely: local contextuality, as in Bohmian mechanics) or free choice (i.e. uncorrelated (...) measurement settings, as in 't Hooft's cellular automaton interpretation of quantum mechanics). The main point is that Bell and others did not exploit the full empirical content of quantum mechanics, which consists of long series of outcomes of repeated measurements (idealized as infinite binary sequences): their arguments only used the long-run relative frequencies derived from such series, and hence merely asked hidden variable theories to reproduce single-case Born probabilities defined by certain entangled bipartite states. If we idealize binary outcome strings of a fair quantum coin flip as infinite sequences, quantum mechanics predicts that these typically (i.e. almost surely) have a property called 1-randomness in logic, which is much stronger than uncomputability. This is the key to my claim, which is admittedly based on a stronger (yet compelling) notion of determinism than what is common in the literature on hidden variable theories. (shrink)