How to solve the knowability paradox with transcendental epistemology

A novel solution to the knowability paradox is proposed based on Kant’s transcendental epistemology. The ‘paradox’ refers to a simple argument from the moderate claim that all truths are knowable to the extreme claim that all truths are known. It is significant because anti-realists have wanted to maintain knowability but reject omniscience. The core of the proposed solution is to concede realism about epistemic statements while maintaining anti-realism about non-epistemic statements. Transcendental epistemology supports such a view by providing for a sharp distinction between how we come to understand and apply epistemic versus non-epistemic concepts, the former through our capacity for a special kind of reflective self-knowledge Kant calls ‘transcendental apperception’. The proposal is a version of restriction strategy: it solves the paradox by restricting the anti-realist’s knowability principle. Restriction strategies have been a common response to the paradox but previous versions face serious difficulties: either they result in a knowability principle too weak to do the work anti-realists want it to, or they succumb to modified forms of the paradox, or they are ad hoc. It is argued that restricting knowability to non-epistemic statements by conceding realism about epistemic statements avoids all versions of the paradox, leaves enough for the anti-realist attack on classical logic, and, with the help of transcendental epistemology, is principled in a way that remains compatible with a thoroughly anti-realist outlook

Axiomatic foundations of quantum mechanics revisited: the case for systems

We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is discussed in this framework. It is shown that there is no contradiction between realism and recent experimental results.Comment: submitted to International Journal of Theoretical Physics, uses Latex, no figure

Hardy's Non-locality Paradox and Possibilistic Conditions for Non-locality

Hardy's non-locality paradox is a proof without inequalities showing that certain non-local correlations violate local realism. It is `possibilistic' in the sense that one only distinguishes between possible outcomes (positive probability) and impossible outcomes (zero probability). Here we show that Hardy's paradox is quite universal: in any (2,2,l) or (2,k,2) Bell scenario, the occurence of Hardy's paradox is a necessary and sufficient condition for possibilistic non-locality. In particular, it subsumes all ladder paradoxes. This universality of Hardy's paradox is not true more generally: we find a new `proof without inequalities' in the (2,3,3) scenario that can witness non-locality even for correlations that do not display the Hardy paradox. We discuss the ramifications of our results for the computational complexity of recognising possibilistic non-locality

Argument for the incompleteness of quantum mechanics based on macroscopic and contextual realism: EPR and GHZ paradoxes with cat states

The Einstein-Rosen-Podolsky (EPR) paradox gives an argument for the incompleteness of quantum mechanics based on the premise of local realism. The general viewpoint is that the argument is compromised, because local realism is falsifiable by Bell or Greenberger-Horne-Zeilinger (GHZ) experiments. In this paper, we challenge this conclusion, by presenting alternative versions of the EPR paradox based on premises not falsifiable by the GHZ and Bell predictions. First, we explain how the Bohm-EPR and GHZ paradoxes can be demonstrated using macroscopic spins $S_\theta$ formed from qubits realized as two macroscopically distinct states. This establishes an 'all or nothing' incompatibility between quantum mechanics and macroscopic realism (MR). However, we note different definitions of MR. For a system in a superposition of two macroscopically distinct eigenstates of $S_\theta$, MR posits a definite value for the outcome of $S_\theta$. Deterministic macroscopic realism (dMR) posits MR regardless of whether the interaction $U_\theta$ determining the measurement setting $\theta$ has occurred. In contrast, the weaker assumption, weak macroscopic realism (wMR), posits MR for the system prepared after $U_\theta$. We show that the GHZ paradox negates dMR but is consistent with wMR. Yet, we show that a Bohm-EPR paradox for the incompleteness of quantum mechanics arises based on either form of MR. Since wMR is not falsified, this raises the question of how to interpret the EPR paradox. We revisit the original EPR paradox and find a similar result: The EPR argument can be based on a contextual version of local realism (wLR) not falsifiable by Bell or GHZ experiments. The premises wLR and wMR posit realism and no-disturbance for systems prepared with respect to a pointer basis (after $U_\theta$), leading to further predictions giving consistency with quantum mechanics

Uncertainty relations for the realisation of macroscopic quantum superpositions and EPR paradoxes

We present a unified approach, based on the use of quantum uncertainty relations, for arriving at criteria for the demonstration of the EPR paradox and macroscopic superpositions. We suggest to view each criterion as a means to demonstrate an EPR-type paradox, where there is an inconsistency between the assumptions of a form of realism, either macroscopic realism (MR) or local realism (LR), and the completeness of quantum mechanics.Comment: 9 pages, 2 figures, to appear Journ Mod Optics work presented at PQE 2007 conferenc

A Neglected Response to the Paradoxes of Confirmation

Hempel‘s paradox of the ravens, and his take on it, are meant to be understood as being restricted to situations where we have no additional background information. According to him, in the absence of any such information, observations of FGs confirm the hypothesis that all Fs are G. In this paper I argue against this principle by way of considering two other paradoxes of confirmation, Goodman‘s 'grue‘ paradox and the 'tacking‘ (or 'irrelevant conjunct‘) paradox. What these paradoxes reveal, I argue, is that a presumption of causal realism is required to ground any confirmation; but once we grant causal realism, we have no reason to accept the central principles giving rise to the paradoxes