Tomasz Bigaj

This is a response to a critical review of my book Non-locality and Possible Worlds (Ontos Verlag, Frankfurt 2006) by Witold Strawiński. I present arguments why counterfactual conditionals are needed in the description of quantum-mechanical phenomena, and in particular in the analysis of the condition of locality. I rebut arguments against my choice of the relation of similarity between possible worlds offered by W. Strawiński and M. Dickson. In the later part of the article I address some other issues raised by my critics, such as the problem of the truth value of the antecedents of true counterfactuals, the problem of the semantic relation between sentences and events, and various shortcomings of my formulations of the condition of locality. In my response to the specific criticism of the definition of free-choice events, I agree with the charge that my definition is satisfied by all actual events. I present a correction to the definition which uses the distinction between actual events and merely possible events.

This paper addresses the issue of the multiplicity of various grades of discernibility that can be defined in model theory. Building upon earlier works on the subject, I first expand the known logical categorizations of discernibility by introducing several symmetry-based concepts of discernibility, including one I call “witness symmetry-discernibility”. Then I argue that only grades of discernibility stronger than this one possess certain intuitive features necessary to individuate objects. Further downsizing of the set of non-equivalent grades of discernibility can be achieved by stipulating that any relation of discernibility should be applied only to those pairs of objects which have been previously distinguished from the rest of the universe. Restricting discernibility to pairs of objects satisfying this condition gives an additional bonus in the form of restoring the transitivity of some types of indiscernibility which have been known to be non-transitive.

In the article I discuss possible amendments and corrections to Lewis’s semantics for counterfactuals that are necessary in order to account for the indeterministic and non-local character of the quantum world. I argue that Lewis’s criteria of similarity between possible worlds produce incorrect valuations for alternate-outcome counterfactuals in the EPR case. Later I discuss an alternative semantics which rejects the notion of miraculous events and relies entirely on the comparison of the agreement with respect to individual facts. However, a controversy exists whether to include future indeterministic events in the criteria of similarity. J. Bennett has suggested that an indeterministic event count toward similarity only if it is a result of the same causal chain as in the actual world. I claim that a much better agreement with the demands of the quantum-mechanical indeterminism can be achieved when we stipulate that possible worlds which differ only with respect to indeterministic facts that take place after the antecedent-event should always be treated as equally similar to the actual world. In the article I analyze and dismiss some common-sense counterexamples to this claim. Finally, I critically evaluate Bennett’s proposal regarding the truth-conditions for true-antecedent counterfactuals.