It is a venerable slogan due to David Hume, and inherited by the empiricist tradition, that the impossible cannot be believed, or even conceived. In Positivismus und Realismus, Moritz Schlick claimed that, while the merely practically impossible is still conceivable, the logically impossible, such as an explicit inconsistency, is simply unthinkable. -/- An opposite philosophical tradition, however, maintains that inconsistencies and logical impossibilities are thinkable, and sometimes believable, too. In the Science of Logic, Hegel already complained against “one of the (...) fundamental prejudices of logic as hitherto understood”, namely that “the contradictory cannot be imagined or thought” (Hegel 1931: 430). Our representational capabilities are not limited to the possible, for we appear to be able to imagine and describe also impossibilities — perhaps without being aware that they are impossible. -/- Such impossibilities and inconsistencies are what this entry is about... (shrink)

The common view has it that there are two families of approaches towards the logical structure of impossible worlds – Australasian and North American. According to the first, impossible worlds are closed under the relation of logical consequence of one of the non-classical logics. The North American approach is more liberal, allowing for impossible worlds where no logic holds. After pointing out the questionable consequences of each view, I propose a third one. While this new perspective allows for worlds where (...) no logical consequence holds, it also imposes some constraints on what worlds are built upon. This renders the proposed view not as restrictive as the Australasian approach and not as liberal as the North American approach. Due to its intermediary nature, I have named this perspective ‘the Pacific’ approach. (shrink)

The paper proposes a solution to the problem of counterfactuals, building on both Rescher’s epistemic and Tichý’s semantic approaches. The core of the proposed solution is the thesis that when expressing a true counterfactual, the speaker assumes a set of background indicative premises as an implicit parameter. When added tacitly to an unreal antecedent, these premises entail the consequent logically or analytically. We draw a distinction between a potentially unreal and an absolutely unreal condition expressed in the antecedent. We view (...) counterfactuals with a positive time vector and an absolute unreal condition as abbreviated deductive retrodictions. Similarly, we consider counterfactuals with a potentially unreal condition to be abbreviated deductive predictions. In a similar manner, we also explain the truth (falsity) of vacuously true counterpossibles or counterpossible conditionals. In the second part, we discuss the enigmatic backtracking counterfactuals. We propose that their negative time direction is due to their being abductive retrodictions, i.e., explanations of unreal effects based on possible causes in which the conditions remain tacit or unexpressed. The backtracking temporal direction of counterfactual abductive retrodictions is in accordance with the thesis on the positive temporal direction from cause to effect. Thus, we demonstrate that in order to explain backtracking counterfactuals, there is no need to assume violations of laws of nature or a special logic. What we need to do is to take into account the third parameter, i.e., a set of tacit or unexpressed additional propositions, as well as the principle of ceteris paribus as the background. (shrink)