What Is Logical Space?

Abstract

As pointed out in the introduction, the phrase “logical space” is extremely frequent in philosophical discussions, yet one hardly finds any article or monograph dedicated to the notion of logical space itself, except when it is taken as synonymous with the space of possible worlds. Wittgenstein, who introduced the phrase to philosophy in the Tractatus, never defines logical space, yet we get a clear and intuitive idea of what it is supposed to be, namely, the space of all possibilities. If that is true, then we are immediately pushed to explain what possibilities are and what it means to say that logical space is the space of all possibilities. Traditionally, it is propositions that are taken as bearers of the modal properties of possibility, necessity, impossibility and contingency, and these modal notions are in turn explained by appeal to truth at a possible world. Logical space, then, is, according to current orthodoxy, a space of possible worlds, and possibilities are propositions true at some possible world, hence, belonging to logical space. Impossibilities will be propositions that are not true at any possible world; hence, they are not in logical space. Contingencies will be propositions that are possible but false at some worlds. Necessities will be propositions that are true at all possible worlds.