Modalities in Representation

Let us say a bit more about a puzzle that came about in previous posts. Let p be "the sum of the angles of a triangle is lower than 180 degrees" and C a modal operator "it is conceivable that". Consider the situation before anyone even conceived of non-euclidean geometries as a consistent alternative to euclidean geometry. Then, intuitively speaking, p was not conceivable (¬Cp). But we now know that p is true of some triangles, because the geometry of the universe is non-euclidean (p). On the other hand, it is quite natural to think that conceptual modality is factive, that is, that if something stems from conceptual necessity, then it is also true (¬C¬p→p), and this implies the converse, that if something is true, then it is conceivable (p→Cp). But these three premises are mutually inconsistent, hence our trilemma: one of the following statements must be false. ¬Cp p p→Cp So, we have exactly three options: (A) either we can claim that p always was conceivab

We have explored so far, in the previous posts, the differences between conceptual, epistemic, metaphysical and natural modalities, arguing that the two first have representational targets, but differ by the mind-dependence of their source, and that the two last have worldly targets. An important common characteristic of all these modalities is factivity: if P is necessary, in any sense of the term, then P is the case. The converse of this theorem of alethic modal logic is that if P is the case, then P is also possible, that is, compatible with the source of necessity. This is notably not the case of deontic and practical modalities: maybe it must be the case that no one walks on the grass according to the norms, but someone is doing it right now, or maybe we must stop the water from flowing into our basement, but we are not actually doing it. Deontic laws, contrarily to natural ones, can be broken. Another way of making the difference is in terms of direction of fit. If someone w

As we have seen in the previous post, we can make sense of the division between subjective and objective modalities in terms of whether they concern worldly objects, or rather our attitudes towards them. The target of necessary constraints (whether they are worldly or representational) matters, not the source of necessity. But what about the finer distinctions: what distinguishes between epistemic and conceptual possibility? And what distinguishes metaphysical and natural necessity? Consider epistemic and conceptual possibilities first. An hypothesis that flows naturally from our previous remarks is that the target of necessity is representational in both cases, but the source of necessity is markedly different in each case. With conceptual and logical necessity, the source of necessity, the origin of the constraint, lies in our representational capacities, in us, while with epistemic necessity, it lies in the external world. This means reintroducing an analytic/synthetic distinctio

Remember our list of kinds of modalities from the previous post: Logico-conceptual (Bachelor cannot be married) Epistemic (she might be at home) Metaphysical (water molecules are of the H2O kind) Natural (heavy objects must fall) Deontic (she must work tonight) Practical (we could use wood to build this plane) The two first modalities above, epistemic and logico-conceptual, are often thought to be mind-dependent or subjective, while the two next ones, metaphysical and natural, are mind-independent or objective (as for the two last ones, let us put them aside for now). Objective modalities are often used in order to analyse explanations or causation. These are the ones typically involved in counterfactual talk (if you had got up earlier, you woudn't have missed your train), although sometimes conceptual necessities are thus expressed as well (if he were a bachelor, he wouldn't be married). The distinction between objective and subjective modalities could be understood as