Eternal Possibilities: A Neutral Ground for Meaning and Existence

3. Relations among Eternal Possibilities: The Nexus

Relations among Eternal Possibilities The Nexus 3 THIS CHAPTER makes several related claims. First, it proposes that there is a specific difference distinguishing eternal possibility from actuality. They differ as the determinable and the determinate. Second, there are certain relations that prevail among properties existing as possibles. These relations are not peculiar to properties existing in that way; but they are more conspicuous in possibility; and it is by reference to the determinability of possibles that we discover why it is that properties need have these relations to one another. The relations themselves are called vertical and lateral. Relations of both kinds are intrinsic to property fields. The identity of a name property derives in part from its dependency on other properties of its field. We explain that by appealing to these relations as they are founded in the determinability of properties. Third, properties having these relations are organized as hierarchical structures. Structures that satisfy certain least conditions are possible worlds. 1. PROPERTIES, we know, are sometimes actual. We have to provide now for these same properties existing as possibles. Possibility and actuality are, apparently, two modes of existence. They are, I believe, the only two modes. It may be that there are other, unsuspected modes, but there is neither evidence of, nor a role for them. Necessity and contingency might be described as 109 Eternal Possibilities other modes; but they are, more accurately, measures of the security with which properties exist as possibilities or actualities. I shall sometimes refer to possibility and actuality as counterpart modes of existence, meaning that they are the mutually exclusive and exhaustive modes, and that properties existing as possibles may also exist as actuals. There is a specific difference by which possibility and actuality, two species of the genus existence, are distinguished from one another. That factor is determinacy; possibility differs from actuality as the determinable differs from the determinate. Actuality is determinate in respect to quality and number. Considered qualitatively, it is not further determinable. We express that point when saying that the difference of the generic and the specific is a distinction of reason and not of fact as it applies to actual states of affairs. There are Airedales, Spaniels, and various mixed breeds running our streets, not simply animals or even dogs; things are scarlet or pink, not merely colored or red. When a property changes, it loses one determinate quality in favor of a different but still determinate one, becoming, for example, a deeper or lighter blue, but never moving from the genus blue to a particular shade of blue, or the reverse. This qualitative determinacy is a first measure of actuality. It extends to each of a property's three marks, e.g., its quality, quantity , and relation. Thus colors instantiated have a certain hue together with being saturated to a definite intensity. They are of course self-identical. Properties which are determinate in these three respects, mathematicals for example, may nevertheless be wanting in respect to one further sort of determinacy that is essential to actuals. The properties may not be particularized as individuals in space and time. For it is not triangularity, however determinate, but particular triangles that are actual. Eternal possibilities differ from actualities because of being determinable in quality and number. All but a significant subset of possibilities are qualitatively determinable ; as I shall be describing them, they are further Relations among Eternal Possibilities 111 determinable. Every possibility is determinable numerically, for it is not itself individuated by having a place in space and time. There is also the further reason that an indefinite number of particulars having spatial and temporal location may come to instantiate it. 2. EVERY definite difference exists, separate from every other, as a possibility. That follows from the principle of plenitude. Whatever is not a contradiction is possible, so that generic properties, no less than qualitatively determinate ones, exist as possibles. These generic properties are not less than definite because of being determinable. Each is determinable because of having a range of lower-order expressions, as the possibilities for circle and square are more determinate instances of the determinable, shape. But a generic property is also definite ; it is the possibility for this or that feature, or set of features. It is determinable, but not vague: it is the possibility for certain least properties, and its identity is distinct from that of every other possibility sanctioned by the...