Modality

Modal notions, such as possibility and necessity, play an important role in metaphysical considerations. Intuitively, we can distinguish two ways of speaking about possibilities. We can say that it is now possible that an object might change in the future. For instance this chair may be painted in a colour different from the one it has right now. This type of possibility can be called temporal. But in a different sense it is possible that the chair might have a different colour right now – if it had been painted this colour before. This kind of possibility, which applies to the present time as well as to the past (I can say that I might have been born in a different town), will be referred to as counterfactual possibility. It is interesting to notice that counterfactual and temporal notions of possibility are logically independent, i.e. one does not imply the other. From the fact that some state of affairs is counterfactually possible it does not follow that this state of affairs is possible temporarily. A given sculpture could have a different shape now, but once it receives its actual shape it cannot be turned into a different statue in the future (Rodin’s sculpture “The kiss” could have been “The thinker” in the counterfactual sense, but not in the temporal sense). Conversely, although a seed can grow into a tree in the future, it could not be a tree right now. It should be added that counterfactual possibility, in spite of what the term suggests, does not exclude actuality. Actual states of affair are considered possible in the counterfactual sense.

Counterfactual possibility is often presented in the language that uses the concept of possible worlds. A proposition is possible if it is true in some possible worlds. Possible worlds themselves are usually interpreted as complexes (sums) of situations (states of affairs). An example of a possible situation may be that Poland has a king now. Possible worlds have to satisfy two conditions: the condition of consistency and the condition of completeness. A situation s is consistent if there is no proposition p such that p and not-p are true in s. A situation s is complete if for all propositions p, either p is true in s or not-p is true in s. From these two conditions it follows that two numerically distinct possible worlds are mutually exclusive (incompatible), i.e. there is a proposition p such that p is true in one world, and p is false in the other one. Situations that are not complete don’t have to be exclusive. An example: that this ball is red and that this ball is round. The world that we live in is called the actual world, and it is interpreted in the same way as other possible worlds. It is natural to assume that the actual world is complete, i.e. every proposition is either true or its negation is true in the actual world.

Let us see how we can use the notion of possible worlds in order to explicate some modal terms, such as possibility, necessity and contingency. These notions can be applied to propositions as well as to objects. Proposition p is possible iff p is true in some possible world. Proposition p is necessary iff p is true in all possible worlds. And p is contingent iff p is true in some possible worlds and it’s false in some possible worlds. Similarly we can define possible, necessary and contingent objects. A possible object is an object that exists in some possible worlds. A necessary object exists in all possible worlds, and a contingent object exists in some worlds, but in some it does not. The usual examples of necessary truths are the laws of logic and of mathematics. Necessary beings, in turn, typically include mathematical objects and other abstract objects. Some also cite God as an example of a necessary being. It is open to a debate whether there are any spatiotemporal necessary objects (perhaps the universe as a whole can satisfy this requirement).

Let us make an important distinction between modality de re and de dicto. Modality de dicto applies to the entire sentence, whereas modality de re is attributed to a given object. The sentence “It is possible that some man is the present king of Poland” belongs to the de dicto type, whereas “Some man is possibly the king of Poland” is de re. The first sentence can be presented in a semi-formal way as “It is possible that for some x, x is a man and x is the king of Poland”, and this sentence in turn is true if and only if there is a possible world in which Poland has a king. The second sentence translates into “For some x, x is a man and it is possible that x is the king of Poland”, and in order for this proposition to be true, there has to exist someone in the actual world who, in another possible world is the king of Poland. (These explications presuppose of course that one and the same object can exist in different possible worlds.) The second proposition logically implies the first, but the implication in the opposite direction is a matter of some controversy (the validity of the so-called Barcan law). Another example illustrating the de re/de dicto distinction is as follows: “The number of planets in the solar system is necessarily divisible by 2” (de re) and “It is necessary that the number of planets in the solar system is divisible by 2” (de dicto). The first translates into “There is an x such that x is the number of planets in the solar system and it is necessary that x is divisible by 2”, and the second reads “It is necessary that there is an x such that x is the number of planets in the solar system and x is divisible by 2”. The truth of the first sentence follows from the simple arithmetical fact that 8 is (necessarily) divisible by 2, but for the second sentence to be true, the number of planets in all possible worlds would have to be even.

We can now define an important notion of an essential property. P is an essential property of object a iff for every possible world w, if a exists in w, a has P in w. Loosely speaking, if an object loses its essential property, it ceases to be itself. Napoleon’s essential property is being a human, but being the victor from Austerlitz belongs to his accidental properties (in some possible worlds Napoleon lost the battle of Austerlitz). It is interesting to ask whether things have individual essences, i.e. essential properties such that only one object can possess them all. More specifically, the individual essence of object a is a set S of essential properties of a such that in any possible world w, if x possesses all properties from S, x is identical with a. Some philosophers claim that the individual essence of an object a is the property of being identical with a. However, this interpretation prevents us from using the notion of essence in order to explicate transworld identity. According to a different view, an object’s individual essence is its origin, i.e. the cause of its existence. In the case of human beings, their essence would be determined by the zygote (the fertilized egg) that developed into a particular person. Yet another version of essentialism insists that an object’s essence is its constitution, i.e. all parts the object consists of.

Further reading:

E.J. Lowe, Chapter 5, “Necessity and identity”, pp. 79-84; Chapter 6 “Essentialism”, pp. 98-114, in: A Survey of Metaphysics.