Types of Possibility and Necessity

Modalities (in the philosophical sense) correspond to types of possibility and necessity.

When something is necessary, it is necessary in some sense or other. There are dierent modes or ways in which a proposition, event, or thing can be necessary. For instance, physical determinists hold that events, things, or propositions are physically necessary given their antecedent conditions. The modality in this case is physical or material, as encapsulated by physical principles. Physical laws on this view determine whether or not the sun will rise next Tuesday and whether or not Jones will have a cup of coee tomorrow.

Physical modality is a good example because the notion is fairly ordinary. One way of capturing physical modality is in terms of consistency with physical laws expressed as propositions. A proposition is physically possible if and only if it is consistent with the laws of nature (perhaps given some antecedent conditions about the current and past state of the world). A proposition is physically necessary if its opposite is inconsistent with the laws of nature. There is a close relationship between physical modality and physical laws.

Natural laws could be dierent. The modality selected by could, in this case, is pre-sumably not along the lines of physical modality. Physical possibility operates under the stipulation that physical laws remain unbroken and are thus unaltered across possibilities.

That the laws of nature could be other than they are requires a change in physical principles across possibilities. Whenever physical laws are not held constant across possibilities, the modality involved is at least partially non-physical. Logically, the laws of nature could be dierent. There are other consistent sets of physical principles aside from those that actually obtain.

Hence, there are dierent ways in which events, propositions and things can be possible or necessary. The example of physical modality also indicates that modalities can often be an-alyzed in terms of consistency with a set or sets of principles expressed as propositions. Log-ical possibility involves consistency with logLog-ical principles, which is consistency simpliciter.

Metaphysical possibility involves consistency with metaphysical principles. Physical

possibil-Logical

Metaphysical Physical

Practical

Figure 2.1.1: Intensional categorization of types of possibility/necessity. This is one way in which some kinds of possibility and necessity may be categorized. The principles of each inner set are properly contained in the principles of each respective outer set.

ity involves consistency with physical principles. Permissibility, ethical possibility, involves consistency with a set of moral rules. Legality, legal possibility, involves consistency with a set of legal principles. Practical possibility involves consistency with a set of practical principles. Et cetera.

Figure 2.1.1 shows a taxonomy of a few common varieties of possibility/necessity in terms of their basic principles. Some philosophers treat metaphysical and logical possibility identically. If logical possibility is associated with consistency, then metaphysical possibility is more restrictive than logical possibility. Metaphysical possibility requires some extra principles, like that no object can be two dierent colors all over at the same time. Such laws are not true on account of their structure; that is, not logically true. The truth of metaphysical laws depends on their content. One might stipulate that metaphysical rules hold in all possible worlds. In that case, logical and metaphysical possibility would be extensionally equivalent since every world would be logically and metaphysically accessible to every other world, although logical principles are a proper subset of metaphysical principles.

For this project, modalities are primarily classied intensionally, in terms of the strictness of their dening principles. So metaphysical possibility is a proper part of logical given that

the rules of the former contain and are stricter than the those of the latter.

Here are some examples illustrating the distinction between types of possibility.

(2.1) An object can be red and green all over at the same time.

This proposition is logically possible, but not metaphysically possible.

(2.2) A glass marble dropped in a vacuum near the Earth's surface will fall away from the Earth.

This proposition is logically possible, but not physically possible.

(2.3) If Jones punches her boss in the face, she will not be red.

This proposition is physically possible, but perhaps not practically possible.

(2.1) is logically possible since there is no logical rule by which an object cannot be red and green all over at the same time. However, given the metaphysical rule that being red and being green are contrary properties, (2.1) is not metaphysically possible. In the case of (2.2), it is not logically absurd that the marble would fall away from the Earth, but for the marble to do so would be inconsistent with the laws of physics. Granted, if the universe were relevantly dierentif there were an incredibly massive object whose center of gravity is close enough to the marblethen the marble might fall away from the Earth. One might want to block such possibilities by involving antecedent conditions about the way the world is or similarly by using ceteris paribus clauses. Finally, in (2.3), the laws of physics do not entail that Jones will be red if she punches her boss in the face. There might be some other set of rules, like laws or mores, by which she cannot drive the punch home and still retain her job.

The propositions corresponding to a modality may even be world-dependent. For in-stance, dierent sets of possible worlds may vary in their physical laws. It is logically possible that empirical constants are other than they are, such as that the speed of light in a vacuum is faster than 3.00× 10⁸m/s. What is physically possible with respect to worlds

with one set of physical principles is not the same as what is physically possible from worlds with dierent physical laws.

A set or sets of principles need not be given explicitly to designate a modality. It is not a requirement that one knows everything about physical laws to speak meaningfully about physical possibilities. It is enough that there is a cohesive set of principles even if no one knows exactly what they are. A thousand years ago, most natural science was relatively underdeveloped. That does not entail that the same physical laws that hold today did not hold a thousand years ago. A thousand years from now, natural science may adhere to dierent theories than the ones held today, but it does not follow that the natural world would operate dierently in the future than it does now.

One type of modality that is especially important for this project is all-things-considered (ATC) possibility/necessity. ATCnecessity goes by several other names, including necessity per accidens, hypothetical necessity, and antecedent necessity. ATC possibility is whatever is required for an event to occur, be actualizable, or be realizable. For instance, Jones can drink coee tomorrow if and only if, all things considered, it is possible for her to do so. ATC possibility is at least as stringent as physical possibility in the sense that ATC possibility requires physical possibility; so the former incorporates the principles of the latter. Unlike some renditions of physical possibility,ATC possibility/necessity changes over time.

Again, ATC possibility is accidental possibility, whatever that amounts to. The most plausible explication ofATC possibility is that the things to be considered are the principles relevant to determining whether or not Jones' coee-drinking, for instance, is genuinely possible, actualizable, or realizable. Physical principles and antecedent conditions are of course relevant. One might impose additional factors when determining things like whether or not Jones will inevitably be red if she punches her boss, but the context-sensitivity of

all things considered is ignored here for simplicity. It is assumed that there is only one ATC possibility.

Ocially, ATC possibility is dened broadly. The reason for the nebulous denition

Figure 2.2.1: Graphical structure of a modal logic model. Possible worlds are nodes and accessibility relations are directed edges between nodes.

of ATC possibility is that what exactly it consists of is at the heart of the debate about logical fatalism. Some readers may nd it convenient to think ofATC possibility as physical possibility in the sense described for branching time systems in Section 2.4.3. Presumably, laws and antecedent conditions should be enough to dictate ATC possibility. It will be made clear when ATC possibility threatens to elude capture by principles and antecedent conditions. ATC possibility will be discussed further throughout this project.