Modal terms such as ‘possible’ and ‘physically possible’ can be understood in different ways.
We do not attempt to overview the enormous philosophical literature: our focus is on the possible worlds approach that understands alethic modal statements that invoke possibility as an existential quantification over possible worlds1. According to this characterization if the statement ‘time travel is physically possible’ were true then it should be understood as the statement that ‘there exists a physically possible world in which time travel happens.’ I submit that this approach is not merely predominant among philosophers and philosophers of science but also among physicists when they talk of possibilities offered by our most fundamental theories. When asked whether time travel is physically possible physicists routinely point to the existence of mathematical models that satisfy Einstein’s equation and feature time travel. Taking the existence of such global models as evidence for physical possibility – even though these models do not resemble and may even be incompatible with our actual world – is best explained by the implicit adoption of the possible worlds approach2.
1Thinking in terms of possible worlds goes back at least to Leibniz; for a modern introduction seeKripke (1959, 1963a,b) and Lewis (1973). There are philosophical approaches, such as that of Meinong (1960), Fine(1994), or Jubien (1996) that do not understand possibility in terms of possible worlds; for a general overview of the literature on possibility and ‘possible objects’ see i.e.Yagisawa(2009).
2The possible worlds approach have not always been so predominant. Planck and many other nineteenth century physicists understood the term (physically) possible as ‘available in the actual world.’ For them the
Ba
Note that physical possibility is not intended as an epistemic notion: physically possible worlds are not to be equated with epistemically possible worlds, that is with possible worlds that are compatible with some state of knowledge of observers. Lack of observers’ knowl-edge may influence their epistemic possibilities but it does not bear upon what systems or interactions are physically possible3.
Thereceived view of physical possibilityis the conjunction of the possible worlds approach with the tenet that it is physical laws that determine what is physically possible. The conjunction, albeit it is widely accepted, is not necessary. One may entertain either of these assumptions without the other: one may accept that the notion of physical possibility should be analyzed via a possible world approach but deny that the set of physically possible worlds
truth of the statement that ‘a perpetual motion machine is physically possible’ depended upon whether we could actually build one given the furniture of our actual world, that is given the systems and interactions that actually are. (For historical notes on different understandings of physical possibility see i.e. Uffink (2001).) Such an actualist account of possibility faces many difficulties, especially if we adopt the view that our actual world is best represented by a distribution of modally thin definite physical quantities on a spacetime structure, which is arguably the way how the actual world is represented by a solution of a differential equation. A system or process then either exists or does not exist in the (modally thin) actual world and hence making room for the possible in the actual is not straightforward (for an alternative research project that represents a possible world as not modally thin seePlacek and Belnap(2012) and its references;
on modal thinness of physical quantities see also (Belot; 2011, p. 108)). Notions such as ‘could actually build’ also carry connotations of agency which is difficult to reconcile with modal thinness, definiteness, and the assumption that agents are also subject to the same physical laws as other systems and interactions.
Despite these worries I ultimately believe that the correct account of physical possibility is actualist, but an analysis would go beyond the scope of the present work.
3The hierarchy of modal notions is convoluted. It is customary to make distinction among logical, epistemic, metaphysical, nomic / natural, and physical possibility, logical possibility being the most and physical possibility being the least permissive. For the purposes of this work we assume that epistemic possibility differs from metaphysical, nomic, and physical possibility; we do not take stance in whether the latter three notions differ but we tend to use them interchangeably. Distinction between physical possibility and physical laws vs. nomological possibility and natural laws becomes important if we contemplate the existence of natural laws which are not (and which do not supervene in an appropriate sense on) physical laws; such distinction is often emphasized by philosophers of mind. Whether nomic and metaphysical possibility coincides is a debate between the so-called necessitarians and contingentist (see Kment (2012)).
There are many other modal notions such as practical, medical, moral, legal etc. possibility that do not enter to our discussion, although we note that some nineteenth century physicists, such as Lord Kelvin and Maxwell, were concerned with a notion of possibility that is dependent upon the human condition (seeUffink (2001)).
Ba
is determined by physical laws (either because there are no physical laws or because physical laws are not sufficient to determine which possible worlds fall into the set of physically possible worlds)4. One may also accept that physical laws determine what is physically possible but deny that what is physically possible should be analyzed in terms of possible worlds5. In the rest of this work we concern ourselves with the received view of physical possibility and we explore strategies to defend the idea that only well posed problems give rise to physically possible worlds in the light of the received view.
The received view makes reference to physical laws; we now take a brief detour to discuss the question: what are physical laws?
4There is a point of contact here with the ongoing debate about the nature of scientific theories. The so-calledsemantic view maintains that one should think of a scientific theory T as a class of modelsMT. The most radical form (SMV5 in the terminology ofEarman(2008)) of the semantic view claims that this class of modelsMT in general can not be obtained as a set ofL-structures (as a set of models in the logical sense) of formulas ∆ of some suitable formal language: MT 6=mod(∆) for any ∆ set of propositions (for such pronouncement see (van Fraassen;1989, pp. 211-212); also see (Earman;2008, p. 20)). If laws of a physical theoryT can be formulated axiomatically then the radical version of the semantic view denies that the set of modelsMT which a physical theory is supposedly identified with are the L-structures that satisfy these physical laws. Since we can also naturally viewMT as the set of models that represent physical possibilities according toT the radical version of the semantic view seems to accept the possible world analysis but deny that the set of physically possible worlds are those that satisfy the physical laws. The radical version of the semantic view may then deny the received view while still entertain a possible world analysis of physical possibility. (Some proponents of the radical version of the semantic view such as van Fraassen indeed must deny the received view as he also denies that laws of nature exist; see later.)
I don’t find the arguments presently cited in favor of the radical version of the semantic view convincing (mainly in agreement with the challenges formulated by Earman (2008); also see Halvorson (2012) for a different line of attack). I note, however, that while reading (B’) of physical possibility (see later)isaccepting of the received view of physical possibility it is also consistent with the radical claim of the semantic view of scientific theories. In reading (B’) the set of physically possible worlds isdeterminedby the physical laws but this set may not coincide with the set of models that satisfythe laws or satisfy some other set of formulas.
Whether this is so depends on the definability of the mapping Λ :L → W that assigns to a set of laws the possible worlds in which those are laws. Undefinability of Λ would imply the radical claim of the semantic view.
5An actualist approach to physical possibility mentioned in a previous footnote would be such a position.
Ba lazs
Gy enis
:Well posednes
sand ph
ysical possibilit
y