Podcast Symposium: Simona Aimar - The Semantics of Potentiality-ascriptions

What Simona Aimar aptly calls 'potentiality ascriptions', or PAs for short, is closely related to, though not quite the same as, what philosophers have more traditionally called 'disposition ascriptions'. PAs are identified by their syntax: roughly, they are sentences that contain in their predicative part a potentiality term , an adjective of the form 'F-ile'/'F-able'/'F-ible' or slight variations of these with the appropriate contractions. Disposition ascriptions are identified by their semantics: they are sentences that ascribe properties of a certain kind, dispositions. (Or alternatively, sentences that ascribe a property picked out by a dispositional concept. In what follows, I will assume that dispositionality is a feature of properties, not of concepts.) The two classes have significant overlap: the potentiality terms 'fragile', 'soluble', and 'irascible' are paradigmatically terms that ascribe dispositions. But the overlap is not complete. 'The taxes are payable' is a PA but hardly a disposition ascription (taxes aren't the right kind of thing to have a disposition). 'The rubber band is elastic' is another paradigmatic example of a disposition ascription but, by its form, not a PA. Nevertheless, philosophers who are interested in dispositions have every reason to be interested in PAs. Many, indeed probably most, dispositions are ascribed with PAs, and semantics cannot float free of syntax. So dispositions had better be the kind of property which, by a reasonable compositional semantics, may be ascribed with a PA.

I will focus, as does Simona Aimar, on those PAs which are also uncontroversially dispositions ascriptions. The majority view among philosophers is that such ascriptions are to be understood in terms of counterfactual conditionals. The minority view is that they are best be understood in terms of possibility statements. One core motivation for the minority view is the fact that disposition ascriptions are typically PAs, and that the syntax of a PA strongly suggests a compositional semantics along the lines of the minority view: in an adjective of the form 'F-able', the verb 'F' typically denotes the disposition's manifestation, while the suffix '-able' is best understood as expressing possibility. In siding with the minority view, Simona Aimar is true to the most natural compositional semantics of disposition ascriptions.

In its simplest version, the minority view says that any PA is equivalent to a possibility claim. This, as Aimar notes, faces an immediate problem. The problem can be brought out by contrasting two different PAs:

(1) This is fragile.

(2) This is breakable.

Both fragility and breakability appear to have the same manifestation: breaking. Both (1) and (2), then, should be equivalent to

(3) This can break.

But while (3) may well do justice to (2), it is too weak to capture (1): for an object to be fragile, it is not enough that the object can break.

My reaction is to adjust the modality expressed in (1). It is not possibility but something a little stronger, which Aimar labels 'likelihood'. Roughly speaking, to be breakable an object need only break in one world; to be fragile, it must break in a few worlds. (1), then, is best understood in terms of something like

(4) This is likely to break.

(As a matter of fact, I think (4) is too strong. I would prefer to speak of an easy possibility of an object's breaking, rather than of its being likely to break. But this will not matter for present purposes, so I adopt Aimar's way of characterizing the view.)

Aimar's reaction, on the contrary, is to retain the modality but adjust its content, i.e. the manifestation of the disposition. (1) is better understood as being equivalent to

(5) This can break-under-low-impact.

Clearly, Aimar's proposal is more elegant than mine: all PAs, on her view, express the same kind of modality, possibility. This not only makes for a much neater semantics; it also avoids the awful problems that we get into as soon as we talk about proportions of possible worlds - after all, on any reasonable conception of possible worlds there are infinitely many of them, and even "a few" of those worlds may be an infinity already. So I would very much like the proposal to succeed. But I am worried that it faces a version of what Manley and Wasserman (2008) have called "Achilles' heel". Manley and Wasserman imagine “a sturdy concrete block that, like Achilles, is almost entirely immune to harm. On many occasions it has been tossed onto the floor or run over by a truck or struck with a sledgehammer. Yet it shows no sign of wear. But, like Achilles, the block has a weak spot. If it is dropped onto a particular corner at just the right angle with exactly the right amount of force, an amazing chain reaction will cause it to break”. We can easily imagine that the ‘right amount of force’ is a low-impact force, so that (5) is true of the block. We can also easily imagine that the ‘amazing chain reaction’ is caused by factors entirely intrinsic to the block, so the case cannot be explained away as one of external interference. Still, it seems obvious that the block is not fragile - (1) is not true of it. Manley and Wasserman use this kind of case to motivate what I take to be the core insight of their (2008): that dispositions, or at any rate many of them, are a matter of proportion. It is not necessary that an object yield the manifestation of a disposition in all the worlds of a specific kind, but neither is it sufficient that the object yield the manifestation in some world. Requiring that a disposition manifest in a few worlds, vague and troublesome as that is, at least precludes the singular freakish case from counting towards an object's fragility. This is why I believe the special treatment for some of the paradigmatic disposition terms - including 'fragile' and 'irascible' - must be upheld.

Aimar, of course, has further arguments in favour of her proposal, and against my alignment of (1) with (4). First, she points out that (1) and (4) are not equivalent - a lump of marble lying on a field prone to earthquakes is likely to break but not fragile. This should not be surprising, given the close relation between the syntactically identified class of PAs and the semantically identified class of disposition ascriptions. (1) is a disposition ascription - it ascribes to an object a particular property, fragility. Its truth-conditions therefore take into account features of that particular object, while ignoring various features of the world around it. (4) is no disposition ascription. It is, on a plausible reading, a sentence stating that there is some not-too-slight chance of a particular object’s breaking. Now the chance of an object’s breaking, but not its intrinsic disposition (its fragility), is influenced by the object’s position in the world, and in particular by whether or not it is lying on a field prone to earthquakes. In aligning (1) with (4), I am making a claim about the kind of modality that is inherent in (1). But apart from expressing modality, (1) also ascribes an intrinsic property to an object, while (4) does not. So it should not be surprising that the two are not equivalent.

Aimar’s second case threatens this very line of response, and with it the thought that fragility is an intrinsic property. I find this case intriguing; it is often assumed that fragility is intrinsic, but Aimar’s second case seems to show that it is not. The case may be thought of as involving two lumps of marble which are perfect duplicates, but one of which is situated on a planet whose atmospheric conditions make it break rather easily, while the other is on a planet (such as earth) whose atmospheric conditions do not make it break easily. The intuition is that (1) can be said truly of the first but not the second lump. Thus fragility, the property attributed in (1), can differ between perfect duplicates; thus it is not an intrinsic property; and thus my line of argument in the previous section fails.

I think the right line of response here is, first, to acknowledge that fragility is indeed extrinsic; and second, to point out that even an extrinsic property may be sensitive to some aspects of an object’s environments while being neutral with regard to others. The extrinsic property of being 200m from a burning barn is sensitive to facts about the presence or absence of burning barns at 200m from its bearer, but it is not sensitive to facts about the presence or absence of a palm tree at a distance of 10m from its bearer. Or to take an example from McKitrick’s (2003) defence of extrinsic dispositions, a key’s extrinsic power to open a particular door d is sensitive to facts about d but not to facts about anything else. What Aimar’s examples show, I believe, is that fragility is an extrinsic disposition which is sensitive to certain kinds of facts about its bearer’s environment -- namely, the atmospheric conditions in its vicinity -- while being insensitive to others -- namely, the probability of earthquakes at its location. Possible worlds semantics provides a way of modelling this kind of sensitivity: while for intrinsic disposition ascriptions, the modal base (the set of accessible worlds) is determined solely by the intrinsic properties of their bearer, the modal base for ascriptions of extrinsic dispositions should be determined by the intrinsic properties of the object in question plus any external circumstances to which the disposition is sensitive. Thus ‘the key has the power to open door d’ is true just in case the key does open door d in some (or a few) possible worlds where the key’s and the door’s intrinsic constitutions are as they are in actuality. And ‘the lump is fragile’ is true just in case the lump breaks in a few possible worlds where its intrinsic constitution and the gravitational field around it are as they actually are. (There are probably other factors to which fragility is sensitive, and which will have to be added to my clause.)

The question remains why fragility is sensitive to gravitational fields but not to the probability of earthquakes in its bearer’s location. This, I think, is not a question for formal semantics to answer, but I will indicate what is at present my best guess. I suspect that the asymmetry has something to do with the practical prospects for moving an object from earthquake-prone fields to safer locations (generally feasible) vis-à-vis those for moving an object from one gravitational field to another (virtually impossible for us). Atmospheric conditions are the kind of conditions that we think of as stable background conditions; after all, space travel is a relatively new invention. An object’s location in space, on the other hand, is the kind of condition that we think of as unstable, transient, easily changed. If that is so, it is not too surprising that the former are held fixed in evaluating certain modal statements - including (1) - while the latter are allowed to vary.

References:

D. Manley and R. Wasserman (2008): On Linking Dispositions and Conditionals. Mind 117, pp. 59-84.

J. McKitrick (2003): A Case for Extrinsic Dispositions. Australasian Journal of Philosophy 81, pp. 155-174.