Abstract
Identity Theory is based on the following core principle:It is a theory with a growing popularity among property theorists (Martin (1997); Martin and Heil (1999); Heil (2003); Strawson (2008); Schroer (2010); Jacobs (2011); Taylor (2013)). My conviction, however, is that the attractiveness of this view is mainly due to its promise to provide a solution to a (allegedly, in my view) serious problem of categorical and dispositional monism; that is, the (alleged) impossibility of purely categorical and purely dispositional properties.
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Notes
- 1.
An alternative solution to this problem is provided by the now largely neglected Double-Aspect Theory. According to this approach, each fundamental natural property has two distinct, though non-separable, aspects: the first contributes to the categoricality of its bearer, while the second to its dispositionality. One may see the search for an adequate explanation of the postulated by Double-Aspect Theory necessary connection between the two aspects of any natural property as paving the way for the Identity Theory. For the latter relies inter alia on the conviction that the best explanation of the necessary compresence of the dispositional and the categorical is that they are identical.
- 2.
There are dissenting voices claiming that laws can be metaphysically contingent even if we grant that all fundamental properties have dispositional essences (see, for example, Hendry and Rowbottom (2009)).
- 3.
For instance, it might be objected that the multi-track account is supported by a notion of manifestation that erroneously makes the presence of any kind of stimulus (be it the instantiation of dispositional or categorical features) necessary for the manifestation of each property. For instance, Esfeld and Sachse (2011, Ch.2) suggest that the manifestation of the dispositionality of electric charge is not the attraction of another opposite charge but rather the spontaneous generation of an electromagnetic field. Thinking, falsely, that the manifestation of charge is the former type of event leads to the false belief that the presence of another charge in the vicinity of the first one is a necessary condition of its manifestation.
- 4.
According to Bird’s (2007) influential account, the most serious version of the regress-of-powers-objection concerns the identity of dispositional properties in a dispositional monistic world. Roughly, if the identity of any dispositional property is determined by its relations to other properties, and those other properties are dispositional as well, then either there is an infinity of properties or there is circularity in this relationship of identities.
- 5.
According to one interpretation, a quiddity of a property is nothing other than the property itself, whereas according to an alternative construal, it is an intrinsic aspect of the property, that is, a second-order property. For more details, see Sect. 4.2.
- 6.
The theory of truthmakers allows doing that without being ontologically structured. A truthmaker is not required to be structured in the way the truth it makes true is.
- 7.
Note once again that the problem is not that we have one truthmaker for more than one truths; the truthmaking relation is not necessarily injective. It rather concerns the grounds we may have to assume that this is the case here.
- 8.
Schroer, qua identity theorist (see Schroer (2013)), does not believe in the existence of distinct kinds of property. For him, any natural property is both categorical and dispositional.
- 9.
For a detailed critique of UA, see Williams (2009).
- 10.
The conclusion of the argument is compatible with McKitrick’s (2003) view. She argues for the possibility of bare dispositions that have no distinct causal basis. For McKitrick, the causal basis of a bare disposition is the disposition itself (in the sense that it causally explains its own manifestation).
- 11.
Mumford is a realist about powers, but, to my knowledge, he is not convinced about an Ellis-like essentialism about natural kinds.
- 12.
My intention is to exclude certain trivial ‘categorical’ descriptions. For instance (arguably), one possible ‘categorical’ description (in the sense of independence of causal roles) of the property ‘electric charge’ is that it is a property possessed by electrons, protons and other charged particles.
- 13.
Variation of the phase of the wave function of a particle is an example of a transformation associated with an internal symmetry.
- 14.
By definition, a representation of a group on a vector space is an action of the group on the space, in which each member of the group acts as a linear transformation. A subspace of the vector space is said to be invariant if, for each vector of the subspace and each member of the group, the action of the group element on the vector yields another vector of the subspace. A representation is called irreducible if the only invariant subspaces of the vector space are the space itself and the subspace containing only the null vector.
- 15.
The Poincaré group (aka inhomogeneous Lorentz group) is associated with the global external symmetry under the action of Lorentz boosts and rotations, and of space–time translations.
- 16.
According to group theory, associated with any irreducible representation of a continuous group are operators (called Casimir operators) which are multiples of the unit operator, and, therefore, commute with all operators in the representation. Casimir operators have fixed numerical values in a given irreducible representation, which can be used as labels characterising the irreducible representation (Hamermesh 1989, 318). The Casimir operators of the Poincaré group are
$$ {C}_1=-{m}^2\kern0.75em {C}_2=-{m}^2s\left(s+1\right) $$Rest mass is the property which appears (as a parameter) in the first Casimir operator; that is, the one which is formalised with the aid of only one parameter (which, of course, represents mass). Having identified mass, we can then identify spin as the property represented by the second parameter which appears in the second Casimir operator (the one which is formalised with the aid of two different parameters).
- 17.
Dispositional Essentialism is a species of Dispositional Realism which primarily concerns the nature of fundamental natural properties. According to Ellis and Lierse (1994, 39), it is a metaphysical position which ‘is realistic about the dispositional properties of the fundamental particles and fields and essentialist for two reasons: first, because it holds that these properties are among the essential properties of these particles and fields and, second, because it holds that it is essential to the natural processes in which these particles and fields may be involved, that they should be displays of these dispositional properties’. Dispositional Essentialism does not hold that all fundamental natural properties are dispositional. According to Bird’s brief definition, Dispositional Essentialism is the metaphysical view that holds that at least some sparse, fundamental natural properties (and relations) have dispositional essences (i.e., have some essence that may be characterised dispositionally).
- 18.
In technical terms, the Lagrangian function L = T − V (where T and V are the kinetic and potential energy respectively) of any massive scalar field φ is invariant under the action of the following transformations:
$$ \phi \to {e}^{-i\varLambda}\phi \kern2em {\phi}^{\ast}\to {e}^{i\varLambda }{\phi}^{\ast } $$where Λ is a real constant and φ* is the complex conjugate of the field φ. These transformations are associated with the group U(1) and the corresponding (global) symmetry is an internal one.
- 19.
Consider the Lagrangian density L of a physical system and the action S related to it. According to Noether’s first theorem, if the action is invariant under a continuous group of transformations depending smoothly on independent constant parameters, then, given that the equations of motion of the system are satisfied, there are continuity equations for currents associated with each parameter on which the symmetry group depends. Given appropriate boundary conditions, each continuity equation corresponds to a conserved quantity. For technical details, see, for instance, Ryder (1985, 87–93).
- 20.
To avoid misunderstandings, by stating this conclusion, I do not endorse Mumford’s conceptual criterion for the dispositional/categorical distinction. I just show that, by Mumford’s own lights, his version of Neutral Monism has nothing to fear from the existence of ungrounded dispositions.
- 21.
For a response to the obvious objection that the suggested characterisation is not independent of causal roles after all, see the relevant discussion in Sect. 4.2.
- 22.
Of course, there is always the option to take such a resemblance as a brute fact.
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Livanios, V. (2017). Against Identity Theory and Neutral Monism. In: Science in Metaphysics . New Directions in the Philosophy of Science. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-41291-7_2
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