Identity of Indiscernibles

In my review of Steven French's The structure of the world. Metaphysics & Representation. OUP, Oxford, 2014 I argue that the author is forced to navigate between the Scilla of Tegmark’s Pitagoreanism (2008) and the Carybdis of “blobobjectivism” (Horgan and Potrč 2008), namely the claim that the whole physical universe is a single concrete structurally complex but partless cosmos (a “blob”).

I argue that there is an ambiguity in the concept of indiscernibility as applied to objects, because there are two different categories of properties, associated with two different ways in which all of the pre-theoretical 'properties' of an object may be identified. In one structural way, identifications of properties are independent of any particular spatial orientation of the object in question, but in another 'field' way, identifications are instead dependent on an object's particular spatial orientation, so that its properties as (...) thus identified in one orientation are distinct from its properties as identified in any other orientation--all of which ‘field’ properties must hence also be distinct from the previous structurally defined properties. -/- To accommodate the two kinds of intrinsic properties, the standard concept of indiscernibility is redefined as structural indiscernibility, while a new concept of field indiscernibility is introduced. I argue among other things that, though two objects may be structurally indiscernible under all orientational (and other) conditions, those objects may nevertheless fail to have field indiscernibility with each other under some orientational conditions. I also briefly discuss the implications of these results for general issues about the nature of properties, and of realist versus nominalist approaches to them. -/- . (shrink)

Ladyman and Ross argue that quantum objects are not individuals and use this idea to ground their metaphysical view, ontic structural realism, according to which relational structures are primary to things. LR acknowledge that there is a version of quantum theory, namely the Bohm theory, according to which particles do have denite trajectories at all times. However, LR interpret the research by Brown et al. as implying that "raw stuff" or haecceities are needed for the individuality of particles of BT, (...) and LR dismiss this as idle metaphysics. In this paper we note that Brown et al.'s research does not imply that haecceities are needed. Thus BT remains as a genuine option for those who seek to understand quantum particles as individuals. However, we go on to discuss some problems with BT which led Bohm and Hiley to modify it. This modified version underlines that, due to features such as context-dependence and non-locality, Bohmian particles have a very limited autonomy in situations where quantum effects are non-negligible. So while BT restores the possibility of quantum individuals, it also underlines the primacy of the whole over the autonomy of the parts. The later sections of the paper also examine the Bohm theory in the general mathematical context of symplectic geometry. This provides yet another way of understanding the subtle, holistic and dynamic nature of Bohmian individuals. We finally briefly consider Bohm's other main line of research, the "implicate order", which is in some ways similar to LR's structural realism. (shrink)

The Principle of the Identity of Indiscernibles , according to which two objects are identical if they share all the same properties, has come in for much criticism. Michael Della Rocca has recently defended PII on the grounds that it is needed to forestall the possibility that where there appears to be only one object present, there is actually a multiplicity of exactly-overlapping such objects. Katherine Hawley has criticized this approach for violating a plausible “ground rule” in applying rules of (...) indiscernibility to questions of identity: where there is putative duplication, it must be qualitatively significant. Hawley further suggests that with this rule in hand, one can tell the difference between the presence of one and two indiscernible objects without recourse to either PII or brute, nonqualitative individuation. In this paper, I critically examine Hawley’s contention and find that her appeal to “qualitatively significant duplication” fails since its application to distinct indiscernibles involves a difference that is primarily quantitative anyway. The upshot is a different proposed set of “ground rules” for applying the criterion of qualitative difference when seeking a grounding or explanation for distinctness and identity. (shrink)

Goetz outlined legal models of identical entities that include natural persons who are identical to a coregency and natural persons who are identical to a general partnership. Those entities cohere with the formula logic of relative identity. This essay outlines the coexistence of relative identity and numerical identity in the models of identical legal entities, which is impure relative identity. These models support the synthesis of Relative Trinitarianism and Social Trinitarianism, which I call Relative-Social Trinitarianism.

A prominent version of mathematical structuralism holds that mathematical objects are at bottom nothing but "positions in structures," purely relational entities without any sort of nature independent of the structure to which they belong. Such an ontology is often presented as a response to Benacerraf's "multiple reductions" problem, or motivated on hermeneutic grounds, as a faithful representation of the discourse and practice of mathematics. In this paper I argue that there are serious difficulties with this kind of view: its proponents (...) rely on a distinction between "essential" and "nonessential" features of mathematical objects, and there's no good way to articulate this distinction which is compatible with basic structuralist commitments. But all is not lost. For I further argue that the insights motivating structuralism (or at least those worth preserving) can be preserved without formulating the view in ontologically committal terms. (shrink)

Composition as identity, as I understand it, is a theory of the composite structure of reality. The theory’s underlying logic is irreducibly plural; its fundamental primitive is a generalized identity relation that takes either plural or singular arguments. Strong versions of the theory that incorporate a generalized version of the indiscernibility of identicals are incompatible with the framework of plural logic, and should be rejected. Weak versions of the theory that are based on the idea that composition is merely analogous (...) to identity are too weak to be interesting, lacking in metaphysical consequence. I defend a moderate version according to which composition is a kind of identity, and argue that the difference is metaphysically substantial, not merely terminological. I then consider whether the notion of generalized identity, though fundamental, can be elucidated in modal terms by reverse engineering Hume’s Dictum. Unfortunately, for realists about possible worlds, such as myself,... (shrink)

This is a short response to Aaron Cotnoir's 'Composition as General Identity', in which I suggest some further applications of his ideas, and try to press the question of why we should think of his 'general identity relation' as a genuine identity relation.

Leibniz was a philosopher of principles: the principles of Contradiction, of Sufficient Reason, of Identity of Indiscernibles, of Plenitude, of the Best, and of Continuity are among the most famous Leibnizian principles. In this article I shall focus on the first three principles; I shall discuss various formulations of the principles (sect. 1), what it means for these theses to have the status of principles or axioms in Leibniz’s philosophy (sect. 2), the fundamental character of the Principles of Contradiction and (...) Sufficient Reason (sect. 3), some attempts to demonstrate the Principles of Contradiction and Sufficient Reason (sect. 4), and one attempt to demonstrate the Principle of Identity of Indiscernibles (sect. 5). The main results of the chapter are summarized in a short conclusion (sect. 6). (shrink)

This essay proposes an ontological model in which a legal person such as a polity possesses natural unity from group properties that emerge in the self-organization of the human population. Also, analysis of customary legal persons and property indicates noncontradictory paradoxes that include Aristotelian essence of an entity, relative identity over time, ubiquitous authority, coinciding authorities, and identical entities. Mathematical modeling helps to explain the logic of the paradoxes.

Orthodox neural materialists think mental states are neural events or orthodox material properties of neutral events. Orthodox material properties are defining properties of the “physical”. A “defining property” of the physical is a type of property that provides a necessary condition for something’s being correctly termed “physical”. In this paper I give an argument against orthodox neural materialism. If successful, the argument would show at least some properties of some mental states are not orthodox material properties of neural events. Opposing (...) philosophical orthodoxy, I show there are no posteriori identities -- identities that cannot be known of a priori. (shrink)

The initial one-third of the paper is devoted to exposing the first chapter (“Sense-Certainty”) of Hegel’s PHENOMENOLOGY OF SPIRIT as a thesis about reference, viz., that singular demonstrative reference is impossible. In the remainder I basically argue that such a view commits one to radically undermining our conceptions of space, time, and substance (concrete individuality), and rests on the central mistake of construing <this> on the model of a predicable (or property).

This paper offers a critical assessment of the current state of the debate about the identity and individuality of material objects. Its main aim, in particular, is to show that, in a sense to be carefully specified, the opposition between the Leibnizian ‘reductionist’ tradition, based on discernibility, and the sort of ‘primitivism’ that denies that facts of identity and individuality must be analysable has become outdated. In particular, it is argued that—contrary to a widespread consensus—‘naturalised’ metaphysics supports both the acceptability (...) of non-qualitatively grounded (both ‘contextual’ and intrinsic) identity and a pluralistic approach to individuality and individuation. A case study is offered that focuses on non-relativistic quantum mechanics, in the context of which primitivism about identity and individuality, rather than being regarded as unscientific, is on the contrary suggested to be preferable to the complicated forms of reductionism that have recently been proposed. More generally, by assuming a plausible form of anti-reductionism about scientific theories and domains, it is claimed that science can be regarded as compatible with, or even as suggesting, the existence of a series of equally plausible grades of individuality. The kind of individuality that prevails in a certain context and at a given level can be ascertained only on the basis of the specific scientific theory at hand. (shrink)

1. The Bundle Theory I shall discuss is a theory about the nature of substances or concrete particulars, like apples, chairs, atoms, stars and people. The point of the Bundle Theory is to avoid undesirable entities like substrata that allegedly constitute particulars. The version of the Bundle Theory I shall discuss takes particulars to be entirely constituted by the universals they instantiate.' Thus particulars are said to be just bundles of universals. Together with the claim that it is necessary that (...) particulars have constituents, the fundamental claim of the Bundle Theory is: (BT) Necessarily, for every particular x and every entity y, y constitutes x if and only ify is a universal and x instantiates y. 2 The standard and supposedly devastating objection to the Bundle Theory is that it entails or is committed to a false version of the Principle of Identity of Indiscernibles (Armstrong 1978: 91, Loux 1998: 107), namely: (Pll) Necessarily, for all particulars x and y and every universal z, if z is instantiated by x if and only if z is instantiated byy, then x is numerically identical with y. The most famous counterexample to the Identity of Indiscernibles is that put forward by Max Black, consisting of a world where there are only two iron spheres two miles apart from each other, having the same diameter, temperature, colour, shape, size, etc (Black 1952: 156). Let us from now on think of the properties of the spheres in this world as universals. The possibility of this world, which I shall hereafter refer to as 'Black's world', makes (Pll) false.' And according to common philosophical opinion this means that the Bundle Theory is false.. (shrink)

If ordinary particulars are bundles of properties, and if properties are said to be universals, then three well-known objections arise : no particular can change, all particulars have all of their properties essentially (even the most insignificant ones), and there cannot be two numerically distinct but qualitatively indiscernible particulars. In this paper, I try to make a little headway on these issues and see how the objections can be met, if one accepts a certain view about persistence through time and (...) across possible worlds – namely, four-dimensionalism and its modal analogue. The paper is especially devoted to the second and third of the three objections. (shrink)

After sketching some aspects of truthmaker doctrines and "truthmaker projects", and canvassing some prima facie objections to the latter, I turn to an issue which might seem to involve confusion about the nature of character of truthmakers if such there be, viz for statements of identity and (specially) distinctness. The real issue here is versions of the Identity of Indiscernibles. I discuss ways of discriminating versions, which are almost certainly true but trivial, which almost certainly substantive but false, and explore (...) an interesting intermediate possibility which might if developed yield a plausibly true yet not-entirely-trivial version of the doctrine: it is equivalent to what I call "the Denial of Bare Distinctness". (shrink)