A and B continue their conversation concerning the Identity of Indiscernibles. Both are aware of recent critiques of the principle that haven’t received replies; B summarizes those critiques, and A offers the replies that are due. B then raises a new worry.

Causal essentialists hold that a property essentially bears its causal and nomic relations. Further, as many causal essentialists have noted, the main motivations for causal essentialism also motivate holding that properties are individuated in terms of their causal and nomic relations. This amounts to a kind of identity of indiscernibles thesis; properties that are indiscernible with respect to their causal and nomic relations are identical. This can be compared with the more well-known identity of indiscernibles thesis, (...) according to which particulars that are qualitatively indiscernible are identical. Robert Adams has developed a well-known objection to this thesis by considering a series of possibilities involving nearly qualitatively indiscernible particulars that naturally leads to a possibility involving qualitatively indiscernible particulars. I argue that we can construct parallel cases involving a series of possibilities involving properties that are nearly indiscernible with respect to their causal and nomic relations that naturally lead to possibilities involving properties that are indiscernible with respect to their causal and nomic relations. The same features that make Adams’ argument forceful also carry over to my cases, giving us a powerful objection to the causal essentialist identity of indiscernibles thesis. (shrink)

The Identity of Indiscernibles is the principle that objects cannot differ only numerically. It is widely held that one interpretation of this principle is trivially true: the claim that objects that bear all of the same properties are identical. This triviality ostensibly arises from haecceities (properties like \textit{is identical to a}). I argue that this is not the case; we do not trivialize the Identity of Indiscernibles with haecceities, because it is impossible to express the haecceities (...) of indiscernible objects. I then argue that this inexpressibility generalizes to all of their trivializing properties. Whether the Identity of Indiscernibles is trivially true ultimately turns on whether we can quantify over properties that we cannot express. (shrink)

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)

The principle of Identity of Indiscernibles has been challenged with various thought experiments involving symmetric universes. In this paper, I describe a fractal universe and argue that, while it is not a symmetric universe in the classical sense, under the assumption of a relational theory of space it nonetheless contains a set of objects indiscernible by pure properties alone. I then argue that the argument against the principle from this new thought experiment resists better than those from classical (...) symmetric universes three main objections put forth against this kind of arguments. (shrink)

Leibniz’s short letter to the mathematician and physicist Ludovico Casati of 1689 is a short but interesting text on the Principle of Identity of Indiscernibles, to which it is entirely dedicated. Since there is no watermark in the paper of the letter, the letter is difficult to date, but it is likely that it was written during Leibniz’s stay in Rome, sometime between April and November of 1689 (A 2 2 287–8). When addressing the letter, Leibniz wrote ‘Casani’, (...) but this seems to be a mistake and the real addressee is thought to be Ludovico Casati, nephew of Paolo Casati, the Jesuit mathematician. The letter, reproduced in the Berlin’s Academy edition of Leibniz’s works, was first published by Gerhardt in the Archiv für Geschichte der Philosophie in 1892 (Gerhardt 1892: 53–54). It also appears in Robinet’s Iter Italicum (Robinet 1988: 134–35). But neither Gerhardt nor Robinet provide a philosophical discussion of the letter, and I am not aware of any other philosophical discussion of it. Furthermore, as far as I know, the letter has never been translated into any language. Thus I shall here provide a transcription (from A 2 2 288–89) and a translation of the letter into English, and a philosophical discussion of its treatment of the Identity of Indiscernibles. (shrink)

The Principle of Identity of Indiscernibles (PII) is the focus of much controversy in the history of Metaphysics and in contemporary Physics. Many questions rover the debate about its truth or falsehood, for example, to which objects the principle applies? Which properties can be counted as discerning properties? Is the principle necessary? In other words, which version of the principle is the correct and is this version true? This thesis aims to answer this questions in order to show (...) that PII is a necessarily true principle of metaphysics. To accomplish this task, the reader will find, in this thesis, an encyclopaedical introduction to the history of PII and to the reasons it matters so much, followed by a presentation of the most famous arguments against it and the defences used against these arguments. Then, the reader finds in-depth discussion of the minutiae involved in postulating the principle as to make clear what is in fact being attacked and defended. With these preliminaries solved, a deeper analysis of these defences is presented aiming to discover which is the most appropriate example to use against the attacks to the principle. This analysis allowed a classification of these defences in four families with different strategies within them. Finally, with these defensive strategies at hand we are able to confront alleged counterexamples to PII in Mathematics with the intention to test these defences. (shrink)

The aim of this paper is to show that topology has a bearing on Leibniz’s Principle of the Identity of Indiscernibles (PII). According to (PII), if, for all properties F, an object a has property F iff object b has property F, then a and b are identical. If any property F whatsoever is permitted in PII, then Leibniz’s principle is trivial, as is shown by “identity properties”. The aim of this paper is to show that topology (...) can make a contribution to the problem of giving criteria of how to restrict the domain of properties to render (PII) non-trivial. In topology a wealth of different Leibnizian principles of identity can be defined - PII turns out to be just the weakest topological separation axiom T0 in disguise, stronger principles of can be defined with the aid of higher separation axioms Ti, i > 0. Topologically defined properties have a variety of nice features, in particular they are stable in a natural sense. Topologically defined properties do not have a monopoly on defining “good” properties. In the final section of the paper it is show that the topological approach is closely related to Gärdenfors’s approach of conceptual spaces based on the concept of convexity. (shrink)

There are mathematical structures with elements that cannot be distinguished by the properties they have within that structure. For instance within the field of complex numbers the two square roots of −1, i and −i, have the same algebraic properties in that field. So how do we distinguish between them? Imbedding the complex numbers in a bigger structure, the quaternions, allows us to algebraically tell them apart. But a similar problem appears for this larger structure. There seems to be always (...) a background and a context that we rely upon. Thus mathematicians naturally make use of Kantian intuition and references fixed by names and denotations. I argue that such features cannot be avoided. (shrink)

I provide a theory of the metaphysical foundations of identity: an account what grounds facts of the form a=b. In particular, I defend the claim that indiscernibility grounds identity. This is typically rejected because it is viciously circular; plausible assumptions about the logic of ground entail that the fact that a=b partially grounds itself. The theory I defend is immune to this circularity.

Abstract -/- The indistinction between repose and uniform movement exposed in the principle of inertia marks one of the most famous dissertations: the discussion between Newton and Leibniz. Through their respective conceptions of space, both seek to solve the problem of indistinction. The relational space of Leibniz, supported by the principle of sufficient reason and the identity of indiscernibles leads to the kinematic solution of the problem of inertia. The objective of this paper is to show the contribution (...) of Leibniz, in terms of relations of order, by distinguishing between equality by identity and equality by equivalence. Under a philosophical approach we link identity, equivalence and equality as relations of order with the indiscernibility between different states of movement. We expose first the principle of sufficient reason and the identity of indiscernibles. Under Bernoulli's principle of indifference, we argue that we distinguish between equality in abstract and equality in concrete. As a third part, we present the relationship between the identity of the indiscernibles and the predicate of equality under logical analysis. Finally we present the conclusions. -/- . (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)

According to the ‘One Object’ reading of Kant's transcendental idealism, the distinction between the appearance and the thing in itself is not a distinction between two objects, but between two ways of considering one and the same object. On the ‘Metaphysical’ version of the One Object reading, it is a distinction between two kinds of properties possessed by one and the same object. Consequently, the Metaphysical One Object view holds that a given appearance, an empirical object, is numerically identical to (...) the thing in itself that appears as that object. I raise various indiscernibility arguments against that view; because an appearance has different spatiotemporal and modal properties than a thing in itself, no appearance can be identical to a thing in itself. I point out that these arguments are similar to arguments against Monism, the view that material objects are numerically identical to the matter of which they are made. I outline some strategies Monists have developed to respond to these indiscernibility arguments and then develop parallel responses on behalf of the Metaphysical One Object view. However, I then raise another indiscernibility argument, to which, I argue, the Metaphysical One Object view cannot respond, even using the resources I have developed thus far. I develop a modified version of the Metaphysical One Object view that can respond to this new indiscernibility argument, but, I argue, this modified version of the One Object view is only a terminological variant of the Two Object view. When the Metaphysical One Object view is fully thought through it becomes the Two Object view. I conclude that Kantian appearances are not numerically identical to the things in themselves that appear to us. (shrink)

There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This paper aims to complete their technical investigation. Grades of indiscernibility are defined in terms of satisfaction of certain first-order formulas. Grades of symmetry are defined in terms of symmetries on a structure. Both of these families of grades of discrimination have been studied in (...) some detail. However, this paper also introduces grades of relativity, defined in terms of relativeness correspondences. This paper explores the relationships between all the grades of discrimination, exhaustively answering several natural questions that have so far received only partial answers. It also establishes which grades can be captured in terms of satisfaction of object-language formulas and draws connections with definability theory. (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)

This paper is about the nature of God’s pre-creation knowledge of possible creatures. I distinguish three theories: non-qualitative singularism, qualitative singularism, and qualitative generalism, which differ in terms of whether the relevant knowledge is qualitative or non-qualitative, and whether God has singular or merely general knowledge of creatures. My main aim is to argue that qualitative singularism does not depend on a version of the Principle of Identity of Indiscernibles to the effect that, necessarily, qualitatively indiscernible individuals are (...) identical. It follows that qualitative singularism does not depend on the view that possible creatures categorically have qualitative individual essences. (shrink)

According to strong composition as identity, the logical principles of one–one and plural identity can and should be extended to the relation between a whole and its parts. Otherwise, composition would not be legitimately regarded as an identity relation. In particular, several defenders of strong CAI have attempted to extend Leibniz’s Law to composition. However, much less attention has been paid to another, not less important feature of standard identity: a standard identity statement is true (...) iff its terms are coreferential. We contend that, if coreferentiality is dropped, indiscernibility is no help in making composition a genuine identity relation. To this aim, we analyse as a case study Cotnoir’s theory of general identity, in which indiscernibility is obtained thanks to a revisionary semantics and true identity statements are allowed to connect non-coreferential terms. We extend Cotnoir’s strategy for indiscernibility to the relation of comaternity, and we show that, neither in the case of composition nor in that of comaternity, indiscernibility contibutes to show that they are genuine identity relations. Finally, we compare Cotnoir’s approach with other versions of strong CAI endorsed by Wallace, Bøhn, and Hovda, and canvass the extent to which they violate coreferentiality. The comparative analysis shows that, in order to preserve coreferentiality, strong CAI is forced to adopt a non-standard semantic treatment of the singular/plural distinction. (shrink)

Aristotle is essentially human; that is, for all possible worlds metaphysically consistent with our own, if Aristotle exists, then he is human. This is a claim about the essential property of an object. The claim that objects have essential properties has been hotly disputed, but for present purposes, we can bracket that issue. In this essay, we are interested, rather, in the question of whether properties themselves have essential properties (or features) for their existence. We call those who suppose they (...) do “property essentialists”; those who do not, “property anti-essentialists,” or “quidditists.” We offer two complementary arguments. Our total argument is under-girded by two assumptions: transworld identity theory and “received view” counterfactual semantics, a la David Lewis. We then argue that, if one presumes that these are true, then one risks running headlong into paradox if one also accepts property anti-essentialism. That's the first argument. By contrast, if one accepts these same assumptions in conjunction with property essentialism, then the paradox is avoided. This is the second argument. We take it that our arguments work to show that, between property essentialism and quidditism, the property essentialist is on better footing. Plausibly, properties themselves do have essential properties for their existence. (shrink)

The subject of this paper is the epistemology of identity: a general theory of knowledge, evidence and justification for the claim that one thing is identical to another. Although identity figures significantly in our epistemic lives, this is a topic that, to the best of my knowledge, has gone entirely unexplored. Initial attempts to integrate such an epistemology into existing theories of evidence---many of which are tailor-made for contingent propositions---are confounded by the necessity of identity. I defend (...) a restricted form of skepticism according to which the only knowable identity claims are trivial. (shrink)

Conditional excluded middle (CEM) is the following principe of counterfactual logic: either, if it were the case that φ, it would be the case that ψ, or, if it were the case that φ, it would be the case that not-ψ. I will first show that CEM entails the identity of indiscernibles, the falsity of physicalism, and the failure of the modal to supervene on the categorical and of the vague to supervene on the precise. I will then (...) argue that we should accept these startling conclusions, since CEM is valid. (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)

I show that intuitive and logical considerations do not justify introducing Leibniz’s Law of the Indiscernibility of Identicals in more than a limited form, as applying to atomic formulas. Once this is accepted, it follows that Leibniz’s Law generalises to all formulas of the first-order Predicate Calculus but not to modal formulas. Among other things, identity turns out to be logically contingent.

Manzotti (2021) surveys recent variants of identity theories, defending his own preferred version, mind-object identity theory (MOI). According to this view, experiences are identical with the external objects, and the mind is thus literally “spread” in the world. Manzotti supports this view with considerations about indiscernibility of properties and other theoretical considerations. He claims that brain-mind accounts of identity commit the “fallacy of the center,” locating conscious mind inside the skull. Amongst other recent works, he comments on (...) our (Polák and Marvan, 2018) article, in which we defended a standard, neurocentrist version of type identity theory, and supplemented it with a sketch of neuro-phenomenal typing. Manzotti holds that although we appeal to neuro-phenomenal types in our account of mind-brain identity, we nevertheless “lack a convincing explanation as to why the type of neural processes should be identical to the type of one's experience.” This is a fair point. We didn't do much in our 2018 article to support our views on the principles of neuro-phenomenal typing, either by detailed theoretical considerations or by empirical evidence. In this short rejoinder, we offer the missing argument. By doing so, we also respond both to Manzotti's cited objection and to the charge of the “fallacy of the center.” -/- . (shrink)

There are well-known quasi-formal arguments that identity is a "strict" relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is (...) very close to the standard classical theory but which does not validate the formal analogues of (1)-(3). The core idea is simple: We weaken the Principle of the Indiscernibility of Identicals from a conditional to an entailment and we adopt a weakly classical logic. This paper investigates this weakly classical theory of identity (and related theories) and discusses its philosophical ramifications. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity. (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)

This paper investigates the metaphysics in higher-order counterfactual logic. I establish the necessity of identity and distinctness and show that the logic is committed to vacuism, which entails that all counteridenticals are true. I prove the Barcan, Converse Barcan, Being Constraint and Necessitism. I then show how to derive the Identity of Indiscernibles in counterfactual logic. I study a form of maximalist ontology which has been claimed to be so expansive as to be inconsistent. I show that (...) it is equivalent to the collapse of the counterfactual into the material conditional---which is itself equivalent to the modal logic TRIV. TRIV is consistent, from which it follows that maximalism is, surprisingly, consistent. I close by arguing that stating the limit assumption requires a higher-order logic. (shrink)

Aquinas, Ockham, and Burdan all claim that a person can be numerically identical over time, despite changes in size, shape, and color. How can we reconcile this with the Indiscernibility of Identicals, the principle that numerical identity implies indiscernibility across time? Almost all contemporary metaphysicians regard the Indiscernibility of Identicals as axiomatic. But I will argue that Aquinas, Ockham, and Burdan would reject it, perhaps in favor of a principle restricted to indiscernibility at a time.

This paper evaluates six contenders which might be invoked by essentialists in order to meet Quine’s challenge, viz., to provide necessary and sufficient conditions for the crossworld identity of individuals: (i) an object’s qualitative character; (ii) matter; (iii) origins; (iv) haecceities or primitive non-qualitative thisness properties; (v) “world-indexed properties”; and (iv) individual forms. The first three candidates, I argue, fail to provide conditions that are both necessary and sufficient for the crossworld identity of individuals; the fourth and fifth (...) criteria are open to the charge that they do not succeed in meeting Quine’s demand in an explanatorily adequate fashion. On balance, then, individual forms, or so I propose, deserve to be taken very seriously as a possible response to Quine’s challenge, especially by neo-Aristotelians who are already committed to a hylomorphic conception of composite concrete particular objects for other reasons. Theorists who also accept a non-modal conception of essence, i.e., a conception according to which essence is not reducible to modality, in addition face the further difficult task, over and above what is required to meet Quine’s challenge, of having to explain how an object’s de re modal profile in some way follows from facts about its essence. Haecceities and world-indexed properties, as I indicate, are unlikely to be of much help with respect to this second challenge, while the forms of hylomorphic compounds are in fact well-suited for this purpose. (shrink)

The materialist version of the mind/brain identity theory has met with considerable challenges from philosophers of mind. The author first dispenses with a popular objection to the theory based on the law of indiscernibility of identicals. By means of discussing the vexatious problem of phenomenal qualities, he explores how the debate may be advanced by seeing each dualist and monist ontology through the lens of an evolutionary epistemology. The author suggests that by regarding each ontology as the core of (...) a scientific research programme, each of these logically irrefutable hypotheses can be tested rationally. (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.

Keränen (2001) raises an argument against realistic (ante rem) structuralism: where a mathematical structure has a non-trivial automorphism, distinct indiscernible positions within the structure cannot be shown to be non-identical using only the properties and relations of that structure. Ladyman (2005) responds by allowing our identity criterion to include 'irreflexive two-place relations'. I note that this does not solve the problem for structures with indistinguishable positions, i.e. positions that have all the same properties as each other and exactly the (...) same relations to all objects (including themselves). I conclude that realistic structuralists must compromise and treat some structures eliminativistically. (shrink)

When the necessity of identity (NI) is combined with composition as identity (CAI), the contingency of composition (CC) is at risk. In the extant literature, either NI is seen as the basis for a refutation of CAI or CAI is associated with a theory of modality, such that: either NI is renounced (if counterpart theory is adopted); or CC is renounced (if the theory of modal parts is adopted). In this paper, we investigate the prospects of a new (...) variety of CAI, which aims to preserve both NI and CC. This new variety of CAI (CCAI, contingent composition as identity) is the quite natural product of the attempt to make sense of CAI on the background of a broadly Kripkean view of modality, such that one and the same entity is allowed to exist at more than one possible world. CCAI introduces a world-relative kind of identity, which is different from standard identity, and claims that composition is this kind of world-relative identity. CCAI manages to preserve NI and CC. We compare CCAI with Gibbard’s and Gallois’ doctrines of contingent identity and we show that CCAI can be sensibly interpreted as a form of Weak CAI, that is of the thesis that composition is not standard identity, yet is significantly similar to it. (shrink)

Spinoza claims that a person’s mind and body are one and the same. But he also claims that minds think and do not move, whereas bodies move and do not think. How can we reconcile these claims? I believe that Spinoza is building on a traditional view about identity over time. According to this view, identity over time is linked to essence, so that a thing that is now resting is identical to a thing that was previously moving, (...) provided that they share the same essence. I believe that Spinoza has a similar view about the identity of minds and bodies. In particular, a thing that is thinking in the attribute of thought is identical to a thing that is moving in the attribute of extension, provided that they share the same essence. (shrink)

The aim of this paper is to show that (elementary) topology may be useful for dealing with problems of epistemology and metaphysics. More precisely, I want to show that the introduction of topological structures may elucidate the role of the spatial structures (in a broad sense) that underly logic and cognition. In some detail I’ll deal with “Cassirer’s problem” that may be characterized as an early forrunner of Goodman’s “grue-bleen” problem. On a larger scale, topology turns out to be useful (...) in elaborating the approach of conceptual spaces that in the last twenty years or so has found quite a few applications in cognitive science, psychology, and linguistics. In particular, topology may help distinguish “natural” from “not-so-natural” concepts. This classical problem that up to now has withstood all efforts to solve (or dissolve) it by purely logical methods. Finally, in order to show that a topological perspective may also offer a fresh look on classical metaphysical problems, it is shown that Leibniz’s famous principle of the identity of indiscernibles is closely related to some well-known topological separation axioms. More precisely, the topological perspective gives rise in a natural way to some novel variations of Leibniz’s principle. (shrink)

In this work, we discuss a formal way of dealing with the properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernibles. This framework allows us to consider a (...) new ontology in order to study the properties of quantum systems. (shrink)

Abstract: There are two traditionally rival views about the nature of time: substantivalism that takes time to be a substance that exists independently of events located in it, and relationism that takes time to be constructed out of events. In this paper, first, I want to make some progress with respect to the debate between these two views, and I do this mainly by examining the strategies they use to face the possibilities of ‘empty time’ and ‘time without change’. As (...) we shall see, the two allegedly very different rival views are much less different than has been thought: their structure is extremely similar, their strategies are extremely similar, and they can both face the possibilities of ‘empty time’ and ‘time without change’ in the same way. Thus, I argue in favour of a certain kind of equivalence between the two views; I discuss a Strong and a Weak version of this claim; and I provide reasons for endorsing the former. I also discuss the parallel between this pair of views about the nature of time and another analogous pair of views: the bundle theory and the substratum theory about the nature of material objects, with respect to the problem with Identity of Indiscernibles. (shrink)

I gather and constructively criticize Nietzsche’s writings on identity. Nietzsche treats identity as a logical fiction. He denies that there are any enduring things (no substances); he denies that there are any indiscernible things in any respect (no universals, no bare particulars). For Nietzsche, the world consists of durationless events bearing non-universal properties and standing to one another in non-universal relations. Events are bundles of tropes. Nietzsche even denies self-identity. His events are self-differing trope-bundles. I link Nietzsche’s (...) denial of self-identity with modern treatments of paradox. (shrink)

The ontological analysis of concrete particulars deals with the relationship between concrete object and their attributes. Both Peter Simons' Nuclear Theory and Aristotelian Substance Theory may present an acceptable explanation for the following three problems: Identity of Indiscernible, Excessive Necessitism and Change. In spite of the superiority of these two theories over the other theories, each has problems need to be addressed. Aristotelian theory does not seem to be very successful in showing that the spices (kinds) are unchangeable or (...) at least does not explain it. Simmons's theory also returns to Aristotelian theory. While outlining the challenges to any theory, the final suggestion of the paper is that with inspiration of Simmons' theory and introducing a relation between the generalities (universal Whatness), create a modification in Aristotelian theory to overcome the challenge of the irreductive challenge of Species (kinds) Simons' theory, in some sense, collapses back to Aristotelian Theory. (shrink)

This draft preprint presents a nine step argument for “Connectionist Structuralism” (CS), an account of the ontology of abstract objects that is neither purely nominalist nor purely platonist. CS is a common, often implicit assumption in parts of the artificial intelligence literature, but such discussions have not presented formal accounts of the position or engaged with metaphysical issues that potentially undermine it. By making the position legible and presenting an initial case for it, we hope to support a constructive dialogue (...) between AI researchers and philosophers of metaphysics that helps both sides to refine the position. -/- CS proposes that each abstract object we can draw on in human analysis corresponds to a particular subset of an individual person’s brain structure whose functionality is isomorphic to a subset of the nodes and connections in a suitable connectionist network. In other words, abstract objects are physically realised, but in individual brains, rather than only in the referent objects (pure nominalism) or in metaphysical universals (pure platonism). -/- This paper’s minimum claim is that CS can account for all abstract object predicables regarding sensible properties, such as “is red” or “is a square”. Using evidence from cognitive neuroscience, machine learning, and evolutionary biology, as well as a fully traceable toy example, we describe how CS can support our core cognitive uses of such sensible properties and can account for our core phenomenal experiences of them. In the former, CS provides sufficient albeit imperfect inferential safety, whose limitations are argued to strengthen rather than weaken the case for CS as describing human behaviour. In the latter, four target phenomenal features are accounted for – abstract objects as feeling intangible, non-located, transparent, and unchanging - along with accounts for further phenomena such as semantic refinement, the Stroop effect, synaesthesia, semantic clarity, sensory overload, and satiation. -/- Our minimum claim concerns the day-to-day usage and felt experience of abstract objects, but we suggest also an extended claim in which CS can form the basis of a pragmatic sufficient logic. As such, the initial outline of a response is provided for five common objections to positions that seek to ground abstract objects without reference to metaphysically stand-alone universals: referential opacity; identity of indiscernibles; infinite regression; non-physical concepts; and necessary truths. These outlines lay the foundation for (but do not seek to formally demonstrate) an extended CS account that addresses other abstract objects, including issues relating to their use in mathematics and formal logic. -/- The CS account leads to a four-layer hierarchy of similarity for whether your “red” is the same as mine. Considering both semantic and phenomenal similarity, we conclude that our “reds” are likely non-identical but can be made close enough for practical purposes. Finally, we describe how future work could elaborate CS as a metaphysical project and how confidence in it could be tested through empirical research. (shrink)

According to the traditional bundle theory, particulars are bundles of compresent universals. I think we should reject the bundle theory for a variety of reasons. But I will argue for the thesis at the core of the bundle theory: that all the facts about particulars are grounded in facts about universals. I begin by showing how to meet the main objection to this thesis (which is also the main objection to the bundle theory): that it is inconsistent with the possibility (...) of distinct qualitative indiscernibles. Here, the key idea appeals to a non-standard theory of haecceities as non-well-founded properties of a certain sort. I will then defend this theory from a number of objections, and finally argue that we should accept it on the basis of considerations of parsimony about the fundamental. (shrink)

I suggest a solution to two puzzles in Spinoza's metaphysics. The first puzzle involves the mind and the idea of the mind, in particular how they can be identical, even though the mind thinks about bodies and nothing else, whereas the idea of the mind thinks about ideas and nothing else. The second puzzle involves the mind and the idea of a thing that belongs to an unknown attribute, in particular how they can be identical, even though the mind thinks (...) about bodies and nothing else, whereas the idea thinks about things belonging to the unknown attribute and nothing else. I suggest that Spinoza would respond to both puzzles by rejecting the Indiscernibility of Identicals. (shrink)

According to actualism about possible worlds everything that exists is actual. Possible worlds and individuals are actually existing abstract parts of the actual world. Aristotelian actualism is a view that there are only actual individuals but no possible ones, nor their individual abstract representatives. Because of that, our actualist account of modality should differ depending on whether it concerns actual individuals or possible ones. The main goal of the dissertation is to develop a metaphysical framework for Aristotelian actualism. Chapter 1 (...) explains basic issues associated with the possible world approach to modality. I overview modal realist and actualist views on possible worlds and explain why I support the actualist approach. Subsequently, I introduce a distinction between Platonic and Aristotelian actualism, and discuss some semantic issues associated with actualism as such. In Chapter 2 I argue that Aristotelian actualism, modeled on linguistic ersatzism, is preferable over its Platonic counterpart. Subsequently, I propose a metaphysical framework for Aristotelian ersatzism which is based on a claim that our modal concepts work differently for actual and possible individuals. In order to explain that claim I introduce three specific differences concerning modal features of actual and possible individuals: (a) Representational Difference, according to which actual and possible individuals are represented differently by possible worlds; (b) Metaphysical Difference, according to which actual and possible individuals are represented by possible worlds as having different metaphysical nature; (c) Modal Difference, which says while there are singular and contingent possibilities involving actual individuals, all possibilities about possible individuals are general and necessary. I propose to interpret those differences in terms of the doctrines of haecceitism, antihaecceitism and existentialism. There is however no consensus on how those views should be characterized. Chapters 3, 4, and 5 focus on providing a precise characterization of those doctrines. Chapter 3 focuses on the doctrines of modal haecceitism and antihaecceitism, which I view as opposite accounts of how possible worlds represent possibilities. According to modal haecceitism what possible worlds say about particular individuals does not supervene on what they say qualitatively. Modal antihaecceitism is a denial of such a claim. Chapter 4 concerns metaphysical haecceitism and antihaecceitism, which I take to be alternative accounts of the fundamental structure of reality. For the metaphysical haecceitist reality contains irreducible singular facts, while for the metaphysical antihaecceitist reality is purely qualitative and general. Chapter 5 focuses on an argument between existentialists and antiexistentialists. Existentialists claim that there are contingent singular propositions, while antiexistentialists deny that. I defend existentialism against antiexistentialist counterarguments, as well as criticize some of the antiexistentialist accounts of singular propositions modeled on the notion of individual essence. In Chapter 6, by appealing to the results of investigations conducted in Chapters 3, 4 and 5, I reconsider Representational, Metaphysical and Modal Differences. According to a view that I propose: (a) Representational Difference entails (extreme) modal haecceitism for actual individuals but (extreme) modal antihaecceitism for possible individuals; (b) Metaphysical Difference entails metaphysical haecceitism (individualism) for actual individuals, but metaphysical antihaecceitism (generalism) for possible individuals; finally (c) Modal Difference entails existentialism: while there are singular and contingent possibilities involving actual individuals, all possibilities about possible individuals are general and necessary. In Chapter 6, I also explain the implications of those views for the various issues, including transworld identity, essentialism, or the modal status of modal space. Lastly, Chapter 7 overviews some semantic and metaphysical applications of Aristotelian ersatzism. I explain how it manages to accommodate Kripkean semantics and how it is able to account for the possibilities of indiscernibles, alien individuals and iterated modalities. I also address some possible objections to my proposal, including an issue of implicit representation and the Humphrey objection. (shrink)

In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard correspondence, which has been well-established between the simply typed lambda-calculus and natural deduction systems for intuitionistic logic, and apply it to a bilateralist proof system displaying two derivability relations, one for proving and one for refuting. The basis will be the natural deduction system (...) of Wansing's bi-intuitionistic logic 2Int, which I will turn into a term-annotated form. Therefore, we need a type theory that extends to a two-sorted typed lambda-calculus. I will present such a term-annotated proof system for 2Int and prove a Dualization Theorem relating proofs and refutations in this system. On the basis of these formal results I will argue that this gives us interesting insights into questions about sense and denotation as well as synonymy and identity of proofs from a bilateralist point of view. (shrink)

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)

Suppose that X and Y can’t possibly exist apart in reality; then—by definition—there’s no real distinction between them, only a conceptual distinction. There’s a conceptual distinction between a rectilinear figure’s triangularity and its trilaterality, for example, but no real distinction. In fundamental metaphysics there is no real distinction between an object’s categorical properties and its dispositional properties. So too there is no real distinction between an object and its properties. And in fundamental metaphysics, for X and Y to be such (...) that there is no real distinction between them is for them to be identical. (shrink)