Introducing Identity

The best-known syntactic account of the logical constants is inferentialism . Following Wittgenstein’s thought that meaning is use, inferentialists argue that meanings of expressions are given by introduction and elimination rules. This is especially plausible for the logical constants, where standard presentations divide inference rules in just this way. But not just any rules will do, as we’ve learnt from Prior’s famous example of tonk, and the usual extra constraint is harmony. Where does this leave identity? It’s usually taken as a logical constant but it doesn’t seem harmonious: standardly, the introduction rule (reflexivity) only concerns a subset of the formulas canvassed by the elimination rule (Leibniz’s law). In response, Read [5, 8] and Klev [3] amend the standard approach. We argue that both attempts fail, in part because of a misconception regarding inferentialism and identity that we aim to identify and clear up.

Una nueva solución al problema de la fundamentación

Let us consider a statue and the piece of clay out of which it is made, and let us suppose that they start to exist and cease to exist at exactly the same time. According to colocationism, the statue and the piece of clay are two different objects: they have different properties (for example, one is a statue and the other a piece of clay) and, according to Leibniz’s Law, the same object cannot have different properties. One of the most difficult questions for colocationism is that of the grounding problem: given that the statue and the piece of clay share many of their properties (their matter, their microscopic composition, their structure, etc.), what is it that grounds the fact that they have different sortal (or modal) properties? Recently, Catherine Sutton has offered a very interesting answer to the question. However, as I will argue, it cannot be applied to all cases of colocated objects and therefore, it is not an adequate solution to the grounding problem. The main objective of this paper is to present a new solution to the grounding problem that integrates some of Sutton’s theses, but that allows us to give a complete answer to the question. To do this, the notion of a process of coming into existence will be crucial. After presenting the new proposal, I will compare it with the proposals by Kit Fine and Noël Saenz.

Frege and saving substitution

Goodman and Lederman (Philos Stud 177(4):947–952, 2020) argue that the traditional Fregean strategy for preserving the validity of Leibniz’s Law of substitution fails when confronted with apparent counterexamples involving proper names embedded under propositional attitude verbs. We argue, on the contrary, that the Fregean strategy succeeds and that Goodman and Lederman’s argument misfires.

Grief and Composition as Identity

‘It feels like I have lost a part of myself’ is frequently uttered by those grieving the death of a loved one. Despite the ubiquity of such utterances, and the palpable sense that they express something true, few philosophers have considered what, if anything, accounts for their truth. Here, I develop a suggestion from Donald Baxter according to which Composition as Identity provides us a means to understand the grief utterances literally. In doing so, I identify and develop a version of Leibniz's Law required for Composition as Identity to account for the truth of the grief utterances. In turn, this principle helps shed light on Composition as Identity's central claim: that the parts are identical to the whole. By considering objections to the resulting view, I construct a list of desiderata for other philosophers interested in accounting for the grief utterances.

SUBSTITUTION IN RELEVANT LOGICS

This essay discusses rules and semantic clauses relating to Substitution—Leibniz’s law in the conjunctive-implicational form $s\dot{ = }t \wedge A\left( s \right) \to A\left( t \right)$—as these are put forward in Priest’s books In Contradiction and An Introduction to Non-Classical Logic: From If to Is. The stated rules and clauses are shown to be too weak in some cases and too strong in others. New ones are presented and shown to be correct. Justification for the various rules is probed and it is argued that Substitution ought to fail.

2. Identity in logic and the classical law of thought

‘Identity in logic and the classical law of thought’ explains that Leibniz’s law of the identity of indiscernibles conforms to the laws of logic. It defines identity as strict self-sameness, but raises the difficult problem of what counts as the same. By framing identity as a semantic problem and introducing a distinction between the meaning of an expression (sense) and what it stands for (reference), Frege provided a partial solution to it, but vagueness continues to pose a major difficulty for the logic of identity. Non-Western logics that differ from the Aristotelian tradition offer an alternative by viewing every concept as including its own negation as a property, rather than the absence of properties.

Metaphysics of composition

Composition occurs when one or more objects are parts of another object. The metaphysics of composition concerns the nature of composition – i.e. what it is, and how it works. Some of the more important questions philosophers have regarding the metaphysics of composition are the following: (1) When does composition occur? This is van Inwagen’s ‘Special Composition Question’. Four prominent answers to this question include: (i) objects compose another object when those former objects are in contact; (ii) any two or more objects compose another object; (iii) objects never compose another object; (iv) objects compose another object when the activities of the former objects constitute a life. (2) Are composite objects identical with their parts? Proponents of ‘composition as identity’ answer ‘yes’ to this question. There are two primary variants of composition as identity, ‘strong’ composition as identity and ‘weak’ composition as identity. The most prominent objection to strong composition as identity is an objection from Leibniz’s Law: composite objects cannot be identical with their parts, since they seem to have properties which their parts do not have. (3) Is it possible for one object to constitute another object? Here ‘constitution’ is the relation which is alleged to obtain between, for example, a clay statue and the lump of clay from which it is formed. We can distinguish between the thesis that constitution is identity, and the thesis that constitution is not identity. The chief motivation which leads some philosophers to reject the thesis that constitution is not identity is the ‘grounding problem’ for that thesis. (4) Are there, in addition to composite objects, the ‘forms’ of those objects, and if so, what is the relationship between composite objects and their forms? We can distinguish between (at least) two variants of hylomorphism (the thesis that objects have forms), with the main distinction between the two views being whether or not they regard forms as being among the parts of composite objects.

Propositional attitude statements

Propositional attitude statements – statements about our beliefs, desires, hopes and fears – exhibit certain logical peculiarities. For example, in apparent violation of Leibniz’s law of the indiscernibility of identicals, we cannot freely substitute expressions which designate the same object within such statements. According to Leibniz’s law, every instance of the following scheme is valid: - a = b - F(a) - Therefore, F(b) The validity of Leibniz’s law seems beyond question. It says, in effect, that if an object has a certain property, then anything identical to that object also has that property. Valid instances abound. But consider the following apparently invalid instance: - Hesperus is Phosphorus - Hammurabi believed that Hesperus often rose in the evening - Therefore, Hammurabi believed that ‘Phosphorus’ often rose in the evening. If we take ‘Hammurabi believed that…often rose in the evening’ to serve as the predicate F and ‘Hesperus’ and ‘Phosphorus’ to be a and b respectively, this argument appears to be an instance of Leibniz’s law. Yet (3) apparently fails to follow from (1) and (2). Hammurabi believed that Hesperus and Phosphorus were two heavenly bodies not one. And he believed that Hesperus did, but that Phosphorus did not rise in the evening. We have derived a false conclusion from true premises and an apparently valid law. If that law is really valid, then our argument had better not be a genuine instance of the law. The tempting conclusion, widely accepted, is that we were wrong to construe propositional attitude statements as simple predications. We should not, that is, construe ‘Hammurabi believed that…often rose in the evening’ to be just a long predicate with the semantic function of attributing some property to the object commonly denoted by ‘Hesperus’ and ‘Phosphorus’. But then the question arises: if attitude reports are not simple predications, what are they? Philosophers have disagreed sharply in their answers. Moreover, their disagreements are intimately connected to a wide range of deep issues about the nature of meaning and reference.

Identity of indiscernibles

The principle of the identity of indiscernibles states that objects which are alike in all respects are identical. It is sometimes called Leibniz’s Law. This name is also frequently used for the converse principle, the indiscernibility of identicals, that objects which are identical are alike in all respects. Both principles together are sometimes taken to define the concept of identity. Unlike the indiscernibility of identicals, which is widely accepted as a logical truth, the identity of indiscernibles principle has frequently been doubted and rejected. The principle is susceptible of more precise formulation in a number of ways, some more dubitable than others.