Rigid designators designate whatever they do in all possible worlds. Mathematical definite descriptions are usually considered paradigmatic examples of such expressions. The main aim of the present paper is to challenge this view. It is argued that mathematical definite descriptions cannot be rigid in the same sense as ordinary empirical definite descriptions because—assuming that mathematical facts are not determined by goings on in possible worlds—mathematical descriptions designate whatever they do independently of possible worlds. Nevertheless, there is a widespread practice of (...) treating mathematical definite descriptions as rigid. Apart from this, there might be theoretical reasons for admitting that they are rigid in some sense. The second part of the paper suggests a way out. Borrowing from ideas proposed by Kit Fine, it develops and defends an extended notion of rigidity, which can be applied to mathematical definite descriptions. Importantly, this notion is fully compatible with the claim that mathematical facts are independent of possible worlds. (shrink)

Saul Kripke in his revolutionary and influential series of lectures from the early 1970s (later published as the book Naming and Necessity) famously resurrected John Stuart Mill's theory of proper names. Kripke at the same time rejected Mill's theory of general terms. According to Kripke, many natural kind terms do not fit Mill's account of general terms and are closer to proper names. Unfortunately, Kripke and his followers ignored key passages in Mill's A System of Logic in which Mill enunciates (...) a sophisticated and detailed theory of natural kind terms that anticipates and is in some ways superior to Kripke's. (shrink)

Rigid expressionism is the view that all natural kind terms and many other kind terms are rigid designators. Rigid expressionists embrace the ‘overgeneralization’ of rigidity, since they hold that not just natural kind terms but all unstructured kind terms are rigid designators. Unfortunately overgeneralization remains a defeating problem for rigid expressionism. It runs together natural kind terms and nominal kind terms in a way that enforces a false semantic uniformity. The Kripke/putnam view of natural kind terms minus the claim of (...) rigidity is correct, but a traditional descriptivist theory is appropriate for nominal kind terms. None of them should be thought of as either rigid or non-rigid, however. (shrink)

Following insights from the New Theory of Reference, it has become widely accepted that theoretical identities like ‘water = H2O' are necessary. However, some have challenged this claim. I propose yet another challenge in the form of a sceptical argument. The argument is based on the contention that the necessity of theoretical identities is dependent upon criteria of identity. Thus, a theoretical identity is necessary given one criterion of identity but contingent given another. Since we do not know which criteria (...) of identity in fact obtain, it follows that, for all we know, theoretical identities may not be necessary. (shrink)

Possible world semantics considers not only what an expression actually refers to but also what it might have referred to in counterfactual circumstances. This has proven exceptionally useful both inside and outside philosophy. The way this is achieved is by using intensions. An intension of an expression is a function that assigns to each possible world the reference of the expression in that world. However, the specific intension of terms has been subject to frequent disputes. How is one to determine (...) the intension of a term? Carnap has shown how the intension of a term depends on the type of that term. Two-dimensional semantics has shown how intensions also depend on the actual state of affairs. I will show how, in addition, intensions are no less dependent on metaphysical criteria of identity. Furthermore, I will reveal how these three factors interact to fix the exact intension of a term. In other words, I propose an outline of the overall mechanism by which intensions are being fixed. (shrink)

Standard Kripke-Putnam semantics is widely taken to entail that theoretical identifications like ‘Brontosauruses are Apatosauruses’ or ‘Gold is 79Au’ are necessary, if true. I offer a new diagnosis as to why this modal consequence ensues. Central to my diagnosis is the concept of a paradigm term. I argue that modal and epistemic peculiarities that are commonly considered as distinctive of natural kind expressions are in fact traits that are shared by paradigm terms in general. Philosophical semantics should broaden its focus (...) from natural kind expressions to paradigm terms. (shrink)

The classification-cum-explanation Kripke assigns to rigidity requires the notion to apply to singular and general terms alike. But Kripke's own notion of rigidity is tailor-made for singular terms, and an extensive debate has not secured a general notion of rigidity apt to provide the classification-cum-explanation Kripke aims for. I propose that we look for a Kripkean alternative to generalized rigidity. I argue that on Kripkean premises, natural kind terms and proper names belong to the meta-semantic category of paradigm terms. I (...) also argue that the property of being a paradigm term effects precisely the classification-cum-explanation Kripke attributes to rigidity. I conclude that Kripkeans should acknowledge that being a paradigm term, rather than designating rigidly, plays the role Kripke delineates, and that we can stop worrying about generalizing rigidity. Kripke's notion works fine for singular terms. And there is no need for rigidity to apply beyond these. (shrink)

Kripke holds the thesis that identity statements containing natural kind terms are if true, necessarily true; these statements can be denominated theoretical identities. Kripke alleges that the necessity of theoretical identities grounds on the linguistic feature that natural kind terms are rigid designators. Nevertheless, I argue that the conception of natural kind terms as rigid designators, in one of their most natural views, hinders the establishment of the truth of theoretical identities and thus of their necessity. However, in Kripke’s works (...) another proposal, not linguistic but metaphysical, is found to justify the presumed necessity of theoretical identities; it grounds on essentialism concerning natural kinds. In this regard, I question some of Kripke’s main claims, focusing on one of the main examples of theoretical identities put forward by Kripke, i.e., “Water is H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}O”. I challenge his a priori claims concerning what should be the essence of a natural kind like water. Furthermore, I adduce that the character of that theoretical identity is not that claimed by Kripke, since in the term flanking the right side of the identity sign it has to be resorted to the notion of similarity or it should have the form of a disjunction of a cluster of substances. (shrink)

In this paper, I present, generalize and develop the extensionalist theory of rigidity for general terms in light of criteria commonly applied to theories of general term rigidity. According to the theory, a general term is rigid if its extension is constant across all possible worlds. This position has been widely dismissed because it conflicts with the seemingly straightforward idea that natural kind terms have varying extensions from world to world. This criticism holds only to the extent that natural kind (...) terms are indeed rigid. If it turns out that we need not view them as rigid, then the extensionalist theory fares well when compared with other theoretical requirements. (shrink)

The Russell-Myhill paradox puts pressure on the Russellian structured view of propositions by showing that it conflicts with certain prima facie attractive ontological and logical principles. I describe several versions of RMP and argue that structurists can appeal to natural assumptions about metaphysical grounding to provide independent reasons for rejecting the ontological principles used in these paradoxes. It remains a task for future work to extend this grounding-based approach to all variants of RMP.

Häggqvist and Wikforss argued that in the case of so-called natural kind terms, semantic externalism relies on an untenable metaphysics of kinds: microessentialism. They further claimed that this metaphysics fails, for largely empirical reasons. Focussing on the case of water, Hoefer and Martí European Journal for the Philosophy of Science, 9, rejoin that suitably construed, microessentialism is correct. I argue that their defence of microessentialism fails.

Causal theories of reference for natural kind terms are widely agreed to play a central role in arguments for the claim that theoretical identity statements such as “Water is H2O” are necessary, if true. However, there is also fairly wide-spread agreement, due to the arguments of Nathan Salmon, that causal theories of reference do not alone establish such essentialism about natural kinds: an independent, non-trivial essentialist premise is also needed. In this paper I will question this latter agreement. I will (...) argue that there is an independently attractive explanation of why such identity statements are metaphysically necessary, if true: an explanation which relies on assumptions about the semantics of natural kind terms, general philosophical assumptions about reference, and straightforward empirical assumptions, but presupposes no non-trivial essentialist premises. (shrink)

Though it is often claimed that some general terms are rigid designators, it has turned out to be difficult to give a satisfying definition that avoids making all general terms rigid, and even if a non-rigid reading is available, makes that non-rigid reading matter. Several authors have attempted to develop examples that meet the trivialization challenge, with Martí and Martínez-Fernández providing what is, perhaps, the most convincing strategy. I show that the type of example Martí and Martínez-Fernández offer nevertheless fails (...) to meet the trivialization challenge and, accordingly, that we should still have serious doubts about whether continuing the search for a non-trivial definition of general term rigidity would be fruitful. (shrink)

Although it is common to claim that certain general terms or kind terms are rigid designators and that their rigidity helps explain their behavior in modal contexts, it has turned out to be surprisingly difficult to define an adequate notion of rigidity for general terms. Such definitions tend, as argued in particular by Scott Soames, to lead to a type of overgeneralization that leaves the purported rigidity of general terms explanatorily inert. In recent years, several attempts have been made to (...) circumvent the problem, and the present article focuses on a particular and potentially powerful strategy developed by Joseph LaPorte in his recent book Rigid Designation and Theoretical Identities for blocking one of the core inferences in Soames’s case against general term rigidity. I argue that the type of response LaPorte promotes is bound to fail; though it might initially appear to circumvent the threat of trivialization described by Soames, it is susceptible to a different and arguably even worse kind of trivialization challenge. In conclusion, Soames’s arguments remain a significant obstacle to identifying a non-trivializing definition of kind term rigidity, and we have good reasons to think that an explanation for the modal status of theoretical identity statements must be sought elsewhere. (shrink)

It is often thought that some general terms or kind terms, in particular natural kind terms, are rigid designators, and that a properly extended notion of singular-term rigidity can help explain the behaviour of such general terms. In this article, I argue that the only legitimate notion of general-term rigidity is a trivial one and identify some crucial asymmetries between a posteriori necessary truths involving names and a posteriori necessary truths involving general terms. If we pay attention to these asymmetries, (...) it becomes clear that attempts to draw a non-trivial rigid/non-rigid distinction for general terms are bound to fail to offer the explanations we expected. As opposed to singular terms, what is interesting about the behaviour of natural kind terms, even in modal contexts, cannot be accounted for by modal distinctions like rigidity/non-rigidity but must rather track non-modal features. (shrink)

The question of transtemporal identity of objects in general and persons in particular is an important issue in both philosophy and psychology. While the focus of philosophers traditionally was on questions of the nature of identity relation and criteria that allow to settle ontological issues about identity, psychologists are mostly concerned with how people think about identity, and how they track identity of objects and people through time. In this article, we critically engage with widespread use of inferring folk judgments (...) of identity from study participants’ use of proper names in response to experimental vignettes. We provide reasons to doubt that using this method one can reliably infer judgments of numerical identity over time and transformations. We also critically examine allegedly-Kripkean justification of this method and find it lacking. Merely assuming that names are rigid designators will not help. A study participant’s use of proper names can be taken to track the participant’s identity judgments only if supported by the participant’s belief that names used in the scenario are used rigidly. (shrink)

Philosophical treatments of natural kinds are embedded in two distinct projects. I call these the philosophy of science approach and the philosophy of language approach. Each is characterized by its own set of philosophical questions, concerns, and assumptions. The kinds studied in the philosophy of science approach are projectible categories that can ground inductive inferences and scientific explanation. The kinds studied in the philosophy of language approach are the referential objects of a special linguistic category—natural kind terms—thought to refer directly. (...) Philosophers may hope for a unified account addresses both sets of concerns. This paper argues that this cannot be done successfully. No single account can satisfy both the semantic objectives of the philosophy of language approach and the explanatory projects of the philosophy of science approach. After analyzing where the tensions arise, I make recommendations about assumptions and projects that are best abandoned, those that should be retained, and those that should go their separate ways. I also recommend adopting the disambiguating terminology of “scientific kinds” and “natural kinds” for the different notions of kinds developed in these different approaches. (shrink)

The question whether the notion of rigidity can be extended in a fruitful way beyond singular terms has received a standard answer in the literature, according to which non-singular terms designate kinds, properties or other abstract singular objects and generalized rigidity is the same thing as singular term rigidity, but for terms designating such objects. I offer some new criticisms of this view and go on to defend an alternative view, on which non-singular terms designate extensions in general, and generalized (...) rigidity is identity of extension across possible worlds. I develop some fundamental positive considerations that make this view virtually inevitable as a view of generalized rigidity, emphasizing its exclusive ability to offer a purely logical justification of the necessity of several kinds of statements that go beyond true identity statements between rigid singular terms. (shrink)

This article is aimed to rephrase and critique the arguments presented by Joseph LaPorte about the truth of theoretical identity statements in natural sciences. LaPorte is classified as an essentialist who accepts the real kinds, but he denies the essence of the kinds to be discovered. His arguments are based on the vagueness of the terms of kinds. In his view while science progress we convention (not discover) what is related to the kinds. I evaluate LaPorte's arguments and show they (...) can be applied only for the border terms in scientific theories and so the generalization of the claim is not defensible. (shrink)

In (1959), Carnap famously attacked Heidegger for having constructed an insane metaphysics based on a misconception of both the logical form and the semantics of ordinary language. In what follows, it will be argued that, once one appropriately (i.e., in a Russellian fashion) reads Heidegger’s famous sentence that should paradigmatically exemplify such a misconception, i.e., “the nothing nothings”, there is nothing either logically or semantically wrong with it. The real controversy as to how that sentence has to be evaluated—not as (...) to its meaning but as to its truth—lies at the metaphysico- ontological level. For in order for the sentence to be true one has to endorse an ontology of impossibilia and Leibniz’s principle of the identity of indiscernibles. (shrink)