Kuhn's alleged taxonomic interpretation of incommensurability is grounded on an ill defined notion of untranslatability and is hence radically incomplete. To supplement it, I reconstruct Kuhn's taxonomic interpretation on the basis of a logical-semantic theory of taxonomy, a semantic theory of truth-value, and a truth-value conditional theory of cross-language communication. According to the reconstruction, two scientific languages are incommensurable when core sentences of one language, which have truth values when considered within its own context, lack truth values when (...) considered within the context of the other due to the unmatchable taxonomic structures underlying them. So constructed, Kuhn's mature interpretation of incommensurability does not depend upon the notion of truth-preserving translatability, but rather depends on the notion of truth-value-status-preserving cross-language communication. The reconstruction makes Kuhn's notion of incommensurability a well grounded, tenable and integrated notion.Author Keywords: Incommensurability; Thomas Kuhn; Taxonomic structures; Lexicons; Truth-value; Untranslatability; Cross-language communication. (shrink)
Since the famous debate between Russell (Mind 14: 479–493, 1905, Mind 66: 385–389, 1957) and Strawson (Mind 59: 320–344, 1950; Introduction to logical theory, 1952; Theoria, 30: 96–118, 1964) linguistic intuitions about truth values have been considered notoriously unreliable as a guide to the semantics of definite descriptions. As a result, most existing semantic analyses of definites leave a large number of intuitions unexplained. In this paper, I explore the nature of the relationship between truth value intuitions and non-referring definites. (...) Inspired by comments in Strawson (Introduction to logical theory, 1964), I argue that given certain systematic considerations, one can provide a structured explanation of conflicting intuitions. I show that the intuitions of falsity, which proponents of a Russellian analysis often appeal to, result from evaluating sentences in relation to specific questions in context. This is shown by developing a method for predicting when sentences containing non-referring definites elicit intuitions of falsity. My proposed analysis draws importantly on Roberts (in: Yoon & Kathol (eds.) OSU working papers in Linguistics: vol. 49: Papers in Semantics 1998; in: Horn & Ward (eds.) Handbook of pragmatics, 2004) and recent research in the semantics and pragmatics of focus. (shrink)
Presupposition, vagueness, and oddness can lead to some sentences failing to have a clear truth value. The homogeneity property of plural predication with definite descriptions may also create truth-value gaps: The books are written in Dutch is true if all relevant books are in Dutch, false if none of them are, and neither true nor false if, say, half of the books are written in Dutch. We study the projection property of homogeneity by deploying methods of general interest to (...) identify truth-value gaps. Method A consists in collecting both truth judgments and, independently, falsity judgments. The second method, employed in experiment series B and C, is based on one-shot ternary judgments: completely true vs. completely false vs. neither. After a calibration of these methods, we use them to demonstrate that homogeneity projects out of negation, the scope of universal sentences and the scope of non-monotonic quantifiers such as exactly two, to some extent. We assess our results in light of different theoretical approaches to homogeneity—approaches based on presuppositions, scalar implicatures, and something like supervaluations, respectively. We identify free parameters in these theories and assess various variants of them based on our results. Our experimental paradigms may be of broader significance insofar as they can be applied to other phenomena which result in the failure of a sentence to have a definite truth value. (shrink)
In his article 'Rejection' (1996), Timothy Smiley had shown how a logical system allowing rules of rejection could provide a categorical axiomatization of the classical propositional calculus. This paper shows how rules of rejection, when placed in a multiple conclusion setting, can also provide categorical axiomatizations of a range of non-classical calculi which permit truth-value gaps, among them the calculus in Smiley's own 'Sense without denotation' (1960).
Truth-value gaps have received little attention from a foundational perspective, a fact which has rightfully opened up gap theories to charges of vacuousness. This paper develops an account of the foundations of gap-like behavior which has some hope of avoiding such charges. I begin by reviewing and sharpening a powerful argument of Dummett’s to constrain the options that gap theorists have to make sense of their views. I then show that within these strictures, we can give an account of (...) gaps by drawing on elements of a broadly Stalnakerian framework for assertion and using gaps to track an amalgamation of assertoric effects. The discussion reveals that we may need special resources in our theories of assertion to posit gaps, that gaps may be unusable in characterizing the structure of mental states, and that gaps may have heterogeneous linguistic sources that result in equally heterogeneous projective and inferential behavior. (shrink)
Among other good things, supervaluation is supposed to allow vague sentences to go without truth values. But Jerry Fodor and Ernest Lepore have recently argued that it cannot allow this - not if it also respects certain conceptual truths. The main point I wish to make here is that they are mistaken. Supervaluation can leave truth-value gaps while respecting the conceptual truths they have in mind.
The fact that a group of axioms use the word 'true' does not guarantee that that group of axioms yields a theory of truth. For Davidson the derivability of certain biconditionals from the axioms is what guarantees this. We argue that the test does not work. In particular, we argue that if the object language has truth-value gaps, the result of applying Davidson''s definition of a theory of truth is that no correct theory of truth for the language is (...) possible. (shrink)
According to the accepted translation-failure interpretation, the problem of incommensurability involves the nature of the meaning-referential relation between scientific languages. The incommensurability thesis is that some competing scientific languages are mutually untranslatable due to the radical variance of meaning or/and reference of the terms they employ. I argue that this interpretation faces many difficulties and cannot give us a tenable, coherent, and integrated notion of incommensurability. It has to be rejected. ;On the basis of two case studies, I find that (...) the confrontations between many classical incommensurable languages are not confrontations between two untranslatable languages with different distribution of truth values, but rather the confrontations between incompatible fundamental presuppositions at the ontological level. We can always identify a truth-value gap between two incommensurable languages. Such a truth-value gap indicates a communication breakdown between the two language communities on the one hand, and is caused by the incompatible fundamental presuppositions underlying them on the other. ;I thereby identify the truth-value functional relationship between sentences, instead of the meaning-referential relationship between terms, as the dominant semantic relation between two incommensurable languages. According to my presuppositional interpretation of incommensurability, the real secret of incommensurability lies in the ontological setup of two competing presuppositional languages. When two presuppositional languages with incompatible factual commitments encounter with each other, the confrontation leads to a truth-value gap, and consequently a communication breakdown between them. Formally put, two scientific languages are incommensurable when core sentences of one language, which have truth values when considered within its own context, lack truth values when considered within the context of the other due to an ontological gap between them. ;The presuppositional interpretation makes many significant contributions to the discussion of the issue of incommensurability and the related metaphysical and epistemological issues: It confirms the existence of the phenomenon of incommensurability and makes it metaphysically and epistemologically significant. It establishes the tenability and integrity of the notion of incommensurability. It avoids many alleged unattractive epistemological and metaphysical consequences of the translation-failure interpretation. (shrink)
An account of the logic of bivalent languages with truth-value gaps is given. This account is keyed to the use of tables introduced by S. C. Kleene. The account has two guiding ideas. First, that the bivalence property insures that the language satisfies classical logic. Second, that the general concepts of a valid sentence and an inconsistent sentence are, respectively, as sentences which are not false in any model and sentences which are not true in any model. What recommends (...) this approach is (1) its relative simplicity, and (2) the fact that it leaves the fundamental features of classical logic intact. (shrink)
We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and selection functions, independently of any strictness assumption.
A number of authors have noted that vagueness engenders degrees of belief, but that these degrees of belief do not behave like subjective probabilities. So should we countenance two different kinds of degree of belief: the kind arising from vagueness, and the familiar kind arising from uncertainty, which obey the laws of probability? I argue that we cannot coherently countenance two different kinds of degree of belief. Instead, I present a framework in which there is a single notion of degree (...) of belief, which in certain circumstances behaves like a subjective probability assignment and in other circumstances does not. The core idea is that one’s degree of belief in a proposition P is one’s expectation of P’s degree of truth. (shrink)
This paper is a reply to Michael Lynch's "Truth, Value and Epistemic Expressivism" in Philosophy and Phenomenological Research for 2009. It argues that Lynch's argument against expressivism fails because of an ambiguity in the employed notion of an 'epistemically disengaged standpoint'.
There are least two different things we might mean when we say that truth is a value: that it is a norm of belief, and that it is an end of inquiry. This paper considers to what extent we might be irrealist about the former claim -- that truth is a norm of belief.
To what extent is possession of truth considered a good thing in the Republic? Certain passages of the dialogue appear to regard truth as a universal good, but others are more circumspect about its value, recommending that truth be withheld on occasion and falsehood disseminated. I seek to resolve this tension by distinguishing two kinds of truths, which I label 'philosophical' and 'non-philosophical'. Philosophical truths, I argue, are considered unqualifiedly good to possess, whereas non-philosophical truths are regarded as worth possessing (...) only to the extent that possession conduces to good behaviour in those who possess them. In the non-philosophical arena it is an open question, to be determined on a case-by-case basis, whether falsehood is more efficacious in furthering this practical aim than truth. (shrink)
The paper aims at a perspicuous representation of Isaac Levi's pragmatist epistemology, spanning from the 1967 classic "Gambling with Truth" to his 2004 book on "Mild Contraction". Based on a formal framework for Levi's notion of inquiry, I analyse his decision-theoretic approach with truth and information as basic cognitive values, and with Shackle measures as emerging structures. Both cognitive values figure prominently in Levi's model of inductive belief expansion, but only the value of information is employed in his model of (...) belief contraction. I argue that the former model is more successful than the latter. (shrink)
Central to any form of Deflationism concerning truth (hereafter ‘DT’) is the claim that truth has no substantial theoretical role to play. For this reason, DT faces the following immediate challenge: if truth can play no substantial theoretical role then how can we model various prevalent kinds of indeterminacy—such as the indeterminacy exhibited by vague predicates, future contingents, liar sentences, truth-teller sentences, incomplete stipulations, cases of presupposition failure, and such-like? It is too hasty to assume that these phenomena are all (...) to be modelled via some epistemic conception of indeterminacy whereby indeterminacy is just some special species of ignorance which arises because of our limited powers of discrimination. Some non-epistemic model is called for—at least for certain species of indeterminacy. On what is perhaps the most enduring and popular non-epistemic model, indeterminacy gives rise to truth-value gaps. But is DT compatible with the possibility of truth-value gaps? Compatibilism says Yes; Incompatibilism says No. The broad goal of this paper is to defend a form of Incompatibilism. If DT is to make sense of various kinds of indeterminacy then truth-value gaps cannot be invoked to do so. The particular goals of this paper are: (i) To set forth a new form of Compatibilism which can address an argument against truth-value gaps given by Williamson (1994, pp. 187-192). (ii) To offer a new argument against truth-value gaps using principles entailed by DT, thereby undermining Compatibilism. (shrink)
Can mystics intuit something of what modern physicists calculate? And if so, how? The question of the relation between the classical mysticisms and modern science is approached in Part I in terms of the multiple forms and definitions of 'truth value'. Intuition/epiphany, pragmatism, coherence, and correspondence are considered as forms of truth that have also been proposed for unitive mystical experience. Since 'correspondence' or 'representation' has been the definition at the core of modern science, it in particular is approached by (...) combining Lakoff and Johnson on the roots of all abstract knowledge in physical metaphor and Gibson on the ecological array of perception as the template from which such metaphors must be drawn. A series of similarities between the maximally inclusive metaphors underlying unitive mystical experience and cosmological physics, as abstracted from an ecological array already resonant with multiple levels of physical reality, suggests a basis for the correspondence between these otherwise distinct cognitive domains. Part II extends this approach to widely posited cross cultural values of spiritual or mystical realization, in terms of gratitude, compassion, faith, and inner freedom. When fully embodied as forms of personal conduct, these are also ultimately derivable from the openness and flow patternings of the ecological array itself. The possibility that the more abstract spiritual values of the major world mysticisms exemplify not only revelatory and pragmatic forms of truth, but are also broadly correspondent with both the principles of immediate concrete perception and modern physics, may eventually allow a contemporary re- formulation of the microcosm-macrocosm unities basic to traditional cultures. (shrink)
It is shown how frege's problematic connection between truth-Value and "bedeutung" (of a sentence) becomes more plausible when set against the background of german language and philosophy, Especially by comparing frege's position with the value-Theoretical school of neo-Kantianism (w windelband).
The rift between science and religion needs to be assessed not merely on pragmatic grounds, on the basis of the effect of scientific versus religious beliefs on people's behavior, as John Caiazza's essay does, but also and above all in regard to the cogency of the respective beliefs in reference to what we can reasonably assume is the true face of reality. About such truth value, the conflict is not irremediable; there are elements of belief regarding the nature of reality (...) that are strikingly similar regardless of whether one arrived at them on the basis of faith in revealed knowledge or on the basis of knowledge acquired by reasoning from or in reference to experience. Two such items are selected here by way of example: belief that in certain states of mind and consciousness individuals can experience union with something larger or deeper than themselves, and belief that the universe we inhabit is the result of an original creative act. (shrink)
Antirealism about the past is apparently in conflict with our acceptance of a set of systematic linkages between the truth-values of differently tensed sentences made at different times. Arguments based on acceptance of these so-called truth-value links seem to show that fully accounting for our use of the past and future tenses will involve use of a notion of truth which is not epistemically constrained and is thus antirealistically unacceptable. I elaborate these difficulties through an examination of work by (...) Dummett and Wright. I agree with Wright's rejection of Dummett's proposal but go on to argue that Wright's account fares no better. Building on what I take to be the failure of Wright's account, I offer a solution for the antirealist which diagnoses the problem as stemming from an equivocation in the meanings assigned to the tensed truth predicates. I close by raising a different problem for antirealist accounts of the past, one which is, however, related to more general difficulties for antirealist theories of meaning. (shrink)
The purpose of the paper is to refute the fregean assumption that declarative sentences refer to truth-Values. A consequence of the assumption is that the truth-Value of a declarative sentence containing another as part remains unchanged when the part is replaced by another sentence having the same truth-Value, Provided that the part as part has only customary reference and expresses a complete thought. The refutation proceeds by demonstrating this consequence to be false.
In introductory logic courses the authors often limit their considerations to the truth-value operators. Then they write that conditionals and biconditionals of natural language ("if" and "if and only if") may be represented as material implications and equivalences ("⊃" and "≡"), respectively. Yet material implications are not suitable for conditionals. Lewis' strict implications are much better for this purpose. Similarly, strict equivalences are better for representing biconditionals (than material equivalences). In this paper we prove that the methods from standard (...) first courses in logic can be used for testing arguments with strict implications, strict equivalences and other operators which may represent connectives from natural language. (shrink)
After summarizing approaches taken previously to the problem of the determination of truth-Value of statements constituting literary works (ryle, Russell, Quine, Strawson, Davidson, Et. Al.) the author argues for a treatment of the problem based upon the linguistic status of such statements as translocutions and their relation to the context in which they occur.
We discuss Sengupta's argumentation according to which Frege was wrong identifying reference with truth-value.After stating various possible interpretations of Frege's principle of substitution, we show that there is no coherent interpretation under which Sengupta's argumentation is valid.Finally we try to show how Frege's distinction can work in the context of modern mathematics and how modern logic grasps it.
This paper examines the concept of ‘areti’ as encountered in the Aristotelian ethical system in order to establish its relationship to the modern concept of virtue as well as to that of moral truth, that is, to identify its truth-value. I intend to show that the Aristotelian ‘areti’ as a developed state of character and as an advanced stage of ethical understanding entails moral truth. ‘Areti’ as a good-in-itself possesses an intrinsic value which reflects moral truth, and as a (...) means for the accomplishment of ‘eudaimonia’ (ultimate happiness) it possesses an instrumental value. I also wish to argue that this position calls for a realist as well as an objectivist (or nonrelativist) approach in Aristotle. To that effect, I examine the elements of ‘areti’ that relate it to truth, and then I use reference to some of theAristotelian virtues, such as ‘andreia’ (courage), ‘philia’ (friendship), ‘dikaiosyne’ (justice), and ‘megalopsychia’ (magnanimity), in order to examine the way moral truth functions. This examination will also try to show that Aristotle’s aretaic approach does not suffer from the ills of virtue ethics theories. (shrink)
In the first half of the 17th century the Aristotelian view that the same statement or belief may be true at one time and false at another and, on the other hand, the conception of a mental proposition as a fully explicit thought that lends a definite meaning to a declarative sentence originated a lively debate concerning the question whether a mental proposition can change its truth-value.In this article it is shown that the defenders of a negative answer and (...) the advocates of a positive answer argued on the basis of different notions of what a mental proposition is:one side taking it as more or less equivalent to a specific utterance?meaning and the other side as more or less equivalent to a generic sentence-meaning. (shrink)
The author recently claimed that Pr(P, Q), where Pr is a probability function and P and Q are two sentences of a formalized language L, qualifies as an estimate--made in the light of Q--of the truth-value of P in L. To substantiate his claim, the author establishes here that the two strategies lying at the opposite extremes of the spectrum of truth-value estimating strategies meet the first five of the six requirements (R1-R6) currently placed upon probability functions and (...) fail to meet the sixth one. He concludes from those two results that the value for P and Q of any function satisfying R1-R5 must rate "minimally satisfactory" and the value for P and Q of any function satisfying R1-R6 must rate "satisfactory" as an estimate--made in the light of Q--of the truth-value of P in L. (shrink)
This thesis is concerned with the challenge truth-value gaps pose to the principle of bivalence. The central question addressed is: are truth-value gaps counterexamples to bivalence and is the supposition of counterexamples coherent? My aim is to examine putative cases of truth-value gaps against an argument by Timothy Williamson, which shows that the supposition of counterexamples to bivalence is contradictory. The upshot of his argument is that either problematic utterances say nothing, or they cannot be neither true (...) nor false. I start by identifying truth-bearers: an utterance, for instance, is a truth-bearer if it says that something is the case. Truth-bearers are evaluable items, with truth- and falsity-conditions statable in corresponding instances of schemas for truth and falsehood. A genuine case of a truth-value gap should be an utterance that is neither true nor false but says something to be the case. But it is inconsistent to accept the schemas for truth and falsehood and the existence of genuine cases of truth-value gaps. Secondly, I expound Williamson’s argument, which explores this inconsistency, and I identify two kinds of strategy to disarm his argument: those that preserve the schemas for truth and falsehood, and those that do not. Neither strategy is found to be persuasive. Thirdly, I argue that cases of reference failure causing truth-value gaps illustrate the upshot of Williamson’s argument. Fourthly, I examine Scott Soames’s account of liar sentences as counterexamples to bivalence. Soames adopts a strategy of the first kind to avoid contradictions. I argue that his solution allows some contradictions to be true, and that he fails to show that liar sentences are truth-bearers. Finally, I examine Charles Travis’s case for isostheneia: an equal balancing of reasons to evaluate a statement as true or as false, in which case a statement is neither. Travis avoids contradictions by adopting a strategy of the second kind. I argue that the schemas for truth and falsehood are immune to Travis’s objections, and that isostheneia fails to identify evaluable items. The cases examined confirm that utterances that are neither true nor false say nothing. My claim is thus that truth-value gaps are not counterexamples to bivalence. (shrink)
Most epistemologists maintain that true beliefs are of final epistemic value. However, Richard Feldman is a rare philosopher who is skeptical that true beliefs are of final epistemic value. The aim of this paper is to evaluate Feldman’s criticisms. I’ll argue that Feldman’s arguments ultimately turn on a view about the relation between epistemic duties and epistemic value that is implausible and underdeveloped.
To say that evidence is normative is to say that what evidence one possesses, and how this evidence relates to any proposition, determines which attitude among believing, dis-believing and withholding one ought to take toward this proposition if one deliberates about whether to believe it. It has been suggested by McHugh that this view can be vindi-cated by resting on the premise that truth is epistemically valuable. In this paper, I modify the strategy sketched by McHugh so as to overcome (...) the initial difficulty that it is unable to vindicate the claim that on counterbalanced evidence with respect to P one ought to con-clude deliberation by withholding on P. However, I describe the more serious difficulty that this strategy rests on principles whose acceptance commits one to acknowledging non-evidential reasons for believing. A way to overcome this second difficulty, against the evidentialists who deny this, is to show that we sometimes manage to believe on the ba-sis of non-epistemic considerations. If this is so, one fundamental motivation behind the evidentialist idea that non-epistemic considerations could not enter as reasons in delib-eration would lose its force. In the second part of this paper I address several strategies proposed in the attempt to show that we sometimes manage to believe on the basis of non-epistemic considerations and show that they all fail. So, I conclude that the strategy inspired by McHugh to ground the normativity of evidence of the value of truth ultimately fails. (shrink)
Truth values are, properly understood, merely proxies for the various relations that can hold between language and the world. Once truth values are understood in this way, consideration of the Liar paradox and the revenge problem shows that our language is indefinitely extensible, as is the class of truth values that statements of our language can take – in short, there is a proper class of such truth values. As a result, important and unexpected connections emerge between the semantic paradoxes (...) and the set-theoretic paradoxes. (shrink)
Chang's MV algebras are the algebras of the infinite-valued sentential calculus of ukasiewicz. We introduce finitely additive measures (called states) on MV algebras with the intent of capturing the notion of average degree of truth of a proposition. Since Boolean algebras coincide with idempotent MV algebras, states yield a generalization of finitely additive measures. Since MV algebras stand to Boolean algebras as AFC*-algebras stand to commutative AFC*-algebras, states are naturally related to noncommutativeC*-algebraic measures.
The question is asked whether one can consistently both be a minimalist about truth, and hold that some meaningful assertoric sentences fail to be either true or false. It is shown that one can, but the issues are delicate, and the price is high: one must either refrain from saying that the sentences lack truth values, or else one must invoke a novel non-contraposing three-valued conditional. Finally it is shown that this does not help in reconciling minimalism with emotivism, where (...) this latter is understood as involving the view that ethical sentences are neither true nor false. (shrink)
The article intends to show: a) that the modist Martin of Dacia sides with the traditional reading of the first chapter of Aristotle’s De interpretatione that we find in masters of arts from the first half of the thirteenth century; and b) that the modist Boethius of Dacia is one of the first thirteenth-century scholars to depart from this reading. In fact, Boethius presents us with an account of propositional verification where the terms’ signification is not operational and where the (...) immediate truth-maker of statements like ‘homo est animal’ is an external state of affairs. In Martin’s case, to the contrary, the terms’ signification is operational in his account of propositional verification and the immediate truth-bearer of such statements is a mental composition or division. (shrink)
This chapter focuses on the question of whether true belief can have final value because it answers our ‘intellectual interest’ or ‘natural curiosity’. The idea is that sometimes we are interested in the truth on some issue not for any ulterior purpose, but simply because we are curious about that issue. It is argued that this approach fails to provide an adequate explanation of the final value of true belief, since there is an unbridgeable gap between our valuing the truth (...) on some issue for its own sake, and that truth's being valuable for its own sake. (shrink)
The symposium »Does the Concept of ›Truth‹ Have Value in the Pursuit of Cross-Cultural Philosophy?« hones on a methodological question which has deep implications on doing philosophy cross-culturally. Drawing on early Confucian writers, the anchor, Henry Rosemont, Jr., attempts to explain why he is skeptical of pat, affirmative answers to this question. His co-symposiasts James Maffie, John Maraldo, and Sonam Thakchoe follow his trail in working out multi-faceted views on truth from Mexican, Japanese Confucian, and Tibetan Buddhist perspectives respectively. As (...) these positions substantiate, the aforementioned non-Anglo-European traditions seem to draw on an integrated view of thinking, feeling, and living a human life. For their practitioners, truth is less of a correspondence with a given external reality. In fact, it enables human beings to strike the right path in living good, social lives. (shrink)
Cappelen and Lepore claim that the English language contains a basic and limited set of context-sensitive expressions, as only expressions within this set pass the truth-related tests that they propose to single out context-sensitive from context-insensitive words. In this paper, I argue that racial and ethnic slurs also pass Cappelen and Lepore’s context sensitivity tests and that, as a result, slurs should also be seen as context-sensitive expressions in a truth-related sense.
In Category Mistakes, Ofra Magidor provides two arguments against the view that category mistakes express propositions that are not truth-evaluable at some world. I argue that her first, Williamsonian argument against this view begs the question, and that her second argument rests on a misleading conception of how semantic defect results in infelicity judgments. I conclude by conceding that she is still correct to stress that the view she opposes face noteworthy foundational and empirical challenges.
Among other things, Odegard urged that a person can be completely justified in believing a false proposition because the truth condition can be shown to be satisfied independently of the satisfaction of the evidence condition for human knowledge. I respond to his argument and other arguments attacking the arguments I previously offered for the view that a person cannot be completely justified in believing a false proposition.
Almeder effectively defends his view that justification entails truth against some earlier objections and offers new arguments for the entailment. Although the arguments make clear that truth claims depend on justification claims, They still fail to establish an entailment.
This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.