Pure quotation, as in ‘cat’ has three letters, is a linguistic device designed for referring to linguistic expressions. I present a uniform recon struction of the four classic philosophical accounts of the phenomenon: the proper name theory, the description theory, the demonstrative theory, and the disquotational theory. I evaluate the strengths and weaknesses of each proposal with respect to fundamental semantic properties like compositionality, productivity, and recursivity.

Consistency of choice is a fundamental and recurring theme in decision theory, social choice theory, behavioral economics, and psychological sciences. The purpose of this paper is to study the consistency of choice independent of the particular decision model at hand. Consistency is viewed as an inherently logical concept that is fundamentally void of connotation and is thus disentangled from traditional rationality or consistency conditions imposed on decision models. The proposed formalization of consistency takes two forms: internal consistency, which refers to (...) the property that a choice model does not generate contradictory statements; and semantic consistency, which refers to the idea that a theory’s predictions are valid with respect to some observed data. In addressing semantic consistency, the relationship between theory and data is analyzed in terms of so-called duality mappings, which allow a passage between the two universes in a way that consistency is preserved. The formalization of consistency concepts relies on adapting the revealed preference theory to the context-dependent setting. The paper concludes by discussing the implications of the proposed framework and how it relates to classical revealed preference theory and other formalizations of the relationship between the theory and reality of choice. (shrink)

This paper is concerned with the reversal in meaning of the word positivism, which has come to mean ‘theory which assumes the existence of a world beyond our ideas’ whereas once it meant ‘theory which is agnostic about the existence of a world beyond our ideas', and with educational writers’ persistent mistakes in using quotation marks, as a consequence of this reversal.

Research into logical syntax provides us the knowledge of the structure of sentences, while logical semantics provides a window into uncovering the truth of sentences. Therefore, it is natural to make sentences and truth the central concern when one deals with the theory of meaning logically. Although their theories of meaning differ greatly, both Michael Dummett’s theory and Donald Davidson’s theory are concerned with sentences and truth and developed in terms of truth. Logical theories and methods first introduced by G. (...) Frege underwent great developments during the past century and have played an important role in expanding these two scholars’ theories of meaning. (shrink)

It is often argued that by assuming the existence of a universal language, one prohibits oneself from conducting semantical investigations. It could thus be thought that Tarski’s stance towards a universal language in his fruitful Wahrheitsbegriff differs essentially from Carnap’s in the latter’s less successful Untersuchungen zur allgemeinen Axiomatik. Yet this is not the case. Rather, these two works differ in whether or not the studied fragments of the universal language are languages themselves, i.e., whether or not they are closed (...) under derivation rules. In Carnap’s case, axiom systems are not closed under derivation rules, which enables him to adopt a substitutional concept of models. His approach is directly rooted in the tradition of formal axiomatics, we argue, and in this contrary to Tarski’s. In comparing these works by Carnap and Tarski, our aim will be to qualify the connection between Tarski’s approach and the tradition of formal axiomatics, which has been overemphasized in the literature. (shrink)

The ethical problems surrounding voluntary assisted suicide remain formidable, and are unlikely to be resolved in pluralist societies. An examination of historical attitudes to suicide suggests that modernity has inherited a formidable complex of religious and moral attitudes to suicide, whether assisted or not. Advocates usually invoke the ending of intolerable suffering as one justification for euthanasia of this kind. This does not provide an adequate justification by itself, because there are (at least theoretically) methods which would relieve suffering without (...) causing the physical death of the suffering person. Carried to extremes, these methods would finish the life worth living, but leave a being which was technically alive. Such acts, however, would provide no moral escape, since they would create beings without meaning. Arguments seeking to justify ending the lives of others need some grounding in concepts of the meaning of a life. The euthanasia discourse therefore needs to take at least some account of the meaning we construct for our lives and the lives of others. (shrink)

Aristotle’s words in the Metaphysics: “to say of what is that it is, or of what is not that it is not, is true” are often understood as indicating a correspondence view of truth: a statement is true if it corresponds to something in the world that makes it true. Aristotle’s words can also be interpreted in a deflationary, i.e., metaphysically less loaded, way. According to the latter view, the concept of truth is contained in platitudes like: ‘It is true (...) that snow is white iff snow is white’, ‘It is true that neutrinos have mass iff neutrinos have mass’, etc. Our understanding of the concept of truth is exhausted by these and similar equivalences. This is all there is to truth. In his book Truth (Second edition 1998), Paul Horwich develops minimalism, a special variant of the deflationary view. According to Horwich’s minimalism, truth is an indefinable property of propositions characterized by what he calls the minimal theory, i.e., all (nonparadoxical) propositions of the form: It is true that p if and only if p. Although the idea of minimalism is simple and straightforward, the proper formulation of Horwich’s theory is no simple matter. In this paper, I shall discuss some of the difficulties of a logical nature that arise. First, I discuss problems that arise when we try to give a rigorous characterization of the theory without presupposing a prior understanding of the notion of truth. Next I turn to Horwich’s treatment of the Liar paradox and a paradox about the totality of all propositions that was first formulated by Russell (1903). My conclusion is that Horwich’s minimal theory cannot deal with these difficulties in an adequate way, and that it has to be revised in fundamental ways in order to do so. Once such revisions have been carried out the theory may, however, have lost some of its appealing simplicity. (shrink)

Complex demonstratives, expressions of the form 'That F', 'These Fs', etc., have traditionally been taken to be referring terms. Yet they exhibit many of the features of quantified noun phrases. This has led some philosophers to suggest that demonstrative determiners are a special kind of quantifier, which can be paraphrased using a context sensitive definite description. Both these views contain elements of the truth, though each is mistaken. We advance a novel account of the semantic form of complex demonstratives that (...) shows how to reconcile the view that they function like quantified noun phrases with the view that simple demonstratives function as context sensitive referring terms wherever they occur. If we are right, previous accounts of complex demonstratives have misconceived their semantic role; and philosophers relying on the majority view in employing complex demonstratives in analysis have proceeded on a false assumption. (shrink)

In this paper, we defend Davidson's program in truth-theoretical semantics against recent criticisms by Scott Soames. We argue that Soames has misunderstood Davidson's project, that in consequence his criticisms miss the mark, that appeal to meanings as entities in the alternative approach that Soames favors does no work, and that the approach is no advance over truth-theoretic semantics.

The goal of this paper is to present and defend an inferentialist account of the meaning of fictional names on the basis of Sellars-Brandom’s inferentialist semantics and a Brandomian anaphoric theory of reference. On this inferentialist account, the meaning of a fictional name is constituted by the relevant language norms which provide the correctness conditions for its use. In addition, the Brandomian anaphoric theory of reference allows us to understand reference in terms of anaphoric word-word relations, rather than substantial word-world (...) relations. In this paper I argue that this inferentialist account has many important merits over its rival theories. One important merit is that it explains why we can use fictional names to make true statements, even if they lack bearers. As a consequence, this theory allows us to use fictional names without committing ourselves to an implausible ontology of fictional entities. Another important merit is that it provides a uniform semantic account of fictional names across different types of statements in which fictional names are involved. (shrink)

Depuis 1967, Donald Davidson defend l'idée qu'une théorie de la signification pour une langue naturelle doit prendre la forme d'une théorie tarskienne de la vérité. Je me propose ici d'exposer les grandes lignes de l a conception davidsonienne de la sémantique des langues naturelles et de chercher à préciser en quel sens une theorie tarskienne de la vérité pour une langue L constitue, selon Davidson, une théorié de la signification pour L. Je ferai pour cela abstraction des obstacles qu'il pourrait (...) y avoir à la réalisation du programme de Davidson. (shrink)

In their (2008) article Liar-Like Paradox and Object Language Features C.S. Jenkins and Daniel Nolan (henceforth, JN) argue that it is possible to construct Liar-like paradox in a metalanguage even though its object language is not semantically closed. I do not take issue with this claim. I find fault though with the following points contained in JN’s article: First, that it is possible to construct Liar-like paradox in a metalanguage, even though this metalanguage is not semantically closed. Second, that the (...) presented examples of Liar-like paradox are supposed to be counterexamples to Tarski’s diagnosis of the classic Liar paradox. Third, that JN fail to notice Tarski’s postulate. And finally, that JN fail to recognize that the world they are pondering is not among the possible worlds. (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)

This is a commentary on MM McCabe's "First Chop your logos... Socrates and the sophists on language, logic, and development". In her paper MM analyses Plato's Euthydemos, in which Plato tackles the problem of falsity in a way that takes into account the speaker and complements the Sophist's discussion of what is said. The dialogue looks as if it is merely a demonstration of the silly consequences of eristic combat. And so it is. But a main point of MM's paper (...) is that there is serious philosophy in the Euthydemos, too. MM argues that to counter the sophist brothers Euthydemos and Dionysodoros, Socrates points out that that there are different aspects to the verb 'to say' that run in parallel to the different aspects of the very 'to learn'. So just as there is continuity rather than ambiguity between 'to learn' and 'to understand', so there is continuity between the different aspects of saying. Thus Socrates puts forward a teleological account of both learning and meaning. Following up on some of MM's thoughts, I argue that the sophists subscribe, despite appearance, to a theory of meaning that respects serious and widely accepted philosophical theses on meaning. -/- Forthcoming in the Australasian Philosophical Review. The curator of the volume is Fiona Leigh, and the committee also has Hugh Benson and Tim Clarke. You can find MM's paper as well as the commentaries by Nicholas Denyer and Russell E. Jones and Ravi Sharma (and myself) by registering. (shrink)

This paper explores applications of concepts from argumentation theory to mathematical proofs. Note is taken of the various contexts in which proofs occur and of the various objectives they may serve. Examples of strategic maneuvering are discussed when surveying, in proofs, the four stages of argumentation distinguished by pragma-dialectics. Derailments of strategies (fallacies) are seen to encompass more than logical fallacies and to occur both in alleged proofs that are completely out of bounds and in alleged proofs that are at (...) least mathematical arguments. These considerations lead to a dialectical and rhetorical view of proofs. (shrink)

We shall try to defend two non-standard views that run counter to two well-entrenched familiar views. The standard views are the universal and existential quantifiers of first-order logic are not modal operators, and the quantifiers are extensional. If that is correct then the counterclaims create genuine problems for some traditional philosophical doctrines.

What exactly does conceptual analysis consist in? Is it empirical or a priori? How does it support philosophical theses? and What kinds of thesis are these? There is no consensus on these questions in contemporary philosophy. This study aims to defend conceptual analysis by showing that it comprises a number of different methods and by explaining their importance in philosophy. After setting out an initial dilemma for conceptual analysis, the study outlines a minimal ecumenical account of concepts, as well as (...) an account of concept possession and concept employment. On the basis of these accounts, the study then argues that there are both empirical and a priori forms of conceptual analysis, and that each can be defended as legitimate methods. The philosophical interest of conceptual analysis, however, resides in relying on all three types of method in the service of answering philosophical concerns. This is illustrated by three sample cases. (shrink)

In this article, I am concerned with the ethical foundations of behavior therapy, that is, with the normative ethics and the meta-ethics underlying behavior therapy. In particular, I am concerned with questions concerning the very possibility of providing an ethical justification for things done in the context of therapy. Because behavior therapists must be able to provide an ethical justification for various actions (if the need arises), certain meta-ethical views widely accepted by behavior therapists must be abandoned: in particular, one (...) must give up ethical subjectivism, ethical skepticism, and ethical relativism. An additional task is to show how it is possible to provide a nonsubjective, nonskeptical, and nonrelativistic moral justification for an ethical statement. Although this is a monumental task, I provide a rough sketch of such a model, one that is congenial to the value judgments underlying behavior therapy. (shrink)

This book is a running commentary of Tarski’s momentous monograph ‘The Concept of Truth in Formalized Languages’, published in Polish in 1933, with special focus on discrepancies...

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen–Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event algebras. We show explicitly that the latter category is equipped with an object of truth values, (...) or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is inherent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature. (shrink)

We give a survey on truth theories for applicative theories. It comprises Frege structures, universes for Frege structures, and a theory of supervaluation. We present the proof-theoretic results for these theories and show their syntactical expressive power. In particular, we present as a novelty a syntactical interpretation of ID1 in a applicative truth theory based on supervaluation.

John Etchemendy has argued that it is but "a fortuitous accident" that Tarski's work on truth has any signifance at all for semantics. I argue, in response, that Etchemendy and others, such as Scott Soames and Hilary Putnam, have been misled by Tarski's emphasis on definitions of truth rather than theories of truth and that, once we appreciate how Tarski understood the relation between these, we can answer Etchemendy's implicit and explicit criticisms of neo-Davidsonian semantics.

Each science has its own domain of investigation, but one and the same science can be formalized in different languages with different universes of discourse. The concept of the domain of a science and the concept of the universe of discourse of a formalization of a science are distinct, although they often coincide in extension. In order to analyse the presuppositions and implications of choices of domain and universe, this article discusses the treatment of omega arguments in three very different (...) formalizations of arithmetic. In Peano's formalization the domain is a restricted class of individuals, while the universe of discourse is the unrestricted class of all individuals. In Gödel's formalization the domain is a restricted class of individuals as in Peano's formalization, but the universe of discourse coincides with the domain. In Whitehead-Russell's formalization the domain is a class of logical notions in Tarski's sense, that are necessarily not individuals, whereas the universe of discourse is the unrestricted class of individuals as in Peano's formalization. The present approach emphasizes the viewpoint that the universe of discourse of a given discourse is important in determining which propositions are expressed by which sentences. (shrink)

Review: Ippoliti, Emiliano, Sterpetti, Fabio, Nickles Thomas : Models and Inferences in Science.

Contra Lewis, it is argued that the correspondence theory is a genuine rival theory of truth: it goes beyond the redundancy theory; it competes with other theories of truth; it is aptly summarized by the slogan 'truth is correspondence to fact'; and it really is a theory of truth.

Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or falsehood of sentences in a language can only be asserted or denied in a higher-order meta-language. However, Tarski’s statement of the truth-schemata themselves involve general truth functions, and in particular (...) the biconditional, defined in terms of truth conditions involving truth values standardly displayed in a truth table. Consistently with his semantic program, all such truth values should also be relativized to particular languages for Tarski. The objection thus points toward the more interesting problem of Tarski’s concept of the exact status of truth predications in a general logic of sentential connectives. Tarski’s three-part solution to the circularity objection which he anticipates is discussed and refuted in detail. (shrink)

Network motifs are small patterns of connections, found over‐represented in gene regulatory networks. An example is the negative feedback loop (e.g. factor A represses itself). This opposes its own state so that when ‘on’ it tends towards ‘off’ – and vice versa. Here, we argue that such self‐opposition, if considered dimensionlessly, is analogous to the liar paradox: ‘This statement is false’. When ‘true’ it implies ‘false’ – and vice versa. Such logical constructs have provided philosophical consternation for over 2000 years. (...) Extending the analogy, other network topologies give strikingly varying outputs over different dimensions. For example, the motif ‘A activates B and A. B inhibits A’ can give switches or oscillators with time only, or can lead to Turing‐type patterns with both space and time (spots, stripes or waves). It is argued here that the dimensionless form reduces to a variant of ‘The following statement is true. The preceding statement is false’. Thus, merely having a static topological description of a gene network can lead to a liar paradox. Network diagrams are only snapshots of dynamic biological processes and apparent paradoxes can reveal important biological mechanisms that are far from paradoxical when considered explicitly in time and space. (shrink)

The paper argues that the liar paradox teaches us these lessons about English. First, the paradox-yielding sentence is a sentence of English that is neither true nor false in English. Second, there is no English name for any such thing as a set of all and only true sentences of English. Third, ‘is true in English’ does not satisfy the axiom of comprehension.

The significance of the semantical paradoxes for natural languages is examined. If Tarski’s reflections on the issue are correct, English is inconsistent. Paul Ziff responds to Tarskian reflections by arguing to the conclusion that no natural language is or can be inconsistent. The authors reject Ziff’s argument, but they defend something similar to its conclusion: no language, natural or otherwise, is or can be inconsistent in the way that Tarski holds languages capable of formulating the Epimenides are inconsistent.

Tarski's theorem essentially says that the Liar paradox is paradoxical in the minimal reflexive frame. We generalise this result to the Liar-like paradox $\lambda^\alpha$ for all ordinal $\alpha\geq 1$. The main result is that for any positive integer $n = 2^i(2j+1)$, the paradox $\lambda^n$ is paradoxical in a frame iff this frame contains at least a cycle the depth of which is not divisible by $2^{i+1}$; and for any ordinal $\alpha \geq \omega$, the paradox $\lambda^\alpha$ is paradoxical in a frame (...) iff this frame contains at least an infinite walk which has an arbitrarily large depth. We thus get that $\lambda^n$ has a degree of paradoxicality no more than $\lambda^m$ iff the multiplicity of 2 in the (unique) prime factorisation of $n$ is no more than that in the prime factorisation of $m$; and all tranfinite $\lambda^\alpha$ has the same degree of paradoxcality but has a higher degree of paradoxicality than any $\lambda^n$. (shrink)

A relativized version of Tarski's T-scheme is introduced as a new principle of the truth predicate. Under the relativized T-scheme, the paradoxical objects, such as the Liar sentence and Jourdain's card sequence, are found to have certain relative contradictoriness. That is, they are contradictory only in some frames in the sense that any valuation admissible for them in these frames will lead to a contradiction. It is proved that for any positive integer n, the n-jump liar sentence is contradictory in (...) and only in those frames containing at least an n-jump odd cycle. In particular, the Liar sentence is contradictory in and only in those frames containing at least an odd cycle. The Liar sentence is also proved to be less contradictory than Jourdain's card sequence: the latter must be contradictory in those frames where the former is so, but not vice versa. Generally, the relative contradictoriness is the common characteristic of the paradoxical objects, but different paradoxical objects may have different relative contradictoriness. (shrink)

Even though disquotationalism is not correct as it is usually formulated, a deep insight lies behind it. Specifically, it can be argued that, modulo implicit commitment to reflection principles, all there is to the notion of truth is given by a simple, natural collection of truth-biconditionals.

The present paper discusses a proposal which says,roughly and with several qualifications, that thecollection of mathematical truths is identical withthe set of theorems of ZFC. It is argued that thisproposal is not as easily dismissed as outright falseor philosophically incoherent as one might think. Some morals of this are drawn for the concept ofmathematical knowledge.

This article contains an overview of the main problems, themes and theories relating to the semantic paradoxes in the twentieth century. From this historical overview I tentatively draw some lessons about the way in which the field may evolve in the next decade.

According to Field’s influential incompleteness objection, Tarski’s semantic theory of truth is unsatisfactory since the definition that forms its basis is incomplete in two distinct senses: (1) it is physicalistically inadequate, and for this reason, (2) it is conceptually deficient. In this paper, I defend the semantic theory of truth against the incompleteness objection by conceding (1) but rejecting (2). After arguing that Davidson and McDowell’s reply to the incompleteness objection fails to pass muster, I argue that, within the constraints (...) of a non-reductive physicalism and a holism concerning the concepts of truth, reference and meaning, conceding Field’s physicalistic inadequacy conclusion while rejecting his conceptual deficiency conclusion is a promising reply to the incompleteness objection. (shrink)

Although there is a prima facie strong case for a close connection between the meaning and inferential role of certain expressions, this connection seems seriously threatened by the semantic and logical paradoxes which rely on these inferential roles. Some philosophers have drawn radical conclusions from the paradoxes for the theory of meaning in general, and for which sentences in our language are true. I criticize these overreactions, and instead propose to distinguish two conceptions of inferential role. This distinction is closely (...) tied to two conceptions of deductive logic, and it is the key, I argue, for understanding first the connection between meaning and inferential role, and second what the paradoxes show more generally. (shrink)

We consider two formalisations of the notion of a compositionalsemantics for a language, and find some equivalent statements in termsof substitutions. We prove a theorem stating necessary and sufficientconditions for the existence of a canonical compositional semanticsextending a given partial semantics, after discussing what features onewould want such an extension to have. The theorem involves someassumptions about semantical categories in the spirit of Husserl andTarski.

The paper analyses what is said and what is presupposed by thePrinciple of Compositionality for semantics, as it is commonly stated. ThePrinciple of Compositionality is an axiom which some semantics satisfy andsome don’t. It says essentially that if two expressions have the same meaning then they make the same contribution to the meanings of expressionscontaining them. This is a sensible axiom only if one combines it with aconverse, that if two expressions make the same contribution to the meanings of sentences (...) containing them, then they have the same meaning;and some assumption that two expressions which can’t meaningfully besubstituted for each other have different meanings. as a full abstraction principle, and as ‘Husserl’s principle’.) Moreoverthe Principle of Compositionality speaks only about when two expressionshave the same meaning; it adds nothing whatever about what that meaningmight be . Some recent discussions by writers in linguistics and logic are assessed. The paper finishes by reviewing thehistory of the notion of compositionality. (shrink)

In its first meaning, a logic is a collection of closely related artificial languages. There are certain languages called first‐order languages, and together they form first‐order logic. In the same spirit, there are several closely related languages called modal languages, and together they form modal logic. Likewise second‐order logic, deontic logic and so forth.

In many actual arguments, the conclusion seems intuitively to follow from the premisses, even though we cannot show that it follows logically. The traditional approach to evaluating such arguments is to suppose that they have an unstated premiss whose explicit addition will produce an argument where the conclusion does follow logically. But there are good reasons for doubting that people so frequently leave the premisses of their arguments unstated. The inclination to suppose that they do stems from the belief that (...) the only way in which an argument's conclusion can follow definitely from its premisses is to follow logically. I argue that this belief is mistaken. I propose a revision of the current generic conception of logical consequence, and its variant specifications, to avoid the paradoxes of strict implication. The revised conception can then be naturally extended to include also what we might call 'enthymematic consequence'. This concept is a kind of consequence, whose properties merit investigation. (shrink)

Within the context of the Quine–Putnam indispensability argument, one discussion about the status of mathematics is concerned with the ‘Enhanced Indispensability Argument’, which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the life cycles of Periodical Cicadas is genuinely mathematical, according to Baker (...) :223–238, 2005; Br J Philos Sci 60:611–633, 2009). Furthermore, the result is then also used to strengthen the platonist position :779–793, 2017a). We pick up the circularity problem brought up by Leng Mathematical reasoning, heuristics and the development of mathematics, King’s College Publications, London, pp 167–189, 2005) and Bangu :13–20, 2008). We will argue that Baker’s attempt to solve this problem fails, if Hume’s Principle is analytic. We will also provide the opponent of the Enhanced Indispensability Argument with the so-called ‘interpretability strategy’, which can be used to come up with alternative explanations in case Hume’s Principle is non-analytic. (shrink)