The rule of universal instantiation appears to be subject to counterexamples, although the rule of existential generalization is not subject to the same doubts. This paper is a survey of ways of responding to this problem, both conservative and revisionist. The conclusion drawn is that logical validity should be defined in terms of assertibility in a context rather than in terms of truth on an interpretation. Contexts are here defined, not in terms of the attitudes of the interlocutors, (...) but in terms of the goals of conversation, and assertibility is explained in terms of cooperation. (shrink)

Given the recent interest in the fragment of system $\mathbf{F}$ where universal instantiation is restricted to atomic formulas, a fragment nowadays named system ${\mathbf{F}}_{\textbf{at}}$, we study directly in system $\mathbf{F}$ new conversions whose purpose is to enforce that restriction. We show some benefits of these new atomization conversions: they help achieving strict simulation of proof reduction by means of the Russell–Prawitz embedding of $\textbf{IPC}$ into system $\mathbf{F}$, they are not stronger than a certain ‘dinaturality’ conversion known to generate (...) a consistent equality of proofs, they provide the bridge between the Russell–Prawitz embedding and another translation, due to the authors, of $\textbf{IPC}$ directly into system ${\mathbf{F}}_{\textbf{at}}$ and they give means for explaining why the Russell–Prawitz translation achieves strict simulation whereas the translation into ${\mathbf{F}}_{\textbf{at}}$ does not. (shrink)

Numerous sex differences in obsessive-compulsive disorder (OCD) instantiations are likely universal, as the associated evolutionary threats and concerns onto which they map were differentially important to the two sexes. Hence, although some ritualized behaviors or thoughts are indeed culture-specific, others are both culturally and temporally invariant as they are rooted in universal Darwinian etiologies (e.g., the sex differences in OCD symptomatology posited here). (Published Online February 8 2007).

Many philosophers believe that there are both particulars and universals. Many of these philosophers, in turn, believe that universals areimmanent. On this view, universals are wholly located where their instances are located. Both Douglas Ehring and E.J. Lowe have argued that immanent universals do not exist on the grounds that nothing can be wholly located in multiple places simultaneously without contradiction. In this paper, I focus on Lowe’s argument, which has received far less attention in the literature. Using the theory (...) of location found in Josh Parsons (2007), I show how Lowe’s argument against immanent universals can be resisted. (shrink)

What all contemporary so-called aristotelian realists have in common has been identified by David Armstrong as the principle of instantiation. This principle has been put forward in different versions, but all of them have the following simple consequence in common: uninstantiated universals do not exist. Such entities are for the lotus-eating Platonist to countenance, but not for any sort of moderate realist. I shall argue that this principle, in any guise, is not the best way to differentiate aristotelianism from (...) Platonism. In its place, I shall suggest that the best way to differentiate the two versions of realism from each other is by means of a far more powerful idea: naturalism. And the surprising conclusion given this means of differentiation will be that contrary to the usual proclamations, Platonism will be the more naturalistic theory, whereas aristotelianism will come to be seen for what it really is, namely, non-naturalistic. (shrink)

In order to avoid the problems faced by standard realist analyses of the “relation” of instantiation, Baxter and, following him, Armstrong each analyze the instantiation of a universal by a particular in terms of their partial identity. I introduce two related conceptions of partial identity, one mereological and one non-mereological, both of which require at least one of the relata of the partial identity “relation” to be complex. I then introduce a second non-mereological conception of partial identity, (...) which allows for both relata to be simple. I take these three conceptions to exhaust the plausible ways of construing two entities as being partially identical. I then argue that there is no analysis (including those offered by Baxter and Armstrong) of a universal and a particular as being partially identical consistent with any of these three conceptions that (i) is coherent, (ii) is consistently realist, (iii) does not lead to absurd consequences, and (iv) offers a “solution” to the problem of instantiation that avoids the problems with the other standard realist responses. In so arguing, I offer a criticism of the analysis of instantiation as partial identity that is independent of the standard criticism that it entails the necessity of predication. (shrink)

Construing the instantiation of a universal by a particular in terms of my theory of aspects resolves the basic mystery of this "non-relational tie", and gives theoretical unity to the four characteristics of instantiation discerned by Armstrong. Taking aspects as distinct in a way akin to Scotus's formal distinction, I suggest that instantiation is the sharing of an aspect by a universal and a particular--a kind of partial identity. This approach allows me to address Plato's (...) multiple location and One over Many problems, Bradley's problem concerning the instantiation of relations, and the problem of change. (shrink)

What is it, metaphysically, for a universal to be instantiated in a concrete particular? Philosophical controversy has been ongoing since the beginning of philosophy itself. I here contribute a novel account of instantiation developed on the basis of Aristotelian premises (but departing from the mainstream interpretation according to which Aristotelian universals are instantiated by ‘combining’ hylomorphically with matter). The key stance is that for Aristotle each substance is one, i.e. single (in addition to also being a non-recurrent particular). (...) I show that for Aristotle, the oneness of substances is primitively assumed, and, importantly, cannot be derived from composition of parts, not even holistic composition. Parts undermine oneness. It follows that instantiated properties are 'not parts' of substances. However, if not parts of the substances they are in, what are they? Aristotle shows they are 'qualifications' of the substances they are in. Don’t qualifications undermine the singleness of a substance? I show that Aristotle makes sure they do not. The way he does it is new, then and now. Instantiated properties are ‘hybrid’ entities: they sacrifice their own discreteness 'qua' properties, while adopting the discreteness of the metaphysical subject they qualify, i.e. the substance. But then, how can a universal quality recur in many substances, if, when instantiated, it assimilates the discreteness of each of these substances? This is a key Aristotelian stance: 'the quality recurs, not its qualifications'. Qualities are abstracted from their instances in similar objects, e.g. ‘wisdom’ is abstracted from many ‘wise’ people; ‘wisdom’ is individuated bottom-up from its instances, by abstraction. (shrink)

This work presents and discusses the conception of instantiation as ‘partial identity’. The theory has been previously proposed in two different guises by Baxter and Armstrong . Attention will be paid mostly to Baxter’s presentation, which seems the best de veloped, and where instantiation is understood as identity of ‘aspects’ of a universal and a particular. The theory seems to offer a solution to the vexed question of Bradley’s Regress, because instantiation is no longer conceived as (...) a relation between numerically different entities. The proposed solution requires an ontology of ‘aspects’ in order to work. Aspects are presented in the form [ x insofar as j] where x is filled by the entity to which the aspect pertains and j is filled by the respect in which the entity in question is considered. Aspects are numerically identical with the entity to which they pertain and with the other aspects of the same entity. Aspects, nonetheless, are not mere ways in which one can conceive an entity. Aspects are objective. Rejection of the principle of indiscernibility of identicals is crucial to this theory. The attributions of one aspect are not also attributions to the other aspects of the same entity. Hence, aspects offer ways to deal with seemingly incoherent attributions to the same entity. Baxter uses them to solve the problem of the multi-location of universals, temporary intrinsics and trans-world identity, besides the nature of instantiation. Several difficulties are presented, both to the general metaphysics of aspects, and to the conception of instantiation as identity of aspects. In general: it is not clear how to distinguish objective aspects from the mere forms in which we conceive an entity; it is not clear what are the conditions of identity of an aspect; and although the necessity of identity is rejected in general, it reappears as necessity of ‘aspectual’ identity. The necessity of aspectual identity raises concerns about the stability of the view. In respect to the specific conception of instantiation as identity of aspects, it will be pointed out that the theory implies the complete identity of universals and particulars that instantiate them and, further, that it implies the identity of everything with everything. (shrink)

This paper is concerned with English noun phrases that denote generalized instances: they do not refer to actual spatio-temporal instances, but to virtual ones that are abstracted from a limited number of actual instances, e.g., a student in Three times, a student complained (Langacker, Foundations of Cognitive Grammar. Volume II: Descriptive application, Stanford University Press, 1991, Dynamicity, fictivity, and scanning: The imaginative basis of logic and linguistic meaning, Cambridge University Press, 2005, forthcoming). Langacker likens generalized instances to generic ones, which (...) constitute “global” generalizations over all actual instances of a type. On the basis of authentic data, I argue that, even though the profiled instance denoted by generic and generalized noun phrases is similar, the way the respective instances are accessed in discourse is very different. My data set consists of English noun phrases that are explicitly marked for generalized instantiation by the addition of a secondary determiner such as same in The twin brothers bought the same car or kind of in There was no way we could match that kind of offer. I compare noun phrases of four sets of secondary determiners, viz. adjectives of multiple exposure (usual), of identity (same, identical), of similarity (similar, comparable) and type noun constructions (kind of/type of/sort of). These data also allow me to refine the concept of generalized instantiation in terms of its semantic subtypes, the semantic interaction between secondary determiner and primary determiner, and the selection criteria for secondary determiners that can express it. (shrink)

Words come into existence through a number of distinct processes including naming, semantic shifts, morphological productivity, and compounding. In accounting for the instantiation and individuation of word-types, two diachronic proposals termed Originalism and History are considered, which view word-types as emerging through a tokening act after which they are subsequently distinguished from others on the basis of having a unique event-like origin. In the following paper I elucidate two central tenets of Originalism and History, which I name essentialism and (...) propagation. Next, I demonstrate that each suffer considerable challenges from evidence pertaining to the systematic generativity of words grounded in universal features of human lexical cognition. A third diachronic theory named Originalism-Plus-Transfer (OPT) is then outlined. I argue that this more nuanced version of Originalism, in its present form, still lacks a thorough explanation of pivotal features of word generativity, word instantiation, and word individuation. A number of ‘synchronic’ constraints on word-hood—phonological, phonotactic, morpho-syntactic, and semantic—are put forward to ground the possible space for word generation. I conclude by exploring the viability of supplementing OPT with synchronic constraints and propose that a union between the two has the potential to provide OPT with greater empirical strength and predictive power. The upshot of this analysis is that there exists great programmatic value for diachronic theories in drawing on synchronic data and that the latter must feature as central to the philosophy of words if such work is to anticipate achieving explanatory adequacy. (shrink)

In his “Are Properties, Particular, Universal, or Neither?” Javier Cumpa argues that science not metaphysics explains how properties are instantiated. I accept this conclusion provided physics can be stated using rather few primitive predicates. In addition, he uses his scientific theory of instantiation to argue for Neutralism, his thesis that the “tie” between properties and their instances implies neither that properties are particular nor that they are universals. Neutralism, I claim, is a thesis that realist about universals have (...) independent reason to accept and their opponents have reason to reject. So, neutralism is not neutral on the topic of whether properties are universals. Nor is Cumpa’s Theory of Instantiation as naturalistic as he claims. I argue that although compatible with Ontological Naturalism, his theory provides a precedent for the non-naturalistic emergence of mental properties. Finally, I argue that because his theory requires a simple physics it presupposes a more rationalist epistemology than that of Methodological Naturalism. (shrink)

I offer a mereological bundle of universals theory of material objects. The theory says that objects are identical to fusions of immanent universals at regions of space. Immanent universals are in the objects that instantiate them, and they can be wholly located at many regions of space. The version of the bundle theory I offer explains these characteristics of immanent universals, and it captures the instantiation relation in terms of the part-whole relation. The version of the theory I offer (...) is simpler and more unified than other mereological bundle theories. Yet, it is not as encompassing as other versions. For I suppose throughout that space is a particular substance, but not a bundle of properties. (shrink)

This book addresses the metaphysics of Armstrongian states of affairs, i.e. instantiations of naturalist universals by particulars. The author argues that states of affairs are the best candidate for truthmakers and, in the spirit of logical atomism, that we need no molecular truthmakers for positive truths. In the book's context, this has the pleasing result that there are no molecular states of affairs. Following this account of truthmaking, the author first shows that the particulars in (first-order) states of affairs are (...) bare particulars. He then argues that the properties in states of affairs are simple, non-relational and concrete universals. Next, he argues that (material) relations in states of affairs are external relations. Lastly, he argues that a state of affairs is unified by a distinctive formal relation without giving rise to Bradley’s regress. (shrink)

The co-instantiation thesis is pivotal to a significant solution to the problem of causal exclusion. But this thesis has been subject to some powerful objections. In this paper, I argue that these difficulties arise because the thesis lacks the necessary metaphysical framework in which its claims should be interpreted and understood. Once this framework is in place, we see that the co-instantiation thesis can answer its critics. The result is a rehabilitated co-instantiation solution to the troubling problem (...) of causal exclusion. But questions remain concerning the viability of certain of its applications. (shrink)

Armstrong holds the Supervenience Theory of instantiation, namely that the instantiation of universals by particulars supervenes upon what particulars and what universals there are, where supervenience is stipulated to be explanatory or dependent supervenience. I begin by rejecting the Supervenience Theory of instantiation. Having done so it is then tempting to take instantiation as primitive. This has, however, an awkward consequence, undermining one of the main advantages universals have over tropes. So I examine another account hinted (...) at by Armstrong. This is the Operator Theory of instantiation, by which I mean the theory that universals are operators, and that a particular instantiates a monadic universal because the universal operates on the particular, resulting in the state of affairs. On this theory the state of affairs supervenes on the instantiation rather than vice versa. In the second part of the paper I develop this theory of universals as operators, including an account of structural universals, which are useful for accounts of modality and of mathematics. (shrink)

Oliver's and Rodriguez-Pereyra's important interpretation of the problem of universals as one concerning truthmakers neglects something crucial: that there is a numerical identity between numerically distinct particulars. The problem of universals is rather how to resolve the apparent contradiction that the same things are both numerically distinct and numerically identical. Baxter's account of instantiation as partial identity resolves the apparent contradiction. A seeming objection to this account is that it appears to make instantiation symmetric, since partial identity is (...) symmetric. Armstrong's standard reply is that the difference between a particular and a universal is what makes instantiation asymmetric. Brown suggests, though, that the instantiation of a universal by a universal is sometimes symmetric. However, the examples on which he relies are not universals. (shrink)

Are properties universal or particular? According to Universalism, properties are universals because there is a certain fundamental tie that makes properties capable of being shareable by more than one thing. On the opposing side, Particularism is the view that properties are particulars due to the existence of a fundamental tie that makes properties incapable of being shared. My aim in this paper is to critically examine the connections between the notions of the fundamental tie and universality and particularity. I (...) argue, first, that universality and particularity can characterize a property if and only if there is a universalist or a particularist fundamental tie, and, second, that it is unclear that these should be the fundamental ties that connect ordinary and scientific properties to their respective bearers. Then I develop an alternative approach to properties and the fundamental tie, which is neutralist because it dispenses with universality and particularity as features of properties, and naturalist because it naturalizes the possession of properties by replacing metaphysical fundamental ties with a scientific one, in particular, a physical process. I show how this approach improves our understanding of properties and instantiation. (shrink)

Universal Bundle Theory holds that objects are fundamentally identical with bundles of universals. Universals are multiply instantiable properties. One popular objection to UBT concerns the possibility of distinct indiscernibles. There are mainly two replies in the literature, corresponding to two representative UBTs, which I shall call the Identity-View and the Instance-View. Each view faces serious problems. This paper proposes a new version of UBT and argues that it is better than these other two versions.

Attempting to provide an ontological framework for the notion of the non-personal Universe of Being proposed elsewhere, this paper – after some basic definitions – focuses on substances, one pillar of that notion. It recognizes only to individual substances a material existence, viewed as the entire complex of the properties instantiated in each of them. It then examines features of the general essence of substances. While such essence can be comprehended via abstract definitions, their individual essence cannot, I argue, because (...) it is not a concept but a reality, which I refer to as Being. This manifests powers, is inexhaustible growth and is one, although expressed differently in each individual. The possible connection of the human being with this reality is the second pillar of the notion of the non-personal Universe of Being, which I summarize and compare to other scenarios at the end. (shrink)

My recently developed Fact-Proposition-Event (FPE) Theory can help to begin the clarification of D.A. Armstrong's account of natural laws-that laws are relationships among certain universals. FPE Theory makes careful description of laws possible, distinguishing them from law propositions (or statements), law facts, and states-of-affairs with which they might be confused. Initial inspection of Armstrong's proposal forces a choice between taking a law to be a certain kind of state (an event- or state-kind) and taking it to be a determinate kind (...) of relation (a relation-kind instantiated by ordered pairs of concrete events and/or states). On both alternatives, new kinds of events and states arise (abstract ones and event-pairs, among others). (shrink)

Typical structural universals are not just the mereological sum of their constituents. Hence, there is the Structure Problem of explaining this non-mereological structure. The Instantiation Problem is that the predicate "U is instantiated by x, y, etc., in that order" is ill-suited to be a primitive, unanalyzed predicate. The proposed solution to these problems is based on the observation that if universal U is said to supervene upon universals V, W, etc., then it is the instantiation of (...) U that supervenes on the instantiation of V, W, etc. Assuming there are few subvenient universals, which is admittedly a speculation, their instantiation may be explained in ways that would be uneconomic if there were too many. (shrink)

Comparing the three-form reasoning of new Hetu-vidya with Western logic, scholars have put forward four perspectives. Combining their strengths and shortcomings, and the examples of Hetu-vidya reasoning, we can conclude that the three-form reasoning should have four forms: (1) the affirmative expression of formal implication; (2) the modus ponens of hypothetical reasoning concerning sufficient conditions after universal instantiation; (3) the negative expression of a formal implication; and (4) the modus tollens of hypothetical reasoning concerning sufficient conditions after (...) class='Hi'>universal instantiation. (shrink)

The global scale of contemporary human life and activity places us in a generic conflict between our identity as individuals and our awareness of the individual's global responsibilities. We face a conflict between the reassuring condition of living according to tradition and the unsettling condition of living in the "new continent" where human self-constitution has global implications. The cohesive set of shared traditional values and ideals is effectively overwritten by the possibility and necessity of innovation in response to global demands. (...) Many paths between the ideal of universahsm and the individual's instantiation in tradition have been contemplated by philosophers and social activists. Given the current dynamics of change, most of these projects, while of good intendon, are nevertheless profoundly naïve in their fundamental assumptions. We are at a crossroads in which we experience a condition of instability that precedes any fundamental bifurcation. But in contrast to the dominant view that instability is by definition negative, we are witnessing an extraordinary explosion of creativity. (shrink)

The task of distinguishing universals from particulars is difficult twice over. It faces a host of first order challenges, since first order proposals about the distinction (e.g. only universals are instantiable, or only universals can be multi-located) tend to be threatened by counterexamples. But it also faces formidable methodological challenges, such as how to decide whether the distinction ought to be exclusive and exhaustive. After discussing the relationships between the distinction and several pairs of pre-philosophical notions, this chapter aims to (...) provide an instructive—albeit non-exhaustive—examination of some principal first order approaches and methodological challenges, respectively. (shrink)

A potentially new interpretation of quantum mechanics posits the state of the universe as a consistent set of facts that are instantiated in the correlations among entangled objects. A fact (or event) occurs exactly when the number or density of future possibilities decreases, and a quantum superposition exists if and only if the facts of the universe are consistent with the superposition. The interpretation sheds light on both in-principle and real-world predictability of the universe.

The lack of academic religious studies in India has several causes: the choice of the secular University of London as model for the first universities in India in 1857, the secular constitution, the secularist approach of the first prime minister of India, Jawaharlal Nehru, and the explosive relation between major faith traditions. However, with the waning of the Indian secularist framework and the continued power and influence of Hindutva ideology, there is a need to discuss different models for religious studies (...) in India. In this article, the point of departure is Banaras Hindu University, one of the few universities in India that has religious studies, but also a faculty of Hindu theology. The focus is on the history of BHU and the recommendations of several educational commission from the 1930s to the 60s, with a note on recent attempts at BHU of renewing value education. The aim is to highlight one alternative for developing religious studies in India, whose primary goal is the formation of good citizens enabled by a set of universal human values instantiated in local traditions. (shrink)

It is generally acknowledged that Kant's political philosophy stands on a par with the great works of the Western liberal tradition. It is also a matter of agreement that the rational principles on which it rests represent an adequate philosophical expression of the progressive agenda that was inaugurated by the Enlightenment and fulfilled, with varying degrees of success, by the French Revolution. Yet Kant's philosophical position is ambiguous when it comes to evaluating that momentous event in modern history. We know, (...) from anecdotal evidence, some surviving letters, several cryptic references in his published works, as well as a number of posthumously published reflections, that Kant was enthusiastic about and strongly approved of the changes that were taking place in France at the time. He certainly condemned, in strong and unequivocal terms, the execution of Louis XVI. But this did not translate into a repudiation of his support for the revolution. And he seems to have found even in this case mitigating circumstances that explained the revolutionaries' decision to execute the monarch, thus in fact excusing their action. Moreover, he argued that all post-revolutionary governments ought to command the same kind of loyalty from their subjects as the ones they replaced, which appears to justify Kant's contention in the Idea for a Universal History that political violence can be a vehicle of progress. Furthermore, in the Contest of Faculties Kant went so far as to identify in the enthusiastic response of the ‘spectators’ to the French Revolution a clear sign of the moral disposition of humankind. (shrink)

Mind-body dualism conceptualizes mind and body as distinct, but there are different ways that dualism may be instantiated. In this study, we examined how Hierarchical Dualism (the belief that mind and body are distinct, and the mind is superior) and Mutual-Influence Dualism (the belief that mind and body are separate but interrelate) related to health behaviors and mental health in three student samples: exclusively queer, exclusively straight, and a mixed university subject pool (N = 535). Participants in each sample endorsed (...) Mutual-Influence Dualism at a higher rate than Hierarchical Dualism. Mutual-Influence dualism was consistently associated with greater engagement in health-promoting behaviors and greater well-being, whereas Hierarchical Dualism differed by sample. These results suggest that dualist beliefs do not uniformly shape the lives of those who hold them: rather, the relation between dualist beliefs and health differs as a function of the type of dualism and the identities we hold. (shrink)

The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. (...) Our assessment of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior’s and Kaplan’s derivations at face value. (shrink)

According to Minkoswki, Einstein's special theory of relativity reveals that ‘space by itself, and time by itself are doomed to fade away into mere shadows’. But perceptual experience represents objects as instantiating shapes like squareness — properties of ‘space by itself’. Thus, STR seems to threaten the veridicality of shape experience. In response to this worry, some have argued that we should analyze the contents of our spatial experiences on the model of traditional secondary qualities. On this picture—defended in recent (...) work by Chalmers —an experience of squareness just represents whatever property usually causes such experiences. This view salvages the veridicality of shape experience, but leaves the nature of the properties we perceive outside our ken. I argue that such a move is unwarranted: STR is compatible with the idea that shape experience acquaints us with the spatial character of our world. In defending this claim, I propose a view on which shape experience presents familiar Euclidean spatial properties veridically, while implicitly representing those properties as instantiated in a particular manner — namely, relative to our own frame of reference. (shrink)

Andrew Bacon, John Hawthorne, and Gabriel Uzquiano have recently argued that free logics—logics that reject or restrict Universal Instantiation—are ultimately not promising approaches to resolving a family of intensional paradoxes due to Arthur Prior. These logics encompass ramified and contextualist approaches to paradoxes, and broadly speaking, there are two kinds of criticism they face. First, they fail to address every version of the Priorean paradoxes. Second, the theoretical considerations behind the logics make absolutely general statements about all propositions, (...) properties of propositions, etc., but because this sort of intensional quantification is always restricted in the logics, they cannot even express those considerations. I present a novel sort of free logic, which rejects the standard Universal Instantiation but validates a restricted form of the rule, and which addresses both kinds of criticism by allowing some propositions to be unrestricted in their quantification. (shrink)

This paper challenges a dualistic picture popularised by Nigel Pleasants at the centre of influential investigations into the possibility of Wittgensteinian forms of moral certainty. The dualistic picture takes it for granted that moral certainty concerns both a series of hinge propositions that are beyond doubt, make no sense to justify and cannot be expressed in ordinary discourse and a phenomenon that is only ever instantiated in our ways of acting. I consider tensions in this account as they relate to (...) ‘Murder is wrong’ as a moral hinge proposition by drawing on the life and lyrics of US hip‐hop artist Kendrick Lamar. My claim is that the Lamar example highlights important tensions in our relation to the wrongness of murder that many would understand to occur within the moral realm, but which are conceptually ruled out from dualistic accounts of moral certainty. The plausibility of the dualistic picture must therefore be reassessed. (shrink)

We discuss the one–many problem as it appears in the Philebus and find that it is not restricted to the usually understood problem about the identity of universals across particulars that instantiate them (the Hylomorphic Dispersal Problem). In fact some of the most interesting aspects of the problem occur purely with respect to the relationship between Forms. We argue that contemporary metaphysicians may draw from the Philebus at least three different one–many relationships between universals themselves: instantiation, subkind and part, (...) and thereby construct three new ‘problems of the one and the many’ (an Eidetic Dispersal Problem, a Genus–Species Problem, and an Eidetic Combination Problem), which are as problematic as the version generally discussed. We then argue that this taxonomy sheds new and interesting light on certain discussions of higher-order universals in recent Australian analytic philosophy. (shrink)

It has been known for six years that the restriction of Girard's polymorphic system $\text{\bfseries\upshape F}$ to atomic universal instantiations interprets the full fragment of the intuitionistic propositional calculus. We firstly observe that Tait's method of “convertibility” applies quite naturally to the proof of strong normalization of the restricted Girard system. We then show that each $\beta$-reduction step of the full intuitionistic propositional calculus translates into one or more $\beta\eta$-reduction steps in the restricted Girard system. As a consequence, we (...) obtain a novel and perspicuous proof of the strong normalization property for the full intuitionistic propositional calculus. It is noticed that this novel proof bestows a crucial role to $\eta$-conversions. (shrink)

The adoption question asks whether there are logical rules that cannot be adopted if one does not already infer in accordance with them. Several philosophers, most famously Saul Kripke and Romina Padró, agree that there are such rules. Accordingly, they agree that there is an adoption problem. However, there is disagreement over which rules are unadoptable. In particular, while most agree that if there is an adoption problem, modus ponens and universal instantiation are in its scope, many would (...) exclude adjunction from the list. In this paper, I argue that adjunction is in the scope of the adoption problem. Then I show that the most straightforward counterargument against adjunction being in the scope of the problem, which tries to reformulate the adjunction rule into a more palatable one, does not work. (shrink)

The Adoption Problem (AP) was a postponed issue for some years (Kripke, 2024; Padró, 2015; Birman, 2024). This problem highlights certain difficulties surrounding the adoption of rules of inference: If anti-exceptionalism is wrong, is it possible to adopt an alternative logic? What is the point of the revision of logic in epistemology? During 2022 Kripke, Padró and Barrio held seminars on AP. The latter two edited the first thematic section on this subject in the journal Análisis Filosófico. It contains “What (...) the Adoption Problem Does Not Show” by Camilo Fiore, subject of this critical note, in which Fiore holds two theses: 1) AP is compatible with the thesis that logica utens is revisable; 2) to assess whether an agent can revise their logic, it is best to consider a different definition of adoption, e.g. weak adoption, according to which Universal Instantiation and Modus Ponens are sometimes adoptable. It then states that (1) and (2) are independent. In this article I will criticize the independence between (1) and (2). To this end, I will point out that thesis (1) and (2) are supported by the examples of Carrie and Barry, respectively, and that the type of logical revision involved in both is the same and local. Therefore, (1) and (2) are not independent. Next, I argue that it is impossible to satisfy another kind of logical revision, e.g. global revision. Therefore, the interdependence between (1) and (2) is not due to the examples proposed. (shrink)

In An Introduction to Non-Classical Logic: From If to Is Graham Priest presents branching rules in Free Logic, Variable Domain Modal Logic, and Intuitionist Logic. I propose a simpler, non-branching rule to replace Priest's rule for universal instantiation in Free Logic, a second, slightly modified version of this rule to replace Priest's rule for universal instantiation in Variable Domain Modal Logic, and third and fourth rules, further modifying the second rule, to replace Priest's branching universal (...) and particular instantiation rules in Intuitionist Logic. In each of these logics the proposed rule leads to tableaux with fewer branches. In Intuitionist logic, the proposed rules allow for the resolution of a particular problem Priest is grappling with throughout the chapter. In this paper, I demonstrate that the proposed rules can greatly simplify tableaux and argue that they should be used in place of the rules given by Priest. (shrink)

This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, it is then shown how we can use pure higher-order (...) logic to ask, and begin to answer, metaphysical questions with non-trivial implications. In particular, while we must reject the popular idea that structural differences between sentences correspond to parallel distinctions in the logical structure of extra-linguistic reality, it may still be possible to give a purely logical characterization of objectual aboutness and related notions. (shrink)

We investigate how the sentence choice semantics for propositional superposition logic developed in Tzouvaras could be extended so as to successfully apply to first-order superposition logic. There are two options for such an extension. The apparently more natural one is the formula choice semantics based on choice functions for pairs of arbitrary formulas of the basis language. It is proved however that the universal instantiation scheme of first-order logic, $\varphi \rightarrow \varphi $, is false, as a scheme of (...) tautologies, with respect to FCS. This causes the total failure of FCS as a candidate semantics. Then we turn to the other option, which is a variant of SCS, since it uses again choice functions for pairs of sentences only. This semantics however presupposes that the applicability of the connective | is restricted to quantifier-free sentences, and thus the class of well-formed formulas and sentences of the language is restricted too. Granted these syntactic restrictions, the usual axiomatizations of FOLS turn out to be sound and conditionally complete with respect to this second semantics, just like the corresponding systems of PLS. (shrink)

A claim by David K. Lewis (1986) that his counterpart theory provides a semantics for intensional languages is critiqued by showing that basic principles of modal logic fail to be valid in counterpart theory & by investigating problematic counterpart-theoretical translations of instances of universal instantiation. From Lewis's postulate that individuals inhabit only one world & have counterparts in other worlds, it follows that the relation between an object & its counterparts is nontransitive & nonsymmetric; consequently, an object does (...) not need to have exactly one counterpart in any world. The failure of modal principles in counterpart theory is ascribed to the possibility that an object has no counterpart in a given world, whereas universal instantiation becomes invalid when an object has more than one counterpart in a given world. 3 References. Adapted from the source document. (shrink)

This article is a clarification of different procedures in natural deduction: universal instantiation, Universal generalisation, Existential generalisation, And existential instantiation. The author discusses rules concerning universal generalisation from copi's "symbolic logic". (staff).

It seems that the Truth-teller is either true or false, but there is no accepted principle determining which it is. From this point of view, the Truth-teller is a hypodox. A hypodox is a conundrum like a paradox, but consistent. Sometimes, accepting an additional principle will convert a hypodox into a paradox. Conversely, in some cases, retracting or restricting a principle will convert a paradox to a hypodox. This last point suggests a new method of avoiding inconsistency. This article provides (...) a significant example. The Liar paradox can be defused to a hypodox by relatively minimally restricting three principles: the T-schema, substitution of identicals and universal instantiation. These restrictions are not arbitrary. For each, I identify the source of a contradiction given some presumptions. Then I propose each restriction as a reasonable way to deal with that source of contradiction. (shrink)

In this paper I argue that pluralism at the level of logical systems requires a certain monism at the meta-logical level, and so, in a sense, there cannot be pluralism all the way down. The adequate alternative logical systems bottom out in a shared basic meta-logic, and as such, logical pluralism is limited. I argue that the content of this basic meta-logic must include the analogue of logical rules Modus Ponens and Universal Instantiation. I show this through a (...) detailed analysis of the ‘adoption problem’, which manifests something special about MP and UI. It appears that MP and UI underwrite the very nature of a logical rule of inference, due to all rules of inference being conditional and universal in their structure. As such, all logical rules presuppose MP and UI, making MP and UI self-governing, basic, unadoptable, and required in the meta-logic for the adequacy of any logical system. (shrink)

After introducing the adoption problem (AP) as the claim that certain basic logical principles cannot be adopted, I offer a characterization of this notion as a two-phase process consisting in (1) the acceptance of a basic logical principle, and (2) the development, in virtue of Phase 1, of a practice of inferring in accordance with that principle. The case of a subject who does not infer in accordance with universal instantiation is considered in detail. I argue that the (...) AP has deep and wide implications for the epistemology of logic, extending well beyond Kripke’s original target, viz. Putnam’s proposal for the empirical revision of logic and its background Quinean epistemology. In particular, the AP questions whether basic logical principles could have a fundamental role in our inferential practices, drawing our attention to the nature of basic inferences and the need to have a clearer conception of them before taking a stand on the matter of the epistemic justification of the logical principles. (shrink)