An appropriate characterization of property types is an important topic for measurement science. On the basis of a set-theoretic model of evaluation and measurement processes, the paper introduces the operative concept of property evaluation type, and discusses how property types are related to, and in fact can be derived from, property evaluation types, by finally analyzing the consequences of these distinctions for the concepts of ‘property’ used in the International Vocabulary of Metrology – Basic (...) and General Concepts and Associated Terms (VIM3). (shrink)

An appropriate characterization of property types is an important topic for measurement science. This paper proposes to derive them from evaluation types, and analyzes the consequences of this position for the VIM3.

In a lengthy review article, C. Anthony Anderson criticizes the approach to property theory developed in Quality and Concept (1982). That approach is first-order, type-free, and broadly Russellian. Anderson favors Alonzo Church’s higher-order, type-theoretic, broadly Fregean approach. His worries concern the way in which the theory of intensional entities is developed. It is shown that the worries can be handled within the approach developed in the book but they remain serious obstacles for the Church approach. The discussion (...) focuses on: (1) the fine-grained/coarse-grained distinction, (2) proper names and definite descriptions, (3) the paradox of analysis and Mates’ puzzle, and (4) the logical, semantical, and intentional paradoxes. (shrink)

In this essay I shall argue that the crucial assumptions of Kripke's argument, i.e. the collapse of the appearance/reality distinction in the case of phenomenal states and the idea of a qualitatively identical epistemic situation, imply an objective principle of identity for mental-state types. This principle, I shall argue, rather than being at odds with physicalism, is actually compatible with both the type-identity theory of the mind and Kripke's semantics and metaphysics. Finally, I shall sketch a version of the (...) type-identity theory. (shrink)

The type-free property-theoretic system EC, based on the mediation view of predication, is presented. According to the mediation view, the copula or exemplification is a necessary component of every proposition. It is explained how the system EC relates to Bradley's Regress regarding predication. Finally, the system EC is applied to the Meinong-Russell debate on non-existent objects and it is shown how EC allows us to preserve some important intuitions of both Meinong and Russell.

This paper describes an axiomatic theory BT, which is a suitable formal theory for developing constructive mathematics, due to its expressive language with countable number of set types and its constructive properties such as the existence and disjunction properties, and consistency with the formal Church thesis. BT has a predicative comprehension axiom and usual combinatorial operations. BT has intuitionistic logic and is consistent with classical logic. BT is mutually interpretable with a so called theory of arithmetical truth PATr and with (...) a second-order arithmetic SA that contains infinitely many sorts of sets of natural numbers. We compare BT with some standard second-order arithmetics and investigate the proof-theoretical strengths of fragments of BT, PATr and SA. (shrink)

The extent to which we generalize a novel property from a sample of familiar instances to novel instances depends on the sample composition. Previous property induction experiments have only used samples consisting of novel types (unique entities). Because real‐world evidence samples often contain redundant tokens (repetitions of the same entity), we studied the effects on property induction of adding types and tokens to an observed sample. In Experiments 1–3, we presented participants with a sample of birds or (...) flowers known to have a novel property and probed whether this property generalized to novel items varying in similarity to the initial sample. Increasing the number of novel types (e.g., new birds with the target property) in a sample produced tightening, promoting property generalization to highly similar stimuli but decreasing generalization to less similar stimuli. On the other hand, increasing the number of tokens (e.g., repeated presentations of the same bird with the target property) had little effect on generalization. Experiment 4 showed that repeated tokens are encoded and can benefit recognition, but appear to be given little weight when inferring property generalization. We modified an existing Bayesian model of induction (Navarro, Dry, & Lee, 2012) to account for both the information added by new types and the discounting of information conveyed by tokens. (shrink)

Visual perception is widely taken to present properties such as redness, roundness, and so on. This in turn might be thought to give rise to accuracy conditions for experience, and so content, regardless of which metaphysical view of perception one endorses. An influential version of this argument—Susanna Siegel’s ’Argument from Appearing’—aims to establish the existence of content as common ground between representational and relational views of perception. This goes against proponents of ‘austere’ relationalism who deny that content plays a substantive (...) role in philosophical explanations of conscious perceptual experience. Though Siegel’s argument purports to be neutral with respect to the metaphysics of perception, it relies upon an equivocation between the presentation of property-types and property-instances. Consequently, the argument begs the question against the austere relational view, and so fails to establish the desired conclusion. So while relationalists can and should allow that experiences have accuracy conditions, it does not follow from this that they have contents of any philosophically interesting or significant kind. (shrink)

This paper presents a type-free property-theoretic system in the spirit of a framework proposed by Menzel and then supplements it with a theory of truth and exemplification. The notions of a truth-relevantly complex (simple) sentence and of a truth-relevant subsentence are introduced and then used in order to motivate the proposed theory. Finally, it is shown how the theory avoids Russell's paradox and similar problems. Some potential applications to the foundations of mathematics and to natural language semantics are (...) sketched in the introduction. (shrink)

According to David Chalmers, the virtual entities found in Virtual Reality (VR) and Augmented Reality (AR) environments instantiate virtual properties of a specific kind. It has recently been objected that such a view (i) can’t extend to all types of properties; (ii) leads to a proliferation of property-types; (iii) implausibly ascribes massive errors to VR and AR users; and (iv) faces an analogue of Jackson’s “many-property problem”. My first objective here is to show that advocates of virtual properties (...) can deal with each of these objections. The other goal of this paper is to examine the consequences of Chalmers’ theory in the particular case of AR. If we countenance virtual properties, AR highlights that non-virtual objects can possess both non-virtual and virtual properties. With AR, it also appears that a same non-virtual object can have different and even incompatible properties across augmented environments. Lastly, considering properties in light of AR highlights the risk of an “augmented solipsism”, and calls forth interesting questions about the persistence conditions of non-virtual objects in AR environments. (shrink)

The general aim of this paper is to propose a reductionist strategy to higher-level property types. Starting from a common ground in the philosophy of science, I shall elaborate on possible realizer differences of higher-level property types. Because of the realizer types' causal heterogeneity, an introduction of functional sub-types of higher-level properties will be suggested. Each higher-level functional sub-type corresponds to one realizer type. This means that there is the theoretical possibility to reach some kind of (...) type-identity and this opens up the way for theory reduction in a more complete manner. This kind of type-identity will go beyond the common ground of the identity of tokens and their reductive explanation. In the second part of the paper, this reductionist strategy will be applied to a specific debate in the philosophy of biology — the reductionist approach to classical genetics from a molecular point of view. (shrink)

Even the most Parmenidean-minded of people recognize that quotidian objects somehow undergo change. This claim, nonetheless, is as clearly intuitive as it is apparently incompatible with one of our most widely believed logical principles, namely, Leibniz's Law. This paper focuses briefly on the metaphysical issue underlying this alleged incompatibility in order to provide elements for exploring its semantical counterpart: the analysis of the logical form of sentences attributing complementary temporal properties to current objects. Four analyses are presented, and the ability (...) of each to account for the linguistic data is explained. The semantical issue is preceded by some introductory remarks on the role of temporal references in the evaluation of declarative sentences. (shrink)

We show that in a stable first-order theory, the failure of higher dimensional type amalgamation can always be witnessed by algebraic structures that we call n-ary polygroupoids. This generalizes a result of Hrushovski in [16] that failures of 4-amalgamation are witnessed by definable groupoids. The n-ary polygroupoids are definable in a mild expansion of the language.

Theories of singular causation have a genuine problem with properties. In virtue of what property do events (or facts) cause other events? One possible answer to this question, Davidson’s, is that causal relations hold between particulars and properties play no role in the way a particular causes another. According to another, recently fashionable answer, in contrast, events cause other events in virtue of having a trope (as opposed to a property-type). Both views face serious objections. My aim (...) in this paper is to combine these two very different solutions to the problem of the properties of singular causation and to argue that this combined view can avoid objections against both of them. (shrink)

Revised and reprinted in Handbook of Philosophical Logic, volume 10, Dov Gabbay and Frans Guenthner (eds.), Dordrecht: Kluwer, (2003). -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented (...) in the course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

Recent discussions of mental causation have focused on three principles: (1) Mental properties are (sometimes) causally relevant to physical effects; (2) mental properties are not physical properties; (3) every physical event has in its causal history only physical events and physical properties. Since these principles seem to be inconsistent, solutions have focused on rejecting one or more of them. But I argue that, in spite of appearances, (1)–(3) are not inconsistent. The reason is that 'properties' is used in different senses (...) in the principles. In (1) and (3), 'properties' should be read as 'tropes' (properties here are particulars), while in (2) 'properties' should read as 'types' (properties here are universals or classes). Although mental types are distinct from physical types, every mental trope is a physical trope. This allows mental properties to be causally relevant to physical effects without violating the closed character of the physical world. (shrink)

Type ‹1, 1› quantifiers are (on each universe) binary relations between sets, and it is natural to inquire how quantirelation denotations behave in terms of ordinary relational properties. This chapter focuses primarily on one such property: symmetry. It turns out that symmetric determiners are very common in natural languages, and such determiners are particularly well-behaved. For example, a symmetric determiner can be seen to denote a property of the intersection of the restriction and the scope, which in (...) turn explains why such expressions often go well in predicate position too. Moreover, symmetry has been advanced as the major factor in explaining which determiners are acceptable in existential-there sentences. This chapter also analyses the semantics of such sentences, including a comparative study of various attempts at explaining acceptability that have been proposed in the literature. It also presents a number of different characterisations of symmetric quantifiers. In particular, it shows that extension for a type ‹1› quantifier amounts to the symmetry of its relativisation. (shrink)

The property theory of musical works says that each musical work is a property that is instantiated by its occurrences, that is, the work's performances and playings. The property theory provides ontological explanations very similar to those given by its popular cousin, the type/token theory of musical works, but it is both simpler and stronger. However, type/token theorists often dismiss the property theory. In this essay, I formulate a version of the property theory (...) that identifies each type (thus, each musical work) with a unique property. I then scrutinize the arguments offered for thinking that types, including musical works, are distinct from properties. I respond that no such argument is forceful and conclude that the property theory of musical works is superior to the type/token theory. (shrink)

This article aims to clarify how aspects of current chemical understanding relate to some important contemporary problems of philosophy. The first section points out that the long-running philosophical debates concerning how properties stay together in substances have neglected the important topic of structure-determining closure. The second part describes several chemically-important types of closure and the third part shows how such closures ground the properties of chemical substances. The fourth section introduces current discussions of structural realism (SR) and contextual emergence: the (...) final sections reconsider the coherence of the properties of substances and concludes that recognition that structures qualify as determinants of specific outcomes—as ‘causes’ as that designation is used in Standard English—clarifies how properties stay together in chemical entities, and by analogy, how characteristics cohere in ordinary items. (shrink)

Due to the advance computer technology, the use of probability distributions has been raised up to solve the real life problems. These applications are found in reliability engineering, computer sciences, economics, psychology, survival analysis, and some others. This study offers a new probability model called Marshall–Olkin Extended Gumbel Type-II which can model various shapes of the failure rate function. The proposed distribution is capable to model increasing, decreasing, reverse J-shaped, and upside down bathtub shapes of the failure rate function. (...) Various statistical properties of the proposed distribution are derived such as alternate expressions for the density and distribution function, special cases of MOEGT-II distribution, quantile function, Lorenz curve, and Bonferroni curve. Estimation of the unknown parameters is carried out by the method of maximum likelihood. A simulation study is conducted using three different iterative methods with different samples of sizes n. The usefulness and potentiality of the MOEGT-II distribution have been shown using three real life data sets. The MOEGT-II distribution has been demonstrated as better fit than Exponentiated Gumbel Type-II, Marshall–Olkin Gumbel Type-II, Gumbel Type-II, Marshall–Olkin–Frechet, Frechet, Burr III, Log Logistic, Beta Inverse Weibull, and Kumaraswamy Inverse Weibull distributions. (shrink)

We discuss the externally definable Ramsey property, a weakening of the Ramsey property for relational structures, where the only colourings considered are those that are externally definable: that is, definable with parameters in an elementary extension. We show a number of basic results analogous to the classical Ramsey theory, and show that, for an ultrahomogeneous structure M with countable age, the externally definable Ramsey property is equivalent to the dynamical statement that, for all $$n \in \mathbb {N} (...) $$, every subflow of the space $$S_n(M)$$ of n-types has a fixed point. We discuss a range of examples, including results regarding the lexicographic product of structures. (shrink)

This book gives an account of a full spectrum of property rights and their relationship to individual liberty. It shows that a purely deontological approach to justice can deal with the most complex questions regarding the property system. Moreover, the author considers the economic, ecological, and technological complexities of our real-world property systems. The result is a more conceptually sound account of natural rights and the property system they demand. If we think that liberty should be (...) at the centre of justice, what does that mean for the property system? Economists and lawyers widely agree that a property system must be composed of many different types of property: the kind of private ownership one has over one's person and immediate possessions, as well as the kinds of common ownership we each have in our local streets, as well as many more. However, theories of property and justice have not given anything approaching an adequate account of the relationship between liberty and any other form of property other than private ownership. It is often thought that a basic commitment to liberty cannot really tell us how to arrange the major complexities of the property system, which diverge from simple private ownership. Property and Justice demonstrates how philosophical rigour coupled with interdisciplinary engagement enables us to think clearly about how to deal with real-world problems. It will be of interest to political philosophers, political theorists, and legal theorists working on property rights and justice. (shrink)

Computational models of meaning trained on naturally occurring text successfully model human performance on tasks involving simple similarity measures, but they characterize meaning in terms of undifferentiated bags of words or topical dimensions. This has led some to question their psychological plausibility (Murphy, 2002;Schunn, 1999). We present here a fully automatic method for extracting a structured and comprehensive set of concept descriptions directly from an English part‐of‐speech‐tagged corpus. Concepts are characterized by weighted properties, enriched with concept–property types that approximate (...) classical relations such as hypernymy and function. Our model outperforms comparable algorithms in cognitive tasks pertaining not only to concept‐internal structures (discovering properties of concepts, grouping properties by property type) but also to inter‐concept relations (clustering into superordinates), suggesting the empirical validity of the property‐based approach. (shrink)

The scope and type of property rights recognized over the effectiveness of antibiotics have a direct effect on how those claiming ownership engage in the exploitation and stewardship of this scarce resource. We examine the different property claims and rights the four major interest groups are asserting on antibiotics: (i) the inventors, (ii) those demanding that the resource be treated like any other transferable commodity, (iii) those advocating usage restrictions based on good stewardship principles and (iv) those (...) considering the resource as common heritage of humankind. (shrink)

We discuss the externally definable Ramsey property, a weakening of the Ramsey property for relational structures, where the only colourings considered are those that are externally definable: that is, definable with parameters in an elementary extension. We show a number of basic results analogous to the classical Ramsey theory, and show that, for an ultrahomogeneous structure _M_ with countable age, the externally definable Ramsey property is equivalent to the dynamical statement that, for all $$n \in \mathbb {N} (...) $$, every subflow of the space $$S_n(M)$$ of _n_-types has a fixed point. We discuss a range of examples, including results regarding the lexicographic product of structures. (shrink)

In set theory without the axiom of choice math formula, three-space type results for the Hahn-Banach property are provided. We deduce that for every Hausdorff compact scattered space K, the Banach space C of real continuous functions on K satisfies the continuous Hahn-Banach property in math formula. We also prove in math formula Rudin's theorem: “Radon measures on Hausdorff compact scattered spaces are discrete”.

Any system for the protection of intellectual property rights (IPRs) has three main kinds of distributive effects. It will determine or influence: (a) the types of objects that will be developed and for which IPRs will be sought; (b) the differential access various people will have to these objects; and (c) the distribution of the IPRs themselves among various actors. What this means to the area of pharmaceutical research is that many urgently needed medicines will not be developed at (...) all, that the existing medicines will not be suitable for countries with a precarious health infrastructure or not target the disease variety that is prevalent in poorer regions. Such effects are commonly captured under the rubric of the “10/90 gap” in biomedical research. High prices will also restrict access to medicines as well endanger compliance to treatment schemes. IPRs are mainly held by multinational corporations situated in the developed world, which not only raises egalitarian concerns, but also severely limits the possibilities of companies in poorer countries to realize improvements on existing inventions, as they cannot financially afford to secure freedom to operate, which systematically shrinks the number of potential innovators. Those inequities lead to an enormous burden for the global poor and since no institution is willing to assume the responsibility to fulfil the right to health and the corresponding right of access to essential medicines, we have to analyse alternatives or additions to the actual intellectual property regimes in order to create new incentives to fill this gap. (shrink)

Quantum theory brings into question the compatibility of the twin desiderata of exact knowability of the present state of the physical world and perfect predictability of its future states. Bohr’s coordination–causality complementarity principle transforms this tension into one between properties (as ordinarily understood in classical physics) and deterministic causality. Here, we develop an explicit model of quantum properties which accommodates this essential tension. Our approach integrates operational, reconstructive, and metaphysical standpoints. In particular, we make use of an operational framework employed (...) in a recent operational reconstruction of Feynman’s formulation of quantum theory; base our property model on an analysis of property types; and use the notions of actuality and potentiality to frame the model. We show that this quantum property model provides a natural resolution of Zeno’s paradox of motion, and provides reliable intuitions about phenomena such as electron diffraction and the non-local behaviour of entangled states of non-identical particles. (shrink)

A critical but underdeveloped part of the libertarian debate about immigration is the question of who, if anyone, owns public property, and the consequences of the answer to this question. Libertarians who favor restrictive immigration policies, such as Hans-Hermann Hoppe, argue that taxpayers own public property, and that the state, while it is in control of such property, should manage it on behalf of taxpayers in the same way private owners would manage their own property. In (...) other words, it should be quite selective about who may enter. Walter Block, who takes an “open borders” position, does not appear to dispute the claim that taxpayers own public property, but nevertheless argues that immigrants are entitled to ignore the state’s control of, and thus may freely enter, such property. In this article I explore the question of public property ownership using Rothbardian property rights principles. I conclude that, at least with respect to a particular type of public property, neither Hoppe’s nor Block’s reasoning is consistent with these principles. I also consider the idea that the state ought to have a role in managing public property in light of some libertarian anarchist ideas about the state. I conclude that supporting a legitimate role for the state as an immigration gatekeeper is inconsistent with Rothbardian and Hoppean libertarian anarchism, as well as with the associated strategy of advocating always and in every instance reductions in the state’s role in society. (shrink)

This book aims to develop a philosophical theory of extrinsic properties – of properties whose instantiation by an object does not only depend on what the object itself is like, but also on features of its environment. Various accounts of the intrinsic/extrinsic distinction are analysed in detail, and it is argued that the most promising approach to defining this distinction is to consider extrinsic properties as a particular type of relational property. Moreover, it is shown that two key (...) notions in the metaphysics of properties, the supervenience relation and the dispositional/categorical distinction, whose scope is usually restricted to intrinsic properties, can fruitfully be applied to extrinsic properties as well. (shrink)

Russell’s type theory has been the standard property theory for years, relying on rigid type distinctions at the grammatical level to circumvent the paradoxes of predication. In recent years it has been convincingly argued by Bealer, Cochiarella, Turner and others that many linguistic and ontological data are best accounted for by using a type-free property theory. In the spirit of exploring alternatives and “to have as many opportunities as possible for theory comparison”, this paper presents (...) another type-free property theory, to be called P*, intended for applications in Montague-style natural language semantics and formal ontology. The theory is philosophically grounded on Gupta’s and Belnap’s revision theory of definitions and its basic idea is viewing predication (exemplification) as a ‘circular concept’ that can be captured by circular definitions. The paper has the following fourteen sections: (1) Introduction; (2) Formal type-free property theory; (3) Applying RTD [revision theory of definitions] to exemplification; (4) The system P*; (5) Some features of P*; (6) A comparison with Turner’s system; (7) Entailment and P*; (8) P* and natural language semantics; (9) Noun phrases; (10) The need for type-freedom in semantics; (11) Arithmetic in P*; (12) Arithmetic in PN*; (13) Complexity of P*; (14) Conclusion, and acknowledgments. (shrink)

The last several decades have seen the emergence of intellectual property rights (IPRs), especially patents, as a key issue in developments across the fields of law, the economy and the biosciences, and as part of the burgeoning "bioeconomy". This paper examines how the categories of nature and knowledge, so vital to IPR regimes that support bioeconomy-type projects, are challenged by the allegation of biopiracy. It reflects on the relationship between nature, IPR and the bioeconomy, and presents an example (...) of how the creation of new categories, in this case genetic resources, come to impact on how we come to understand nature in relation to the economy and IPRs. The paper then follows this with an analysis of how knowledge is treated in those same systems, focusing specifically on some of the challenges that arise when attempting to bring traditional knowledge (TK) under the rubric of the IPR system. Finally, it examines the allegation of biopiracy in greater depth, and reflects on how it critiques the way the bioeconomy and the IPR regime treat nature, culture, knowledge, and the relationship between them. (shrink)

We introduce a natural class of quantifiersTh containing all monadic type quantifiers, all quantifiers for linear orders, quantifiers for isomorphism, Ramsey type quantifiers, and plenty more, showing that no sublogic ofL ωω (Th) or countably compact regular sublogic ofL ∞ω (Th), properly extendingL ωω, satisfies the uniform reduction property for quotients. As a consequence, none of these logics satisfies eitherΔ-interpolation or Beth's definability theorem when closed under relativizations. We also show the failure of both properties for any (...) sublogic ofL ∞ω (Th) in which Chang's quantifier or some cardinality quantifierQ α, with α≧1, is definable. (shrink)

There are two major theories of properties that employ resemblance classes to avoid commitment to universals.1 Object-resemblance nominalism ~ORN! faces the notorious companionship and imperfect community difficulties, though some costly remedies have been proposed. Trope-resemblance nominalism ~TRN!, in contrast, is commonly supposed to avoid these difficulties altogether. My contention is that both versions of resemblance nominalism are subject to companionship and imperfect community difficulties. If I am right, ~1! trope theory loses one of its primary selling points, and ~2! resemblance (...) nominalists of either type must appeal to the troublesome remedies that I discuss below. (shrink)

After some suggestions about how to clarify the confused metaphysical distinctions between dispositional and non-dispositional or categorical properties, I review some of the main interpretations of QM in order to show that – with the relevant exception of Bohm’s minimalist interpretation – quantum ontology is irreducibly dispositional. Such an irreducible character of dispositions must be explained differently in different interpretations, but the reducibility of the contextual properties in the case of Bohmian mechanics is guaranteed by the fact that the positions (...) of particles play the role of the categorical basis, a role that in other interpretations cannot be filled by anything else. In Bohr’s and Everett-type interpretations, dispositionalism is instrumentalism in disguise. (shrink)

By what types of properties do we specify twinges, toothaches, and other kinds of mental states? Wittgenstein considers two methods. Procedure one, direct, private acquaintance: A person connects a word to the sensation it specifies through noticing what that sensation is like in his own experience. Procedure two, outward signs: A person pins his use of a word to outward, pre-verbal signs of the sensation. I identify and explain a third procedure and show we in fact specify many kinds of (...) mental states in this way. (shrink)

All of the attempts to date to find a set of necessary and sufficient conditions for life, in order to provide an essential definition of life, have failed. We only have at our disposal series of lists that contain diverse characteristics usually found in living beings. Some authors have drawn from this fact the conclusion that life is not a natural kind. It will be argued here that this conclusion is too hasty and that if life is understood as a (...) natural kind in the non-essentialist sense of a homeostatic property cluster, it is easy to see why the attempts to find a unique and essentialist definition of life have failed. Understanding life in this way would imply that the pretension to find such a type of definition should be abandoned. (shrink)

This paper argues that Twin Earth twins belong to the same psychological natural kind, but that the reason for this is not that the causal powers of mental states supervene on local neural structure. Fodor’s argument for this latter thesis is criticized and found to rest on a confusion between it and the claim that Putnamian and Burgean type relational psychological properties do not affect the causal powers of the mental states that have them. While it is true that (...) Putnamian and Burgean type relational psychological properties do not affect causal powers, it is false that no relational psychological properties do. Examples of relational psychological properties that do affect causal powers are given and psychological laws are sketched that subsume twins in virtue of them instantiating these relational properties rather than them sharing the narrow contents of their thoughts. (shrink)

An algebraic type of structure is shown forth which is such that if it is a characteristic matrix for a logic, then that logic satisfies Meyer's weak variable sharing property. As a corollary, it is shown that RM and all its odd-valued extensions \(\mathbf{RM}_{2n\mathord{-}1}\) satisfy the weak variable sharing property. It is also shown that a proof to the effect that the "fuzzy" version of the relevant logic R satisfies the property is incorrect.

Computer games are artifacts designed to exhibit forms of meaning to their players in response to their actions during play. The aim of this paper is to outline and examine main theoretical conceptions for how they perform this function. This chapter identifies three major conceptions of computer games that are implicit in much thinking about them: a nominalist, a representationalist and a ludic. It argues that the representationalist conception gives the wrong account of in-game player action and that the ludic (...) conception is unable to explain the manner in which a game system guides actions. As an alternative to all three conceptions the chapter proposes a motivational conception, according to which computer games are systems designed to support a special kind of autonomous in-game agential properties. It argues that the artistic potential of computer games is found in how they implement action types and goal attainment structures to be performed for their own sake. (shrink)

Contrary to views that diagnose the paradoxes of truth and related notions in terms of sentences not expressing propositions, or expressing non-paradoxical propositions different from the propositions they appear to express, or expressing multiple propositions none of which are paradoxical, the paper argues that the basic paradoxes are paradoxes of propositions; or alternatively, of sentential quantification. Similarly for the paradoxes of satisfaction: the basic paradoxes arise for properties, or for quantification into predicate position. (In the latter case, it’s argued that (...) adopting the syntactic restrictions of Russellian type theory is not the best way to go.). The basic paradoxes can be handled either in classical or non-classical logic, but the paper focuses mostly on non-classical options. (shrink)

Numerous philosophers are committed to fine-grained accounts of properties, propositions, and relations. One approach gaining traction in recent decades is the structuralist view, which claims that properties and propositions with distinct constituents are distinct. However, the Russell-Myhill paradox has been proposed as evidence that this view is inconsistent within higher-order logic. Based on the previous work of other philosophers, my article-based dissertation is dedicated to the conceptual foundation and mathematical implementation of a framework, called generativism, which aims to retain the (...) structuralist view and counter the paradox in a well-motivated way. -/- Generativism is grounded on the idea that structured entities are iteratively generated, thereby circumventing the paradox. According to this view, the universe of structured properties and propositions is never fully available, but continuously expands through a hierarchy of stages. The key aspect of my approach is advocating for a predicative turn in higher-order logic, suggesting that the quantifiers used when generating new entities should only range over entities available at each stage of the generative process. So, the main aim of my dissertation is to propose a more thoroughgoing study of predicativism in the context of structured properties and propositions. -/- I develop and discuss two mathematical implementations of these ideas. One is historically well-known in the logical and philosophical literature on predicativity: it is Russell's ramified theory of types. The other is Boolos' stage theory, which has received significant attention in the philosophy of set theory, but its applicability for structured propositions has been seriously underestimated. Ramified type theory is often deemed clunky and not explanatory, so my preferred approach for giving formal precision to generativism is the stage theory. The reason is that it provides greater flexibility, enhanced clarity, stronger theoretical justification, and a more streamlined framework, by bypassing the complications tied to ramified types and the use of modal operators, which are typical of potentialist views. (shrink)