This is the only complete logic for properties, relations, and propositions (PRPS) that has been formulated to date. First, an intensional abstraction operation is adjoined to first-order quantifier logic, Then, a new algebraic semantic method is developed. The heuristic used is not that of possible worlds but rather that of PRPS taken at face value. Unlike the possible worlds approach to intensional logic, this approach yields a logic for intentional (psychological) matters, as well as modal matters. At the close (...) of the paper, the origin of incompleteness in logic is investigated. The culprit is found to be the predication relation, a relation on properties and relations that is expressed in natural language by the copula. (shrink)

The definition of capitalist exploitation that I put forth was as follows. Let a society be divided into a coalition S and its complement S’. S is exploited and S’ is exploiting if: S would be better off if it withdrew with its per capita share of productive, alienable assets; S’ would be worse off if it withdrew with its per capita share of productive, alienable assets; and S’ would be worse off if S withdrew from society with its own (...) assets. Call this the property relations definition of exploitation. I favored the PR definition over the traditional approach, which focuses upon the relationship between capitalist and worker mediated by a labor market and consummated at the point of production, because the classical approach fails to locate the source of exploitation in the unequal and unfair distribution of the productive assets. (shrink)

Many theories assimilate the idioms of modality to those of quantification; they hold that so-and-so is possible iff there is a "world" at which it is true that so-and-so. "Modal realism" identifies worlds with certain concrete particulars, and truth at a world with what is true of it. Rival "ersatz" theories identify worlds with certain abstract entities and identify what is true at them with what they represent. ;David Lewis argues that pre-theoretic modal intuitions are best explained by modal realism. (...) I try to make a case for ersatzism. ;First, I argue that modal realism is flawed on the grounds that it entails the impossibility of certain intuitively possible spatiotemporal structures; it fails to explain fully even those intuitions with which it is compatible; and it renders the origin of modal knowledge mysterious. ;Next, I argue that objections to ersatzism are not conclusive. ;Lewis objects that even a generic version of ersatzism requires an unnameable and maybe unintelligible primitive relation. I suggest that the problems with naming are perfectly general; they have nothing to do with metaphysical theories of modality in particular. And I suggest a solution taken from Lewis himself. I also argue that any purported unintelligibility is due to illegitimately assimilating the relation to spatiotemporal relations. ;Finally, I consider some difficulties with a version of ersatzism that aims to reduce modality to impure set-theory. One concerns the accommodation of intuitions about properties that are not, but might have been, instantiated. Another concerns accommodation of intuitions about relations of exclusion and entailment among properties. I suggest that these difficulties are due to faulty assumptions about the nature of properties rather than any fundamental flaws in this ersatz approach. So I propose an account of properties that when incorporated into ersatzism circumvents these difficulties and allows it to claim the advantages of modal realism without its drawbacks. Unlike traditional accounts, this takes the essence of a property to consist in its role in imposing a certain classificational structure on the particulars that instantiate it, rather than in any unique and irreducible "quiddity". (shrink)

Higher-order theories of properties, relations, and propositions are known to be essentially incomplete relative to their standard notions of validity. It turns out that the first-order theory of PRPs that results when first-order logic is supplemented with a generalized intensional abstraction operation is complete. The construction involves the development of an intensional algebraic semantic method that does not appeal to possible worlds, but rather takes PRPs as primitive entities. This allows for a satisfactory treatment of both the modalities and (...) the propositional attitudes, and it suggests a general strategy for developing a comprehensive treatment of intensional logic. (shrink)

Many properties of compacta have “textbook” definitions which are phrased in lattice-theoretic terms that, ostensibly, apply only to the full closed-set lattice of a space. We provide a simple criterion for identifying such definitions that may be paraphrased in terms that apply to all lattice bases of the space, thereby making model-theoretic tools available to study the defined properties. In this note we are primarily interested in properties of continua related to unicoherence; i.e., properties that speak to the existence of (...) “holes” in a continuum and in certain of its subcontinua. (shrink)

This paper argues that social trust is the emergent product of a complex system of property relations, backed up by a sub-system of mutual monitoring. This happens in a context similar to Ostrom’s commons, where cooperation is necessary for the management of resources, in the absence of external authorities to enforce sanctions. I show that social trust emerges in this context because of an institutional structure that enables individuals to develop a generalized disposition to internalize the external effects (...) of their actions. This is made possible by the “patrimonial” nature of this structure. (shrink)

This paper provides an analysis of the intrinsic/extrinsic distinction, as applied both to properties and to relations. In contrast to other accounts, the approach taken here locates the source of a property’s intrinsicality or extrinsicality in the manner in which that property is ‘logically constituted’, and thus – plausibly – in its nature or essence, rather than in e.g. its modal profile. Another respect in which the present proposal differs from many extant analyses lies in the fact (...) that it does not seek to analyse the ‘global’ distinction between intrinsic and extrinsic properties on the basis of the ‘local’ distinction between having a property intrinsically and having it extrinsically. Instead, the latter distinction is explicated on the basis of the former. (shrink)

In this paper I examine the role of dispositional properties in the most frequently discussed interpretations of non-relativistic quantum mechanics. After offering some motivation for this project, I briefly characterize the distinction between non-dispositional and dispositional properties in the context of quantum mechanics by suggesting a necessary condition for dispositionality – namely contextuality – and, consequently, a sufficient condition for non-dispositionality, namely non-contextuality. Having made sure that the distinction is conceptually sound, I then analyze the plausibility of the widespread, monistic (...) ontological thesis about the reducibility of dispositional properties to categorical properties in the context of the philosophy of quantum mechanics. I conclude that with the exception of Bohmian mechanics, the other “minimally realist” views of quantum mechanics require essential dispositions, i.e., dispositions of a non-reducible kind. Interestingly, seen behind the lenses of dispositionalism, Bohr’s and Bohm’s interpretations of quantum mechanics are much closer than it is usually recognized, a fact that could teach us something about the way the quantum world is. (shrink)

This essay presents an interpretation of the juridical thought of Cicero, Hugo Grotius and Adam Smith. Focussing upon questions of property, capital accumulation and violence, the essay traces a tension within their writings between a social ethic of human fellowship and compassion, and, a theory of the utility of ‘unsocial’ commercial self-interest. This tension forms a key problem for the tradition of liberal international law. For Grotius and Smith one response to this tension is to attempt to reign in (...) capitalist markets by asserting a range of moral duties to individuals and to the nation-state. The importance of stressing such an interpretation is to reject the flattening-out of the liberal political and juridical tradition by contemporary neoliberal thought, and to reclaim a number of ways of thinking about the global economy and international law in which moral action and political intervention are understood as playing a necessary and essential role. (shrink)

This paper is concerned with two concepts of qualitativeness that apply to intensional entities. I propose an account of pure qualitativeness that largely follows the traditional understanding established by Carnap, and try to shed light on its ontological presuppositions. On this account, an intensional entity is purely qualitative iff it does not ‘involve’ any particular. An alternative notion of qualitativeness—which I propose to refer to as a concept of strict qualitativeness—has recently been introduced by Chad Carmichael. However, Carmichael’s definition presupposes (...) a highly fine-grained conception of properties and relations. To eliminate this presupposition, I tentatively suggest a different definition that rests on a concept of perspicuous denotation. In the penultimate section, both concepts of qualitativeness are put to work in distinguishing between different ‘grades’ of qualitative discriminability. (shrink)

The present study investigates the relations between L2-English proficiency and L1-Turkish lexical property evaluations. We asked whether L2 proficiency affects lexical properties, including imageability and concreteness ratings of 600 Turkish words selected from the Word Frequency Dictionary of Written Turkish. Seventy-two participants provided ratings of concreteness and imageability for 600 words on a 7-point scale. In order to assess their L2 proficiency, we administered Peabody Picture Vocabulary Test-IV. We divided categories into two subcategories as high and low for (...) the frequency, concreteness, imageability, and age of acquisition. The relationship between these subcategories and imageability-concreteness was examined by mixed effects linear regression analyses. We found that L2 proficiency and imageability ratings were positively correlated and specifically, this positive association was evident for low-frequency words and later acquired words. Results are in line with the interaction of bilingual representation under the dual-coding theory which suggests that bilinguals develop an interconnected imaginal representation for two languages as opposed to separate verbal representations. As L2 proficiency increased, the imageability also increased. These findings have implications for literature investigating the relationship between L2 proficiency and linguistic outcomes. Additionally, findings point to the importance of considering the L2 proficiency of participants when lexical tasks that involve cue words or word lists are used. (shrink)

Various types of continuity for preference relations on a metric space are examined constructively. In particular, necessary and sufficient conditions are given for an order-dense, strongly extensional preference relation on a complete metric space to be continuous. It is also shown, in the spirit of constructive reverse mathematics, that the continuity of sequentially continuous, order-dense preference relations on complete, separable metric spaces is connected to Ishihara's principleBD-ℕ, and therefore is not provable within Bishop-style constructive mathematics alone.

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)

I think it would be fair to say that, until about 1900, philosophers were generally reluctant to admit the existence of what are nowadays called polyadic properties.1 It is important to recognize, however, that this reluctance on the part of pre-twentieth-century philosophers did not prevent them from theorizing about relations. On the contrary, philosophers from the ancient through the modern period have had much to say about both the nature and the ontological status of relations. In this paper (...) I examine the views of one such philosopher, namely, Albert the Great. (shrink)

Assuming that we find the concept of naturalness coherent, we shall no doubt wish to allow that certain relations count as highly natural. Many of us will think that various spatio-temporal and causal relations—is the cause of, is spatially separated from, is later than—are highly natural. Some of us will think that various basic semantic and mentalistic relations—refers to, attends to, believes.…--- are highly natural. Some will think that various logico-mathematical relations—being the successor of, being identical (...) to…—are highly natural. (shrink)

Hird, G.R., Recursive properties of relations on models, Annals of Pure and Applied Logic 63 241–269. We prove general existence theorems for recursive models on which various relations have specified recursive properties. These capture common features of results in the literature for particular algebraic structures. For a useful class of models with new relations R, S, where S is r.e., we characterize those for which there is a recursive model isomorphic to on which the relation corresponding to (...) S remains r.e., while that corresponding to R is not r.e.; immune; hyperimmune. The results are applied to vector spaces, Boolean algebras and abelian groups. In the case of vector spaces, this leads to a new kind supermaximal subspace of V∞. (shrink)

I demonstrate that the pre-Critical Kant is essentialist and intellectualist about the relational properties of substances. That is to say, God can choose whether or not to create a substance, and whether or not to connect this substance with other substances, so as to create a world: but God cannot choose what the nature of the relational properties is, once the substance is created and connected. The divine will is constrained by the essences of substances. Nonetheless, Kant considers that essences (...) depend upon God, in that they depend upon the divine intellect. I conclude by gesturing towards some possible implications of this interpretation, when considering the role that might be played by God – both historically and conceptually – in relation to the notion of ‘laws of nature’, and when understanding Kant's transcendental idealism and his Critical conception of freedom. (shrink)

Assuming that we find the concept of naturalness coherent, we shall no doubt wish to allow that certain relations count as highly natural. Many of us will think that various spatio-temporal and causal relations—is the cause of, is spatially separated from, is later than—are highly natural. Some of us will think that various basic semantic and mentalistic relations—refers to, attends to, believes.…--- are highly natural. Some will think that various logico-mathematical relations—being the successor of, being identical (...) to…—are highly natural. (shrink)

The question whether qualities are metaphysically more fundamental than or mere limiting cases of relations can be addressed in an applied symbolic logic. There exists a logical equivalence between qualitative and relational predications, in which qualities are represented as one-argument-place property predicates, and relations as more-than-one-argument-place predicates. An interpretation is first considered, according to which the logical equivalence of qualitative and relational predications logically permits us ontically to eliminate qualities in favor of relations, or relations (...) in favor of qualities. If metaphysics is understood at least in part as an exercise in ontic economy, then we may be encouraged to adopt a property ontology of qualities without quality-irreducible relations, or relations without relation-irreducible qualities. If either strategy is followed, the choice of reducing qualities to relations or relations to qualities will need to be justified on extra-logical grounds. These might include a perceived greater intuitiveness, explanatory fecundity, compatibility with cognitive ontogeny or developmental psychology, expressive or explanatory elegance or cumbersomeness, and an open-ended list of philosophical motivations that could reasonably favor the ontic prioritization of qualities over relations or relations over qualities. Despite its intuitive appeal, the thesis that logical equivalence together with extra-logical preferences justifies unidirectional ontic reduction of relations to qualities or qualities to relations is rejected in light of the more defensible proposition that the logical equivalence of qualitative and relational predications actually supports the opposite conclusion, that both qualities and relations are logically indispensable to a complete ontology of properties. The logical equivalence of qualitative and relational predications, insofar as we continue to observe the distinction, makes it logically necessary ontically for both qualities and relations to exist whenever either one exists. That logically equivalent qualitative and relational predications have as their truth-makers the exemplification by objects of both qualities and relations as equi-foundational properties further suggests that there is no deeper logical distinction between qualities and relations, but only two convenient lexical-grammatical designations for property predications involving one- versus more-than-one-argument-place. (shrink)

This paper presents an account of what it is for a property or relation (or ‘attribute’ for short) to be logically simple. Based on this account, it is shown, among other things, that the logically simple attributes are in at least one important way sparse. This in turn lends support to the view that the concept of a logically simple attribute can be regarded as a promising substitute for Lewis’s concept of a perfectly natural attribute. At least in part, (...) the advantage of using the former concept lies in the fact that it is amenable to analysis, where that analysis—i.e., the account put forward in this paper—requires the adoption neither of an Armstrongian theory of universals nor of a primitive notion of naturalness, fundamentality, or grounding. (shrink)

Slater’s method is an integral part of the undergraduate experience. In actuality, Slater’s method is part of an atomic model and not simply a set of rules. Slater’s rules are a simple means for computing the effective nuclear charge experienced by an orbital. These rules are based on the shell-like structure of the Slater atom in which outer shell electrons are incapable of shielding inner electrons. Slater’s model provides a qualitative description of the valence electrons in multi-electron atoms with tremendous (...) ease. The model is useful for explaining atomic properties such as ionisation energy, electron affinity and atomic radius qualitatively. Slater’s rules also correctly reproduce the Madelung rule of filling and the ionisation sequence (4s before 3d); however, these rules are not able to reproduce the anomalous configurations of atoms such as Cr and Cu. It is found that the atomic properties that Slater’s model reproduces are all related to the exponential decay factor of the Slater orbital. We find—from estimating the polarity of a diatomic molecule using a simple model—that molecular polarity is related to the difference in the exponential decay factors of the valence orbitals of the two atoms, implying that the decay factor acts as the electronegativity of the atom. (shrink)

Frege famously argued that truth is not a property or relation. In the “Notes on Logic” Wittgenstein emphasised the bi-polarity of propositions which he called their sense. He argued that “propositions by virtue of sense cannot have predicates or relations.” This led to his fundamental thought that the logical constants do not represent predicates or relations. The idea, however, has wider ramifications than that. It is not just that propositions cannot have relations to other propositions but (...) also that they cannot have relations to anything at all. The paper explores the consequences of this insight for the way in which we should read the Tractatus. In the “Notes on Logic” the insight led to Wittgenstein's emphasis on “facts” in any attempt to understand the nature of symbolism. This emphasis is continued in the Tractatus. It is central to his view that propositions are facts which picture facts which prevent us from construing such picturing as a relation between what pictures and what is pictured. It illuminates the importance of context principle with regard to the distinction between showing and saying to which Wittgenstein attached so much importance and it underlies the non-relational view of psychological propositions which he advocates. Finally, if propositions by virtue of sense cannot have predicates or relations the paradox at the end of a work which consist largely of propositions about propositions becomes intelligible. (shrink)

This paper reexamines the central thesis of Gadamer’s theory of interpretation that objectivity is not a suitable ideal for understanding a text, historical event or cultural phenomenon because there exists no one correct interpretation of such phenomena. Because Gadamer fails to make clear the grounds for this claim, I consider three possible arguments. The first, predominant in the secondary literature, is built on the premise that we cannot surpass our historically situated prejudgments. I reject this argument as insufficient. I also (...) reject a second argument concerning the heuristics of understanding. I then articulate a third argument that the object of understanding changes according to the conditions under which it is grasped. I appeal to the notion of relational properties to make sense of this claim and to defend it against two objections: that it conflates meaning and significance; and that it is saddled with an indefensible relativism. (shrink)

This paper is a contribution to the study of the rôle of disjunction inAlgebraic Logic. Several kinds of (generalized) disjunctions, usually defined using a suitable variant of the proof by cases property, were introduced and extensively studied in the literature mainly in the context of finitary logics. The goals of this paper are to extend these results to all logics, to systematize the multitude of notions of disjunction (both those already considered in the literature and those introduced in this (...) paper), and to show several interesting applications allowed by the presence of a suitable disjunction in a given logic. (shrink)

The most important question concerning picture perception is: what perceptual state are we in when we see an object in a picture? In order to answer this question, philosophers have used the results of the two visual systems model, according to which our visual system can be divided into two streams, a ventral stream for object recognition, allowing one to perceive from an allocentric frame of reference, and a dorsal stream for visually guided motor interaction, thus allowing one to perceive (...) from an egocentric frame of reference. Following this model, philosophers denied that we can be in a dorsal perceptual state when perceiving a depicted object. This is because a depicted object is not physically graspable or manipulable and, in turn, it cannot be egocentrically localized, as a normal object, by the dorsal stream. Thus, the impossibility of manipulating depicted objects and of localizing them from an egocentric frame of reference has led some people to be sceptical about the possibility of a representation of action properties in the perception of objects in pictures, which pertains to the dorsal visual system. The aim of the present paper is to show that it is possible for the depicted object to be represented by dorsal perception. That means that we can ascribe action properties to depicted objects as well, even if depicted objects cannot be egocentrically localized—at least, not as much as normal objects can. (shrink)

We prove the finite model property (fmp) for BCI and BCI with additive conjunction, which answers some open questions in Meyer and Ono [11]. We also obtain similar results for some restricted versions of these systems in the style of the Lambek calculus [10, 3]. The key tool is the method of barriers which was earlier introduced by the author to prove fmp for the product-free Lambek calculus [2] and the commutative product-free Lambek calculus [4].