In 1968, Orevkov presented proofs of conservativity of classical over intuitionistic and minimal predicate logic with equality for seven classes of sequents, what are known as Glivenko classes. The proofs of these results, important in the literature on the constructive content of classical theories, have remained somehow cryptic. In this paper, direct proofs for more general extensions are given for each class by exploiting the structural properties of G3 sequent calculi; for five of the seven classes the results are (...) strengthened to height-preserving statements, and it is further shown that the constructive and minimal proofs are identical in structure to the classical proof from which they are obtained. (shrink)

The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given (generalizing the results of [9]) in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. (...) We include examples to show how we can apply the results to describe free algebras in some well known varieties of involutive MTL-algebras and of pseudocomplemented MTL-algebras. (shrink)

The aim of this paper is to give a description of the free algebras in some varieties of Glivenko MTL-algebras having the Boolean retraction property. This description is given (generalizing the results of [9]) in terms of weak Boolean products over Cantor spaces. We prove that in some cases the stalks can be obtained in a constructive way from free kernel DL-algebras, which are the maximal radical of directly indecomposable Glivenko MTL-algebras satisfying the equation in the title. (...) We include examples to show how we can apply the results to describe free algebras in some well known varieties of involutive MTL-algebras and of pseudocomplemented MTL-algebras. (shrink)

This paper is devoted to the investigation of term-definable connexive implications in substructural logics with exchange and, on the semantical perspective, in sub-varieties of commutative residuated lattices (FL ${}_{\scriptsize\mbox{e}}$ -algebras). In particular, we inquire into sufficient and necessary conditions under which generalizations of the connexive implication-like operation defined in [6] for Heyting algebras still satisfy connexive theses. It will turn out that, in most cases, connexive principles are equivalent to the equational Glivenko property with respect to Boolean algebras. (...) Furthermore, we provide some philosophical upshots like, e.g., a discussion on the relevance of the above operation in relationship with G. Polya’s logic of plausible inference, and some characterization results on weak and strong connexivity. (shrink)

A residuated lattice is said to be integrally closed if it satisfies the quasiequations \ and \, or equivalently, the equations \ and \. Every integral, cancellative, or divisible residuated lattice is integrally closed, and, conversely, every bounded integrally closed residuated lattice is integral. It is proved that the mapping \\backslash {\mathrm {e}}\) on any integrally closed residuated lattice is a homomorphism onto a lattice-ordered group. A Glivenko-style property is then established for varieties of integrally closed residuated lattices (...) with respect to varieties of lattice-ordered groups, showing in particular that integrally closed residuated lattices form the largest variety of residuated lattices admitting this property with respect to lattice-ordered groups. The Glivenko property is used to obtain a sequent calculus admitting cut-elimination for the variety of integrally closed residuated lattices and to establish the decidability, indeed PSPACE-completenes, of its equational theory. Finally, these results are related to previous work on BCI-algebras, semi-integral residuated pomonoids, and Casari’s comparative logic. (shrink)

States have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in [0,1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0,1], in this paper we introduce Bosbach states defined on residuated lattices with values in residuated lattices. We are led to two types of generalized Bosbach states, with distinct behaviours. Properties of generalized states are useful for the development of an (...) algebraic theory of probabilistic models for non-commutative fuzzy logics. (shrink)

In this work, an intuitionistic propositional logic with a Galois connection is introduced. In addition to the intuitionistic logic axioms and inference rule of modus ponens, the logic contains only two rules of inference mimicking the performance of Galois connections. Both Kripke-style and algebraic semantics are presented for IntGC, and IntGC is proved to be complete with respect to both of these semantics. We show that IntGC has the finite model property and is decidable, but Glivenko's Theorem does (...) not hold. Duality between algebraic and Kripke semantics is presented, and a representation theorem for Heyting algebras with Galois connections is proved. In addition, an application to rough L-valued sets is presented. (shrink)

In this paper we continue the study of the variety \ of monadic Gödel algebras. These algebras are the equivalent algebraic semantics of the S5-modal expansion of Gödel logic, which is equivalent to the one-variable monadic fragment of first-order Gödel logic. We show three families of locally finite subvarieties of \ and give their equational bases. We also introduce a topological duality for monadic Gödel algebras and, as an application of this representation theorem, we characterize congruences and give characterizations of (...) the locally finite subvarieties mentioned above by means of their dual spaces. Finally, we study some further properties of the subvariety generated by monadic Gödel chains: we present a characteristic chain for this variety, we prove that a Glivenko-type theorem holds for these algebras and we characterize free algebras over n generators. (shrink)

We provide a natural extension of the intuitionistic natural deduction system NJ with at most two consequences, which we call a binary conclusion natural deduction system. The classical natural deduction system NK is defined as NJ together with the law of the excluded middle or the double negation principle. However, in contrast to NK, the new BCN system has no such classical rule, but has two kinds of rules managing two consequences. One is to eliminate one consequence and the other (...) is to introduce another consequence. Except on this point, BCN proofs are derived in exactly the same way as those in NJ. It is shown that with respect to the propositional fragment of NK, the BCN system is sound and sufficiently complete to prove classical propositional theorems. Moreover, as a corollary we obtain a general form of Glivenko's theorem and disjunction property for one of the two consequences. We also show the normalization theorem for BCN. Finally, we study some extensions of BCN to classical predicate logic. (shrink)

Although John Locke’s theory of appropriation is undoubtedly influential, no one seems to agree about exactly what he was trying to say. It is unlikely that someone will write the interpretation that effectively ends the controversy. Instead of trying to find the one definitive interpretation of Locke’s property theory, this article attempts to identify the range of reasonable interpretations and extensions of Lockean property theory that exist in the contemporary literature with an emphasis on his argument for unilateral (...) appropriation. It goes through Locke’s argument point-by-point discussing the controversy over what he said and over what he perhaps should have said to make the most valuable and coherent argument. The result is an outline of Lockean theories of property: a menu of options by which one might use appropriation to justify property rights. Supporters only need to pick the version they find most plausible, but opponents should be aware of the entire menu. Anyone claiming to refute appropriation-based property rights must address not only one but all potentially valid versions of it. (shrink)

Social contract thought has always contained multiple and mutually conflicting lines of argument; the minimalist contractarianism so influential today represents the weaker of two main constellations of claims. I make the case for a Kantian contract theory that emphasizes the bedrock principle of consent of the governed instead of the mere heuristic device of the exit from the state of nature. Such a shift in emphasis resolves two classic difficulties: tradi- tional contract theory’s ahistorical presumption of a pre-political settlement, and (...) its impossibly high demands on citizens seeking to practice self-rule. Kant’s solutions to these problems of property rights and citizenship are found in his political works, rather than the ethical works through which Kant’s political theory is usually interpreted. (shrink)

Strong property representationalism, as applied to visual experience, is the thesis that the phenomenal character of a visual experience is one and the same as the property complex or ‘sensible profile’ represented by that experience. Speaks discusses the following argument against this thesis:Let ‘RED’ stand for the phenomenal character of the experience of red.(1) Red = RED (strong property representationalism).(2) My pen has no representational properties, but is red.Hence,(3) My pen has a phenomenal character but no representational (...) properties.Since (3) is false, (1) is false too.(3) Follows from (1) and (2) only on the assumption that what it is for something to have a phenomenal character is for it to instantiate a certain property just as what it is for my pen to have the color red is for it to instantiate the property of being red. The property instantiation model of having a phenomenal character is not the only possible model, however, and I reject it.An alternative model is t. (shrink)

Can the right to private property be claimed as one of the `rights of mankind'? This is the central question of this comprehensive and critical examination of the subject of private property. Jeremy Waldron contrasts two types of arguments about rights: those based on historical entitlement, and those based on the importance of property to freedom. He provides a detailed discussion of the theories of property found in Locke's Second Treatise and Hegel's Philosophy of Right to (...) illustrate this contrast. The book contains original analyses of the concept of ownership, the ideas of rights, and the relation between property and equality. The author's overriding determination throughout is to follow through the arguments and values used to justify private ownership. He finds that the traditional arguments about property yield some surprisingly radical conclusions. (shrink)

This chapter defends the property dualism argument. The term “semantic premise” mentioned is used to refers to an assumption identified by Brian Loar that antiphysicalist arguments, such as the property dualism argument, tacitly assume that a statement of property identity that links conceptually independent concepts is true only if at least one concept picks out the property it refers to by connoting a contingent property of that property. It is argued that, the property (...) that does the work in explaining the possibility of a posteriori identities need not be a first-order property of the referent in question. On his view, the property dualism argument requires only a weaker semantic premise, which allows that the property in question be a higher order property. A refined version of the property dualism argument is formulated, which uses the weaker premise, and defends the argument against various objections. (shrink)

We study those relational structures S with the property that each partition of S contains a block isomorphic to S. We show that the Fraïsse limits of parametric classes K. have property ; over a binary language, every countable structure in K satisfying along with a condition on 1-extensions must be isomorphic to this limit.

Mainstream analytic epistemology regards knowledge as the property of individuals, rather ‎than groups. Drawing on insights from the reality of knowledge production and dissemination ‎in the sciences, I argue, from within the analytic framework, that this view is wrong. I defend ‎the thesis of ‘knowledge-level justification communalism’, which states that at least some ‎knowledge, typically knowledge obtained from expert testimony, is the property of a ‎community and possibly none of its individual members, in that only the community or (...) some ‎members of it collectively possesses knowledge-level justification for its individual members’ ‎beliefs. I address several objections that individuals, qua individuals, have or are able to ‎acquire knowledge-level justification for all the beliefs they obtain from expert testimony. I ‎argue that the problem I identify with individualism is invariant under any specific account of ‎justification, internalist or externalist. ‎. (shrink)

This paper defends the Blockian Proviso against its critics, Kinsella in particular, and interprets it as a law of non-contradiction in the theory of just property rights. I demonstrate that one may not lawfully appropriate in such a way as to forestall others from appropriating an unowned land because such appropriation would result in conflict-generating norms, and conflict-generating norms are not rationally justifiable and just norms. The Blockian Proviso, which precludes forestalling, operates therefore at the level of original appropriation (...) and determines, according to the homestead principle of justice in first acquisition, what may and what may not be lawfully appropriated. Hence, the Blockian Proviso is not an add-on to the homestead principle but part and parcel thereof. (shrink)

In this paper we give a rather detailed algebraic investigation of interpolation and Beth’s property in propositional many-valued logics extending Hájek’s Basic Logic [P. Hájek, Metamathematics of Fuzzy Logic, Kluwer, 1998], and we connect such properties with amalgamation and strong amalgamation in the corresponding varieties of algebras. It turns out that, while the most interesting extensions of in the language of have deductive interpolation, very few of them have Beth’s property or Craig interpolation. Thus in the last part (...) of the paper we look for conservative extensions of having such properties. (shrink)

This paper provides an entrance into central discussions regarding Kant’s account of property. The first section shows how Kant engages and transforms important, related proposals from Hobbes and Locke as well as how the ‘libertarian’ and ‘liberal republican’ interpretive traditions differ in their readings on these points. Since Kantian theories for a long time didn’t focus on Kant’s Doctrine of Right but instead followed Rawls’s lead by developing Kantian theories grounded on Kant’s (meta-) ethical writings, the second section focuses (...) on property discussions found in the Rawlsian tradition. The final section shows how important contemporary work in the Kantian tradition goes beyond Rawlsian, libertarian, and liberal republican concerns of distributive justice among free and equal citizens, to include questions central to, for example, the philosophy of care, feminist philosophy, philosophy of race, philosophy of sex and love, and environmental philosophy. (shrink)

An argument against treating our bodies as commodities No one wants to be treated like an object, regarded as an item of property, or put up for sale. Yet many people frame personal autonomy in terms of self-ownership, representing themselves as property owners with the right to do as they wish with their bodies. Others do not use the language of property, but are similarly insistent on the rights of free individuals to decide for themselves whether to (...) engage in commercial transactions for sex, reproduction, or organ sales. Drawing on analyses of rape, surrogacy, and markets in human organs, Our Bodies, Whose Property? challenges notions of freedom based on ownership of our bodies and argues against the normalization of markets in bodily services and parts. Anne Phillips explores the risks associated with metaphors of property and the reasons why the commodification of the body remains problematic. What, she asks, is wrong with thinking of oneself as the owner of one's body? What is wrong with making our bodies available for rent or sale? What, if anything, is the difference between markets in sex, reproduction, or human body parts, and the other markets we commonly applaud? Phillips contends that body markets occupy the outer edges of a continuum that is, in some way, a feature of all labor markets. But she also emphasizes that we all have bodies, and considers the implications of this otherwise banal fact for equality. Bodies remind us of shared vulnerability, alerting us to the common experience of living as embodied beings in the same world. Examining the complex issue of body exceptionalism, Our Bodies, Whose Property? demonstrates that treating the body as property makes human equality harder to comprehend. (shrink)

This book provides a detailed account of the role of property in German Idealism. It puts the concept of property in the center of the philosophical systems of Kant, Fichte, and Hegel and shows how property remains tied to their conceptions of freedom, right, and recognition. The book begins with a critical genealogy of the concept of property in modern legal philosophy, followed by a reconstruction of the theory of property in Kant's Doctrine of Right, (...) Fichte's Foundations of Natural Right, and Hegel's Jena Realphilosophie. By turning to the tradition of German Rechtsphilosophie, as opposed to the more standard libertarian and utilitarian frameworks of property, it explores the metaphysical, normative, political, and material questions that make property intelligible as a social relation. The book formulates a normative theory of property rooted in practical reason, mutual recognition, and social freedom. This relational theory of property, inspired by German Idealism, brings a fresh angle to contemporary property theory. Additionally, it provides crucial philosophical background to 19th century debates on private property, inequality, labor, socialism, capitalism, and the state. The Concept of Property in Kant, Fichte, and Hegel will appeal to scholars and advanced students interested in 19th Century German philosophy, social and political philosophy, philosophy of law, political theory, and political economy. (shrink)

This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system, and gives reduction procedures for them. It is then shown that deductions in the system convert into normal form, i.e. deductions that contain neither maximal formulas nor maximal segments, and that deductions in normal form satisfy the subformula property. Tarski’s Rule is treated as a general introduction rule for (...) implication. The general introduction rule for negation has a similar form. Maximal formulas with implication or negation as main operator require reduction procedures of a more intricate kind not present in normalisation for intuitionist logic. (shrink)

Let T be a strongly minimal theory with quantifier elimination. We show that the class of existentially closed models of T{“σ is an automorphism”} is an elementary class if and only if T has the definable multiplicity property, as long as T is a finite cover of a strongly minimal theory which does have the definable multiplicity property. We obtain cleaner results working with several automorphisms, and prove: the class of existentially closed models of T{“σi is an automorphism”: (...) i=1,2} is an elementary class if and only if T has the definable multiplicity property. (shrink)

Property-owning democracies combine the regulative and redistributive functions of the welfare state with the governmental aim of ensuring that wealth and capital are widely dispersed. John Rawls, political philosophy’s most famous property-owning democrat, argued that property-owning democracy was one of two regime types that best realized his two principles of justice, though he was notoriously vague about how a property-owning democracy’s institutions are meant to realize his principles. To compensate for this deficiency, a number of Rawlsian (...) political philosophers have tried to add institutional and policy content to the idea. While their efforts have advanced the discussion, few have criticized the soundness of these attempts. This article attempts to fill the void. I claim that, in comparison to welfare-state capitalism, property-owning democracy is both prohibitively impractical and unjust on Rawlsian grounds. I first argue that property-owning democracy is economically ineffective. Even granting the assumptions of Rawlsian ideal theory, property-owning democracies generate bad incentives and face severe information problems in comparison to more market-friendly welfare states. Further, in nonideal theory the motivations of political officials and citizens will likely be corrupted by the temptation to abuse the awesome state power at their disposal. Second, I argue that property-owning democracy is unjust relative to welfare-state capitalism. The three principles used to defend property-owning democracy—the difference principle, the principle of fair equality of opportunity and the “political liberty” proviso—do not vindicate property-owning democracy and may even prohibit it. Welfare-state capitalism does much better. (shrink)

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)

Physicalists about the mind are committed to claims about property identities. Following Kripke's well-known discussion, modal arguments have emerged as major threats to such claims. This paper argues that modal arguments can be resisted by adopting a counterpart theoretic account of modal claims, and in particular modal claims involving properties. Thus physicalists have a powerful motive to adopt non-Kripkean accounts of the metaphysics of modality and the semantics of modal expressions.

After Marx, dissenting economics almost always used 'the labour theory' as a theory of value. This paper develops a modern treatment of the alternative labour theory of property that is essentially the property theoretic application of the juridical principle of responsibility: impute legal responsibility in accordance with who was in fact responsible. To understand descriptively how assets and liabilities are appropriated in normal production, a 'fundamental myth' needs to be cleared away, and then the market mechanism of appropriation (...) can be understood. On the normative side, neoclassical theory represents marginal productivity theory as showing that (a metaphorical version of) the imputation principle is satisfied ('people get what they produce') in competitive enterprises. Since that shows the moral commitment of neoclassical economics to the imputation principle, the labour theory of property is presented here as the actual non-metaphorical application of the imputation principle to property appropriation. The property-theoretic analysis at the firm level shows how the neoclassical (and much heterodox) analysis in terms of 'distributive shares' wholly misframed the basic questions. Finally, the paper shows how the imputation principle (modernised labour theory of property) is systematically violated in the present wage labour system of renting persons. The paper can be seen as taking up the recent challenge posed by Donald Katzner for a dialogue between neoclassical and heterodox microeconomics. (shrink)

We initiate a systematic study of the class of theories without the tree property of the second kind — NTP2. Most importantly, we show: the burden is “sub-multiplicative” in arbitrary theories ; NTP2 is equivalent to the generalized Kimʼs lemma and to the boundedness of ist-weight; the dp-rank of a type in an arbitrary theory is witnessed by mutually indiscernible sequences of realizations of the type, after adding some parameters — so the dp-rank of a 1-type in any theory (...) is always witnessed by sequences of singletons; in NTP2 theories, simple types are co-simple, characterized by the co-independence theorem, and forking between the realizations of a simple type and arbitrary elements satisfies full symmetry; a Henselian valued field of characteristic is NTP2 if and only if the residue field is NTP2 , so in particular any ultraproduct of p-adics is NTP2; adding a generic predicate to a geometric NTP2 theory preserves NTP2. (shrink)