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)

The positions on private landownership of two libertarian scholars thought to have a wide following in that movement are examined The libertarians —Murray Rothbard and Robert Nozick—hold positions which are untenable. Rothbard's theory is almost indistinguishable from John Locke's and rests on the labor theory of ownership and the admixture theory of labor; standards which are too vague. Nozick believes that making something valuable gives a right of ownership, but again the standard is too ambiguous. And it is necessary to (...) appropriate a thing before one can improve it. The value added theory permits a utilitarian justification of landownership involving the payment of compensation to non-owners. (shrink)

Whether or not we have any natural right to landownership, like life and liberty, the institution of private property is agood. The utility produced by private property in land is overshadowed by the evils produced by the speculative withholding of supramarginal land unless compensatory payments are required of landowners. Such payments should be made to those living in the same “rental area” and should be of an amount that will eliminate all incentive to land speculation. It is not (...) always either desirable or possible to require that all of one's land value be paid in compensation. and even if such payments could be accomplished, they would not always be enough to redistribute the product stemming from the “monopolization” of real property The proper compensatory payment should reflect real increases in the value of real estate since its purchase, minus the value of improvements to the site made by the owner. (shrink)

American philosopher Everett W. Hall was among the first epistemologists writing in English to have promoted “representationism,” a currently popular explanation of cognition. According to this school, there are no private sense-data or qualia, because the ascription of public properties that are exemplified in the world of common sense is believed to be sufficient to explain mental content. In this timely volume, Walter Horn, perhaps the foremost living expert on Hall’s philosophy, not only provides copious excerpts from Hall’s works (...) in epistemology, metaphysics, and the philosophy of language--as well as his own commentaries on those writings--but also includes articles by Richard Rorty, Amie Thomasson, Fred Dretske, Thomas Natsoulas, and Romane Clark that are pertinent to Hall’s unique blend of linguistic idealism and intentional, common-sense realism. Covering metaphilosophy, the intentionality of perception, naïve realism, linguistic relativism, and Hall's public disagreements with such luminaries as Moore, Carnap, Wittgenstein, Quine, and Sellars, The Roots of Representationism is essential reading for students of 20th Century analytic philosophy. (shrink)

What is a number? Answering this will answer questions about its philosophical foundations - rational numbers, the complex numbers, imaginary numbers. If we are to write or talk about something, it is helpful to know whether it exists, how it exists, and why it exists, just from a common-sense point of view [Quine, 1948, p. 6]. Generally, there does not seem to be any disagreement among mathematicians, scientists, and logicians about numbers existing in some way, but currently, in the mainstream (...) arena only definitions, descriptions of properties, and effects are presented as evidence. Enough historical description of numbers in history provides an empirical basis of number, although a case can be made that numbers do not exist by themselves empirically. Correspondingly, numbers exist as abstractions. All the while, though, these "descriptions" beg the question of what numbers are ontologically. Advocates for numbers being the ultimate reality have the problem of wrestling with the nature of reality. I start on the road to discovering the ontology of number by looking at where people have talked about numbers as already existing: history. Of course, we need to know not only what ontology is but the problems of identifying one, leading to the selection between metaphysics and provisional approaches. While we seem to be dimensionally limited, at least we can identify a more suitable bootstrapping ontology than mere definitions, leading us to the unity of opposites. The rest of the paper details how this is done and modifies Peano's Postulates. (shrink)

Many philosophers have argued that moral disagreement raises metaphysical and/or epistemological challenges for moral realism. In this paper, I consider whether widespread moral disagreement raises a different sort of challenge by threatening the semantic commitments of moral realism. In particular, I suggest that the character of many moral disagreements gives us reason to suspect that not all competent moral speakers pick out the same properties as one another when they use moral terms. If this is so, both sides of a (...) moral dispute may speak truly, and the standard realist diagnosis of such disputes—that at most one party can be correct—is mistaken. My argumentative strategy is to first isolate some features of linguistic exchanges that provide evidence of a lack of co-reference, and then argue that many moral disputes have these features. I conclude by suggesting that there are plausible accounts of moral disputes that do not require co-reference. (shrink)

Epistemological realists have long struggled to explain perceptual error without introducing a tertium quid between perceivers and physical objects. Two leading realist philosophers, Thomas Reid and Everett Hall, agreed in denying that mental entities are the immediate objects of perceptions of the external world, but each relied upon strange metaphysical entities of his own in the construction of a realist philosophy of perception. Reid added ‘visible figures’ to sensory impressions and specific sorts of mental events, while Hall utilized an array (...) of ways that he maintained properties may participate in the world. This paper assesses each realist's attempt to explain perceptual relativity and illusion without contradicting either the science of his time or the structure of common sense. (shrink)

In Property Rights and Poverty, / argued that seventeenth? to mid?nineteenth?century liberal theories of the natural right to property included both the ability to exclude others from resources lawfully acquired and the ability to claim as property the resources necessary for life and livelihood. Virtually every defense of the right to exclude written during this period carried limits which allowed and even required the government to enforce the rights of those without resources to the property of (...) others. But although Locke, among others, was a theorist of welfare rights, it is a mistake to describe him as a radical, as Richard Ashcraft does, which identifies Locke's purposes too closely with the legitimately radical theorists of the early nineteenth century who were deeply influenced by his work. (shrink)

A proof is offered according to which if a psychological premise held by many diverse philosophers through the centuries to the effect that any represented physical property will be held to be exemplified unless some conflicting physical property is simultaneously represented is considered to be necessary, then there are physical objects in every possible world.

Two arguments Paul Snowdon has brought against the causal theory of perception are examined. One involves the claim that, based on the phenomenology of perceptual situations, it cannot be the case that perception is an essentially causal concept. The other is a reductio , according to which causal theorists’ arguments imply that a proposition Snowdon takes to be obviously non-causal ( A is married to B ) can be analyzed into some sort of indefinite ‘spousal connection’ plus a causal ingredient (...) . I conclude that neither argument is sound. The reason that Snowdon’s critiques fail is that, since causal theories need not be about ‘effect ends’ that are internally manifest to perceivers, no such ostensibly separable, non-causal property as it being to S as if he were perceiving O need be an essential element in a causal theory of perception. (shrink)

Most people presume that government is always responsible for providing solutions to pollution problems, including transportation pollution. This paper examines the validity of this argument from a minarchist libertarian, property rights principles perspective, and concludes that government cannot solve these problems using command-and-control legislation. The primary policy suggested for government to adopt is the strict adherence to property rights protection and enforcement regarding polluters, including themselves. Further encouragement of market forces could be accomplished by stopping interference within the (...) market at critical points, namely the production of roads, production and sales of automobiles, and the subsidization of alternative fuels. (shrink)

In this essay, it is argued that Leibniz’s theodicy is even stronger than it might first appear, but only if we also take into account his super-essentialism, the view that every property of a substance is essential to it, and theory of compossibility, the notion that possible worlds are intrinsically possible just in case they are compossible—that is, they are internally consistent. After describing how we should understand these principles in Leibniz’s thought, I argue that although there are obvious (...) cases of evil in the best of all possible worlds, if such cases of evil did not occur, then the overall goodness of the actual world be diminished. Due to the unique nature of his solution to the problem of evil, Leibniz remains an important interlocutor even today in metaphysics, theology, and philosophy of religion. (shrink)

Do young children have a teleological conception of the essence of natural kinds? We tested this by examining how the preservation or alteration of an animal’s purpose affected children’s persistence judgments (N = 40, ages 4 - 12, Mean Age = 7.04, 61% female). We found that even when surface-level features of an animal (e.g., a bee) were preserved, if the entity’s purpose changed (e.g., the bee now spins webs), children were more likely to categorize the entity as a member (...) of a different natural kind (e.g., a spider) and these effects were similar in magnitude to altering the surface-features of a natural kind. Our results suggest that we might view teleological properties as partially constitutive of the essence of natural kinds. (shrink)

Background: Patients prescribed with medication that treats mental health conditions benefit the most compared to those prescribed with other types of medication. However, they are also the most difficult to adhere. The development of mobile health (mHealth) applications (‘apps’) to help patients monitor their adherence is fast growing but with limited evidence on their efficacy. There is no evidence on the content of these apps for patients taking psychotropic medication. The aim of this study is to identify and evaluate the (...) aims and functioning of available apps that are aiming to help and educate patients to adhere to medication that treats mental health conditions. Method: Three platform descriptions (Apple, Google and Microsoft) were searched between October 2015 and February 2016. Included apps need to focus on adherence to medication that treats mental health conditions and use at least a reinforcement strategy. Descriptive information was extracted and apps evaluated on a number of assessment criteria using content analysis. Results: Sixteen apps were identified. All apps included self-monitoring properties like reminders and psycho-educational properties like mood logs. It was unclear how the latter were used or how adherence was measured. Major barriers to medication adherence like patients’ illness and medication beliefs and attitudes were not considered nor where information to patients about mediation side effects. Very few apps were tailored and none was developed based on established theories explaining the processes for successful medication adherence like cognitions and beliefs. Reported information on app development and validation was poor. Discussion: A variety of apps with different properties that tackle both intentional and unintentional non-adherence from a different perspective are identified. An evidence-based approach and co-creation with patients is needed. This will ensure that the apps increase the possibility to impact on non-adherence. Theories like social cognition models can be useful in ensuring that patients’ education, motivation, skills, beliefs and type of adherence are taken into consideration when developing the apps. Findings from this study can help clinicians and patients make informed choices and pursue policy-makers to integrate evidence when developing future apps. Quality-assurance tools are needed to ensure the apps are systematically evaluated. (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)

In the paper we give a sucient condition of the Interpolation Property in propositional calculi; then we establish the power of the class of the systems with Craig's property. Next we show that there does not exist a minimal R0-system with Craig-Godel-Lindenbaum's property. Finally, we generalize Sobocinski-Tarskis theorem concerning Sobocinski-Tarski's property.

The paper studies closure properties of classes of fuzzy structures defined by fuzzy implicational theories, i.e. theories whose formulas are implications between fuzzy identities. We present generalizations of results from the bivalent case. Namely, we characterize model classes of general implicational theories, finitary implicational theories, and Horn theories by means of closedness under suitable algebraic constructions.

This note corrects an error in my paper 'Normalisation and Subformula Property for a System of Classical Logic with Tarski's Rule' (Archive for Mathematical Logic 61 (2022): 105-129, DOI 10.1007/s00153-021-00775-6): Theorem 2 is mistaken, and so is a corollary drawn from it as well as a corollary that was concluded by the same mistake. Luckily this does not affect the main result of the paper.

Contrary to Thomas Horne's propensity to consider arguments concerning property rights and poverty as exclusive and self?contained topics within the political discourse of liberalism, they should be seen as part of the defense of democratic and market institutions that is central to the historical development of liberalism. The problems arising from the relationship of property rights to poverty, therefore, need to be included in any assessment of the success or failure of the institutions of a democratic market society (...) to realize their objectives. (shrink)

Tarski's model-theoretic truth definition of the 1950s differs from his 1930s truth definition by allowing the language to have a set of parameters that are interpreted by means of structures. The paper traces how the model-theoretic theorems that Tarski and others were proving in the period between these two truth definitions became increasingly difficult to fit into the framework of the earlier truth definition, making the later one more or less inevitable. The paper also maintains that neither recursiveness (...) nor satisfaction are essential features of the truth definition . The recursive form was a ‘practical’ step towards the explicit definition that was Tarski's target. There are model-theoretic languages for which satisfaction is provably too crude a notion for expressing those properties of formulas that are needed for determining the truth of sentences. (shrink)

A hallmark of correspondence theories of truth is the principle that sentences are made true by some truth-makers. A well-known objection to treating Tarski’s definition of truth as a correspondence theory has been put forward by Donald Davidson. He argued that Tarski’s approach does not relate sentences to any entities (like facts) to which true sentences might correspond. From the historical viewpoint, it is interesting to observe that Tarski’s philosophical teacher Tadeusz Kotarbinski advocated an ontological doctrine of (...) reism which accepted only concrete individuals and rejected all such abstract entities as facts, states of affairs, properties, and sets. Kotarbinski’s physicalism influenced Tarski who also avoided concepts like “fact” and “property” in his theory of truth, but—unlike Kotarbinski—he used freely set-theoretical terminology. In his mature work in model theory in the 1950s, Tarski used systematically the notion of a relational system (i.e., a domain of objects with designated elements, subsets, and relations). Wilfrid Hodges has argued that the notions of “structure” and “truth in a structure” appeared in Tarski’s work only in 1950. In my view, one can find the main ingredients of the model-theoretic account of truth already in the 1930s. These considerations suggest, against Davidson, that Tarski’s definition presupposes that material truth is always related to some kind of truth-maker. Further, facts as truth-makers can be reconstructed by employing the resources of model theory. (shrink)

The paper deals with fuzzy Horn logic which is a fragment of predicate fuzzy logic with evaluated syntax. Formulas of FHL are of the form of simple implications between identities. We show that one can have Pavelka-style completeness of FHL w.r.t. semantics over the unit interval [0, 1] with left-continuous t-norm and a residuated implication, provided that only certain fuzzy sets of formulas are considered. The model classes of fuzzy structures of FHL are characterized by closure properties. We also (...) give comments on related topics proposed by N. Weaver. (shrink)

A.1. Some philosophers, including Tarski and Russell, have concluded from a study of various versions of the Liar Paradox ‘that there must be a hierarchy of languages, and that the words “true” and “false”, as applied to statements in any given language, are themselves words belonging to a language of higher order’. In his famous essay on truth Tarski claimed that ‘colloquial’ language is inconsistent as a result of its property of ‘universality’: that is, whatever can be (...) said at all can in principle be said in it, with an extended vocabularly if necessary. Thus, in English we can talk about English expressions, what they denote, what they say, whether what they say is true or false, and so on: English contains its own metalanguage. This universality enables us to construct sentences which say of themselves that they are false, and by applying the law of excluded middle to them we easily derive a contradiction. Tarski concludes that ‘these antinomies seem to provide a proof that every language which is universal in the above sense, and for which the normal laws of logic hold, must be inconsistent’ . He then proposes to avoid such contradictions by the use of a hierarchy of languages such that statements about any one language can be made only in a different language at a higher level. (shrink)

Deflationsism about truth is a pot-pourri, variously claiming that truth is redundant, or is constituted by the totality of 'T-sentences', or is a purely logical device (required solely for disquotational purposes or for re-expressing finitarily infinite conjunctions and/or disjunctions). In 1980, Hartry Field proposed what might be called a 'deflationary theory of mathematics', in which it is alleged that all uses of mathematics within science are dispensable. Field's criterion for the dispensability of mathematics turns on a property of theories, (...) called conservativeness. I present some technical results, some of which may be found in Tarski (1936), concerning the logical properties of truth theories; in particular, concerning the conservativeness of adding a truth theory for an object level language to any theory expressed in it. It transpires that various deflationary truth theories behave somewhat differently from the standard Tarskian truth theory. These results suggest that Tarskian theories of truth are not redundant or dispensable. Finally, I hint at an analogy between the behaviour of mathematical theories and of standard (Tarskian) theories of truth with respect to their indispensability to, as Quine would put, our 'scientific world-view'. (shrink)

In the present commentary, I argue that Foster has attacked an uncharitable reconstruction of Etchemendy's argument against Tarski's account of the logical properties. I provide an alternative, more charitable reconstruction of that argument that withstands Foster's objections.

In ‘The Trouble with Tarski’, The Philosophical Quarterly, 48 (1998), pp. 1–22, Jonathan Harrison attacks ‘Tarski‐style’ truth theories for both formalized and natural languages, on the grounds that (1) truth cannot be a property of sentences; (2) if it could be, T‐sentences would have to be necessary truths, which they are not; and (3) T‐sentences are not necessarily true and can even can be false. I reply that (1) cannot be an objection to Tarskian truth theories, since (...) these can be formulated in terms of whatever truth bearers might be. Thesis (2) is unjustified: Harrison's argument for it depends on an equivocation. Thesis (3) is false, since the right‐hand side of a T‐sentence is a meta‐language translation of the object‐language sentence described on the left‐hand side, and this guarantees its truth. (shrink)

A first-order theory T has the Independence Property provided deduction of a statement of type (quantifiers) (P -> (P1 or P2 or .. or Pn)) in T implies that (quantifiers) (P -> Pi) can be deduced in T for some i, 1 <= i <= n). Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first-order theory has the Independence Property for the class of basic (...) formulas provided it can be axiomatized with Horn sentences. The existence of free models is a useful intermediate result. The independence Property is also a tool to decide that a sentence cannot be deduced. We illustrate this with the case of the classical Caratheodory theorem for Pasch-Peano geometries. (shrink)

This article outlines the work of a group of US mathematicians called the American Postulate Theorists and their influence on Tarski's work in the 1930s that was to be foundational for model theory. The American Postulate Theorists were influenced by the European foundational work of the period around 1900, such as that of Peano and Hilbert. In the period roughly from 1900???1940, they developed an indigenous American approach to foundational investigations. This made use of interpretations of precisely formulated axiomatic (...) theories to prove such metatheoretic properties as independence, consistency, categoricity and, in some cases, completeness of axiom sets. This approach to foundations was in many respects similar to that later taken by Tarski, who frequently cites the work of American Postulate Theorists. Their work served as paradigm examples of the theories and concepts investigated in model theory. The article also examines the possibility of a more specific impetus to Tarski's model theoretic investigation, arising from his having studied in 1927???1929 a paper by C. H. Langford proving completeness for various axiom sets for linear orders. This used the method of elimination of quantifiers. The article concludes with an examination of one example of Langford's methods to indicate how their correct formulation seems to call for model-theoretic concepts. (shrink)

A Greenberger, Horne and Zeilinger - type construction is realized in the position properties of three particles whose wave functions are distributed over three two - chambered boxes. The same system is modeled more realistically using three spatially separated, singly ionized hydrogen molecules.

In an earlier paper we proved that a universal Horn class generated by finitely many finite structures has a model companion. If the language has only finitely many fundamental operations then the theory of the model companion admits a primitive recursive elimination of quantifiers and is primitive recursive. The theory of the model companion is ℵ 0 -categorical iff it is complete iff the universal Horn class has the joint embedding property iff the universal Horn class (...) is generated by a single finite structure. In the last section we look at structure theorems for the model companions of universal Horn classes generated by functionally complete algebras, in particular for the cases of rings and groups. (shrink)

In his classic 1936 essay "On the Concept of Logical Consequence", Alfred Tarski used the notion of satisfaction to give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic characterization of the logical properties familiar to us today. However, in his book, The Concept of Logical Consequence, Etchemendy argues that Tarski's account is inadequate for quite a number of reasons, and is actually incompatible with the standard model-theoretic account. Many of his (...) criticisms are meant to apply to the model-theoretic account as well. In this paper, I discuss the following four critical charges that Etchemendy makes against Tarski and his account of the logical properties: (1) (a) Tarski's account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right. (b) Tarski's account cannot be brought into line with the model-theoretic account, because the two are fundamentally incompatible. (2) There are simple counterexamples (enumerated by Etchemendy) which show that Tarski's account is wrong. (3) Tarski committed a modal fallacy when arguing that his account captures our pre-theoretical concept of logical consequence, and so obscured an essential weakness of the account. (4) Tarski's account depends on there being a distinction between the "logical terms" and the "non-logical terms" of a language, but (according to Etchemendy) there are very simple (even first-order) languages for which no such distinction can be made. Etchemendy's critique raises historical and philosophical questions about important foundational work. However, Etchemendy is mistaken about each of these central criticisms. In the course of justifying that claim, I give a sustained explication and defense of Tarski's account. Moreover, since I will argue that Tarski's account and the model theoretic account really do come to the same thing, my subsequent defense of Tarski's account against Etchemendy's other attacks doubles as a defense against criticisms that would apply equally to the familiar model-theoretic account of the logical properties. (shrink)

The purpose of this paper is to examine some passages of Tarski‘s paper ’On the concept of logical consequence’ and to show that some recent readings of those passages are wrong. John Etchemendy has claimed that in those passages Tarski gave an argument purporting to show that the notion of logical consequence defined by him (as opposed to some pretheoretic notion of logical consequence) possesses certain modal properties. Etchemendy further claims that the argument he attributes to Tarski (...) is fallacious. Some of Etchemendy’s critics have granted him that Tarski did give an argument purporting to show that the defined notion possesses certain modal properties ; but they have claimed that Tarski’s argument was not a fallacious one. I will show that both Etchemendy and his critics are wrong; in the relevant passages, Tarski did not offer (nor did he intend to offer) an argument that the defined notion of logical consequence possesses any modal properties. (shrink)

The paper presents the main idea of point-free theories of space based on Tarski's system of point-free geometry. First, the general idea of the so-called point-free ontology was discussed, as well as the epistemological and methodological reasons for its adoption. Next, Whitehead's method of extensive abstraction, which is the methodological basis for the construction of point-free theories of space, is presented, and the fundamental concepts of mereology are discussed. The main part of the paper is a discussion of (...) class='Hi'>Tarski’s geometry of solids, its postulates and metatheoretical properties. The paper ends with a short description of the contribution of Polish researchers to the development of research on point-free theories of space. (shrink)

There is a well-established correspondence between interpolation and amalgamation for algebraizable logics that satisfy certain additional assumptions. In this paper, we introduce the Robinson property of a logic and show that a conditionally algebraizable logic without any additional assumptions has the Robinson property if and only if the corresponding class of Lindenbaum–Tarski algebras has the amalgamation property. Moreover, we give the logical characterization of the strong amalgamation property, solving an open problem of Andréka–Németi–Sain. It is (...) also shown that given the mentioned extra assumptions the Robinson property implies the interpolation property. As conditionally algebraizable logics cover algebraizable logics as well as various quantifier logics such as classical first order logic, our results yield a generalization of some of the results concerning interpolation and amalgamation. (shrink)

Boolean logic deals with {0, 1}-observables and yes–no events, as many-valued logic does for continuous ones. Since every measurement has an error, continuity ensures that small measurement errors on elementary observables have small effects on compound observables. Continuity is irrelevant for {0, 1}-observables. Functional completeness no longer holds when n-ary connectives are understood as [0, 1]-valued maps defined on [0, 1] n . So one must envisage suitable selection criteria for [0, 1]-connectives. Łukasiewicz implication has a well known characterization as (...) the only continuous connective \ satisfying the following conditions: \= y\Rightarrow}\) and \ . Then syntactic consequence can be defined purely algorithmically using the Łukasiewicz axioms and Modus Ponens. As discussed in this paper, to recover a strongly complete semantics one may use differential valuations. (shrink)