CORCORAN REVIEWS THE 4 VOLUMES OF TARSKI’S COLLECTED PAPERS Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but (...) most of the Aristotelian corpus is not about logic, whereas virtually everything written by Tarski concerns logic more or less directly. There is no doubt that Tarski wrote more on logic than any other author; he started publishing on logic in 1921 at the age of 20 and continued until his death at the age of 82. (shrink)

Recently, a number of philosophers have argued that we can and should “consequentialize” non-consequentialist moral theories, putting them into a consequentialist framework. I argue that these philosophers, usually treated as a group, in fact offer three separate arguments, two of which are incompatible. I show that none represent significant threats to a committed non-consequentialist, and that the literature has suffered due to a failure to distinguish these arguments. I conclude by showing that the failure of the consequentializers’ arguments has (...) implications for disciplines, such as economics, logic, decision theory, and linguistics, which sometimes use a consequentialist structure to represent non-consequentialist ethical theories. (shrink)

The thought-experiment presented by Bernard Williams in 'The self and the future' continues to draw the attention of writers in the debate about personal identity. While few of them agree on what implications it has for the debate, almost all agree that those implications are significant ones. Some have even claimed that it has consequences not only for personal identity, but also concerning the viability of thought-experiment as a method. This paper surveys what these consequences might be at both levels (...) - as a substantive contribution to the debate on identity, and as to what it shows about the usefulness of thought-experiments. It argues ultimately that thought-experiments like Williams's do provide a useful philosophical tool as long as we temper our expectations of them, and that it offers some support to a view of personal identity but one which is at odds with Williams's own view. (shrink)

The republican tradition has long been ambivalent about markets and commercial society more generally: from the contrasting positions of Rousseau and Smith in the eighteenth century to recent neorepublican debates about capitalism, republicans have staked out diverse positions on fundamental issues of political economy. Rather than offering a systematic historical survey of these discussions, this chapter will instead focus on the leading neo-republican theory—that of Philip Pettit—and consider its implications for market society. As I will argue, Pettit’s theory is even (...) friendlier to markets than most have believed: far from condemning commercial society, his theory recognizes that competitive markets and their institutional preconditions are an alternative means to limit arbitrary power across the domestic, economic, and even political spheres. While most republican theorists have focused on political means to limit such power—including both constitutional means (e.g., separation of powers, judicial review, the rule of law, federalism) and participatory ones (democratic elections and oversight)—I will examine here an economic model of republicanism that can complement, substitute for, and at times displace the standard political model. Whether we look at spousal markets, labor markets, or residential markets within federal systems, state policies that heighten competition among their participants and resource exit from abusive relationships within them can advance freedom as non-domination as effectively or even more effectively than social-democratic approaches that have recently gained enthusiasts among republicans. These conclusions suggest that democracy, be it social or political, is just one means among others for restraining arbitrary power and is consequently less central to (certain versions of) republicanism than we may have expected. So long as they counteract domination, economic inroads into notionally democratic territory are no more worrisome than constitutional ones. (shrink)

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework (...) recognizes multiple universes of discourse serving as different ranges of the individual variables in different interpretations?as in post-WWII model theory. In the early 1960s, many logicians?mistakenly, as we show?held the ?contrary alternative? that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege?Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski's philosophy underwent many other radical changes. (shrink)

We address the need for a model by considering two competing theories regarding the origin of life: (i) the Metabolism First theory, and (ii) the RNA World theory. We discuss two interrelated points, namely: (i) Models are valuable tools for understanding both the processes and intricacies of origin-of-life issues, and (ii) Insights from models also help us to evaluate the core objection to origin-of-life theories, called “the inefficiency objection”, which is commonly raised by proponents of both the Metabolism (...) First theory and the RNA World theory against each other. We use Simpson’s Paradox (SP) as a tool for challenging this objection. We will use models in various senses, ranging from taking them as representations of reality to treating them as theories/accounts that provide heuristics for probing reality. In this paper, we will frequently use models and theories interchangeably. Additionally, we investigate Conway’s Game of Life and contrast it with our SP-based approach to emergence-of-life issues. Finally, we discuss some of the consequences of our view. A scientific model is testable in three senses: (i) a logical sense, (ii) a nomological sense, and (iii) a current technological sense. The SP-based model is testable in the first two senses but it is not feasible to test it using current technology. (shrink)

“Bodily autonomy” has received significant attention in bioethics, medical ethics, and medical law in terms of the general inviolability of a patient’s bodily sovereignty and the rights of patients to make choices (e.g., reproductive choices) that concern their own body. However, the role of the body in terms of how it can or does contribute to a patient’s capacity for, or exercises of their autonomy in clinical decision-making situations has not been explicitly addressed. The approach to autonomy in this paper (...) is aligned with traditional theories that conceive autonomy in terms of an individual’s capacities for, and exercises of rational reflection. However, at the same time, this paper extends these accounts by arguing that autonomy is, in part, embodied. Specifically, by drawing on phenomenological conceptions of the experience of autonomy, we argue that, in principle, the body is a necessary component of the capacity for autonomy. Secondly, through the presentation of two different cases, we highlight ways in which a patient’s body can contribute to the autonomy of treatment choices. Ultimately, we hope to encourage others to explore additional conditions under which a concept of embodied autonomy should be employed in medical decision making, how its underlying principles might be operationalised in clinical situations, and its consequences for approaches to patient autonomy in healthcare practice, policy, and law. (shrink)

I wish to defend the claim that given the content and structure of any moral theory we are likely to find palatable, there is no way of uniquely breaking down that theory into either consequentialist or deontological elements. Indeed, once we examine the actual structure of any such theory more closely, we see that it can be classified in either way arbitrarily. Hence if we ignore the metaethical pronouncements often made by adherents of the consequentialist-deontological distinction, we are quickly led (...) to the conclusion that this distinction contributes nothing of consequence to an understanding of moral theory. I will try to show that there are basically two reasons for this. First, what we mean by the terms endemic to the consequentialist-deontological distinction have no unique references to particular states of affairs in actual cases of moral decision making. Hence we may justify any such concrete moral decision by reference to typically consequentialist or deontological reasoning indifferently. Second, scrutiny of actual and viable moral theories reveals a much finer-grained structure than the consequentialist-deontological taxonomy can capture. And it is this structure, rather than simple attention to consequences or principles, that determines practical moral decision making. We would thus do better to develop the richer vocabulary of causes and constituents, goals and effects, states and events (mental, social, or physical). So in the end, the consequentialist-deontological distinction is irrelevant at the normative level of actual moral reasoning, whereas at the metaethical level it crudely schematizes two opposing types of dummy theory, neither of which is convincing, upon reflection, to any practicing moral philosopher. (shrink)

In this paprer a class of so called mathematically acceptable (shortly MA) languages is introduced First-order formal languages containing natural numbers and numerals belong to that class. MA languages which are contained in a given fully interpreted MA language augmented by a monadic predicate are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of these languages. MTT makes them fully interpreted MA languages which posses their own truth predicates, yielding consequences to philosophy of mathematics. MTT is (...) shown to conform well with the eight norms presented for theories of truth in the paper 'What Theories of Truth Should be Like (but Cannot be)' by Hannes Leitgeb. MTT is also free from infinite regress, providing a proper framework to study the regress problem. (shrink)

Nugayev’s book is one of the first Soviet monographs treating the theory change problem. The gist of epistemological model consists in consequent account of intertheoretical relations. His book is based on the works of Soviet authors, as well as on Western studies (K.R. Popper, T.S. Kuhn, I. Lakatos, P. Feyerabend et al.) Key words: epistemological model, Soviet philosophy, Western studies .

Many commentators on Alfred Tarski have, following Hartry Field, claimed that Tarski's truth-definition was motivated by physicalism—the doctrine that all facts, including semantic facts, must be reducible to physical facts. I claim, instead, that Tarski did not aim to reduce semantic facts to physical ones. Thus, Field's criticism that Tarski's truth-definition fails to fulfill physicalist ambitions does not reveal Tarski to be inconsistent, since Tarski's goal is not to vindicate physicalism. I argue that Tarski's only published remarks that speak approvingly (...) of physicalism were written in unusual circumstances: Tarski was likely attempting to appease an audience of physicalists that he viewed as hostile to his ideas. In later sections I develop positive accounts of: (1) Tarski's reduction of semantic concepts; (2) Tarski's motivation to develop formal semantics in the particular way he does; and (3) the role physicalism plays in Tarski's thought. (shrink)

I want to examine the implications of a metaphysical thesis which is presupposed in various objections to Rawls' theory of justice.Although their criticisms differ in many respects, they concur in employing what I shall refer to as the continuity thesis. This consists of the following claims conjointly: (1) The parties in the original position (henceforth the OP) are, and know themselves to be, fully mature persons who will be among the members of the well-ordered society (henceforth the WOS) which is (...) generated by their choice of principles of justice. (2) The OP is a conscious event among others, integrated (compatibly with the constraints on knowledge and motivation imposed on the parties) into the regular continuity of experience that comprises each of their ongoing constitutes lives. (3) The parties in the OP thus are, and regard themselves as, psychologically continuing persons, partially determined in personality and interests by prior experiences, capable of recollection and regret concerning the past, anticipation and apprehensiveness regarding the future, and so on. Although the continuity thesis as stated above is not at odds with any of the conditions that define the OP, its exegetical validity is a matter for discussion. I shall be concerned to argue that if it is indeed contained in or a consequence of Rawls' theory, then it casts into doubt the capacity of the OP to generate or justify any principles of justice at all. On the other hand, if the continuity thesis is viewed as dispensable and unnecessary to the Rawlsian enterprise, then Rawls is correct in maintaining the irrelevance of the question of personal identity to the construction of his moral theory. In this case, the contract-theoretic, instrumentalist justification for the two principles of justice (henceforth the 2PJ) needs to be supplanted by a modified conception of wide reflective equilibrium. The considerations that form the bulk of this discussion then may be understood as providing a rationale for Rawls' recent revisions in the model of justification on which his theory of justice rests, and for his increasing emphasis on us as moral mediators between the OP and the WOS. Now I want to consider the question of whether or not, given the textual evidence, anything like the continuity thesis is stated or implied by Rawls, and what problems for his theory, if any, turn on a positive or negative answer to this question. -/- . (shrink)

This discussion treats a set of familiar social derelictions as consequences of the perversion of a universalistic moral theory in the service of an ill-considered or insufficiently examined personal agenda.The set includes racism, sexism, anti-Semitism, homophobia, and class elitism, among other similar pathologies, under the general heading of discrimination. The perversion of moral theory from which these derelictions arise, I argue, involves restricting its scope of application to some preferred subgroup of the moral community of human beings. -/- The following (...) analysis of higher-order discrimination suggests that we often select the individuals who constitute such subgroups for reasons that we ourselves would reject on moral grounds were we to examine them carefully, but that we choose instead to put our rational resources in the service of avoiding any such examination at all costs. The implication is that arguments that truncate the scope of moral theory in fact justify bestowing the gift of moral treatment on a select few who deserve it no more than the many from whom we withhold it. Therefore, it would be precipitous to conclude that universalistic moral theory can be legitimately restricted in its practical scope of application in any way at all. (shrink)

Most readers believe that it is difficult, verging on the impossible, to extract concrete prescriptions from the ethics of Emmanuel Levinas. Although this view is largely correct, Levinas’ philosophy can, with some assistance, generate specific duties on the part of legal actors. In this paper, I argue that the fundamental premises of Levinas’ theory of justice can be used to construct a prohibition against capital punishment. After analyzing Levinas’ concepts of justice, responsibility, and interruption, I turn toward his scattered remarks (...) on legal institutions, arguing that they enable a sense of interruption specific to the legal domain. It is here that we find the conceptual resources most important to my Levinasian abolition. I argue that the interruption of legal justice by responsibility implies what I call the principle of revisability. The principle of revisability states a necessary condition of just legal institutions: To be just, legal institutions must ensure the possibility of revising any and all of their rules, principles, and judgments. From this, the argument against capital punishment easily follows. Execution is a legal act, perhaps the only legal act, that cannot be undone. An application of the principle of revisability to this fact leads to the conclusion that legal institutions cannot justly impose capital punishment. After defending these points at length, I conclude with some observations on the consequences of the principle of revisability for law more generally. (shrink)

In 1951 John Rawls expressed these convictions about the fundamental issues in metaethics: [T]he objectivity or the subjectivity of moral knowledge turns, not on the question whether ideal value entities exist or whether moral judgments are caused by emotions or whether there is a variety of moral codes the world over, but simply on the question: does there exist a reasonable method for validating and invalidating given or proposed moral rules and those decisions made on the basis of them? For (...) to say of scientific knowledge that it is objective is to say that the propositions expressed therein may be evidenced to be true by a reasonable and reliable method, that is, by the rules and procedures of what we may call "inductive logic"; and, similarly, to establish the objectivity of moral rules, and the decisions based upon them, we must exhibit the decision procedure, which can be shown to be both reasonable and reliable, at least in some cases, for deciding between moral rules and lines of conduct consequent to them.1 In this passage Rawls reconfigured the issue of moral objectivity and so reoriented the practice of metaethics from linguistic analysis to rational methodology. In so doing, his work has provided inspiration to philosophers as disparate in normative views as Thomas Nagel,2 Richard Brandt3, Alan Gewirth4, and David Gauthier.5 Rawls replaced the Moorean question, Do moral terms refer? with the Rawlsian question, Can moral judgments be the outcome of a rational and reliable procedure? He later gave a resoundingly positive answer to this question6 and later still, a more tentative one.7 Rawls' considered qualification of his earlier enthusiasm about the extent to which moral philosophy could be "part of the theory of rational choice"8 is a tribute to the seriousness with which he took his critics' objections. (shrink)

The focus in this essay will be upon the paradoxes, and foremostly in set theory. A central result is that the librationist set theory £ extension \Pfund $\mathscr{HR}(\mathbf{D})$ of \pounds \ accounts for \textbf{Neumann-Bernays-Gödel} set theory with the \textbf{Axiom of Choice} and \textbf{Tarski's Axiom}. Moreover, \Pfund \ succeeds with defining an impredicative manifestation set $\mathbf{W}$, \emph{die Welt}, so that \Pfund$\mathscr{H}(\mathbf{W})$ %is a model accounts for Quine's \textbf{New Foundations}. Nevertheless, the points of view developed support the view that the truth-paradoxes and (...) the set-paradoxes have common origins, so that the librationist resolutions of the set theoretic paradoxes are at the same time resolutions of the truth theoretic paradoxes. Both the librationist resolutions of the set theoretic paradoxes and the truth theoretic paradoxes have non-trivial philosophical implications: librationist set theories have the consequence that there are no absolutely uncountable sets, and librationist truth theories allow the use of syntactical modalities in ways which circumvent limitations as those of \parencite{Montague1963}, and a truth predicate which is useful for more precise philosophical discourse. (shrink)

Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but most of the Aristotelian corpus is not about logic, whereas (...) virtually everything written by Tarski concerns logic more or less directly. There is no doubt that Tarski wrote more on logic than any other author; he started publishing on logic in 1921 at the age of 20 and continued until his death at the age of 82. Two of his works appeared posthumously [Hist. Philos. Logic 7 (1986), no. 2, 143--154; MR0868748 (88b:03010); Tarski and Givant, A formalization of set theory without variables, Amer. Math. Soc., Providence, RI, 1987; MR0920815 (89g:03012)]. Tarski's voluminous writings were widely scattered in numerous journals, some quite rare. It has been extremely difficult to study the development of Tarski's thought and to trace the interconnections and interdependence of his various papers. Thanks to the present collection all this has changed, and it is likely that the increased accessibility of Tarski's papers will have the effect of increasing Tarski's already enormous influence. (shrink)

The paper explores the logical structure of Rawlsian justice principles in order to see whether their justificatory or explanatory conditions are unproblematic. To facilitate this purpose, drawing on readers of Rawls, the author shows that the Aristotelian principle is used to explain the principles of rational choice, particularly the principle of inclusiveness. Then, on the basis of the Aristotelian principle, Rawls justifies his conclusion, via the principles of rational choice and the theory of primary goods. After figuring out the logical (...) structure of justice as fairness, the author deals with the central objective of the paper, where he exposes some problems suffered by the motivational basis of the principles of justice. The foundation on which Rawls grounds his principles of justice is problematic, and consequently, they remain as matters of contention as of today. (shrink)

In this paper, two axiomatic theories T− and T′ are constructed, which are dual to Tarski’s theory T+ (1930) of deductive systems based on classical propositional calculus. While in Tarski’s theory T+ the primitive notion is the classical consequence function (entailment) Cn+, in the dual theory T− it is replaced by the notion of Słupecki’s rejection consequence Cn− and in the dual theory T′ it is replaced by the notion of the family Incons of inconsistent (...) sets. The author has proved that the theories T+, T−, and T′ are equivalent. (shrink)

Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of (...) the meaning of true that attribution of being true to a given thing presupposes the thing is a sentence. Beta’s importance is further highlighted by the fact that alpha can be satisfied using the recursively definable concept of being satisfied by every infinite sequence, which Tarski explicitly rejects. Moreover, in Definition 23, the famous truth-definition, Tarski supplements “being satisfied by every infinite sequence” by adding the condition “being a sentence”. Even where truth is undefinable and treated by Tarski axiomatically, he adds as an explicit axiom a sentence to the effect that every truth is a sentence. Surprisingly, the sentence just before the presentation of Convention T seems to imply that alpha alone might be sufficient. Even more surprising is the sentence just after Convention T saying beta “is not essential”. Why include a condition if it is not essential? Tarski says nothing about this dissonance. Considering the broader context, the Polish original, the German translation from which the English was derived, and other sources, we attempt to determine what Tarski might have intended by the two troubling sentences which, as they stand, are contrary to the spirit, if not the letter, of several other passages in Tarski’s corpus. (shrink)

The paper is devoted to the study of determinants determined the level of financial security of economic systems. It is shown that the financial security of an economic system implies the achievement of a level of financial stability that will contribute to simultaneously maintaining financial equilibrium and ensuring targeted growth in line with the development strategy. The level of financial security of rail transport in Ukraine was analyzed and it was determined that the decline in its security was the result (...) of a complex interaction of external and internal factors, the main of which were tight government regulation, shifting the financial burden of social responsibilities to Ukrzaliznytsya, PJSC, lack of competition in the transportation of the main nomenclature of cargo and the unsatisfactory state of non-current assets. Based on the Argenti’s method, it is shown that the consequence of the inefficient financial management of Ukrzaliznytsia, PJSC are the reduction of its insolvency. Three main determinants of the financial security of rail enterprises were identified: a reduction in traffic volumes, an unstable capital structure and the impossibility of timely repayment of current liabilities. An additive model for assessing the impact of selected determinants on the level of financial security of Ukrzaliznytsia, PJSC is proposed. The analysis of the model parameters showed that the greatest impact has the index of industrial production, which is due to the predominant formation of its own financial resources of rail transport due to income from freight traffic. A complex of measures designed to improve the financial condition of rail enterprises was proposed. It is substantiated that in order to equalize existing threats, it is necessary to take political decisions aimed at improving the financial condition of Ukrzaliznytsia, PJSC by reducing the intensity of leaching of its financial resources, as well as implementing an anti-crisis financial strategy aimed at optimizing the capital structure and financial rehabilitation of rail enterprises. (shrink)

The monograph contains three works on research on the concept of a rejected sentence. This research, conducted under the supervision of Prof. Jerzy Słupecki by U. Wybraniec-Skardowska (1) "Theory of rejected sentences" and G. Bryll (2) "Some supplements of theory of rejected sentences" and (3) "Logical relations between sentences of empirical sciences" led to the construction of a theory rejected sentences and made it possible to formalize certain issues in the methodology of empirical sciences. The concept of a rejected sentence (...) was introduced by J. Łukasiewicz in the course of his inquiry into Aristotelian Syllogistic. It was essentialy generelized by J. Słupecki who, with reference to Tarski's axiomatic theory of deductive systems (1930), gave the formal definition of the rejection function Cn' according to which a sentence y is rejected on the base of a set of sentences X iff at least one sentence which belongs to X can be deduced from the sentence y. Słupecki proved (1959) that the function Cn', which assignes to the set X the set of sentences rejected on the basis of X, is additive and satisfies the axioms of Tarski's general theory of deductive systems. Work (1) uses not only Tarski's general theory of systems but also his the so-called enlarged theory of systems (1930). It constructs a theory T of rejected sentences (propositions), which is created from Tarski's richer theory of systems by adding one axiom and a number of definitions; among them the definition of the rejection function Cn' is fundamental one. Cn' is a function which assignes to every set X of false sentences the set Cn'X whose members are exclusively false senteces. A number of theorems which describes properties of defined concepts have been proved in T. Some of them are necessary for conducting considertions of the concluding section of (1) devoted to the empirical sentences. Section 2 of (1) deals with the theory of the unit consequenses. It is characterized by an axiom from which follow all axioms of Tarski's general theory of deductive systems, additivity and the property that the unit consequence of the set X of sentences is a unit consequence only one sentence of X. An example of unit consequence is the rejection consequence Cn'. In section 3 of (1) the dual theory T' equivalent to T is presented. In T' the primitive concept is the rejection function Cn'. The fundamental axiom of T' states that Cn' is a unit consequence. The concluding section brings a few examples of applications of the definitions and theorems of T in the domain of the scientific methodology. Work (2) corresonds to J. Słupecki paper (1959) and the theory T of rejected propositions given in work (1). In this paper some suplements of the theory T are given. Work (3) is an extension of the theory of rejected propositios given in the paper (1). It is an attempt of formalization some problems of methodology of the empirical sciences which concern to such concepts as: empirical sentence, similar sentence, generalization, inductive conclusion etc. (shrink)

Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz (Ajdukiewicz in Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). Translated as: Pragmatic Logic. Reidel & PWN, Dordrecht, 1975). The author of this paper, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and additionally two (...) types of them in each of the two, depending on the manner of combining their premises with the conclusion through the relation of classical logical entailment. Consequently, the four types of reasoning: unilateral deductive (incl. its sub-types: deductive inference and proof), bilateral deductive (incl. complete induction), and reductive (incl. the sub-types: explanation and verification), logically nonvaluable (incl. inference by analogy, statistic inference), correspond to four operators of derivability. They are defined formally on the ground of Tarski’s axiomatic theory of deductive systems, by means of the consequence operation _Cn_ (Tarski in Monatshefte Math Phys 37:361–404, 1930a, C R Soc Sci Lett Vars 23:22–29, 1930b). Also, certain metalogical properties of these operators are given, as well as their relations with Tarski’s consequence operations \(Cn^+\) ( \(Cn^+ = Cn\) ) and dual consequences \(Cn^{-1}\) (Słupecki in Zeszyty Naukowe Uniwersytetu Wrocławskiego Seria B Nr 3:33–40, 1959, Słupecki et al. in Stud Log 29:76–123, 1971, Wybraniec-Skardowska, in: Wybraniec-Skardowska, Bryll (eds) Z badań nad teorią zdań odrzuconych [Studies in the Theory of Rejected Propositions], Series B, Studia i Monografie, Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Opole, 1969), and \(Cn^-\) (Wójcicki in Bull Sect Log 2(2):54–57, 1973)). (shrink)

It might come as a surprise for someone who has only a superficial knowledge of Donald Davidson’s philosophy that he has claimed literary language to be ‘a prime test of the adequacy of any view on the nature of language’.1 The claim, however, captures well the transformation that has happened in Davidson’s thinking on language since he began in the 1960’s to develop a truth-conditional semantic theory for natural languages in the lines of Alfred Tarski’s semantic conception of truth. (...) About twenty years afterwards, this project was replaced with a view that highlights the flexible nature of language and, in consequence, the importance of the speaker’s intentions for a theory of meaning, culminating in Davidson’s staggering claim that ‘there is no such thing as a language’. (shrink)

In his seminal work “The Concept of Truth in Formalized Languages”, Alfred Tarski showed how to construct a formally correct and materially adequate definition of true sentence for certain formalized languages. These results have, eventually, been accepted and applauded by philosophers and logicians nearly in unison. Its Postscript, written two years later, however, has given rise to a considerable amount of controversy. There is an ongoing debate on what Tarski really said in the postscript. These discussions often regard Tarski as (...) putatively changing his logical framework from type theory to set theory. In what follows, we will compare the original results with those presented two years later. After a brief outline of Carnap’s program in The Logical Syntax of Language we will determine its significance for Tarski’s final results. (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)

It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to be shown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusion follows and using a countermodel to show that a conclusion does not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These (...) practices presuppose, respectively, a criterion of validity and a criterion of invalidity each of which has been extended and refined by modern logicians: deductions are studied in formal syntax (proof theory) and coun¬termodels are studied in formal semantics (model theory). The purpose of this paper is to compare these two criteria to the corresponding criteria employed in Boole’s first logical work, The Mathematical Analysis of Logic (1847). In particular, this paper presents a detailed study of the relevant metalogical passages and an analysis of Boole’s symbolic derivations. It is well known, of course, that Boole’s logical analysis of compound terms (involving ‘not’, ‘and’, ‘or’, ‘except’, etc.) contributed to the enlargement of the class of propositions and arguments formally treatable in logic. The present study shows, in addition, that Boole made significant contributions to the study of deduc¬tive reasoning. He identified the role of logical axioms (as opposed to inference rules) in formal deductions, he conceived of the idea of an axiomatic deductive sys¬tem (which yields logical truths by itself and which yields consequences when ap¬plied to arbitrary premises). Nevertheless, surprisingly, Boole’s attempt to imple¬ment his idea of an axiomatic deductive system involved striking omissions: Boole does not use his own formal deductions to establish validity. Boole does give symbolic derivations, several of which are vitiated by “Boole’s Solutions Fallacy”: the fallacy of supposing that a solution to an equation is necessarily a logical consequence of the equation. This fallacy seems to have led Boole to confuse equational calculi (i.e., methods for gen-erating solutions) with deduction procedures (i.e., methods for generating consequences). The methodological confusion is closely related to the fact, shown in detail below, that Boole had adopted an unsound criterion of validity. It is also shown that Boole totally ignored the countermodel criterion of invalid¬ity. Careful examination of the text does not reveal with certainty a test for invalidity which was adopted by Boole. However, we have isolated a test that he seems to use in this way and we show that this test is ineffectual in the sense that it does not serve to identify invalid arguments. We go beyond the simple goal stated above. Besides comparing Boole’s earliest criteria of validity and invalidity with those traditionally (and still generally) employed, this paper also investigates the framework and details of THE MATHEMATICAL ANALYSIS OF LOGIC. (shrink)

This paper addresses Prinz's naturalistic theory of conceptual content, which he has defended in several works (Prinz, 2000; 2002; 2006). More precisely, I present in detail and critically assess his account of referential content, which he distinguishes from nominal or cognitive content. The paper argues that Prinz's theory faces four important difficulties, which might have significant consequences for his overall empiricist project.

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection (...) of sentences, above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.

The aim of this dissertation is to offer and defend a correspondence theory of truth. I begin by critically examining the coherence, pragmatic, simple, redundancy, disquotational, minimal, and prosentential theories of truth. Special attention is paid to several versions of disquotationalism, whose plausibility has led to its fairly constant support since the pioneering work of Alfred Tarski, through that by W. V. Quine, and recently in the work of Paul Horwich. I argue that none of these theories meets (...) the correspondence intuition---that a true sentence or proposition in some way corresponds to reality---despite the explicit claims by each to capture this intuition. I distinguish six versions of the correspondence theory, and defend two against traditional objections, standardly taken as decisive against them, and show, plainly, that these two theories capture the correspondence intuition. Due to the importance of meeting this intuition, only these two theories stands a chance of being a satisfactory theory of truth. I argue that the version of the correspondence theory incorporating a simple semantic representation relation is preferable to its rival, for which the representation relation is complex. I present and argue for a novel version of this correspondence theory according to which truth is a correspondence property sensitive to semantic context. One consequence of this context-sensitivity is that an ungrounded sentence does not express a proposition. In addition to accounting for the similarity between the Liar and Truth-Teller sentences, this theory of truth is immune to the Liar Paradox, including empirical versions. It is argued that the Liar Paradox is devastating to all of the other theories above, and even formal theories of truth designed to solve it, such as the revision and vagueness theories. Customized versions of the Liar Paradox besetting this theory are handled by its context-sensitivity, and by enforcing the distinction between truth and truth value. This same pair of considerations also yields solutions to Lob's Paradox and Grelling's Paradox. Arguments similar to those given to defend this correspondence theory show that with one minor alteration, Kripke's fixed point theory may be used to model this correspondence notion of truth. (shrink)

This is the PhD dissertation, written under supervision of Professor Jerzy Słupecki, published in the book: U.Wybraniec-Skardowska i Grzegorz Bryll "Z badań nad teorią zdań odrzuconych" ( "Studies of theory of rejected sentences"), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Seria B: Studia i Monografie nr 22, pp. 5-131. It is the first, original publication on the theory of rejected sentences on which are based, among other, papers: "Theory of rejected propositions. I"and "Theory of rejected propositions II" with Jerzy Słupecki (...) and Grzegorz Bryll. -/- -/- . (shrink)

According to Brandom’s conceptual role semantics, to grasp a concept involves a commitment to drawing certain inferences. This is a consequence of the inferentialist thesis that the meaning of a term is given by its justification through assertibility conditions. Inferential commitments come out from a material notion of inference which underwrites human rational discourse and activity. In this paper I discuss a problem of Brandom’s semantics allegedly exposed in an argument by Paul Boghossian against Dummett’s and Brandom’s substantive conception (...) of meaning. I contend that Boghossian’s analysis is dubious because it overlooks an important difference between Dummett’s and Brandom’s positions related respectively to a monotonic and a non-monotonic view of the norm underwriting meaning. (shrink)

Tarski’s pioneering work on truth has been thought by some to motivate a robust, correspondence-style theory of truth, and by others to motivate a deflationary attitude toward truth. I argue that Tarski’s work suggests neither; if it motivates any contemporary theory of truth, it motivates conceptual primitivism, the view that truth is a fundamental, indefinable concept. After outlining conceptual primitivism and Tarski’s theory of truth, I show how the two approaches to truth share much in common. While (...) Tarski does not explicitly accept primitivism, the view is open to him, and fits better with his formal work on truth than do correspondence or deflationary theories. Primitivists, in turn, may rely on Tarski’s insights in motivating their own perspective on truth. I conclude by showing how viewing Tarski through the primitivist lens provides a fresh response to some familiar charges from Putnam and Etchemendy. (shrink)

With his critical theory of resonance, Hartmut Rosa has proposed the basis of a model for normatively criticizing and practically addressing the consequences of social acceleration, and its inherent tendency towards growth and innovation. This model has brought a fresh perspective to Critical Theory, offering a framework to examine a dynamic that permeates virtually all social activities. However, it has also been associated with certain characteristics that could potentially justify two labels always reproached by Critical Theory: paternalism and totalitarianism. To (...) contribute to the ongoing debates sparked by Rosa's work, this article aims to demonstrate how Rosa's approach actively seeks to avoid these accusations, primarily by incorporating the concept of Weltbeziehung [relationships with the world]. (shrink)

Leibniz’s claim that possibles strive towards existence has led to diverging interpretations. According to the metaphorical interpretation, only the divine will is causally efficacious in bringing possibles into exisence. According to the literal interpretation, God endows possibles with causal powers of their own. The present article suggests a solution to this interpretative impass by suggesting that the doctrine of the striving possibles can be understood as a consequence of Leibniz’s early cognitivist theory of volition. According to this theory, thinking (...) the degree of goodness of something is identical with wanting it to this degree. Arguably, this analysis of volition is relevant not only for Leibniz’s early analysis of the human mind but also for his early analysis of the divine mind. (shrink)

This paper challenges Francis Hutcheson's and John Clarke of Hull's alleged demonstrations that William Wollaston's moral theory is inconsistent. It also present a form of the inconsistency objection that fares better than theirs, namely, that of Thomas Bott (1688-1754). Ultimately, the paper shows that Wollaston's moral standard is not what some have thought it to be; that consequently, his philosophy withstands the best-known efforts to expose it as inconsistent; and further, that one of the least-known British moralists is more important (...) than hitherto thought, in that he uncovers the inconsistency Clarke and Hutcheson try in vain to elicit. (shrink)

Alfred Tarski was one of the greatest logicians of the twentieth century. His influence comes not merely through his own work but from the legion of students who pursued his projects, both in Poland and Berkeley. This chapter focuses on three key areas of Tarski's research, beginning with his groundbreaking studies of the concept of truth. Tarski's work led to the creation of the area of mathematical logic known as model theory and prefigured semantic approaches in the philosophy of language (...) and philosophical logic, such as Kripke's possible worlds semantics for modal logic. We also examine the paradoxical decomposition of the sphere known as the Banach–Tarski paradox. Finally we examine Tarski's work on decidable and undecidable theories, which he carried out in collaboration with students such as Mostowski, Presburger, Robinson and others. (shrink)

The phenomenon of ambivalence is an important one for any philosophy of action. Despite this importance, there is a lack of a fully satisfactory analysis of the phenomenon. Although many contemporary philosophers recognize the phenomenon, and address topics related to it, only Harry Frankfurt has given the phenomenon full treatment in the context of action theory - providing an analysis of how it relates to the structure and freedom of the will. In this paper, I develop objections to Frankfurt's account, (...) all revolving around the charge that his account contains a serious ambiguity between willing and identifying. With such objections in place, I then develop an analysis that avoids the difficulties and ambiguities that Frankfurt's analysis is prey to. I briefly distinguish ambivalence from other types of internal conflict. This paper aims to offer conceptual clarification on the phenomenon of ambivalence, which will then allow for discussions about the normative merits and demerits of ambivalence, the effects of ambivalence on autonomous action, and methods of resolution of ambivalence. (shrink)

Define teleology as the view that requirements hold in virtue of facts about value or goodness. Teleological views are quite popular, and in fact some philosophers (e.g. Dreier, Smith) argue that all (plausible) moral theories can be understood teleologically. I argue, however, that certain well-known cases show that the teleologist must at minimum assume that there are certain facts that an agent ought to know, and that this means that requirements can't, in general, hold in virtue of facts about (...) value or goodness. I then show that even if we grant those 'ought's teleology still runs into problems. A positive justification of teleology looks like it will require an argument of this form: O(X); if X, then O(Y); therefore O(Y). But this form of argument isn't in general valid. I conclude by offering two positive suggestions for those attracted to a teleological outlook. (shrink)

G. E. Moore’s critical analysis of right action in utilitarian ethics and his consequentialist concept of right action is a starting point for a theory of moral/right action in ethics of social consequences. The terms right and wrong have different meanings in these theories. The author explores different aspects of right and wrong actions in ethics of social consequences and compares them with Moore’s ideas. He positively evaluates Moore’s contributions to the development his theory of moral/right action.

Unifying physics by describing a variety of interactions – or even all interactions – within a common framework has long been an alluring goal for physicists. One of the most ambitious attempts at unification was made in the 1910s by Gustav Mie. Mie aimed to derive electromagnetism, gravitation, and aspects of the emerging quantum theory from a single variational principle and a well-chosen Lagrangian. Mie’s main innovation was to consider nonlinear field equations to allow for stable particle-like solutions (now called (...) solitons), and he clarified the use of variational principles in the context of special relativity. The following brief introduction to Mie’s work has three main objectives. The first is to explain how Mie’s project fit into the contemporary development of the electromagnetic world view. Part of Mie’s project was to develop a relativistic theory of gravitation as a consequence of his generalized electromagnetic theory, and our second goal is to briefly assess this work, which reflects the conceptual resources available for developing a new account of gravitation by analogy with electromagnetism. Finally, Mie was a vocal critic of other approaches to the problem of gravitation. Mie’s criticisms of Einstein, in particular, bring out the subtlety and novelty of the ideas that Einstein used to guide his development of general relativity. (shrink)

The aim of this article is to outline a pragmatist image of science following Rorty’s discussions and critics of epistemology and to develop some consequences of it in the philosophical analysis and its relations to culture. I will deal with some aspects of how scientific practice is construed and understood, and also outline the shift in Philosophy of Science from epistemological to ethical-political concerns that are implied in his proposal. I will contend that this perspective suggests an interesting way of (...) analysing scientific practices, theories, and public policies of it. Furthermore, I will suggest that it successfully connects the most interesting proposals of contemporary scientific views in philosophy. Finally, I will use some examples in physics and biology to illustrate my assertions. (shrink)

Is capitalism inherently predatory? Must there be winners and losers? Is public interest outdated and free-riding rational? Is consumer choice the same as self-determination? Must bargainers abandon the no-harm principle? Prisoners of Reason recalls that classical liberal capitalism exalted the no-harm principle. Although imperfect and exclusionary, modern liberalism recognized individual human dignity alongside individuals' responsibility to respect others. Neoliberalism, by contrast, views life as ceaseless struggle. Agents vie for scarce resources in antagonistic competition in which every individual seeks dominance. This (...) political theory is codified in non-cooperative game theory; the neoliberal citizen and consumer is the strategic rational actor. Rational choice justifies ends irrespective of means. Money becomes the medium of all value. Solidarity and good will are invalidated. Relationships are conducted on a quid pro quo basis. However, agents can freely opt out of this cynical race to the bottom by embracing a more expansive range of coherent action. (shrink)

The broad scope and coherence of Natural Beauty are among its major strengths. Moore's syncretic theory tries to integrate diverse and sometimes conflicting theoretical strands. Of special importance is his recognition that the natural world is a social institution embodying perceptions that are conditioned, experiences communicated through language, and social beliefs and conventions. These lead him to consider the natural world as actually artifactual, and he terms it the 'natureworld'. Among the consequences of this is the reciprocity of natural and (...) artistic beauty, one indication of the inclusiveness that runs through his theory. My central concern is whether Moore's syncretic theory can successfully combine disparate features of conflicting theories, such as cognitivism and non-cognitivism, and subjectivism and objectivism. Another concern is whether his syncretism can resolve problems such as the apparent inconsistencies raised by his discussion of framing. Here, alternatives that Moore had presumably settled reappear, as when objects, which had presumably been replaced by experiences, re-emerge in his discussion of framing. These comments identify such difficulties and ask whether the way out may be to reframe not natural beauty but the terms of the question. (shrink)

The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. (...) Her development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

Alfred Tarski seems to endorse a partial conception of truth, the T-schema, which he believes might be clarified by the application of empirical methods, specifically citing the experimental results of Arne Næss (1938a). The aim of this paper is to argue that Næss’ empirical work confirmed Tarski’s semantic conception of truth, among others. In the first part, I lay out the case for believing that Tarski’s T-schema, while not the formal and generalizable Convention-T, provides a partial account of (...) truth that may be buttressed by an examination of the ordinary person’s views of truth. Then, I address a concern raised by Tarski’s contemporaries who saw Næss’ results as refuting Tarski’s semantic conception. Following that, I summarize Næss’ results. Finally, I will contend with a few objections that suggest a strict interpretation of Næss’ results might recommend an overturning of Tarski’s theory. (shrink)

Hilary Putnam's famous arguments criticizing Tarski's theory of truth are evaluated. It is argued that they do not succeed to undermine Tarski's approach. One of the arguments is based on the problematic idea of a false instance of T-schema. The other ignores various issues essential for Tarski's setting such as language-relativity of truth definition.