In this paper I present a new theory of propositions, according to which propositions are abstract mathematical objects: well-formed formulas together with models. I distinguish the theory from a number of existing views and explain some of its advantages  chief amongst which are the following. On this view, propositions are unified and intrinsically truth-bearing. They are mind- and language-independent and they are governed by logic. The theory of propositions is ontologically innocent. It makes room for an (...) appropriate interface with formal semantics and it does not enforce an overly fine or overly coarse level of granularity. (shrink)

A new reduction class is presented for the satisfiability problem for well-formed formulas of the first-order predicate calculus. The members of this class are closed prenex formulas of the form ∀ x∀ yC. The matrix C is in conjunctive normal form and has no disjuncts with more than three literals, in fact all but one conjunct is unary. Furthermore C contains but one predicate symbol, that being unary, and one function symbol which symbol is binary.

Consider the following argument: All men are mortal; Socrates is a man; therefore, Socrates is mortal. Intuitively, what makes this a valid argument has nothing to do with Socrates, men, or mortality. Rather, each sentence in the argument exhibits a certain logical form, which, together with the forms of the other two, constitute a pattern that, of itself, guarantees the truth of the conclusion given the truth of the premises. More generally, then, the logical form of a sentence of natural (...) language is what determines both its logical properties and its logical relations to other sentences. The logical form of a sentence of natural language is typically represented in a theory of logical form by a well-formed formula in a ‘logically pure’ language whose only meaningful symbols are expressions with fixed, distinctly logical meanings (e.g., quantifiers). Thus, the logical forms of the sentences in the above argument would be represented in a theory based on pure predicate logic by the formulas ‘∀x(Fx ⊃ Gx)’, ‘Fy’, and ‘Gy’, respectively, where ‘F’, ‘G’, and ‘y’ are all free variables. The argument’s intuitive validity is then explained in virtue of the fact that the logical forms of the premises formally entail the logical form of the conclusion. The primary goal of a theory of logical form is to explain as broad a range of such intuitive logical phenomena as possible in terms of the logical forms that it assigns to sentences of natural language. (shrink)

A many-valued (aka multiple- or multi-valued) semantics, in the strict sense, is one which employs more than two truth values; in the loose sense it is one which countenances more than two truth statuses. So if, for example, we say that there are only two truth values—True and False—but allow that as well as possessing the value True and possessing the value False, propositions may also have a third truth status—possessing neither truth value—then we have a many-valued semantics in (...) the loose but not the strict sense. A many-valued logic is one which arises from a many-valued semantics and does not also arise from any two-valued semantics [Malinowski, 1993, 30]. By a ‘logic’ here we mean either a set of tautologies, or a consequence relation. We can best explain these ideas by considering the case of classical propositional logic. The language contains the usual basic symbols (propositional constants p, q, r, . . .; connectives ¬, ∧, ∨, →, ↔; and parentheses) and well-formed formulas are defined in the standard way. With the language thus specified—as a set of well-formed formulas—its semantics is then given in three parts. (i) A model of a logical language consists in a free assignment of semantic values to basic items of the non-logical vocabulary. Here the basic items of the non-logical vocabulary are the propositional constants. The appropriate kind of semantic value for a proposition is a truth value, and so a model of the language consists in a free assignment of truth values to basic propositions. Two truth values are countenanced: 1 (representing truth) and 0 (representing falsity). (ii) Rules are presented which determine a truth value for every proposition of the language, given a model. The most common way of presenting these rules is via truth tables (Figure 1). Another way of stating such rules—which will be useful below—is first to introduce functions on the truth values themselves: a unary function ¬ and four binary functions ∧, ∨, → and ↔ (Figure 2).. (shrink)

Let K = (p, q...; &, ∨, ~) be a zeroth-order formal language with sentence variables p, q..., two place connectives & (and), ∨ (or) and negation sign ~, and let F be the formula algebra (set of well-formed formulas in K defined in the standard way by induction from the sentence variables). If v is an assignment of truth values 1(true), 0(f alse) to the sentence variables p, q..., then classical propositional logic is characterized by extending (...) v by induction from p, q... to the formula algebra F in such a manner that the extension (called interpretation and also denoted by v) be a “homomorphism” from F into the two-element Boolean algebra B 2 ≡ (1, 0, ⋂, ⋃, ⊥), where “homomorphism” means that the following hold υ(q&p)=υ(q)∩υ(p)υ(q∨p)=υ(q)∪υ(p)υ(∼q)=υ(q)⊥. (shrink)

Let K = (p, q...; &, ∨, ~) be a zeroth-order formal language with sentence variables p, q..., two place connectives & (and), ∨ (or) and negation sign ~, and let F be the formula algebra (set of well-formed formulas in K defined in the standard way by induction from the sentence variables). If v is an assignment of truth values 1(true), 0(f alse) to the sentence variables p, q..., then classical propositional logic is characterized by extending (...) v by induction from p, q... to the formula algebra F in such a manner that the extension (called interpretation and also denoted by v) be a “homomorphism” from F into the two-element Boolean algebra B 2 ≡ (1, 0, ⋂, ⋃, ⊥), where “homomorphism” means that the following hold υ(q&p)=υ(q)∩υ(p)υ(q∨p)=υ(q)∪υ(p)υ(∼q)=υ(q)⊥. (shrink)

This Perspective traces the evolution of certain central notions in the theory of Generative Grammar (GG). The founding documents of the field suggested a relation between the grammar, construed as recursively enumerating an infinite set of sentences, and the idealized native speaker that was essentially equivalent to the relation between a formal language (a set of well-formed formulas) and an automaton that recognizes strings as belonging to the language or not. But this early view was later abandoned, (...) when the focus of the field shifted to the grammar's strong generative capacity as recursive generation of hierarchically structured objects as opposed to strings. The grammar is now no longer seen as specifying a set of well-formed expressions and in fact necessarily constructs expressions of any degree of intuitive “acceptability.” The field of GG, however, has not sufficiently acknowledged the significance of this shift in perspective, as evidenced by the fact that (informal and experimentally-controlled) observations about string acceptability continue to be treated as bona fide data and generalizations for the theory of GG. The focus on strong generative capacity, it is argued, requires a new discussion of what constitutes valid empirical evidence for GG beyond observations pertaining to weak generation. (shrink)

The tree-based data structure of -tree for propositional formulas is introduced in an improved and optimised form. The -trees allow a compact representation for negation normal forms as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. These reduction strategies are divided into two subsets (meaning- and satisfiability-preserving transformations) and can be used to decrease the size of a negation normal (...) form A at (at most) quadratic cost. The reduction strategies are aimed at decreasing the number of required branchings and, therefore, these strategies allow to limit the size of the search space for the SAT problem. (shrink)

We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is (...) endowed with atruth value defined classically, and everyaf is endowed with ajustification value, defined in terms of the intuitive notion of proof and depending on the truth values of its radical subformulas. In this framework, we define the notion ofpragmatic validity in P and yield a list of criteria of pragmatic validity which hold under the assumption that only classical metalinguistic procedures of proof be accepted. We translate the classical propositional calculus (CPC) and the intuitionistic propositional calculus (IPC) into the assertive part of P and show that this translation allows us to interpret Intuitionistic Logic as an axiomatic theory of the constructive proof concept rather than an alternative to Classical Logic. Finally, we show that our framework provides a suitable background for discussing classical problems in the philosophy of logic. (shrink)

Nominalism in formal ontology is still the thesis that the only acceptable domain of quantification is the first-order domain of particulars. Nominalists may assert that second-order well-formed formulas can be fully and completely interpreted within the first-order domain, thereby avoiding any ontological commitment to second-order entities, by means of an appropriate semantics called “substitutional”. In this paper I argue that the success of this strategy depends on the ability of Nominalists to maintain that identity, and equivalence relations (...) more in general, is first-order and invariant. Firstly, I explain why Nominalists are formally bound to this first-order concept of identity. Secondly, I show that the resources needed to justify identity, a certain conception of identity invariance, are out of the Nominalist’s reach. (shrink)

Let K = (p, q...; &, ∨, ~) be a zeroth-order formal language with sentence variables p, q..., two place connectives & (and), ∨ (or) and negation sign ~, and let F be the formula algebra (set of well-formed formulas in K defined in the standard way by induction from the sentence variables). If v is an assignment of truth values 1(true), 0(f alse) to the sentence variables p, q..., then classical propositional logic is characterized by extending (...) v by induction from p, q... to the formula algebra F in such a manner that the extension (called interpretation and also denoted by v) be a “homomorphism” from F into the two-element Boolean algebra B 2 ≡ (1, 0, ⋂, ⋃, ⊥), where “homomorphism” means that the following hold υ(q&p)=υ(q)∩υ(p)υ(q∨p)=υ(q)∪υ(p)υ(∼q)=υ(q)⊥. (shrink)

Akama et al. [1] systematically studied an arithmetical hierarchy of the law of excluded middle and related principles in the context of first-order arithmetic. In that paper, they first provide a prenex normal form theorem as a justification of their semi-classical principles restricted to prenex formulas. However, there are some errors in their proof. In this paper, we provide a simple counterexample of their prenex normal form theorem [1, Theorem 2.7], then modify it in an appropriate way which still (...) serves to largely justify the arithmetical hierarchy. In addition, we characterize a variety of prenex normal form theorems by logical principles in the arithmetical hierarchy. The characterization results reveal that our prenex normal form theorems are optimal. For the characterization results, we establish a new conservation theorem on semi-classical arithmetic. The theorem generalizes a well-known fact that classical arithmetic is $\Pi _2$ -conservative over intuitionistic arithmetic. (shrink)

We study instantiated abstract argumentation frames of the form, where is an abstract argumentation frame and where the arguments x of S are instantiated by I as well formed formulas of a well known logic, for example as Boolean formulas or as predicate logic formulas or as modal logic formulas. We use the method of conceptual analysis to derive the properties of our proposed system. We seek to define the notion of complete extensions (...) for such systems and provide algorithms for finding such extensions. We further develop a theory of instantiation in the abstract, using the framework of Boolean attack formations and of conjunctive and disjunctive attacks. We discuss applications and compare critically with the existing related literature. (shrink)

We study here equiformity, the standard identity criterion for sentences. This notion was put forward by Lesniewski, mentioned by Tarski and defined explicitly by Presburger. At the practical level this criterion seems workable but if the notion of sentence is taken as a fundamental basis for logic and mathematics, it seems that this principle cannot be maintained without vicious circle. It seems also that equiformity has some semantical features ; maybe this is not so clear for individual signs but sentences (...) are often considered as meaningful combinations of signs. If meaning has to play a role, we are thus maybe in no better position than when dealing with identity criterion for propositions. In formal logic, one speaks rather about well-formed formulas, but closed formulas are called sentences because they are meaningful in the sense that they can be true or false. Formulas look better like mathematical objects than material inscriptions and equiformity does not seem to apply to them. Various congruencies can be considered as identities between formulas and in particular "to have the same logical form". One can say that the objects of study of logic are rather logical forms than sentences conceived as material inscriptions. (shrink)

A constructive proof is given which shows that every nonrecursive r.e. many-one degree is represented by the family of decision problems for partial implicational propositional calculi whose well-formed formulas contain at most two distinct variable symbols.

We investigate how the sentence choice semantics for propositional superposition logic developed in Tzouvaras could be extended so as to successfully apply to first-order superposition logic. There are two options for such an extension. The apparently more natural one is the formula choice semantics based on choice functions for pairs of arbitrary formulas of the basis language. It is proved however that the universal instantiation scheme of first-order logic, $\varphi \rightarrow \varphi $, is false, as a scheme of tautologies, (...) with respect to FCS. This causes the total failure of FCS as a candidate semantics. Then we turn to the other option, which is a variant of SCS, since it uses again choice functions for pairs of sentences only. This semantics however presupposes that the applicability of the connective | is restricted to quantifier-free sentences, and thus the class of well-formed formulas and sentences of the language is restricted too. Granted these syntactic restrictions, the usual axiomatizations of FOLS turn out to be sound and conditionally complete with respect to this second semantics, just like the corresponding systems of PLS. (shrink)

We present a multi-conclusion natural deduction calculus characterizing the dynamic reasoning typical of Adaptive Logics. The resulting system AdaptiveND is sound and complete with respect to the propositional fragment of adaptive logics based on CLuN. This appears to be the first tree-format presentation of the standard linear dynamic proof system typical of Adaptive Logics. It offers the advantage of full transparency in the formulation of locally derivable rules, a connection between restricted inference-rules and their adaptive counterpart, and the formulation of (...) abnormalities as a subtype of well-formed formulas. These features of the proposed calculus allow us to clarify the relation between defeasible and multiple-conclusion approaches to classical recapture. (shrink)

Analysis of quantifiers in Wittgenstein's Tractatus. A critical survey In the Tractatus Logico-Philosophicus, Wittgenstein distinguishes between what can and cannot be said in any language by the general form of propositions. I explain Wittgenstein's method and discuss Robert J. Fogelin's criticism of what he takes to be the incompleteness of Wittgenstein's general form of propositions in his exposition of the 'Naive Constructivism of the Tractatus.' I argue that Fogelin's objection is mistaken, and that, contrary to Fogelin's claim, Wittgenstein's method when (...) properly applied produces all of the well-formed formulas with mixed multiple quantification that Fogelin maintains it cannot provide. I conclude by offering a critical comparison of similar solutions proposed, among others, by P.T. Geach, Scott Soames, and Matthias Varga von Kibéd. (shrink)

The dissertation deals with problems in "logic", more precisely, it deals with particular formal systems aiming at capturing patterns of valid reasoning. Sequent calculi were proposed to characterize logical connectives via introduction rules. These systems customarily also have structural rules which allow one to rearrange the set of premises and conclusions. In the "structurally free logic" of Dunn and Meyer the structural rules are replaced by combinatory rules which allow the same reshuffling of formulae, and additionally introduce an explicit marker (...) for the application of the rule---the combinator. The dissertation gives syntactic extensions of such systems introducing conjunction and disjunction . Cut elimination is proved for these systems. ;Syntactic systems as a rule are accompanied by a semantics which interprets them. The extended systems are supplied with semantics using algebraic methods. First, the Lindenbaum algebras are formed, and then these algebras are represented in an algebra of sets. This gives a so called Kripke-style semantics for the systems. The representation for the distributive extension utilizes well-known techniques; it uses sets of prime filters and set theoretical operations on them to deal with conjunction and disjunction, plus a ternary accessibility relation to accommodate the intensional operators as fusion and implication. The representation theorem is proven generally, i.e., for arbitrary sets of combinators using the "squeeze lemma" of Routley and Meyer. ;The non-distributive calculi require a different representation since union and intersection are distributive. Two previous representations for lattices are overviewed, and a modification of the Hartonas-Dunn representation is successfully augmented with the intensional operations. Instead of sets of filters, sets of pairs of minimally inconsistent filters and ideals are used and the representation theorem is proven. The representation results provide soundness and completeness for the systems. The dissertation also investigates properties of dual combinators , proving a series of lemmas about dual combinatory systems not being Church-Rosser and being inconsistent. Combinatorially definable classes of lambda-terms are considered as well. (shrink)

We consider a quantifier-free language in which there are terms as well as formulas. The proposition-forming propositional operators are the usual ones, and the term-making term operators are the usual lattice theoretical ones. In addition there is a formula-making term operator, does. We study a new logic in which does is claimed to approximate some features of the informal concept the agent performs the action.

A logical system is studied whose well-formed representations consist of diagrams rather than formulas. The system, due to Shin [2, 3], is shown to be complete by an argument concerning maximally consistent sets of diagrams. The argument is complicated by the lack of a straight forward counterpart of atomic formulas for diagrams, and by the lack of a counterpart of negation for most diagrams.

A well-known result states that, over basic Kalmar elementary arithmetic EA, the induction schema for ∑n formulas is equivalent to the uniform reflection principle for ∑n + 1 formulas . We show that fragments of arithmetic axiomatized by various forms of induction rules admit a precise axiomatization in terms of reflection principles as well. Thus, the closure of EA under the induction rule for ∑n formulas is equivalent to ω times iterated ∑n reflection principle. Moreover, (...) for k < ω, k times iterated ∑n reflection principle over EA precisely corresponds to the extension of EA by k nested applications of ∑n induction rule.The above relationship holds in greater generality than just stated. In fact, we give general formulas characterizing in terms of iterated reflection principles the extension of any given theory by k nested applications of ∑n or Πn induction rules. In particular, the closure of a theory T under just one application of ∑1 induction rule is equivalent to T together with ∑1 reflection principle for each finite Π2 axiomatized subtheory of T.These results have closely parallel ones in the theory of subrecursive function classes. The rules under study correspond, in a canonical way, to natural closure operators on the classes of provably recursive functions. Thus, ∑1 induction rule precisely corresponds to the primitive recursive closure operator, and ∑1 collection rule, introduced below, corresponds to the elementary closure operator. (shrink)

A structure which generalizes formulas by including substitution terms is used to represent proofs in classical logic. These structures, called expansion trees, can be most easily understood as describing a tautologous substitution instance of a theorem. They also provide a computationally useful representation of classical proofs as first-class values. As values they are compact and can easily be manipulated and transformed. For example, we present an explicit transformations between expansion tree proofs and cut-free sequential proofs. A theorem prover which (...) represents proofs using expansion trees can use this transformation to present its proofs in more human-readable form. Also a very simple computation on expansion trees can transform them into Craig-style linear reasoning and into interpolants when they exist. We have chosen a sublogic of the Simple Theory of Types for our classical logic because it elegantly represents substitutions at all finite types through the use of the typed -calculus. Since all the proof-theoretic results we shall study depend heavily on properties of substitutions, using this logic has allowed us to strengthen and extend prior results: we are able to prove a strengthen form of the firstorder interpolation theorem as well as provide a correct description of Skolem functions and the Herbrand Universe. The latter are not straightforward generalization of their first-order definitions. (shrink)

The tableaux-constructions have a number of properties which advantageously distinguish them from equivalent axiomatic systems . The proofs in the form of tableaux-constructions have a full accordance with semantic interpretation and subformula property in the sense of Gentzen’s Hauptsatz. Method of tatleaux-construction gives a good substitute of Gentzen’s methods and thus opens a good perspective for the investigations of theoretical as well as applied aspects of logical calculi. It should be noted that application of tableau method in modal, tense, (...) relevant and other non-classical logics is connected with serious difficulties. Tableaux variants are constructed only for a few normal modal systems. As to relevant and paraconsistent logic, the absence of its tableau variants may be considered as a question of special interest. We shall formulate the tableaux for propositional modal system S4.1, S4.2, S4.3, S4.4 and relevant R∗ and E ∗ using Beth’s tableaux construction with indexed formulas. (shrink)

In Human Well-Being and the Natural Environment, Partha Dasgupta explores ways to measure the quality of life. In developing quality-of-life indices, he pays particular attention to the natural environment, illustrating how it can be incorporated, more generally, into economic reasoning in a seamless manner. Professor Dasgupta puts the theory that he develops to use in extended commentaries on the economics of population, poverty traps, global warming, structural adjustment programmes, and free trade, particularly in relation to poor countries. The result (...) is a treatise that goes beyond quality-of-life measures and offers a comprehensive account of the newly emergent subject of ecological economics.With the publication of this new paperback edition, Professor Dasgupta has taken the opportunity to update and revise his text in a number of ways, including developments to facilitate its current use on a number of gradate courses in environmental and resource economics. The treatment of the welfare economics of imperfect economies has been developed using new findings, and the Appendix has been expanded to include applications of the theory to a number of institutions, and to develop approximate formulae for estimating the value of environmental natural resources. (shrink)

Predicate modal formulas are considered as schemata of arithmetical formulas, where is interpreted as the standard formula of provability in a fixed sufficiently rich theory T in the language of arithmetic. QL T(T) and QL T are the sets of schemata of T-provable and true formulas, correspondingly. Solovay's well-known result — construction an arithmetical counterinterpretation by Kripke countermodel — is generalized on the predicate modal language; axiomatizations of the restrictions of QL T(T) and QL T by (...) formulas, which contain no variables different from x, are given by means of decidable prepositional bimodal systems; under the assumption that T is 1-complete, there is established the enumerability of the restrictions of QL T(T) and QL T by: 1) formulas in which the domains of different occurrences of don't intersect and 2) formulas of the form n A. (shrink)

Derived from Heidegger's interpretation of attractive force with a high volume of inspired beauty care and a master not only the followers. And in order to maintain this special, he followed the great classical psychologists: Ferdinand learning. He also won in the traditional school psychology professor at the certificate, but his real motive is not subject to the ancient hope臘Heidegger was carried out by the interpretation of the full amount of impact force. Nevertheless, Heidegger's classic is still up to the (...) United States: "true management and methods" to maintain significant influence over. Up to the United States as a major interpreter of Heidegger's thinking, and faithful friend. In about two more people, I turned to introduce three other in Heidegger, Gadamer's major research on the influence of the philosopher: Park Latin chart, sub-km Aristotle and Hegel. First we look at the future Park Latin chart, I think the focus on conversation and dialogue up to the United States and the "dialectic dialogue" concept. The relative importance of making it true, so true that people with reasonable doubt and dialogue. Although there are many plans to pull up to the United States Park effect, but I make up as two points and a U.S. interlocutor's talent and try to prove. I have given up by the United States with three coming from Aristotle's concept of sub-km: wise , mimetic and tragedy. Wise is to predict the results of practical wisdom for the rational, he does not see a formula-based learning, as can be, but based on life experience. That mimic the Department of Aristotle in the sub-km only copy, and is reasonable in real life, the ultimate communicator. Finally, the tragedy is not the only sub-km Aristotle considers the six parts of the structure, but compassion and fear the experience of change in the audience angle of view, it is up to the United States in view of the viewer's experience of understanding and application, is a kind of tragedy action meaningful participation and experience. Beneficiary of up to U.S. history in Hegel's awareness of personal, Hegel's dialectic, as well as their knowledge to the arts is the current acceptance of the senses. He does not agree with Hegel referred to the "art of the past things," Hegel explains how this point. Shortly we will be able to see the remarkable work of art as a nervous balcony. Let me give you a visit in Heidelberg, Heidegger's experience in the United States up to the lecture, he objected to clarify and to hide his own dialectic and Hegel's dialectic with links, because at the end of Hegel's philosophy of total abstraction knowledge. In the second part of this lecture, I turned to the analysis of Gadamer's thesis on the art of "the relevance of the United States," and Heidegger in this direction is the famous "Art works of origin> thesis compared. In the late writings, Heidegger shows that there is not his main independent and self-study will be presented in the art of the earth and the world as a tension. In Gadamer's thesis in art, he follows Heidegger in the hope臘by establishing the art of human culture, learn the origin of works of art ontology analysis. He discussed all the cultural roots of the game , the difference between symbolic meaning and religious ceremonies. But he formed an art theory of the problem to analyze, it also clarifies the classical art and contemporary abstract art. In these three elements: the game, symbols and festivals, art up to the United States to find a structure is more deep cultural roots. As in the early hope臘ceremony, dance performances and tragedy. Gadamer's encounter with the magnetic force of Heidegger's interpretations made him cautious not to become simply a follower of the great master. To maintain his independence, he studied with Paul Friedländer, the great classical philologist. He attained certification in classical philology to teach in the secondary schools, but his true motive was to be able to resist the powerful interpretations of Greek philosophy put forward by Heidegger. Nevertheless, Heidegger remained a major leavening influence on Gadamer's classic, Truth and Method, and Gadamer became a major interpreter of Heidegger's thought, and a constant friend. After a few comparisons between them, I turn to three major philosophers other than Heidegger who contributed concepts to Gadamer's masterwork: Plato, Aristotle, and Hegel. Regarding Plato, I point to the emphasis in Gadamer on dialogue and conversation and the concept of eumeneis elenchoi, the respect the opponent that recognizes that he could be right, so they join together in dialogue in quest of the truth. Although there are many other debts to Plato in Gadamer, I point to these two and testify to Gadamer's gifts as a conversationalist and debater. I single out three concepts of Aristotle that Gadamer used: phronesis, mimesis, and tragedy. Phronesis is the practical wisdom that goes beyond calculative reason. It is based not on formulas that can be learned but on experience of life . Mimesis in Aristotle is not just copying, but on a recognition that ultimately conveyed truth about life. Finally, tragedy for Aristotle is not just a structure with six parts but an experience of pity and terror that transformed the perspective of the viewer. This was important in the hermeneutics of Gadamer that looked at the viewer's experience of recognition and application, a participatory experience of the meaning of the action of the tragedy. Gadamer is indebted to Hegel for the historical character of consciousness, the Hegelian dialectic, and the recognition that that art is a sensuous representation of the real. He did not agree with Hegel that art was a thing of the past, and also explained what Hegel meant by this: we no longer saw art as a disclosure of the divine. I mention an experience I had of Heidegger's visit to Heidelberg, where he spoke after Gadamer's lecture rejecting his effort to connect his dialect of clearing and concealing with Hegelian dialectic, because Hegel's philosophy always ended in absolute knowledge. For the second major part of the lecture, I turn to an analysis of Gadamer's essay on art, The Relevance of the Beautiful , comparable in a way to Heidegger's famous lectures on The Origin of the Work of Art . In the latter work, Heidegger declares his independence of his masterwork and presents art in terms of the tension between earth and world. In Gadamer's essay on art, he goes beyond the Heideggerian emphasis on the ontology of the artwork by seeking to establish the anthropological roots of art in Greek culture. He discusses the roots of all culture in play, the significance of the symbol, and the meaning of religious festivals. But he begins with an analysis of the problem of formulating a theory of art that does justice both to classical art and contemporary nonrepresentational art. In all three elements, play, symbol, and festival, Gadamer finds a foundation for art in the deep roots of our culture as found in the ritual, dance, and tragic plays of ancient Greece. (shrink)

The Knowability Paradox is a logical argument that, starting from the plainly innocent assumption that every true proposition is knowable, reaches the strong conclusion that every true proposition is known; i.e. if there are unknown truths, there are unknowable truths. The paradox has been considered a problem for every theory assuming the Knowability Principle, according to which all truths are knowable and, in particular, for semantic anti-realist theories. A well known criticism to the Knowability Paradox is the so called (...) restriction strategy. It bounds the scope of the universal quantification in (KP) to a set of formulas whose logical form avoids the paradoxical conclusion. Specifically, Tennant suggests to restrict the quantifier in (KP) to propositions whose knowledge is provably inconsistent. He calls them Anti-Cartesian propositions and distinguished them in three kinds. In this paper we will not be concerned with the soundness of the restriction proposal and the criticisms it has received. Rather, we are interested in analyzing the proposed distinction. We argue that Tennant’s distinction is problematic because it is not completely clear, it is not grounded on an adequate logical analysis, and it is incomplete. We suggest an alternative distinction, and we give some reasons for accepting it: it results logically grounded and more complete than Tennant’s one, inclusive of it and independent from non-epistemic notions. (shrink)

Formal verification involves the use of logical and computational methods to establish claims that are expressed in precise mathematical terms. These can include ordinary mathematical theorems, as well as claims that pieces of hardware or software, network protocols, and mechanical and hybrid systems meet their specifications. In practice, there is not a sharp distinction between verifying a piece of mathematics and verifying the correctness of a system: formal verification requires describing hardware and software systems in mathematical terms, at which (...) point establishing claims as to their correctness becomes a form of theorem proving. Conversely, the proof of a mathematical theorem may require a lengthy computation, in which case verifying the truth of the theorem requires verifying that the computation does what it is supposed to do. The gold standard for supporting a mathematical claim is to provide a proof, and twentieth-century developments in logic show most if not all conventional proof methods can be reduced to a small set of axioms and rules in any of a number of foundational systems. With this reduction, there are two ways that a computer can help establish a claim: it can help find a proof in the first place, and it can help verify that a purported proof is correct. Automated theorem proving focuses on the “finding” aspect. Resolution theorem provers, tableau theorem provers, fast satisfiability solvers, and so on provide means of establishing the validity of formulas in propositional and first-order logic. Other systems provide search procedures and decision procedures for specific languages and domains, such as linear or nonlinear expressions over the integers or the real numbers. Architectures like SMT combine domain-general search methods with domain-specific procedures. Computer algebra systems and specialized mathematical software packages provide means of carrying out mathematical computations, establishing mathematical bounds, or finding mathematical objects. A calculation can be viewed as a proof as well, and these systems, too, help establish mathematical claims. Automated reasoning systems strive for power and efficiency, often at the expense of guaranteed soundness. Such systems can have bugs, and it can be difficult to ensure that the results they deliver are correct. In contrast, interactive theorem proving focuses on the “verification” aspect of theorem proving, requiring that every claim is supported by a proof in a suitable axiomatic foundation. This sets a very high standard: every rule of inference and every step of a calculation has to be justified by appealing to prior definitions and theorems, all the way down to basic axioms and rules. In fact, most such systems provide fully elaborated “proof objects” that can be communicated to other systems and checked independently. Constructing such proofs typically requires much more input and interaction from users, but it allows us to obtain deeper and more complex proofs. The Lean Theorem Prover aims to bridge the gap between interactive and automated theorem proving, by situating automated tools and methods in a framework that supports user interaction and the construction of fully specified axiomatic proofs. The goal is to support both mathematical reasoning and reasoning about complex systems, and to verify claims in both domains. (shrink)

Dynamic predicate logic (DPL), presented in [5] as a formalism for representing anaphoric linking in natural language, can be viewed as a fragment of a well known formalism for reasoning about imperative programming [6]. An interesting difference from other forms of dynamic logic is that the distinction between formulas and programs gets dropped: DPL formulas can be viewed as programs. In this paper we show that DPL is in fact the basis of a hierarchy of formulas-as-programs (...) languages. (shrink)

ABSTRACT The welcome expansion of kairos beyond its traditional locus in public debate to a broad range of discourse forms and persuasive actions has not been matched by a reevaluation of the temporal logic of kairos, which is still seen as located in teleologic time. This article suggests that Walter Benjamin’s understanding of time could refigure kairos as a nonteleological relationship among past, present, and future. Benjamin provides a theoretical rationale for kairotic action that is distributed in time and space (...) and accounts for kairos of objects, places, technologies, and works of art. These temporal affordances, usually developed separately in contemporary theory, are deeply connected in Benjamin’s writing; his understanding of time therefore integrates currently unconnected lines of research and supports a fluid but coherent understanding of kairotic agency. (shrink)

Rachel Wells turns to the examination of three recent artistic practices, which integrate facts in their work not as an antagonistic other but as a constitutive element to their efficacy and ethics. She argues, that in introducing news, factual actions, or objects with traces of factual events, Alfredo Jaar, Jeremy Deller and Martin Creed use facts in order to retract from the position of art as an expression of artistic freedom and subjectivity and thus as the opposite of fact. Instead, (...) she states that by introducing the factual the artists underline each in their own way the instability of given eptistemological and ethical frameworks. Far from being a mere relativist pose, Wells understands this denial of a stable subjectivist position as a reconfigured sense of “decision”—perhaps in the sense of Nancy’s articulation of a “decision of existence—that lets the factual take precedence over the control in and of the artwork as a heightened form of responsiveness and responsibility. Whereas Jaar uses the factual to engage overt political action, Deller presents facts that avoid taking an overtly critical perspective forcing the viewer to think about political events. Creed in contrast seeks for the interpretation of the past altogether, would avoid to take over the responsibility of taking a position. Whereas David Hume stated famously, that reasoning concerning matter of fact is founded in causality and Immanuel Kant concludes, that responsibility and freedom begins where causality ends, Wells understands the positions of Jaar, Deller and Creed as an attempt to reconcile the realm of the factual and the realm of the moral. Responsibility would then arise exactly out of the insight in the impossibility to ground moral stances in rationality and causality and in an attempt to use causality to demonstrate this impossibility. (shrink)

Turing's analysis of computation is a fundamental part of the background of cognitive science. In this paper it is argued that a re‐interpretation of Turing's work is required to underpin theorizing about cognitive architecture. It is claimed that the symbol systems view of the mind, which is the conventional way of understanding how Turing's work impacts on cognitive science, is deeply flawed. There is an alternative interpretation that is more faithful to Turing's original insights, avoids the criticisms made of the (...) symbol systems approach and is compatible with the growing interest in agent‐environment interaction. It is argued that this interpretation should form the basis for theories of cognitive architecture. (shrink)

The article will argue that Charles Sanders Peirce's concepts of the ‘Dynamics of Belief and Doubt’, the ‘Fixation of Belief’ as well as ‘habits of belief’ taken together comprise a theory of learning. The ‘dynamics of belief and doubt’ are Peirce's explanation for the process of changing from one belief to another. Teaching, then, would be an attempt to control that process. Teaching critical thinking represents an attempt to teach the learner to regulate and discipline his or her own (...) ‘settlement of belief’. The ‘settlement of belief’ takes four different forms based on doubt. Peirce's concept of the ‘habits of belief’ refers to the inner and outer constraints placed both on belief as such and belief as it becomes action. The article may be read as both an exegesis of learning and as a pedagogical guide for teaching critical thinking to college students. (shrink)

Unifiability of terms (and formulas) and structural completeness in the variety of relation algebras RA and in the products of modal logic S5 is investigated. Nonunifiable terms (formulas) which are satisfiable in varieties (in logics) are exhibited. Consequently, RA and products of S5 as well as representable diagonal-free n-dimensional cylindric algebras, RDfn, are almost structurally complete but not structurally complete. In case of S5n a basis for admissible rules and the form of all passive rules are provided.

It is well known that there is a categorical equivalence between lattice-ordered Abelian groups (or l-groups) and conical BCK-algebras (see [COR 80]). The aim of this paper is to study this equivalence from the perspective of logic, in particular, to study the relationship between two deductive systems: conical logic Co and a logic of l-groups, Balo. In [GAL 04] the authors introduce a system Bal which models the logic of balance of opposing forces with a single distinguished truth value, (...) that represents equilibrium. Its equivalent algebraic semantics BAL (via Blok-Pigozzi's construction) is definitionally equivalent to the variety of l-groups. In this paper we define the system Balo which is equivalent to Bal and whose Lindenbaum-Tarski algebra is an l-group. On the other hand, we define the conic logic Co and we prove that it can be naturally merged in the system Balo. Also, we prove that every formula of Balo has a normal form that depends on translations of formulas of Co. (shrink)

This book is conceived as part of a systematic philosophy of values. Neither philosophies of value nor systematic philosophies are in fashion. It is hoped that this work will make a contribution toward their reappraisal. Classically, political philosophy was considered a part of philosophic systems, as the basic ideas of the philosophy applied to politics. Its relative neglect by the predominant school of philosophy in America and Britain has meant that certain ideas and issues in philosophy are in danger of (...) erasure by default. The neglect of political philosophy has meant, however, that ideologies dominate political discussion. The field of political discourse has, in effect, been yielded or ceded to the ideologues. Their views, concepts, statements of the issues, and solutions—in a word, the ultimate legitimacy of their approach—have been tacitly accepted. Many philosophers have never discussed ideology in relation to, and in the context of political philosophy in our time. More importantly, the connection between ideology and contemporary events has not received serious philosophic examination. One basis for this attitude may be the ideal of a "value free" social science. The well known thesis of Daniel Bell's book, "the end of ideology," has diverted attention from its study. Yet ideological politics is still with us in the form of ideologically defined political parties and political conflicts in which the ideology of the conflicting groups define the issues. Part I examines the link between ideology, totalitarianism and Plato’s ideal of the “philosopher-king.” Ideology is articulated by intellectuals seeking power, or attached to a party or faction seeking power. It is applied totalistically through bureaucracy and technology. We will go on in Part II to a critique of political essentialism. Essential models, combined with political motives and ideological formulas are the basis for total politicization. Thus totalitarianism will have been analyzed into root essential models, articulated into totalistic ideologies, by politically minded intellectuals, using a formula which politicizes all categories. Chapter five contrasts the moral values of political philosophy with the politicized standards of ideology. Chapter six contrasts the privacy and freedom requisite to evaluation of personal values, and to genuine happiness, with the total publicity of ideology. An entirely new grounding relation for politics is explicated in this book. (shrink)

We consider a family of logical systems for representing entailment relations of various kinds. This family has its root in the logic of first-degree entailment formulated as a binary consequence system, i.e. a proof system dealing with the expressions of the form \, where both \ and \ are single formulas. We generalize this approach by constructing consequence systems that allow manipulating with sets of formulas, either to the right or left of the turnstile. In this way, it (...) is possible to capture proof-theoretically not only the entailment relation of the standard four-valued Belnap’s logic, but also its dual version, as well as some of their interesting extensions. The proof systems we propose are, in a sense, of a hybrid Hilbert–Gentzen nature. We examine some important properties of these systems and establish their completeness with respect to the corresponding entailment relations. (shrink)

The expectation is fulfilled, but in an unexpected way. 'The first studies toward this book were addressed to topics in the field of ethics' ; but our author, like Wagner composing 'Der Ring des Nibelungen', found himself becoming preoccupied with prolegomena. To these the present volume is wholly devoted. In order to establish its fundamental thesis that valuation is a form of empirical knowledge, two preparatory discussions are called for. An analysis of empirical knowledge in general is one of these; (...) but there is an inquiry properly prior even to this, an examination of the topic of meaning. The articulation of the book is accordingly tripartite; and Book I Meaning and Analytic Truth, Book II Empirical Knowledge, and Book III Valuation are of roughly equal length. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 35.2 (2002) 120-137 [Access article in PDF] Discursive Mobility and Double Consciousness in S. Weir Mitchell and W.E.B. Du Bois 1 Susan Wells Here are two stories about double consciousness: they will become, eventually, stories about the public sphere: W. E. B. Du Bois formulating the theory of double consciousness, and S. Weir Mitchell presenting Mary Reynolds's case history, an instance of a mental disorder known (...) in the nineteenth century as double consciousness. I will begin with Du Bois's story, by far the most familiar to us: few texts are more central to contemporary rhetoric or cultural studies than the discussion of double consciousness in the opening pages of The Souls of Black Folk. 2 In the theory of double consciousness, Du Bois concentrated his contradictory experiences of scholarship, activism, social isolation, and active cosmopolitanism. Double consciousness was a methodological constraint that enabled Du Bois to build into the structure of The Souls of Black Folk a recognition that the complexity of African American life requires more than one perspective. And double consciousness was also a technique of writing, shaping the ironic and urgent voice of the book, by turns indignant and tender, eloquent and colloquial, a form of double address to both African American and Caucasian readers that allowed Du Bois to be two places at once. Double consciousness therefore controlled both the development and the presentation of The Souls of Black Folk, from the arc of its argument to its formal elements, includingDu Bois's famous use of chapter epigraphs to link canonic poetry with the melodies of the sorrow songs. Like the most relentlessly formal high modernist poem, the book continually enacts in its form not only its informing idea, but the circumstances of its composition and the constraints that shape its reading.The book's initial essay, "Of Our Spiritual Strivings," offers an analysis of double consciousness as it is shaped by three central categories of modernity: temporality, embodiment, and expertise. Double consciousness is located in time, in history; it is placed in a story of the epochal succession [End Page 120] of races, and in the specific history of slavery. Double consciousness emerges as strategically shaping African American responses to the problems of disenfranchisement, poverty, and the denial of civil rights after the suppression of Reconstruction. The historical sections of The Souls of Black Folk, therefore, do not simply rectify the facts, setting the record straight on Reconstruction or Afrocentric scholar and theorist Alexander Crumell. These local arguments all motivate an understanding of consciousness as temporally constituted, so that the work of previous generations can be effective only when it is appropriated in the present. Such appropriation is supported and mediated by the form of the book: Du Bois ends with an invocation to "God the Reader," who alone can ensure that "these crooked marks on a fragile leaf be not indeed THE END" (19).Double consciousness is also connected with embodiment, specifically the embodiment of African Americans, externalized and displaced in two images: blood, which I will discuss later in the essay, and the veil or caul that grants second sight. Like skin color, the caul is an inconsequential physical object invested with enormous symbolic power (8); it is a mark of origins that foretells the future. The "second sight" offered to the Negro is a vision of "two warring ideals," a vision that can barely be supported by "one dark body, whose dogged strength alone keeps it from being torn asunder"(9). At moments in The Souls of Black Folk, the veil is generalized, and becomes a physical barrier between the white world and the world of African American culture; the work of separating these worlds, of rendering them invisible to one another, is staged on the bodies of African Americans. The veil is usually seen as a separation between the races, something that has happened ("Feeling deeply and keenly the tendencies and opportunities of the age in which they live, their souls are bitter at the fate which drops the Veil... (shrink)

I reconstruct J. H. Lambert’s views on how practical grounds relate to epistemic features, such as certainty. I argue, first, that Lambert’s account of moral certainty does not involve any distinctively practical influence on theoretical belief. However, it does present an interesting form of fallibilism about justification as well as a denial of a tight link between knowledge and action. Second, I argue that for Lambert, the persistence principle that underwrites induction is supported by practical reasons to believe; this (...) indicates that Lambert is a moderate pragmatist about reasons for theoretical belief. (shrink)

The paper begins as a response to Tom Rockmore's thesis that contemporary pragmatism is a healthy “confusion” of disparate views. While Rockmore sees the need of some of today's pragmatists to provide a motivation for what he calls “epistemic optimism,” I contend that the crucial question of pragmatism, the problem of pragmatism, is the ontological status of pragmatic meaning. Thus rather than a mere “epistemic optimism,” I call upon pragmatists to assert a fallible yet unabashedly metaphysical optimism. The argument supporting (...) this claim is made in the context of Peirce's “The Architecture of Theories.” In “The Architecture of Theories” Peirce opens the door to a pragmatic metaphysics while at the same time committing the error of subordinating truths and reality to “the long run of inquiry.” Rockmore suggest that the solution may lie in a return to Kant's notion of the “powers of the mind.” However, it is my contention that a solution to this problem cannot be found within Kant at all. I shall argue here that until contemporary pragmatism decisively extracts itself from the Kantian paradigm, the pragmatic philosophic value of pragmatic meaning will always be qualified, conditional and ontologically subordinated, having the same effect upon the standing of pragmatism as a philosophy as well. Moreover, I shall endeavor to show that when the Kantian paradigm is finally abandoned, pragmatism's classic difficulties with realism and what Peircc called “the long run” of scientific inquiry can also be resolved. Kantian “powers of the mind” and constructivist “epistemological optimism” would then be transformed into what I shall call unrestricted pragmatism. On the other hand if the Kantian impediment is not overcome, these difficulties will continue to form the basis of a more sceptical and traditionally restricted pragmatism, one which lacks the confidence desired by both Rockmore and myself. (shrink)

A defense of Kant’s moral philosophy. The author seeks to counteract those interpretations of Kant that restrict their focus to the Groundwork of the Metaphysics of Morals. He argues that one must look at the whole of Kant’s writings, the earlier and later ethical writings as well as the theoretical works. This makes it possible for him to challenge the popular misconceptions of Kant’s teaching: the overemphasis on the correct motive of an action, the mistaken impression that consequences are (...) of no consequence when evaluating the moral worth of an act, and the overattention paid to logical contradiction as the test of a maxim’s morality. The Groundwork is not simply a conclusion of Kant’s early reflections on morality, but it also represents a new departure whose full significance is not seen until the later works. With the Groundwork Kant realizes that morality cannot be established on the grounds set out by the Critique of Pure Reason but requires an independent foundation. His new concept of practical necessity represents a revolution in morality. It is a mistake, then, to read the practical philosophy solely in the light of the theoretical critique. Though founded on a blind "fact of reason," Kant’s teaching is yet not abstract, overly formalistic, or rigoristic. "One must go through all the different formulas [of the categorical imperative] to understand the concept of moral judgment". Rossvaer’s rethinking brings him to stress that "the categorical imperative has no validity beyond being the form of... sensuous striving". This contention that the intellectual and sensuous faculties are not to be radically divorced leads to the ultimate intent of Rossvaer’s work. He argues that the categorical imperative is a principle of execution and only assumes its fullest form in a social philosophy. Consideration of Kant’s notion of the highest good, especially as it is developed in the later works on religion and history, allows Rossvaer to argue for the social and historical relevance of Kant’s teaching. "Since the highest good cannot be justified within an individualistic perspective, but only within a philosophy which takes up society as a problem, morality is meaningless from a human point of view unless we consider ourselves obligated to realize a universal, ethical community". With this, the kingdom of ends is transformed into an historical idealism, practical philosophy becomes a theory of action, and Kant turns out to be not so different from his detractors, Fichte, Hegel, Marx, Habermas, and others. Yet the historicization of the moral agent is yet not complete in Kant. The moral agent retains his critical standpoint, that is the distinction between rationality and the social system. Yet one is brought to ask how this critical distance can be maintained. To what extent does Kant’s overstepping the bounds of theoretical reason also entail the loss of that critical validity won by the first Critique? And, if one is forced in the end to justify one’s practical philosophy only by a social philosophy which does not find its foundation in a theoretical critique, then is the original fear of the first Critique confirmed, that morality may be meaningless after all? (shrink)

This article provides an overview of computer based catalogue systems designed for use by library clients, seeing present day ‘discovery systems’ on the same trajectory as the older ‘online public access catalogues’ which they are gradually replacing, both in technical development and their approach to client use scenarios. It traces the history of the OPAC/discovery system from its origins in the library automation of the 1960s through to the present and discusses the main technical standards which have formed its (...) development. The article goes on to consider questions relating to the usability of electronic library catalogues and highlights semiotic and ethical issues inherent to their design. It concludes with reflections on the future of the OPAC/discovery system in an information universe apparently dominated by the internet search engine. (shrink)

This conceptual paper explores the theoretical possibilities of posthumanism and presents ecologies of repair as a heuristic device to explore the association modes of different entities, which, when confronted with the effects of human-induced destructive events, seek to repair the damage and transform the conditions of coexistence of various life forms. The central idea is that severe socio-environmental crisis caused by an intensification of industrial activity are conducive to observing new sociomaterial configurations and affective dispositions that, through the reorganization of (...) practices of resistance, remediation, and mutual care, are oriented to generating reparative and/or transformative processes from damaged ecologies and communities. Crises constitute true ontological experimentation processes where the presence of other-than-human natures, and of artifacts or devices that participate in reparative actions, become visible. A post-human approach to nature allows us to use languages and methodologies that do not restrict the emergence of assemblages under the assumption of theira prioriontological separation, but rather examine their reparative potential based on the efficacy of situated relationships. Methodologically, transdisciplinarity is relevant, with ethnography and other engaged methods applied over units of observation and experience called socio-geo-ecologies. The relevant attributes of these socio-geo-ecologies, beyond the individual, community, or institutional aspects, are the specific geological characteristics that make possible an entanglement of interdependent relationships between human and non-human agents. The conceptual analysis is illustrated with empirical examples stemming from socio-geo-ecologies researched in Southern Chile. (shrink)