ABSTRACT This paper deals with two cases of acquisition and construction of Van de Graaff accelerators in 1950s Latin America, at the National Autonomous University of Mexico and the University of São Paulo, respectively. A comparative approach allows us to appreciate the significance of this particular technology within scientific, cultural, commercial, and political processes. Van de Graaff accelerators appeared as an affordable technology to engage in experimental nuclear physics and to be part of the atomic age. The circumstances that (...) motivated physics communities in Brazil and Mexico to choose this specific technology took shape in close interactions with US institutions and scientists. These inter-American alliances involved precisely the main companies and groups that competed for the market of this technology around the world. These accelerators also intertwined with the building of campuses for two major Latin American universities, occupying then a singular place (physically and symbolically) within their execution. This paper engages with comparison for the common goal of going beyond frameworks and methodologies tied to the nation, while integrating the study of connections and interactions, as well as the interplay of multiple scales. (shrink)

There exists a countable structure of Scott rank where and where the -theory of is not ω-categorical. The Scott rank of a model is the least ordinal β where the model is prime in its -theory. Most well-known models with unbounded atoms below also realize a non-principal -type; such a model that preserves the Σ1-admissibility of will have Scott rank . Makkai [M. Makkai, An example concerning Scott heights, J. Symbolic Logic 46 301–318. [4]] produces a hyperarithmetical model of Scott (...) rank whose -theory is ω-categorical. A computable variant of Makkai’s example is produced in [W. Calvert, S.S. Goncharov, J.F. Knight, J. Millar, Categoricity of computable infinitary theories, Arch. Math. Logic . [1]; J. Knight, J. Millar, Computable structures of rank J. Math. Logic . [2]]. (shrink)

Let me attempt a drastic summary, or symbolic reduction, of Mr. Foss's adeptly metaphorical exposition. The use of the copula is, implicit in the appositive series, will do some violence to the complexity of the argument, but since causes and parts are frowned on by the same argument, the simpler arrangement cannot be altogether out of keeping. In logical and grammatical terms, we have on two sides of a profound ledger: "symbolic reduction," the divisive subject and predicate,--and "metaphoric process," the (...) underlying and unifying energy of the proposition, the subjectum. The negations of dialectic operate to show the insufficiency of symbolic concepts and are the "door to philosophic truth." And in ontological terms, we have on the one hand number, time, space, cause and effect, coincidence and contingency; and on the other the different, the naught, the apeiron, the potential, the tension of process, freedom and necessity in metaphoric lawful unity. There are two closely similar extremes of reduction between which one locates the transcendent philosophy of metaphor: that of sensationalism, the philosophy of the brute and atomic, and that of rationalism, the philosophy of expedient action. And in more or less theological terms, we have on the one hand the environment and its complement the ego, purposive and possessive; on the other, World, the I and the Thou, prayer, sin and grace in the metaphorical unity of consciousness, the widening power of personality in intercession or metaphorical representation. On the one hand, birth and death, past and future, and a present extending ad libitum into either; on the other, the eternal present of the integrated process stretching over past and future, expressed in its purest form in art. And so in aesthetic terms: on the one hand catharsis, a rationalized mixture of the ego's pleasure and pain, asceticism and hedonism, play; on the other, drama--especially tragedy, which par excellence action--Eudaimonia, purification, artistic distance, stylization, imagination, conscience, love. On the one hand, comedy in the sense of farce, environment symbolically reduced, actions and persons according to type, the mechanism of means and ends, rules, rituals, tricks, chance, the caricature of symbolic fixation--producing laughter: on the other hand, true and great comedy, the attempt to understand life in all its contradictions, producing the smile. (shrink)

Assume T is stable, small and Φ(x) is a formula of L(T). We study the impact on $T\lceil\Phi$ of naming finitely many elements of a model of T. We consider the cases of $T\lceil\Phi$ which is ω-stable or superstable of finite rank. In these cases we prove that if T has $ countable models and Q = Φ(M) is countable and atomic or saturated, then any good type in S(Q) is τ-stable. If $T\lceil\Phi$ is ω-stable and (bounded, 1-based or (...) of finite rank) with $I(T, \aleph_0) , then we prove that every good p ∈ S(Q) is τ-stable for any countable Q. The proofs of these results lead to several new properties of small stable theories, particularly of types of finite weight in such theories. (shrink)

The organization of the mobile atomic exhibition, Mostra Atomica, designed by the United States Information Service to travel through Italy in 1954–55, had to meet technical, scientific, artistic, and political challenges. The head of the group in charge of the exhibition was architect Peter G. Harnden whose pedigree in the intelligence and training in architecture were an ideal match for leading the unit dedicated to exhibitions. The political sensitivity of the Mostra Atomica also required the intervention of the Italian (...) Ministry of the Interior to guarantee safe mobility and secure shows. In every major town, American and British diplomats attended the local opening ceremony, while the very symbol of science diplomacy was Enrico Fermi, whose recorded message praised international cooperation. All in all, the USIS campaign promoting peaceful applications of nuclear physics was successful in reaching and involving Italian society. Visual and spatial aesthetics were particularly relevant: the geometrical design of the exposition rooms conveyed a strong sense of modernity that contrasted with the artistic heritage of Italian cities. The present article is based on archival files, newspaper reports, and photographs that document who was responsible for planning, setting up, and reporting this Cold War propaganda event. (shrink)

It has been known for six years that the restriction of Girard's polymorphic system $\text{\bfseries\upshape F}$ to atomic universal instantiations interprets the full fragment of the intuitionistic propositional calculus. We firstly observe that Tait's method of “convertibility” applies quite naturally to the proof of strong normalization of the restricted Girard system. We then show that each $\beta$-reduction step of the full intuitionistic propositional calculus translates into one or more $\beta\eta$-reduction steps in the restricted Girard system. As a consequence, we (...) obtain a novel and perspicuous proof of the strong normalization property for the full intuitionistic propositional calculus. It is noticed that this novel proof bestows a crucial role to $\eta$-conversions. (shrink)

We give an example of a countable theory $T$ such that for every cardinal $\lambda \geq \aleph_2$ there is a fully indiscernible set $A$ of power $\lambda$ such that the principal types are dense over $A$, yet there is no atomic model of $T$ over $A$. In particular, $T$ is a theory of size $\lambda$ where the principal types are dense, yet $T$ has no atomic model.

The Czechoslovak-Soviet exhibition ‘Atoms for Peace’ was held in Prague and Bratislava in 1956. This exhibition became a symbol of Czechoslovak-Soviet ‘friendship’ and Soviet influence on the Czechoslovak nuclear programme. At the Brussels World’s Fair in 1958 (Expo 58), one of the most popular Czechoslovak exhibits was the betatron, which would become a symbol of Czechoslovak nuclear pride. The article analyzes the planning, creation and reception of these two exhibitions, as well as the popular image of the Czechoslovak betatron in (...) the Czechoslovak press and literature of that time. It shows how, in Czechoslovakia, the paradigm of Czechoslovak-Soviet friendship and Soviet dominance converged and became entangled with the effort to present Czechoslovakia as an industrially developed country capable of building the nation’s nuclear industry (partly) on its own. One of the results of this entanglement was the betatron – a highly successful and celebrated Czechoslovak nuclear exhibit that captivated both domestic and international audiences. (shrink)

This chapter focuses on one historically important approach to computationalism about thought. According to "the classical computational theory of mind" (CTM), thinking involves the algorithmic manipulation of mental symbols. The chapter reviews CTM and the related language of thought (LOT) position, urging that the orthodox position, associated with the groundbreaking work of Jerry Fodor, has failed to specify a key component: the notion of a mental symbol. It clarifies the notion of a LOT symbol and explores an approach different (...) from the orthodox, Fodorian LOT/CTM. The LOT position is a leading approach to the computational nature of thought. A key feature of LOT is that its mental representations have a combinatorial syntax. A representational system has a combinatorial syntax when it employs a finite store of atomic representations, which can be combined to form compound representations, which can then be combined to form further compound representations. (shrink)

A wide range of systems appear to perform computation: what common features do they share? I consider three examples, a digital computer, a neural network and an analogue route finding system based on soap-bubbles. The common feature of these systems is that they have autonomous dynamics — their states will change over time without additional external influence. We can take advantage of these dynamics if we understand them well enough to map a problem we want to solve onto them. Programming (...) consists of arranging the starting state of a system so that the effects of the system''s dynamics on some of its variables corresponds to the effects of the equations which describe the problem to be solved on their variables. The measured dynamics of a system, and hence the computation it may be performing, depend on the variables of the system we choose to attend to. Although we cannot determine which are the appropriate variables to measure in a system whose computation basis is unknown to us I go on to discuss how grammatical classifications of computational tasks and symbolic machine reconstruction techniques may allow us to rule out some measurements of a system from contributing to computation of particular tasks. Finally I suggest that these arguments and techniques imply that symbolic descriptions of the computation underlying cognition should be stochastic and that symbols in these descriptions may not be atomic but may have contents in alternative descriptions. (shrink)

It is common to distinguish two great families of representation. Symbolic representations include logical and mathematical symbols, words, and complex linguistic expressions. Iconic representations include dials, diagrams, maps, pictures, 3-dimensional models, and depictive gestures. This essay describes and motivates a new way of distinguishing iconic from symbolic representation. It locates the difference not in the signs themselves, nor in the contents they express, but in the semantic rules by which signs are associated with contents. The two kinds of rule (...) have divergent forms, occupying opposite poles on a spectrum of naturalness. Symbolic rules are composed entirely of primitive juxtapositions of sign types with contents, while iconic rules determine contents entirely by uniform natural relations with sign types. This distinction is marked explicitly in the formal semantics of familiar sign systems, both for atomic first-order representations, like words, pixel colors, and dials, and for complex second-order representations, like sentences, diagrams, and pictures. (shrink)

A cylindric algebra atom structure is said to be strongly representable if all atomic cylindric algebras with that atom structure are representable. This is equivalent to saying that the full complex algebra of the atom structure is a representable cylindric algebra. We show that for any finite n >3, the class of all strongly representable n-dimensional cylindric algebra atom structures is not closed under ultraproducts and is therefore not elementary. Our proof is based on the following construction. From an (...) arbitrary undirected, loop-free graph Γ, we construct an n-dimensional atom structure E(Γ), and prove, for infinite Γ, that E(Γ) is a strongly representable cylindric algebra atom structure if and only if the chromatic number of Γ is infinite. A construction of Erdős shows that there are graphs (k < ω)with infinite chromatic number, but having a non-principal ultraproduct $\prod _D\Gamma _k $ whose chromatic number is just two. It follows that $E(\Gamma _k )$ is strongly representable (each k < ω) but $\Pi _D E(\Gamma _k)$ is not. (shrink)

Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material inference and Greg Restall’s (...) bilateralist interpretation of the multiple conclusion sequent calculus, I present a proof-theoretic semantics for atomic sentences and their constituent names and predicates. The resulting system has several interesting features: (1) the rules are harmonious and stable; (2) the rules create a structure analogous to familiar model-theoretic semantics; and (3) the semantics is compositional, in that the rules for atomic sentences are determined by those for their constituent names and predicates. (shrink)

The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De Morgan monoids may (...) be mapped by noninjective homomorphisms. The homomorphic preimages of C4 within DMM constitute a proper quasivariety, which is shown to have a largest subvariety U. The covers of the variety within U are revealed here. There are just ten of them. In exactly six of these ten varieties, all nontrivial members have C4 as a retract. In the varietal join of those six classes, every subquasivariety is a variety—in fact, every finite subdirectly irreducible algebra is projective. Beyond U, all covers of [or of ] within DMM are discriminator varieties. Of these, we identify infinitely many that are finitely generated, and some that are not. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids. (shrink)

In this paper, an extension of first order logic is introduced. In such logics atomic formulas may have infinite lengths. An Omitting Types Theorem is proved.

An examination of the earliest creation traditions and symbols of China and their similarities to those of other ancient cultures Reveals the deep parallels between early Chinese words and those of other ancient creation traditions such as the hieroglyphics of ancient Egypt Explores the 8 stages of creation in Taoism and the cosmological origins of Chinese ancestor worship, the zodiac, the mandala, and the I Ching Provides further evidence that the cosmology of all ancient cultures arose from a single (...) now-lost source Building on his extensive research into the sacred symbols and creation myths of the Dogon of Africa and those of ancient Egypt, India, and Tibet, Laird Scranton investigates the myths, symbols, and traditions of prehistoric China, providing further evidence that the cosmology of all ancient cultures arose from a single now-lost source. Scranton explores the fundamental similarities between the language that defined ancient Chinese cosmology and that of other creation traditions, revealing the connections between the phonetic structure of the words, their glyphs, and their use. He demonstrates striking parallels between the earliest systems of writing in China and the hieroglyphs of ancient Egypt. He examines the 8 levels of creation in Taoism and the cosmological origins of Chinese ancestor worship, mythical emperors, the zodiac, the mandala, and the I Ching. He details the fundamental principles of land-use in ancient China in relation to the symbolism of a Buddhist stupa and the Dogon granary, ritual shrines that are also the central symbol of other creation traditions. Understanding the true meanings of these symbol complexes also reveals the sophisticated scientific understanding of these ancient cultures, for these creation symbols directly correlate with our modern understanding of atoms and the energetic makeup of matter. In exploring Chinese cosmological traditions, Scranton sheds new light on the contention that the sacred knowledge of the ancients is the legacy of an earlier culture who gave primitive humanity the tools they needed to birth the first known civilizations. (shrink)

To be, or not to be, that is the question…In his wonderful Facts and Mysteries, Martinus Veltman terminates a section with an anecdote: “When quarks were not immediately discovered after the introduction by Gell-Mann he took to calling them symbolic, saying they were indices. In the early seventies I met him at CERN and he again said something in that spirit. I then jumped up, coming down with some impact that made the floor tremble, and asked him: Do I look (...) like a heap of indices? This visibly rattled him, and indeed after that he no more advocated this vision, at least not as far as I know” (see page 240 in Veltman 2003). Although it is probable that Murray Gell-Mann, the inventor of quarks, has changed his mind regarding the reality of his symbols after this tough conversation, even later in the start of eighties the reality of quarks, as basic constituents of protons and neutrons, was a matter of disputes and exchanges (Shrader-Frechette 1982a, b; Albright 1982; Gruender 1982). A g. (shrink)

In 1971, President Richard Nixon declared a “war against cancer,” stating that “the same kind of concentrated effort that split the atom and took man to the moon should be turned toward conquering this dread disease.” Nixon signed the National Cancer Act, and shortly thereafter the first national registry listing all ongoing clinical trials for cancer therapies was published by the National Cancer Institute. The registry was proposed by Mary Lasker (“a patroness and advocate of clinical research”) to help doctors (...) find open trials in which to enroll their patients and to help researchers maintain a steady supply of research participants. The registry appeared to be a win for doctors, patients, researchers, and pharmaceutical companies alike. However, it ended up exposing corrupt practices and tensions between ethics, the corporate need for profits, and public health goals. How did this happen? (shrink)

This paper examines the negative response to Dalton’s atomic symbols by situating them in the context of the normative eighteenth-century representational system of affinity tables. Aesthetic analysis of the affinity tables reveals them as schema embedded with a potent functionalist empiricism. In contrast, the aesthetics of Dalton's symbols is associated with hypothetico-deductivism and alchemical iconicism.

The topic of this dissertation is what thought must be like in order for the laws and generalizations of psychology to be true. I address a number of contemporary problems in the philosophy of mind concerning the nature and structure of concepts and the ontological status of mental content. Drawing on empirical work in psychology, I develop a number of new conceptual tools for theorizing about concepts, including a counterpart model of concepts' role in linguistic communication, and a deflationary theory (...) of concepts' formal features. I also suggest some new answers to old problems, arguing, for example, that content realism is not hostage to a naturalized semantics. This dissertation can, as a whole, be read as a sympathetic re-evaluation of the language of thought hypothesis (LOT). LOT claims that thoughts are sentences in a mental language of computation, and are composed of meaningful, atomic symbols—concepts—which are individuated entirely by their formal features. Each chapter either defends various components of LOT from recent criticism, or fills in gaps in the theory. I begin the dissertation by introducing the language of thought project, and motivating and explaining each of its central components. In chapter 2, I discuss a recent competitor to atomism—neo-empiricism—and argue that it fails to meet several key desiderata on theories of concepts, and defend atomism from similar charges. In chapter 3, I argue against a view common to both philosophy and psychology: that concepts must be shareable. If true, atomism is in jeopardy. I find shareability to be unmotivated, and suggest an alternative counterpart model of concepts that does a better job of explaining the things shareability was supposed to explain. Chapter 4 takes up the question of what formal features are and how mental symbols are individuated. I develop a reductive account, arguing that formal features are certain sorts of physical properties and symbol types are sets of these properties. I turn to the topic of content in chapter 5, and defend a very strong version of content realism against recent criticism. (shrink)

Hybridization is a method invented by Arthur Prior for extending the expressive power of modal languages. Although developed in interesting ways by Robert Bull, and by the Sofia school , the method remains little known. In our view this has deprived temporal logic of a valuable tool.The aim of the paper is to explain why hybridization is useful in temporal logic. We make two major points, the first technical, the second conceptual. First, we show that hybridization gives rise to well-behaved (...) logics that exhibit an interesting synergy between modal and classical ideas. This synergy, obvious for hybrid languages with full first-order expressive strength, is demonstrated for a weaker local language capable of defining the Until operator; we provide a minimal axiomatization, and show that in a wide range of temporally interesting cases extended completeness results can be obtained automatically. Second, we argue that the idea of sorted atomic symbols which underpins the hybrid enterprise can be developed further. To illustrate this, we discuss the advantages and disadvantages of a simple hybrid language which can quantify over paths. (shrink)

Two more or less standard methods exist for the systematic, logical construction of classical mathematics, the so-called theory of types, due in the main to Russell, and the Zermelo axiomatic set theory. In systems based upon either of these, the connective of membership, “ε”, plays a fundamental role. Usually although not always it figures as a primitive or undefined symbol.Following the familiar simplification of Russell's theory, let us mean by alogical typein the strict sense any one of the following: (i) (...) the totality consisting exclusively of individuals, (ii) the totality consisting exclusively of classes whose members are exclusively individuals, (iii) the totality consisting exclusively of classes whose members are exclusively classes whose members in turn are exclusively individuals, and so on. Any entity from (ii) is said to beone type higherthan any entity from (i), any entity from (iii), one type higher than any entity from (ii), and so on. In systems based upon this simplified theory of types, the only significant atomic formulae involving “ε” are those asserting the membership of an entity in an entity one type higher. Thus any expression of the form “(x∈y)” is meaningless except where “y” denotes an entity of just one type higher than the type of the entity denoted by “x” It is by means of general type restrictions of this kind that the Russell and other paradoxes are avoided. (shrink)

This is an attempt to view the most basic and fundamental part of modern logic from a perspective which shares no grounds with any established schools of philosophical logic, in that the truth and falsehood as judged by means of human interventions is denied and the notion of logical dimensions is introduced. It establishes the minimum irrefutable logical structure and proceeds to found the relations between logic and geometry. The description of symmetry creates and simultaneously constrains the logical structure, whereas (...) symmetry itself can only be postulated. (shrink)

B a c k g r o u n d. The article is devoted to the analysis of the key directions of the study of the possible influence of the specifics of Chinese language culture on the content and nature of intellectual discourse, which is recognized as philosophical. Logic and ontology are the key areas of analysis of the possible influence of linguistic determinants on the intellectual discourse of China. Three main topics that attract the attention of researchers are the (...) structure of judgment, the semantics of lexical units, and the specificity of the pragmatics of the Chinese language. M e t h o d s. The author applied general scientific methods of analysis, synthesis, comparison and description of the works of researchers of Chinese philosophy, which justify and argue the fruitfulness of studying the peculiarities of Chinese language to explain the reasons of the fundamental difference between the problems actualized in the history of Chinese philosophy and those that formed the basis of the development of the history of philosophy in the Western world. R e s u l t s. It is generally accepted that for the worldview of representatives of Chinese culture, the world is a structural whole, consisting of elements that continuously interact in the dynamics of changes and transformations, we find a reflection of this feature in the semantics of the corresponding symbolic system. Polysemy in the Chinese language mostly reveals a complex and multi-layered "web" of associative and correlative connections between meanings, which in fact cannot be argued outside the context of the relevant cultural tradition indicating common features or similarities of the signified. The doubt about the typicality of understanding the denotations as fixed and atomized for the Chinese language culture is reasonable, even in those cases when it comes to the designation of empirically accessible objectivity. The main specific features of polysemy in the Chinese language are the complete heterogeneity of what is signified, and the lack of transparent grounds for identifying the genus-species subordination of the scope of general concepts. This can also serve as an explanation for the fact that we do not find a completely obvious and nondisputable analogue of the problem of universals of the Western model in the history of Chinese philosophy. C o n c l u s i o n s. Based on the peculiarities of the Chinese language culture, we can recognize as a reasonable a statement that the seemingly natural understanding of the essence – the subject, as something that remains the same (at least for a certain time), but it undergoes some changes through its manifestations – a predicate (properties and actions). It is not as necessary and axiomatic for Chinese thinkers as, for example, for ancient Greek philosophers. In addition, we can recognize the fact that the verb "to exist" does not fulfill the role of a necessary copula in judgments in the Chinese language, as a probable reason for the lack of fundamental problematization of the concept of "being" in the Chinese history of philosophy. In general, the context of the use of a certain word-sign in the Chinese language plays a determining role. The actualization of one or another meaning in an expression is formed not only by its integration into a certain text, but also by its purpose in accordance with the specific practice of application. Therefore, this can serve as an explanation for the absence of an original and axiomatic interpretation of truth as absolute, that is, unchanging and non-relative in the history of Chinese philosophy. (shrink)

This essay from 1999, republished in Notre Dame Magazine online in July 2023, explores how the 1950s were a time of fundamental transformations in American society, a time when the United States went fully megatechnic. The hugely increased power of military, corporate-industrial and “big science” institutions developed during the 1950s signaled the transformation to megatechnic America, with atomic bombs and nuclear testing, automobiles and televisions as key symbols of that transformation. Figures such as J. Robert Oppenheimer and Edward (...) Teller illustrated the battle between national security dictates controlling nuclear bomb testing and responsible science. -/- Since the Second World War the United States has been problematically guided by a power-oriented culture, which, in the names of national security and convenience, has tended to reshape America toward an increasingly hierarchical model of society based on the system requirements of a machine. This same era gave birth to a generalized economic prosperity in the United States, to the civil rights movement, to feminism, literary and artistic innovations, and to other openings of public equality and freedom. Yet the magnification of bureaucratic-corporate structures in that postwar, cold war prosperity has ultimately tended to restructure America against the basic requirements of democratic community. (shrink)

In most modal logics, atomic propositional symbols are directly representing the meaning of sentences (such as sets of possible worlds). In other words, they use only rigid propositional designators. This means they are not able to handle uncertainty in meaning directly at the sentential level. In this paper, we offer a modal language involving non-rigid propositional designators which can also carefully distinguish de re and de dicto use of these designators. Then, we axiomatize the logics in this language (...) with respect to all Kripke models with multiple modalities and with respect to S5 Kripke models with a single modality. (shrink)

This chapter focuses on picture theory, which is sometimes spoken of as a theory of the proposition. By a proposition, Wittgenstein like Frege means something that determines its sense by means of a correlation between the mode of combination of its constituent symbols and the structure of its sense. It has been an orthodoxy amongst Tractatus interpreters, and continues to be such in the wider philosophical community, that Wittgenstein follows the Russell in offering a correspondence theory of truth. The (...) expression of a Tractarian fact provides that fact's mode of combination, and from here there can be no further question as to the ontological types of its constituents. Tractarian facts, it is however added, are not truth conditions but items whose existence explains the obtaining of truth conditions: a Tractarian atomic fact is not a truth condition but a truthmaker. (shrink)

We establish several first- or second-order properties of models of first-order theories by considering their elements as atoms of a new universe of set theory and by extending naturally any structure of Boolean model on the atoms to the whole universe. For example, complete f-rings are "boundedly algebraically compact" in the language $(+,-,\cdot,\wedge,\vee,\leq)$ , and the positive cone of a complete l-group with infinity adjoined is algebraically compact in the language (+, ∨, ≤). We also give an example with any (...) first-order language. The proofs can be translated into "naive set theory" in a uniform way. (shrink)

Guarded fragments of first-order logic were recently introduced by Andreka, van Benthem and Nemeti; they consist of relational first-order formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful model-theoretic properties and especially because they are decidable classes that avoid the usual syntactic restrictions (on the arity of relation symbols, the quantifier pattern or the number of variables) of almost all other known (...) decidable fragments of first-order logic. Here, we investigate the computational complexity of these fragments. We prove that the satisfiability problems for the guarded fragment (GF) and the loosely guarded fragment (LGF) of first-order logic are complete for deterministic double exponential time. For the subfragments that have only a bounded number of variables or only relation symbols of bounded arity, satisfiability is EXPTIME-complete. We further establish a tree model property for both the guarded fragment and the loosely guarded fragment, and give a proof of the finite model property of the guarded fragment. It is also shown that some natural, modest extensions of the guarded fragments are undecidable. (shrink)

Cognitive theories have expressed their components using an artificial symbolic language, such as first-order predicate logic, and the atoms in such representations are non-decomposable letter strings. A neural theory merely demonstrates how to implement a classical symbol system using neurons: this is actually an argument against the importance of the neural description. The fact that symbol systems are physically instantiated in neurons becomes a mere implementational detail, since there is a direct way to translate from the symbolic description to the (...) more neurally plausible one. It might then be argued that, while the neural aspects of the theory identify how behavior arises, they are not fundamentally important for understanding that behavior. Classical symbol systems would continue to be seen as the right kinds of description for psychological processes. (shrink)

This monograph is designed to provide an introduction to the principal areas of tense logic. Many of the developments in this ever-growing field have been intentionally excluded to fulfill this aim. Length also dictated a choice between the alternative notations of A. N. Prior and Nicholas Rescher - two pioneers of the subject. I choose Prior's because of the syntactical parallels with the language it symbolizes and its close ties with other branches of logi cal theory, especially modal logic. The (...) first chapter presents a wider view of the material than later chapters. Several lines of development are consequently not followed through the remainder of the book, most notably metric systems. Although it is import ant to recognize that the unadorned Prior-symbolism can be enriched in vari ous ways it is an advanced subject as to how to actually carry off these enrichments. Readers desiring more information are referred to the appropri ate literature. Specialists will notice that only the first of several quantifi cational versions of tense logic is proven complete in the final chapter. Again constraints of space are partly to blame. The proof for the 'star' systems is wildly complex and at the time of this writing is not yet ready for publi cation. (shrink)

This article initially presents Ernst Mach's anti-realist or instrumentalist stance that underpin his opposition to atomism and reveal his idea that science should be based totally on objectively observable facts. Then, the details of Mach's phenomenalist arguments which recognize only sensations as real are revealed. Phenomenalist thought is not compatible with the idea of realism, which evaluates unobservable entities such as atom, molecule and quark as mind-independent things. In this context, Mach considers the atom as a thought symbol or a (...) metaphysical fiction. This results in the idea that the existence of matter or entity is not independent of the perceiving minds, which is considered Mach’s subjective idealism. As a result of these arguments, the article argues that it would not be wrong to associate Mach's thoughts with solipsism, a radical form of subjective idealism. -/- Bu makalede ilk olarak Ernst Mach’ın atomun varlığına ilişkin itirazının temelini oluşturan ve bilimin sadece gözlemlenebilir olgulara dayandırılması gerektiği yönündeki düşüncelerini ortaya koyan anti-realist ya da enstrümantalist görüşlerine yer verilmektedir. Ardından Mach’ın enstrümantalist tavrının alt metninde bulunan ve yalnızca duyumları gerçek olarak kabul eden fenomenalist argümanlarının ayrıntıları serimlenecektir. Fenomenalist düşünce atom, molekül ve kuark gibi gözlemlenemeyen varlıkları zihinden bağımsız şeyler olarak değerlendiren realizm düşüncesi ile uyuşmamaktadır. Bu bağlamda yapılan incelemeler, Mach’ın atomu bir düşünce sembolü ya da metafiziksel bir kurgu olarak değerlendirmesine ve dış dünyadaki varlıkların var olmasını, onların bir zihin tarafından duyumsanması koşuluna bağlaması ile sonuçlanmaktadır. Makalede Mach’ın öznel idealizmi olarak ele alabileceğimiz bu argümanlarının radikal bir sonucu olarak onun düşüncelerini solipsizm ile ilişkilendirmenin yanlış olmayacağı sonucuna varılmaktadır. (shrink)

The article presents an analysis of the main aspects of the Christian theology of childhood based on the works of outstanding theologians of the 20th century: Dietrich Bonhoeffer, Hans Urs von Balthasar, Karl Rahner, Paul Tillich, and Jurgen Moltmann. The preoccupation with understanding the figure of the child in Western Christianity is motivated by several factors: the undeniable importance of theology as a tradition of interpreting the existential constraints of the human condition, the deep influence of Christian teaching on secular (...) concepts of childhood, as well as the need to stand in defense of theological knowledge against its reactionary appropriation. It is proposed to begin reflection on the problems of the theology of childhood with the question of secularization, which Bonhoeffer characterized as the world's coming of age. The symptoms of such maturation are a crisis of responsibility in an atomized society, powerlessness, and despair from being doomed to remain in a self-closed system moving towards its own destruction. In the eyes of theologians, the figure of the child turns out to be a symbol of the incompleteness of the history of the world and, in the context of Christian eschatology, of the possibility of saving humanity. For a world that has lost its historical dimension, the child comes across, in Moltmann's words, as a metaphor of hope. Theology emphasizes the intrinsic value and uniqueness of every individual childhood experience, while at the same time seeing it as an analogy of the universal relationship between the human community and God. The model of this relationship implies not only acceptance of the world and its law, but also reprehension leading to liberation from the law in divine love. In theological interpretations the Christian imperative to be like children appears as the cornerstone of universal ethics and political practice, which is necessary for humanity to overcome the catastrophic historical situation. (shrink)