This note is about the “calculational style” of presenting proofs introduced by Dijkstra and Scholten and adopted in some books on theoretical computer science. We define the concept of a calculation, which is a formal counterpart of the idea of a calculational proof. The definition is in terms of a new formalization DS of predicate logic. Any proof tree in the system DS can be represented as a sequence of calculations. This fact shows that any logically valid predicate (...) formula has a calculational proof. (shrink)

The calculus of Natural Calculation is introduced as an extension of Natural Deduction by proper term rules. Such term rules provide the capacity of dealing directly with terms in the calculus instead of the usual reasoning based on equations, and therefore the capacity of a natural representation of informal mathematical calculations. Basic proof theoretic results are communicated, in particular completeness and soundness of the calculus; normalisation is briefly investigated. The philosophical impact on a proof theoretic account of the notion (...) of meaning is considered. (shrink)

Zero pronominals challenge Type Logical Grammar in two ways. One, TLG displays a linear resource management regime for semantic composition, meaning that pronominals call for special treatment if they want to do resource multiplication. Two, as a grammar of lexicalism, TLG applies to phonologically realized lexical entries only, illegitimating the phonetically null items during syntactic derivation. Jägor extends the inventory of category-forming connectives of TLG by a third kind of implication that creates categories of anaphoric items and solves the first (...) problem above. This article goes a step further to tackle the second one. In order to formalize the constructions with zero pronominals, we design a ternary category A B C and include the latter into Jägor’s system. The proposed system is proof-theoretically well-behaved. It is complete, sound, and decidable. More importantly, zero pronominals of various forms can be derived in the system. (shrink)

This paper studies algorithmic learning theory applied to algebraic structures. In previous papers, we have defined our framework, where a learner, given a family of structures, receives larger and larger pieces of an arbitrary copy of a structure in the family and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. The learning is successful if there is a learner that eventually stabilizes to a correct conjecture. Here, we analyze the number of (...) mind changes that are needed to learn a given family K. We give a descriptive set-theoretic interpretation of such mind change complexity. We also study how bounding the Turing degree of learners affects the mind change complexity of a given family of algebraic structures. (shrink)

Astral microtubules are rapidly elongated during anaphase and telophase in sea urchin eggs. The number of microtubules extending to the cell surface was calculated with a computer. For the calculations, microtubules were assumed to radiate from the astral center uniformly over angles. Although microtubules from two asters freely overlapped around the equator, the number per the unit area, i.e. the surface density, was larger in the polar region than in the equatorial region. The ratio of the theoretically calculated numbers (...) in the two regions was close to the ratio obtained from the ultrastructural observations by Asnes and Schroeder in 1979. When counted in the longitudinal section including two astral centers, the microtubule number was a little larger in the equatorial region than in the polar region. However, the numbers do not represent the surface density because the two-dimensional section contains only a small portion of all the microtubules spreading in the three-dimensional space. The fluorescence image for tubulin, in most cases, provides the microtubule distribution in the longitudinal section. Therefore, from such an image, we cannot judge whether the surface density of astral microtubules is larger at the pole or at the equator. (shrink)

This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we (...) calculate a canonical characteristic fomula H of S (char(S)) so that ⊢G ∼ H → (∼S) and ⊢GL-LIN ∼ H, and the complexity σ of ∼ H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of ∼ H with H = char(S) and σ(∼ H) = d(S, G). (shrink)

A set of qubit channels has a classical representation when it is isomorphic to the convex closure of a group of classical channels. From Crowder and Martin (Proceedings of Quantum Physics and Logic, Electronic Notes in Theoretical Computer Science, 2009), we know that up to isomorphism there are five such sets, each corresponding to either a subgroup of the alternating group on four letters, or a subgroup of the symmetric group on three letters. In this paper, we show that (...) the classical representation of a qubit channel also carries its information theoretic data—in particular, both the Holevo capacity and the scope of a unital qubit channel can be completely calculated from a systematically determined classical channel. (shrink)

In the article, I discuss some ideas of the type theoretical grammar of Aarne Ranta and the analysis of the problem of Quine (Ralph and Ortcutt), which Oleg Domanov implemented by means of this theory. There are more similarities than differences in TT grammar with well-known ideas, including “fine grinding” of meanings, counterparts, procedural understanding of – intensions. The main problem, which, in my opinion, exists in the TT grammar, consists in understanding how another agent’s epistemic attitudes can be (...) justified for me. Ranta proceeds from the metaphor of the agent as a calculator, which for the general case is unacceptable. I believe that the interpretation of the epistemic attitudes of another agent must be externalistic, that is, referring not to the agent’s worlds, but to his actions in the actual world: “agent X believes that A” is true when the interpreter sees the behavior of the agent in situations that the interpreter would consider adequate for himself if he believed A and would be “in place” of X. To formalize here, it would take complicated tools which are used for describing actions. I’ve come to the conclusion that an understanding of the type in TT grammar makes it intensional in some extended sense, since the working with the naming relation is already an element of a specific pragmatics. (shrink)

The mathematical dynamic model of oxidative phosphorylation in muscle mitochondria developed previously was used to calculate the flux control coefficients of particular steps of this process in isolated mitochondria at different amounts of hexokinase and oxygen concentrations. The pattern of control was completely different under different conditions. For normoxic concentration, the main controlling steps in state 4, state 3.5 and state 3 were proton leak, ATP usage (hexokinase) and complex III, respectively. The pattern of control in state 4 was not (...) changed at hypoxic oxygen concentration, while in state 3.5 and state 3 much of the control was shifted from other steps to cytochrome oxidase. The implications of the theoretical results obtained for the regulation of oxidative phosphorylation in intact muscle are discussed. (shrink)

Actual AI research began auspiciously around 1955 with Allen Newell and Herbert Simon's work at the RAND Corporation. Newell and Simon proved that computers could do more than calculate. They demonstrated that computers were physical symbol systems whose symbols could be made to stand for anything, including features of the real world, and whose programs could be used as rules for relating these features. In this way computers could be used to simulate certain important aspects intelligence. Thus the information-processing model (...) of the mind was born. But, looking back over these fifty years, it seems that theoretical AI with its promise of a robot like HAL appears to be a perfect example of what Imre Lakatos has called a "degenerating research program". (shrink)

Events regarding individuals’ preferences that do not always follow from standard measures such as “value of statistical life” or “quality-adjusted life years” as well as events that occur in some market-related settings which distort the information conveyed by price mechanisms, suggest that a notable chunk of what Hayek called “local knowledge” remains inaccessible by scientific tools and that only the individuals who interact in these local frameworks can have access to it. This casts serious doubt on the epistemic possibility of (...) economic calculation for if events in the local world do not observe the economic models, it is hard to see how central planners can have knowledge on them. Refined modeling strategies and cutting-edge Artificial Intelligence systems do not manage to overcome this hurdle. They may provide huge datasets in a data model, but since not all events represented in the data model are embeddable in known economic models, the knowledge problem is not evaded. Even if a theory ever manages to capture all possible events as they appear in the data model then we are left with a relationship between models (the theoretical model and the data model) with no direct access to the local world and thus the problem of accessibility of local knowledge remains unresolved. (shrink)

When disability-adjusted life years are used to measure the burden of disease on a population in a time interval, they can be calculated in several different ways: from an incidence, pure prevalence, or hybrid perspective. I show that these calculation methods are not equivalent and discuss some of the formal difficulties each method faces. I show that if we don’t discount the value of future health, there is a sense in which the choice of calculation method is a mere question (...) of accounting. Such questions can be important, but they don’t raise deep theoretical concerns. If we do discount, however, choice of calculation method can change the relative burden attributed to different conditions over time. I conclude by recommending that studies involving disability-adjusted life years be explicit in noting what calculation method is being employed and in explaining why that calculation method has been chosen. (shrink)

SummaryLooking at proof theory as an attempt to ‘code’ the general pattern of the logical steps of a mathematical proof, the question of what kind of rules can make the meaning of a logical connective completely explicit does not seem to have been answered satisfactorily. The lambda calculus seems to have been more coherent simply because the use of ‘λ’ together with its projection 'apply' is specified by what can be called a 'reduction' rule: β‐conversion. We attempt to analyse the (...) role of proof rules, making use of a set of formal rules designed to capture both the notions of proof theory and those of the lambda‐calculus: Martin‐Löf's Intuitionistic Type Theory.RésuméSi on considère la théorie de la démonstration comme une tentative de ‘codifier’ les pas logiques d'une démonstration mathématique, on se rendra compte qu'on n'a pas répondu de façon satisfaisante à la question suivante: quelles sont les règies qui rendent complètement explicite le sens d'un connecteur logique? Le lambda‐calcul a été apparemment plus cohérent, tout simplement parce que l'utilisation du‘λ’ avec sa projection 'apply' est spécifiée par une regie de 'réduction': β‐conversion. Nous essayons d'analyser le rôle des règies de démonstration, en utilisant un système formel de règies conçu pour englober à la fois les notions de la théorie de la démonstration et celles du lambda‐calcul: la Théorie Intuitionniste des Types de Martin‐Löf.ZusammenfassungWenn man Beweistheorie als einen Versuch, ein allgemeines Muster der logischen Schritte in einem mathematischen Beweis zu kodifizieren, betrachtet, so scheint die Frage nach der Art von Regeln , die die Bedeutung von logischen Operatoren vollständig beschreiben, nicht zufriedenstellend beantwortet. Der Lambda‐Kalkül erscheint, kohärenter, einfach deshalb weil der Gebrauch von ‘λ’ zusammen mit dessen Projektion 'apply' durch Regeln bestimmt wird, die man 'Reduktions'‐Regeln nennen kann: β‐Konversion. Wir versuchen, die Rolle von Beweisregeln zu analysieren, indem wir ein Regelsystem verwenden, das sowohl die Begriffe der Beweistheorie als auch diejenigen des Lambda‐Kalküls erfasst, nämlich die Martin‐Löfsche Typentheorie. (shrink)

Earlier in this century, many philosophers of science (for example, Rudolf Carnap) drew a fairly sharp distinction between theory and observation, between theoretical terms like 'mass' and 'electron', and observation terms like 'measures three meters in length' and 'is _2° Celsius'. By simply looking at our instruments we can ascertain what numbers our measurements yield. Creatures like mass are different: we determine mass by calculation; we never directly observe a mass. Nor an electron: this term is introduced in order (...) to explain what we observe. This (once standard) distinction between theory and observation was eventually found to be wanting. First, if the distinction holds, it is difficult to see what can characterize the relationship between theory :md observation. How can theoretical terms explain that which is itself in no way theorized? The second point leads out of the first: are not the instruments that provide us with observational material themselves creatures of theory? Is it really possible to have an observation language that is entirely barren of theory? The theory-Iadenness of observation languages is now an accept ed feature of the logic of science. Many regard such dependence of observation on theory as a virtue. If our instruments of observation do not derive their meaning from theories, whence comes that meaning? Surely - in science - we have nothing else but theories to tell us what to try to observe. (shrink)

Andrés Rivadulla argues for an instrumentalist approach to the use of theoretical models in the physical sciences, which, on his view, have not to be conceived of as intended representations of the phenomena, but just as useful tools for explaining and predicting those phenomena. He analyses two examples of theoretical models employed for those aims. The first one is the supernova model, intended mainly as explanatory. The second one is the atomic central field shell model, where the postulated (...) internal structure for atoms—their electronic configuration- made the prediction and discovery of new noble gases possible. He concludes that theoretical models can be regarded as artifacts designed with the specific purpose of facilitating calculations. (shrink)

Theoretical minimal RNA rings attempt to mimick life’s primitive RNAs. At most 25 22-nucleotide-long RNA rings code once for each biotic amino acid, a start and a stop codon and form a stem-loop hairpin, resembling consensus tRNAs. We calculated, for each RNA ring’s 22 potential splicing positions, similarities of predicted secondary structures with tRNA vs. rRNA secondary structures. Assuming rRNAs partly derived from tRNA accretions, we predict positive associations between relative secondary structure similarities with rRNAs over tRNAs and genetic (...) code integration orders of RNA ring anticodon cognate amino acids. Analyses consider for each secondary structure all nucleotide triplets as potential anticodon. Anticodons for ancient, chemically inert cognate amino acids are most frequent in the 25 RNA rings. For RNA rings with primordial cognate amino acids according to tRNA-homology-derived anticodons, tRNA-homology and coding sequences coincide, these are separate for predicted cognate amino acids that presumably integrated late the genetic code. RNA ring secondary structure similarity with rRNA over tRNA secondary structures associates best with genetic code integration orders of anticodon cognate amino acids when assuming split anticodons (one and two nucleotides at the spliced RNA ring 5′ and 3′ extremities, respectively), and at predicted anticodon location in the spliced RNA ring’s midst. Results confirm RNA ring homologies with tRNAs and CDs, ancestral status of tRNA half genes split at anticodons, the tRNA-rRNA axis of RNA evolution, and that single theoretical minimal RNA rings potentially produce near-complete proto-tRNA sets. Hence genetic code pre-existence determines 25 short circular gene- and tRNA-like RNAs. Accounting for each potential splicing position, each RNA ring potentially translates most amino acids, realistically mimicks evolution of the tRNA-rRNA translation machinery. These RNA rings ‘of creation’ remind the uroboros’ (snake biting its tail) symbolism for creative regeneration. (shrink)

Otto Neurath is well known as a founding member of the Vienna Circle, one of several points of origin of logical empiricism or neopositivism. While Neurath’s distinctive contribution to the philosophy of science and epistemology in general has come to be recognised after long neglect, his economic thought remains relatively unexplored. A striking fact has thus remained long obscured: Neurath is not the “positivist” economist one might expect. To throw this point into further relief, the question I want to explore (...) here is whether and to what extent, if any, it makes sense to look at Neurath as an “Austrian” economist. Aware of the danger of treading a thin line between blatant absurdity and Pickwickian banality, my hope is that this way of proceeding will unlock some of the still topical originality of Neurath’s economics.What would seem to render my leading thought absurd is, of course, the acrimonious debate between Ludwig von Mises and Neurath . This early phase of the socialist calculation debate pitched Neurath very much against thirdgeneration representatives of the so-called Austrian School of Theoretical Economics. And what seems to render my leading thought Pickwickian is the unspectacular fact that Neurath was of Austrian nationality. It is true, of course, that he was a self-consciously “Austrian philosopher”, but that does not make him an Austrian economist in the relevant sense. Yet when we delve into the depths of the debate with Mises, things begin to look quite different. (shrink)

This study investigates the engagement of family firms in corporate social responsibility. We first compare their corporate social performance to non-family firms. Then, following recent evidence on the heterogeneity of family firms, we examine two factors that may influence CSP within family firms: the level of family control and the governance orientation of the country in which they operate. This research is based on a theoretical framework which considers both agency and socioemotional wealth influences on family firms CSR engagements. (...) Overall, we find that family firms exhibit lower CSP than non-family firms. But when focusing on family firms, our analyses show a curvilinear relationship between family control and CSP. At lower levels of control, family owners invest more in social initiatives to protect their SEW. Beyond a threshold level of control that we estimate at 36 % in our sample, economic considerations prevail over SEW and social performance starts decreasing. We also find that family firms operating in stakeholder-oriented countries are more attentive to social concerns than those operating in more shareholder-oriented countries. (shrink)

To determine what the speaker in a cooperative dialog meant with his assertion, on top of what he explicitly said, it is crucial that we assume that the assertion he gave was optimal. In determining optimal assertions we assume that dialogs are embedded in decision problems (van Rooij 2003) and use backwards induction for calculating them (Benz 2006). In this paper, we show that in terms of our framework we can account for several types of implicatures in a uniform way, (...) suggesting that there is no need for an independent linguistic theory of generalized implicatures. In the final section, we show how we can embed our theory in the framework of signaling games, and how it relates with other game theoretic analyses of implicatures. (shrink)

While the principal ideas of a systems theory for the molecular sciences have been introduced in part I (Reiher, 2003), illustrative examples for the ingredients of this systems chemistry are discussed in greater detail in this work. The potential wealth of systems chemistry is then demonstrated for a recently developed approach for the calculation of hydrogen bond energies in non-decomposable systems.

In this article we provide an intrinsic characterization of the famous Howard–Bachmann ordinal in terms of a natural well-partial-ordering by showing that this ordinal can be realized as a maximal order type of a class of generalized trees with respect to a homeomorphic embeddability relation. We use our calculations to draw some conclusions about some corresponding subsystems of second order arithmetic. All these subsystems deal with versions of light-face Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varPi ^1_1$$\end{document}-comprehension.

To determine what the speaker in a cooperative dialog meant with his assertion, on top of what he explicitly said, it is crucial that we assume that the assertion he gave was optimal. In determining optimal assertions we assume that dialogs are embedded in decision problems (van Rooij 2003) and use backwards induction for calculating them (Benz 2006). In this paper, we show that in terms of our framework we can account for several types of implicatures in a uniform way, (...) suggesting that there is no need for an independent linguistic theory of generalized implicatures. In the final section, we show how we can embed our theory in the framework of signaling games, and how it relates with other game theoretic analyses of implicatures. (shrink)

This chapter explores some fundamental consequences of the correspondence between physical process and computations. Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be considered formally undecidable. The behavior of a physical system may always be calculated by simulating explicitly each step in its evolution. Much of theoretical physics has, however, been concerned with devising shorter methods of (...) calculation that reproduce the outcome without tracing each step. Computational irreducibility is common among the systems investigated in mathematics and computation theory, but it may well be the exception rather than the rule, since most physical questions may be answerable only through irreducible amounts of computation. (shrink)

We trace two logical ideas further back than they have previously been traced. One is the idea of using diagrams to prove that certain logical premises do—or don’t—have certain logical consequences. This idea is usually credited to Venn, and before him Euler, and before him Leibniz. We find the idea correctly and vigorously used by Abū al-Barakāt in 12th century Baghdad. The second is the idea that in formal logic, P logically entails Q if and only if every model of (...) P is a model of Q. This idea is usually credited to Tarski, and before him Bolzano. But again we find Abū al-Barakāt already exploiting the idea for logical calculations. Abū al-Barakāt’s work follows on from related but inchoate research of Ibn Sīnā in eleventh century Persia. We briefly trace the notion of model-theoretical consequence back through Paul the Persian and in some form back to Aristotle himself. (shrink)

Moral theory is no substitute for virtue, but virtue is no substitute for moral theory. Many critics of moral theory, with Richard Posner being one prominent recent example, complain that moral theory is too abstract, that it cannot generally be used to derive particular rights and wrongs, and that it does not improve people's characters. Posner complains that it is thus of no use to legal theorists. This article defends moral theory, and to some degree, philosophical inquiry in general, against (...) such pragmatic complaints. I argue that the primary goal of moral theorizing is not pragmatic, but theoretical. Moral theory aims at explanation, at answering certain kinds of questions about morality. Moral theory is meant to deepen our insight into morality but, to count as deepening our insight, it need not provide a formula for calculating what to do in a particular circumstance, nor must it make us more virtuous. I provide an account of the scope and nature of explanation provided by moral theory as well as an account of why such explanations can be worth having, even if they were to have few pragmatic consequences. (shrink)

The “erasing race” effect is the reduction of the salience of “race” as an alliance cue when recalling coalition membership, once more accurate information about coalition structure is presented. We conducted a random-effects model meta-analysis of this effect using five United States studies (containing nine independent effect sizes). The effect was found (ρ = 0.137, K = 9, 95% CI = 0.085 to 0.188). However, no decline effect or moderation effects were found (a “decline effect” in this context would be (...) a decrease in the effect size over time). Furthermore, we found little evidence of publication bias. Synthetically correcting the effect size for bias stemming from the use of an older method for calculating error base rates reduced the magnitude of the effect, but the it remained significant. Taken together, these findings indicate that the “erasing race” effect generalizes quite well across experimental contexts and would, therefore, appear to be quite robust. We reinterpret the theoretical basis for these effects in line with Brunswikian evolutionary-developmental theory and present a series of predictions to guide future research in this area. (shrink)

A traditional aspect of model theory has been the interplay between formal languages and mathematical structures. This dissertation is concerned, in particular, with the relationship between the languages of relevant logic and Routley-Meyer models. One fundamental question is treated: what is the expressive power of relevant languages in the Routley-Meyer framework? In the case of finitary relevant propositional languages, two answers are provided. The first is that finitary propositional relevant languages are the fragments of first order logic preserved under relevant (...) directed bisimulations. The second is that, when we restrict our attention to what can be labelled as De Morgan models, we can obtain an analogue of Lindström's theorem for finitary propositional relevant languages. Furthermore, it is shown that a preservation theorem characterizing the expressive power of infinitary relevant languages in classical infinitary languages follows as a consequence of an interpolation theorem for classical infinitary logic. In addition, algebraic characterizations of the classes of Routley-Meyer models axiomatizable in relevant propositional languages, incompactness of infinitary relevant propositional languages and the expressive power of quantificational relevant languages are discussed. A final chapter is devoted to the study of relevant languages as second order frame languages. In particular we devote our attention to the problem of which properties expressible by relevant languages are elementary and which are not. An algebraic characterization of such elementary properties together with some examples of non first order properties axiomatizable in relevant logic are given. Finally, a Sahlqvist-van Benthem algorithm showing that relevant formulas with a certain syntactic form express calculable first order properties at the level of frames is established. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Contemplating the Beautiful: The Practical Importance of Theoretical Excellence in Aristotle’s EthicsJames L. Wood (bio)Aristotle, unlike plato, famously distinguishes φρόνησις from, practical from theoretical wisdom, in Book VI of the Nicomachean Ethics. He distinguishes them on the basis of both their objects and their psychic spheres: is the excellence or virtue (ἀρετή) of the scientific faculty, τὸ ἐπιστημονικόν, “by which we contemplate [θεωρου̑μεν] the sort of beings (...) whose principles [ἀρχαί] do not admit of being otherwise,” while φρόνησις is an excellence of the calculative faculty, τὸ λογιστικόν, by which we contemplate “the sort of beings that admit of being otherwise” (VI.1, 1139a6–8).1 Φρόνησις is skilled and experienced deliberation about human action and emotion, and in particular about “the sort of things that relate to (πρός) living well in general” (VI.5,1140a28); so φρόνησις guides right action, and as it turns out, directly entails excellence of character, ἠθική ἀρετή (VI.13, 1145a1–2)., on the other hand, while necessary for complete happiness (VI.12, 1144a1–6), “contemplates none of the things that make a human being happy” (VI.12, 1143b19–20), because it contemplates not changeable human affairs, circumstances, and actions, but eternal and unchanging realities (VI.6–7; X.7–8; cf. On the Soul, III.9, 432b26–433a1). Θεωρία, contemplation itself, is defined with reference to in Book X, where contemplation is made the basis of the highest human happiness as the excellent activity of intellect (νου̑ς) by which “beautiful and divine” realities are apprehended (X.7, 1177a15–18 and following). In contrast, the excellence of practical activity (both φρόνησις and ἠθική ἀρετή) is explicitly distinguished from the excellent theoretical activity of νου̑ς in θεωρία and relegated to a merely “secondary” importance (X.8, 1178a9 and following).2 [End Page 391]We might well conclude from this account that theoretical activity has nothing to do with practical activity, even if each is independently necessary for complete human happiness, and even if, as Aristotle says, practical excellence is somehow necessary to prepare the way for theoretical excellence (cf. VI.13, 1145a6–11). I wish to counter this impression, however, by showing that there is a theoretical dimension to excellent practical activity.3 More precisely, I will argue that theoretical activity contributes to practical excellence by furnishing the principles (ἀρχαί) of practical reasoning to the calculative faculty and the motivating end (τέλος) of action to the irrational-appetitive (τὸ; ἄλογον) part of the soul. The intellectual faculty that performs this theoretical activity is νου̑ς; the principles that νου̑ς apprehends are the first premises of ethical and political deliberation; and the τέλος that νου̑ς holds up to the appetitive soul as an orienting and motivating object is το καλόν.4 What distinguishes this activity from the theoretical activity that furnishes the principles of scientific reasoning (ἐπιστήμη) for the sake of knowledge is both the kinds of objects studied and the purpose of the study. One typically studies mathematics or astronomy in order to gain knowledge, not to act virtuously; however, one can certainly study the principles of human nature for the sake of virtuous action (as well as knowledge), as Aristotle himself does in the Ethics and other treatises (cf. II.2, 1103b27–29).5 Moreover, the theoretical study of the most “beautiful and divine” realities, described in Book X of the Ethics and Book XII of the Metaphysics, raises the possibility of a direct contribution of θεωρία at the highest levels to πρα̑ξις through the mediating activity of νου̑ς in the contemplation of the highest beauty and divinity.In what follows I will develop and defend these points through a close examination of Aristotle’s discussion of these concepts. My argument has three main parts. The first examines the role of thought in excellent action, the second brings out [End Page 392] the significance of το καλόν as the universal object of practical excellence, and the third argues in three subsections for the contribution in different ways of theoretical to practical excellence.1. The Dependence of Desire on Thought in Excellent ActionAs is clear from his concluding remarks in Book VI, where he declares that the possession of φρόνησις entails the possession of all the virtues of character (VI.13, 1145a1–2), Aristotle holds that the ἀρεταί of practical thought and character, φρόνησις and ἠθική ἀρετή, are interdependent and mutually implicating in virtuous choice and action. Thought needs desire in order to be practically effective... (shrink)

Given a class \ of models, a binary relation \ between models, and a model-theoretic language L, we consider the modal logic and the modal algebra of the theory of \ in L where the modal operator is interpreted via \. We discuss how modal theories of \ and \ depend on the model-theoretic language, their Kripke completeness, and expressibility of the modality inside L. We calculate such theories for the submodel and the quotient relations. We prove a downward Löwenheim–Skolem (...) theorem for first-order language expanded with the modal operator for the extension relation between models. (shrink)

It is shown by means of general principles and specific examples that, contrary to a long-standing misconception, the modern mathematical physics of compressible fluid dynamics provides a generally consistent and efficient language for describing many seemingly fundamental physical phenomena. It is shown to be appropriate for describing electric and gravitational force fields, the quantized structure of charged elementary particles, the speed of light propagation, relativistic phenomena, the inertia of matter, the expansion of the universe, and the physical nature of time. (...) New avenues and opportunities for fundamental theoretical research are thereby illuminated. (shrink)

In my presentation, I will try to develop a picture of scientific research in terms of heremeneutic phenomenology. I will claim that theoretical objects of science do exist at once as "inscriptions" on the horizon of possibilities for doing research, and as "traces" left by practices of formalization, experimentation, calibration, measurement, and calculation. The possibilities become appropriated in the research process, whereby a conceptual structure of scientific domain gradually takes shape. According to this, the horizon of possibilities remains always (...) an open fore-structure of interpretation concerning the structure of the domain. In elaborating on this view, I will sketch out a phenomenological program of "cognitive existentialism". (shrink)

The Müller-Lyer illusion is the natural consequence of the construction of the vertebrate eye, retina and visual processing system. Due to imperfections in the vertebrate eye and retina and due to the subsequent processing in the system by ever increasing receptive fields, the visual information becomes less and less precise with respect to exact location and size. The consequence of this is that eventually the brain has to calculate a weighted mean value of the information, which is spread out over (...) a population of neurons. In the case of the Müller-Lyer illusion this inevitably leads to extension of one and reduction of the other line. The arguments presented explain several published experimental results concerning the Müller-Lyer illusion and shed new light upon the philosophical neutrality of observation sentences. (shrink)

The tradition of Lughz and muʿammā in Arab poetry has an important place. Ibn al-Fāriḍ (d. 632/1235) is a divine love poet that lived in the Ayyubids period. He is an important point in the process of change and transformation of Arabic poetry language. This research aims to carry out a theoretical and anecdotal examination of the Lughzes in Ibn al-Fāriḍ’s Dīwān. The work explains, firstly, the concept of Lughz in terms of conceptual content and theoretical structure and (...) summarizes its own method to be applied in solving and evaluating Lughzes in ten articles. The paper indicates whether the Lughzes in Dīwānhave a theoretical structure or not. In this context, it distinguishes the Lughzes from the number of layers, simple and compound structure maintenance. It examines the theoretical and functional contributions of the tahsīl, takmīl, tashīland tazyīlmethods, the stages of the establishment and the solution of the Lughzes.Abstract: Abū Hafs Sharafuddīn Omar b. Ali al-Hamavī al-Mısrī (d. 632/1235) known as the king of lovers, and called Ibn al-Fārid, is a divine love poet that lived in Egypt during the Ayyubids period (1171-1462). He is an important figure in the process of change and transformation of poetry language in Arabic literature. The lughz and muʿammā (enigma, enigmetic speech, allusion, inversion riddle, poetry puzzle, synecdoche and metaphoric language) means a word pointing to a name or something by symbol and sign. Numerous books have been written about lughzes. These include Arabic poetry, Persian poetry, Classical Turkish poetry, Arabic grammar, Islamic law, hadith, mathematics and inheritance law. The lughz and muʿammā have some linguistic features related to phonetics, statistical linguistics, morphology, lexicology, grammar, syntax, semantics and prosody. This tradition has an important place in Arabic poetry. The research aims to carry out a theoretical and anecdotal examination of the lughzes and muʿammās in Ibn al-Fārız’s Dīwān. The paper explains, firstly, the concept of lughz in terms of conceptual content and theoretical structure. The article summarizes its own method to be applied in analyzing and evaluating lughzes within ten items. The research examines the series of lughzes in Dīwānand divides them into parts according to the original question in the riddles. This work examines the secondary lughzes given in the details of poems in solution parts. The paper indicates whether the lughzes in Dīwānhave a theoretical structure or not. In this context, the research examines lughzes in terms of language and structure, especially in terms of the processes of establishment and solution. This paper categorizes the lughzes according to the number of layers and to whether they have a simple or compound structure. This paper examines the theoretical and functional contributions of the amal al-tahsīlī, amal al-takmīlī, amal al-tashīlī and amal al-tazyīlī methods in the stages of the establishment and the solution of the lughzes. The work applies the theoretical perspectives of these methods to each lughz. The research also examines the contribution of these four methods to the lughzes.There are many lughzes in Ibn al-Fārid’s poems. In Ibn al-Fārid’s Dīwān, in general, fifty-four things are asked. Fifty-one of them are words. Three of them are verbs. One of the verbs is in the order structure and two in the past tense. His lughzes have a theoretical and methodical structure. In terms of organizational structure, lughzes are generally multi-layered, intricate, compound and integrated. Composite lughzes are multi-layered, simple poems are single-layered. Approximately twenty words are asked in the lughzes. These words are always in the first layer of lughz, whether simple or compound. Thirty-seven words in the lughz are secondary lughz with an auxiliary and complementary nature. They are located between the second and sixth layers. Seventeen of the lughzes asked in the auxiliary nature are located in the second layer, thirteen in the third layer, five in the fourth layer, one in the fifth layer and one in the sixth layer. One of the lughzes is six-layered, one of them are five-layered, four of them are four-layered, eight are three-layered, four are double-layered and three are single-layered. According to this, the majority of lughzes in Ibn al-Fārid’s poems are in the unified form and multilayered.The lughzes are formed in terms of word, composition, phrase, grammar and meaning levels. The lughzes have both lexical and semantic characteristics. Ibn al-Fārid uses the configuration (amal al-tahsīlī), completion (amal al-takmīlī), facilitation (amal al-tashīlī) and addition (amal al-tazyīlī) methods to design the lughzes. The structure in the lughzes is shaped by these methods. The words in his lughzes constitute eleven categories, consisting of names, acts and noun verbs. The answers of the questions asked in the poems consist in general of prophet names, surah names, tribal names, administrator’s surnames, letters, cities, animals, food and drink names, attributes and actions. Verbs are in the past time or order form. Some of the lughzes in Ibn al-Fārid’s poems are built in an extraordinary style beyond being interesting. Not all the sentences used in couplets are part of the lughzes. These elements are mentioned in order to complete the lughzes in terms of rhythm and meaning. To be able to solve the lughzes of Ibn al-Fārid, one must be knowledgeable about the language and narrative features of Arabic and Islamic culture, as well as subjects such as the Quran, Sufism, abjad calculation, mathematics, geometry, geography, biology, botany and zoology. His poems contributes to the development and transformation of Arabic poetry. (shrink)

The new kid on the block in cognitive science these days is dynamic systems. This way of thinking about the mind is, as usual, radically opposed to computationalism - - the hypothesis that thinking is computing. The use of dynamic systems is just the latest in a series of attempts, from Searle's Chinese Room Argument, through the weirdnesses of postmodernism, to overthrown computationalism, which as we all know is a perfectly nice hypothesis about the mind that never hurt anyone.

The notion that manual gestures played an important role in the evolution of human language was strengthened by the discovery of mirror neurons in monkey area F5, the proposed homologue of human Broca's area. This idea is central to the thesis developed by Arbib, and lending further support to a link between motor resonance mechanisms and language/communication development is the case of autism and congenital blindness. We provide an account of how these conditions may relate to the aforementioned theory.

This book starts from the premise that methodology has always dominated archaeology to the detriment of broader social theory.

This paper is the second part of an investigation into Babylonian non-mathematical astronomical texts and the relationships between Babylonian observational and predicted astronomical data. Part I (Gray and Steele 2008) showed that the predictions found in the Almanacs and Normal Star Almanacs were almost certainly made by applying Goal-Year periods to observations recorded in the Goal-Year Texts. The paper showed that the differences in dates of records between the Goal-Year Texts and the Almanacs or Normal Star Almanacs were consistent with (...) the date corrections of a few days which, according to theoretical calculations, should be added to allow for the inexactness of Goal-Year periods. The current paper follows on from our earlier study to consider the effect of the Babylonian calendar on Goal-Year methods of prediction. Due to the fact that the Babylonian calendar year can contain either 12 or 13 months, a Goal-Year period can occasionally be month longer or shorter than usual. This suggests that there should in theory be certain points in the Metonic intercalation cycle where a predicted event occurs one Babylonian month earlier or later than the corresponding event a Goal-Year period later. By comparing dates of lunar and planetary records in the Astronomical Diaries, Goal-Year Texts, Almanacs and Normal Star Almanacs, we show that these month differences between the observational records and the predictions occur in the expected years. This lends further support to the theory that the Almanacs’ and Normal Star Almanacs’ predictions originated from records in the Goal-Year Texts, and clarifies how the Goal-Year periods were used in practice. (shrink)