Husserl endeavoured to establish phenomenology as a ‘rigorous science’ and therefore linked its development to methodological considerations from the very beginning. Such considerations are often lacking in current debates on political phenomenology. This article aims to remedy this deficit. It argues that political phenomenology reinterprets Husserl’s methodological principles of epoché and reduction and transforms them into what can be termed interrogation and exposition. In addition, a further, often overlooked, principle of Husserl’s method is uncovered, which is referred to here (...) as demonstration. It is through this triad of interrogation, exposition and demonstration that contemporary political phenomenology adapts and transforms the method of classical phenomenology. The topics of whiteness and race are employed to show how these principles can facilitate the analysis of political struggles. (shrink)

We propose an experimental method to study the possible emergence of sensemaking in artificial agents. This method involves analyzing the agent's behavior in a test bed environment that presents regularities in the possibilities of interaction afforded to the agent, while the agent has no presuppositions about the underlying functioning of the environment that explains such regularities. We propose a particular environment that permits such an experiment, called the Small Loop Problem. We argue that the agent's behavior demonstrates sensemaking (...) if the agent learns to exploit regularities of interaction to fulfill its self-motivation as if it understood (at least partially) the underlying functioning of the environment. As a corollary, we argue that sensemaking and self-motivation come together. We propose a new method to generate self-motivation in an artificial agent called interactional motivation. An interactionally motivated agent seeks to perform interactions with predefined positive values and avoid.. (shrink)

RESUMEN El artículo reconstruye la concepción metodológica de Leibniz de finales del periodo parisino, que subyace al tratado Sobre la cuadratura aritmética del círculo, la elipse y la hipérbola (1676). Se muestra que Leibniz concibió un procedimiento en el cual el hallazgo de nuevos conocimientos de alguna manera coincide con su demostración, y en el que los procesos de análisis y síntesis se emplean de diversas maneras. ABSTRACT The article reconstructs Leibniz's methodological conception of the late Parisian period underlying the (...) treatise On the Arithmetical Squaring of the Circle, the Ellipse, and the Hyperbola (1676). It is shown that Leibniz conceived of a procedure where the finding of new knowledge somehow coincided with its demonstration and in which the processes of analysis and synthesis were employed in various ways. (shrink)

For those who teach students in psychology, education, and the social sciences, the _Handbook of Demonstrations and Activities in the Teaching of Psychology, Second Edition_ provides practical applications and rich sources of ideas. Revised to include a wealth of new material, these invaluable reference books contain the collective experience of teachers who have successfully dealt with students' difficulty in mastering important concepts about human behavior. Each volume features a table that lists the articles and identifies the primary and secondary courses (...) in which readers can use each demonstration. Additionally, the subject index facilitates retrieval of articles according to topical headings, and the appendix notes the source as it originally appeared in _Teaching of Psychology_, the official journal of the Society for the Teaching of Psychology, Division Two of the American Psychological Association. Volume I consists of 97 articles about strategies for teaching introductory psychology, statistics, research methods, and the history of psychology classes. Divided into four sections, the book suggests ways to stimulate interest, promote participation, grasp psychological terminology, and master necessary scientific skills. (shrink)

Phenomenological psychology has emphasized that experience as it is immediately "given" to the experiencing individual is an appropriate subject matter for psychological investigation. Consideration of the methodological implications of this stance suggests that certain text analytic and cluster analytic methods could be used to discern the identifying properties of different types of experience. We present results of a study in which textual analysis was used to identify recurrent properties of participants' verbal accounts of their experience, cluster analysis was used to (...) classify participants' accounts according to the similarity of their profiles of properties, and the resulting clusters were examined for their more or less characteristic prpoerties. Using these methods, three distinct types of experience of a Renaissance painting were identified and described. This demonstration of numerically aided phenomenological methods indicates the compatibility of rigorous and sensitive descriptions of experiential accounts. (shrink)

Having been neglected or maligned for most of this century, Newton's method of 'deduction from the phenomena' has recently attracted renewed attention and support. John Norton, for example, has argued that this method has been applied with notable success in a variety of cases in the history of physics and that this explains why the massive underdetermination of theory by evidence, seemingly entailed by hypothetico-deductive methods, is invisible to working physicists. This paper, through a detailed analysis of Newton's (...) deduction of one particular 'proposition' in optics 'from the phenomena', gives a clearer account than hitherto of the method - highlighting the fact that it is really one of deduction from the phenomena plus 'background knowledge'. It argues, that, although the method has certain heuristic virtues, examination of its putative accreditational strengths reveals a range of important problems that its defenders have yet adequately to address. (shrink)

Presupposition, vagueness, and oddness can lead to some sentences failing to have a clear truth value. The homogeneity property of plural predication with definite descriptions may also create truth-value gaps: The books are written in Dutch is true if all relevant books are in Dutch, false if none of them are, and neither true nor false if, say, half of the books are written in Dutch. We study the projection property of homogeneity by deploying methods of general interest to identify (...) truth-value gaps. Method A consists in collecting both truth judgments and, independently, falsity judgments. The second method, employed in experiment series B and C, is based on one-shot ternary judgments: completely true vs. completely false vs. neither. After a calibration of these methods, we use them to demonstrate that homogeneity projects out of negation, the scope of universal sentences and the scope of non-monotonic quantifiers such as exactly two, to some extent. We assess our results in light of different theoretical approaches to homogeneity—approaches based on presuppositions, scalar implicatures, and something like supervaluations, respectively. We identify free parameters in these theories and assess various variants of them based on our results. Our experimental paradigms may be of broader significance insofar as they can be applied to other phenomena which result in the failure of a sentence to have a definite truth value. (shrink)

The central theme running throughout this outstanding new survey is the nature of the philosophical debate created by modern science's foundation in experimental and mathematical method. More recently, recognition that reasoning in science is probabilistic generated intense debate about whether and how it should be constrained so as to ensure the practical certainty of the conclusions drawn. These debates brought to light issues of a philosophical nature which form the core of many scientific controversies today. _Scientific Method: A (...) Historical and Philosophical Introduction_ presents these debates through clear and comparative discussion of key figures in the history of science. Key chapters critically discuss * Galileo's demonstrative method, Bacon's inductive method, and Newton's rules of reasoning * the rise of probabilistic `Bayesian' methods in the eighteenth century * the method of hypotheses through the work of Herschel, Mill and Whewell * the conventionalist views of Poincaré and Duhem * the inductivism of Peirce, Russell and Keynes * Popper's falsification compared with Reichenbach's enumerative induction * Carnap's scientific method as Bayesian reasoning The debates are brought up to date in the final chapters by considering the ways in which ideas about method in the physical and biological sciences have affected thinking about method in the social sciences. This debate is analyzed through the ideas of key theorists such as Kuhn, Lakatos, and Feyerabend. (shrink)

The central theme running throughout this outstanding new survey is the nature of the philosophical debate created by modern science's foundation in experimental and mathematical method. More recently, recognition that reasoning in science is probabilistic generated intense debate about whether and how it should be constrained so as to ensure the practical certainty of the conclusions drawn. These debates brought to light issues of a philosophical nature which form the core of many scientific controversies today. _Scientific Method: A (...) Historical and Philosophical Introduction_ presents these debates through clear and comparative discussion of key figures in the history of science. Key chapters critically discuss * Galileo's demonstrative method, Bacon's inductive method, and Newton's rules of reasoning * the rise of probabilistic `Bayesian' methods in the eighteenth century * the method of hypotheses through the work of Herschel, Mill and Whewell * the conventionalist views of Poincaré and Duhem * the inductivism of Peirce, Russell and Keynes * Popper's falsification compared with Reichenbach's enumerative induction * Carnap's scientific method as Bayesian reasoning The debates are brought up to date in the final chapters by considering the ways in which ideas about method in the physical and biological sciences have affected thinking about method in the social sciences. This debate is analyzed through the ideas of key theorists such as Kuhn, Lakatos, and Feyerabend. (shrink)

Graciela De Pierris presents a novel interpretation of the relationship between skepticism and naturalism in Hume's epistemology, and a new appraisal of Hume's place within early modern thought. Contrary to dominant readings, she argues that Hume does offer skeptical arguments concerning causation and induction in Book I, Part III of the Treatise, and presents a detailed reading of the skeptical argument she finds there and how this argument initiates a train of skeptical reasoning that begins in Part III and culminates (...) in Part IV. She goes on to demonstrate that Hume was committed to the Newtonian inductive method while rejecting the place of the supernatural in our understanding of nature. (shrink)

The method of contrast is used within philosophy of perception in order to demonstrate that a specific property could be part of our perception. The method is based on two passages. I argue that the method succeeds in its task only if the intuition of the difference, which constitutes the core of the first passage, has two specific traits. The second passage of the method consists in the evaluation of the available explanations of this difference. Among (...) the three outlined options, I will demonstrate that only in the third option – as we shall see, the case of the scenario that remains the same but is perceived in two different ways by the same perceiver – the intuition purports a difference that posses the necessary characteristics, namely being immediately evident and extremely complex and multifaceted, which determine its tensive nature. The application within auditory perception of this third option will generate two cases, a diachronic one and a synchronic one, which clearly show that we can auditorily perceive causality as a link between two sonorous episodes. The causal explanation is the only possible explanation among the many evaluated within the second passage of the method of contrast. (shrink)

It is well known that Maimonides rejects the Kalam argument for the existence of God because it assumes the temporal creation of the world, a premise for which he says there is no “cogent demonstration (burhan qat'i) except among those who do not know the difference between demonstration, dialectics, and sophistic argument.”Moses Maimonides, The Guide of the Perplexed, trans. Shlomo Pines (Chicago: University of Chicago Press, 1963), I:71:180. All references are to this translation; parenthetic in-text references are to (...) part, chapter, and page. By contrast, he claims to establish belief in the existence of God “through a demonstrative method as to which there is no disagreement in any respect” (I:71:182). Taken at his word, Maimonides’ proofs for the existence of the deity, like Aquinas’s five ways, have traditionally been read as models of medieval natural theology: of the power of human reason to independently establish revealed truth. In recent years, however, the same demonstrations have assumed a second kind of significance. For scholars, like myself, who argue that Maimonides holds severe views about the limitations of human knowledge of divine science and metaphysics, these demonstrations are the strongest conceivable counterevidence.The locus classicus for this view is Shlomo Pines, “The Limitations of Human Knowledge According to Al-Farabi, Ibn Bajja, and Maimonides,” in Studies in Medieval Jewish History and Literature, ed. I Twersky, 3 vols. (Cambridge: Harvard University Press, 1979), I:82–109. See also his “Les Limites de la Métaphysique selon Al-Farabi, ibn Bajja et Maimonide; Sources et Antitheses de ces Doctrines chez Alexandre d’Aphrodise et Chez Themistius,” Miscellanea Mediaevalia 13 (1981): 211–25; “Dieu et L’Etre Selon Maimonide: Exégese d’Exode 3,14 et doctrine connexe,” in Celui qui est: Interprétations juives et chrétiennes d’Exode 3, 14, ed. A. de Libera et E. Zum Brunn (Paris: Les Editions du Cerf [Collection “Patrimoines”], 1986), 15–24; and “The Relation between Maimonides’ Halakhic and non-Halakhic Works,” in Maimonides and Philosophy, ed., S. Pines and Y. Yovel (Dordrecht: Martinus Nijhoff, 1987). Pines concludes, on the basis of the limitations of the intellect with respect to knowledge of metaphysics, that Maimonides, like Kant, gives priority to the practical over the theoretical. For arguments drawing different ‘skeptical’ conclusions, see my “Maimonides in the Skeptical Tradition,” ms.; “Maimonides on the Growth of Knowledge and the Limitations of the Intellect,” to appear in Tony Levy, ed., Maimonide: Traditions philosophiques et scientifiques médievales arabe, hébraique, latine; “Logical Syntax as a Key to a Secret of the Guide of the Perplexed,” (in Heb.), Iyyun 38 (1989): 137–66; “Maimonides on Language and the Science of Language,” in Maimonides and the Sciences, ed., H. Levine and R. Cohen (Dordrecht: Kluwer, 2000), pp. 173–226; and The Matter and Form of Maimonides’ Guide (forthcoming). If Maimonides really held that humans cannot apprehend metaphysical truths about the deity, how could he have demonstrated (or even thought he could demonstrate) the existence of God? If he does demonstrate it, then humans evidently do have knowledge of metaphysics. As one distinguished scholar has recently protested, it is nothing less than “perverse” to interpret Maimonides as “meaning that the existence of God is unknowable when he in fact prides himself on having demonstrated the existence of God in four different ways.”Herbert A. Davidson, “Maimonides on Metaphysical Knowledge,” Maimonidean Studies 3 (1992–1993): 49–103, 86. See also Alfred L. Ivry, “The Logical and Scientific Premises of Maimonides’ Thought,” in Perspectives on Jewish Thought and Mysticism, ed. Alfred L. Ivry, Elliot R. Wolfson, and Allan Arkush (Amsterdam: Harwood Publishers, 1998), pp. 63–97, 70. (shrink)

This article presents Aristotelian scientific demonstration as a method for attaining intuitive theoria of essential natures. Such insight is attained through the discursive demonstrative syllogism. Science is understood as knowledge of causes through their effects, as opposed to an operative knowledge of the consequences of causes. This understanding is thus counter-reductionist.

Among Plato's works, the Statesman is usually seen as transitional between the Republic and the Laws. This book argues that the dialogue deserves a special place of its own. Whereas Plato is usually thought of as defending unchanging knowledge, Dr Lane demonstrates how, by placing change at the heart of political affairs, Plato reconceives the link between knowledge and authority. The statesman is shown to master the timing of affairs of state, and to use this expertise in managing the conflict (...) of opposed civic factions. To this political argument corresponds a methodological approach which is seen to rely not only on the familiar method of 'division', but equally on the unfamiliar centrality of the use of 'example'. The demonstration that method and politics are interrelated transforms our understanding of the Statesman and its fellow dialogues. (shrink)

In elite sport, the advantages demonstrated by expert performers over novices are sometimes due in part to their superior physical fitness or to their greater technical precision in executing specialist motor skills. However at the very highest levels, all competitors typically share extraordinary physical capacities and have supremely well-honed techniques. Among the extra factors which can differentiate between the best performers, psychological skills are paramount. These range from the capacities to cope under pressure and to bounce back from setbacks, to (...) the knowledge of themselves, opponents, and the domain, which experts access and apply in performance. In the companion chapter on breadth and depth of knowledge in expert sport (see Chapter 11), we discussed the forms or kinds of knowledge deployed by elite athletes, and described some lines of research which seek to tap and study such expert knowledge (McPherson & MacMahon, 2008; McRobert, Ward, Eccles & Williams, 2011). In this chapter we focus more directly on questions about methods for measuring or more accurately assessing expert knowledge, in particular addressing a wider range of methods to help us understand what experts know. Suggesting that sport researchers can productively adopt and adapt existing qualitative methodologies for integration with more standard quantitative methods, we introduce and survey a number of areas of qualitative research in psychology. (shrink)

Descartes’s Method: The Formation of the Subject of Science provides a systematic interpretation of Descartes’s method in Rules for the Direction of the Mind and related texts. The book reconstructs Descartes’s method in its entirety and concretely demonstrates both the efficacy of the method in the sciences as well as the unity of the method from Rules for the Direction of the Mind (1620s) to Principles of Philosophy (1644). The principal thesis of the book is (...) that Descartes’s method is a problem-solving cognitive disposition (or habitus) that can be actualized in a variety of well-defined ways, depending always on the nature of problem. The book divides into five parts and eleven chapters. Parts I–II (Chapters 1–4) develop an interpretation of the historical and conceptual foundations of Descartes’s method (its operations and acquisition), while the remainder of the book (Parts III–V, which include Chapters 5–11) demonstrates the fruits of the method in solutions to problems in the sciences (above all, mathematics and optics). (shrink)

The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. The literature on judgment aggregation refers to such a problem as the \textit{discursive dilemma}. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, we address the question of how good (...) the various approaches are at selecting the right conclusion. We focus on two approaches: distance-based procedures and a Bayesian analysis. They correspond to group-internal and group-external decision-making, respectively. We compare those methods in a probabilistic model, demonstrate the robustness of our results over various generalizations and discuss their applicability in different situations. The findings vindicate (i) that in judgment aggregation problems, reasons should carry higher weight than conclusions and (ii) that considering members of an advisory board to be highly competent is a better strategy than to underestimate their advice.". (shrink)

It is a common view that arguments from analogy can only be evaluated on a case-by-case basis. However, while this reflects an important insight, I propose instead a relatively simple method for their evaluation based on just (i) their general form and (ii) four core questions. One clear advantage of this proposal is that it does not depend on any substantial (and controversial) view of similarity, unlike influential current alternative methods, such as Walton’s. Following some initial clarification of the (...) notion of analogy and similarity, I demonstrate the strength of this method by analysing and evaluating three prominent arguments from analogy. (shrink)

Clustering plays an important role in data mining, pattern recognition, and machine learning. Single-valued neutrosophic sets are useful means to describe and handle indeterminate and inconsistent information that fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. To cluster the data represented by single-valued neutrosophic information, this article proposes single-valued neutrosophic clustering methods based on similarity measures between SVNSs. First, we define a generalized distance measure between SVNSs and propose two distance-based similarity measures of SVNSs. Then, we present (...) a clustering algorithm based on the similarity measures of SVNSs to cluster single-valued neutrosophic data. Finally, an illustrative example is given to demonstrate the application and effectiveness of the developed clustering methods. (shrink)

The potential for public engagement to democratise science has come under increasing scrutiny amid concerns that conflicting motivations have led to confusion about what engagement means to those who mediate science and publics. This raises important yet relatively unexplored questions regarding how publics are constituted by different forms of engagement used by intermediary scholars and other actors. It is possible to identify at least two possible ‘rationalities of mediation’ that mobilise different versions of the public and the roles they are (...) assumed to play, as ‘citizens’ or ‘users’, in discussions around technology. However, combinations of rationalities are found in practice and these have significant implications for the ‘new’ scientific democracy. (shrink)

Descartes' methodical doubt is being criticized by naïve realists and others who don't find doubt as a good starting point for metaphysical thought, however, the philosophical achievements of his method have been absorbed in all later philosophies. The objective of this paper is to demonstrate how an inevitable question concerning the foundation of Descartes' mathesis universalis, which led him to investigate this foundation by applying this very method in Metaphysics, has finally enabled him to discover his most important (...) philosophical principle, i.e., the necessary relation between being and reason in the identity of the "I". To demonstrate this, after summarizing the fundamental ideas of mathesis uneversalis, and showing the inner necessity of introducing the methodical doubt to fortify these ideas, the decisive role of metaphysical doubt as the third step of the methodical doubt, and malicious demon as its second phase would be highighted. It would also become clear that the metaphysical doubt has a great importance as a turning point from different aspects: as a knot that ties mathesis universalis with its underlying Metaphysics; as a bridge from within the psychological "I" to the metaphysical "I". (shrink)

This study examines the methods students use to cheat on class examinations and suggests ways of deterring using an international sample from Australia, China, Ireland, and the United States. We also examine the level of cheating and reasons for cheating that prior research has highlighted as a method of demonstrating that our sample is equivalent to those in prior studies. Our results confirm the results of prior research that primarily employs students from the United States. The data indicate that (...) actions such as having multiple versions of the examination and scrambling the questions on these versions would deter cheating. In addition, given the increased level of cheating and students' increased perception of the social acceptability of cheating in college, the data provided by our international sample also suggest that some relatively simple precautions by instructors could dramatically reduce the level of cheating on in-class examinations. (shrink)

We owe most scientific knowledge to methods of inquiry that are never formally analyzed. The analysis of behavior does not call for hypothetico-deductive methods. Statistics, taught in lieu of scientific method, is incompatible with major features of much laboratory research. Squeezing significance out of ambiguous data discourages the more promising step of scrapping the experiment and starting again. As a consequence, psychologists have taken flight from the laboratory. They have fled to Real People and the human interest of “real (...) life,” to Mathematical Models and the elegance of symbolic treatments, to the Inner Man and the explanatory preoccupation with inferred internal mechanisms, and to Laymanship and its appeal to “common sense.” An experimental analysis provides an alternative to these divertissements.The “theories” to which objection is raised here are not the basic assumptions essential to any scientific activity or statements that are not yet facts, but rather explanations which appeal to events taking place somewhere else, at some other level of observation, described in different terms, and measured, if at all, in different dimensions. Three types of learning theories satisfy this definition: physiological theories attempting to reduce behavior to events in the nervous system; mentalistic theories appealing to inferred inner events; and theories of the Conceptual Nervous System offered as explanatory models of behavior. It would be foolhardy to deny the achievements of such theories in the history of science. The question of whether they are necessary, however, has other implications.Experimental material in three areas illustrates the function of theory more concretely. Alternatives to behavior ratios, excitatory potentials, and so on demonstrate the utility of rate or probability of response as the basic datum in learning. Functional relations between behavior and environmental variables provide an account of why learning occurs. Activities such as preferring, choosing, discriminating, and matching can be dealt with solely in terms of behavior, without referring to processes in another dimensional system. The experiments are not offered as demonstrating that theories are not necessary but to suggest an alternative. Theory is possible in another sense. Beyond the collection of uniform relationships lies the need for a formal representation of the data reduced to a minimal number of terms. A theoretical construction may yield greater generality than any assemblage of facts; such a construction will not refer to another dimensional system. (shrink)

In this book, Peter Achinstein proposes and defends several objective concepts of evidence. He then explores the question of whether a scientific method, such as that represented in the four "Rules for the Study of Natural Philosophy" that Isaac Newton invoked in proving his law of gravity, can be employed in demonstrating how the proposed definitions of evidence are to be applied to real scientific cases.

Clinical populations sometimes demonstrate difficulties forgetting stimuli related to their trauma-related disorder, perhaps because their intense personal connection to these stimuli produce deficits in the inhibitory control abilities necessary for forgetting. The present work examined this possibility for people who have high levels of traits implicated in borderline personality disorder (BPD). In two well-powered studies, we found no evidence for deficits in forgetting specific to BPD traits, even for people with clinically significant levels of the traits, contrary to previous studies. (...) The present experiments updated the designs from earlier experiments to employ the most contemporary methods to examine directed forgetting recommended by recent reviews. With these improved methods, Study 1 found that participants showed significant directed forgetting for BPD-related words independent of their level of BPD traits, perhaps because the BPD-related words were so strongly associated with one another. Study 2 found that when we removed the strong relatedness between the stimuli, forgetting of BPD-relevant words was significant and did not interact with BPD symptomology. We concluded that in contrast to people with PTSD who show specific inhibitory deficits for trauma-related works, people with BPD show normal, intact inhibitory control even for words that they should find threatening. (shrink)

The first article in this issue attempts to refute the concept of Altruism and calls it akin to Selfishness. The arguments are logically set in the way like that of Spinoza’s method of demonstration, with Axioms, Definitions, Propositions and Notes: so as to make them exact and precise. Interestingly, the writer introduces a new concept of Credit and through various other original propositions and examples rebuts the altruistic nature which is generally ascribed to humans.

The encounter between two fundamentally different approaches in seminal research in molecular biology-the problems, aims, methods and metaphysics - is delineated and analyzed. They are exemplified by the microbiologist Oswald T. Avery who, in line with the reductionist mechanistic metaphysics of Jacques Loeb, attempted to explain basic life phenomena through chemistry; and the theoretical physicist Max Delbrück who, influenced by Bohr’s antimechanistic views, preferred to explain these phenomena without chemistry. Avery’s and Delbrück’s most important studies took place concurrently. Thus analysis (...) of their contrasting approaches lends itself to examination of the Weltanschauungen view concerning the role of fundamental (metaphysical) assumptions in scientific change, that is, the view that empirical research cannot be neutral in regard to the worldviews of the researchers. This study shows that the initial ostensible disparity (non-integratibility) of the two approaches lasted for just a short time. Ironically it was a student of Delbrück’s school, James Watson, who (with Crick) proposed a chemical model, the DNA double helix, as a solution to Delbrück’s problem. The structure of DNA has not been seriously challenged over the past half century. Moreover, Watson’s and Crick’s work did not call into question the validity of Delbrück’s research, but opened it up to entirely new approaches. The case of Avery and Delbrück demonstrates that after initial obstacles were overcome the different fundamental attitudes and the resulting research practices were capable of integration. © 2008 Stazione Zoologica Anton Dohrn. (shrink)

Peirce’s triadic logic has been under discussion since its discovery in the 1960s by Fisch and Turquette. The experiments with matrices of three-valued logic are recorded in a few pages of unpublished manuscripts dated 1909, a decade before similar systems have been developed by logicians. The purposes of Peirce’s work on such logic, as well as semantical aspects of his system, are disputable. In the most extensive work about it, Turquette suggested that the matrices are related in dual pairs of (...) axiomatic Hilbert-style systems. In this paper, we present a simple tableau proof for a fragment of Peirce three-valued logic, called P3, based on similar approaches in many-valued literature. We demonstrated that this proof is sound and complete. Besides that, taking the false as the only undesignated value and adding non-classical negations to the calculus, we can explore paraconsistent and paracompleteness theories into P3. Keywords: Charles S. Peirce, many-valued logics, theory of proof, tableau method. (shrink)

In this paper I will present a visual method that I have created to demonstrate the validity of propositional arguments and predicates, based on the traditional Venn diagrams. This idea was born after becoming aware of how useful visual methods are in other scientific fields, such as geometrical representations of arithmetic and algebraic concepts. This method illustrates the relationship between propositional logic, predicate logic and set theory, and it can be used to explain linguistic semantic concepts such as (...) synonymy, antonymy, hyponymy, entailment, and lexical substitution. (shrink)

I begin by briefly recalling two facts of seventeenth century intellectual history: not only is a fourth part devoted to method added to the three parts traditionally contained in logic treatises, but in a number of texts the terms "logic" and "method" are blurred. I then give an explanation of these two facts with the following ideas: 1/ Since the criticism of Aristotelian sciences at the beginning of the seventeenth century was in particular focused on logic, the question (...) was asked as to what could replace or supplement it. 2/ Although method was very generally supposed to fulfil this function, its objectives were not clear. I propose a distinction between four ideas of method, which I call method-disposition, method-demonstration, method-invention and method-purification. 3/ The blurring between logic and method comes partly from the fact that some of these ideas take up elements of the then existant logic, but, in a context marked by the reception of Descartes's work, we must also take into account the fact that, since Descartes had not composed a logic and since he had not really explain what his method was, his successors were looking for what both might have been. (shrink)

The Theme. Strong forcing axioms like Martin’s Maximum give a reasonably satisfactory structural analysis of $H(\omega _2)$. A broad program in modern Set Theory is searching for strong forcing axioms beyond $\omega _1$. In other words, one would like to figure out the structural properties of taller initial segments of the universe. However, the classical techniques of forcing iterations seem unable to bypass the obstacles, as the resulting forcings axioms beyond $\omega _1$ have not thus far been strong enough! However, (...) with his celebrated work on generalised side conditions, I. Neeman introduced us to a novel paradigm to iterate forcings. In particular, he could, among other things, reprove the consistency of the Proper Forcing Axiom using an iterated forcing with finite supports. In 2015, using his technology of virtual models, Veličković built up an iteration of semi-proper forcings with finite supports, hence reproving the consistency of Martin’s Maximum, an achievement leading to the notion of a virtual model.In this thesis, we are interested in constructing forcing notions with finitely many virtual models as side conditions to preserve three uncountable cardinals. The thesis constitutes six chapters and three appendices that amount to 118 pages, where Section 1 is devoted to preliminaries, and Section 2 is a warm-up about the scaffolding poset of a proper forcing. In Section 3, we present the general theory of virtual models in the context of forcing with sets of models of two types, where we, e.g., define the “meet” between two virtual models and prove its properties.The main results are joint with Boban Veličković, and partly appeared in Guessing models and the approachability ideal, J. Math. Log. 21 (2021).Pure Side Conditions. In Section 4, we use two types of virtual models (countable and large non-transitive ones induced by a supercompact cardinal, which we call Magidor models) to construct our forcing with pure side conditions. The forcing covertly uses a third type of models that are transitive. We also add decorations to the conditions to add many clubs in the generic $\omega _2$. In contrast to Neeman’s method, we do not have a single chain, but $\alpha $ -chains, for an ordinal $\alpha $ with $V_\alpha \prec V_\lambda $. Thus, starting from suitable large cardinals $\kappa <\lambda $, we construct a forcing notion whose conditions are finite sets of virtual models described earlier. The forcing is strongly proper, preserves $\kappa $, and has the $\lambda $ -Knaster property. The relevant quotients of the forcing are strongly proper, which helps us prove strong guessing model principles. The construction is generalisable to a ${<}\mu $ -closed forcing, for any given cardinal $\mu $ with $\mu ^{<\mu }=\mu <\kappa $.The Iteration Theorem. In Section 5, we use the forcing with pure side conditions to iterate a subclass of proper and $\aleph _2$ -c.c. forcings and obtain a forcing axiom at the level of $\aleph _2$. The iterable class is closely related to Asperó–Mota’s forcing axiom for finitely proper forcings.Guessing Model Principles. Section 6 encompasses the main parts of the thesis. We prove the consistency of the guessing principle $\mathrm {GMP}^+(\omega _3,\omega _1)$ that states for any cardinal ${\theta \geq \omega _3}$, the set of $\aleph _2$ -sized elementary submodels M of $H(\theta )$, which are the union of an $\omega _1$ -continuous $\in $ -chain of $\omega _1$ -guessing, I.C. models is stationary in $\mathcal P_{\omega _3}(H(\theta ))$. The consistency and consequences of this principle are demonstrated in the following diagram. We also prove that one can obtain the above guessing models in a way that the $\omega _1$ -sized $\omega _1$ -guessing models remain $\omega _1$ -guessing model in any outer transitive model with the same $\omega _1$, and we denote this principle by $\rm{SGMP}^+(\omega_3,\omega_1)$.In the following diagram, $\mathrm{TP}$ stands for the tree property; $w\mathrm{KH}$ stands for the weak Kurepa Hypothesis; $\mathrm{MP}$ stands for Mitchell property, i.e., the approachability ideal is trivial modulo the nonstationary ideal; $\mathrm{AP}$ stands for the approachability property; $\mathrm {AMTP}(\kappa ^+)$ states that if $2^\kappa <\aleph _{\kappa ^+}$, then every forcing which adds a new subset of $\kappa ^+$ whose initial segments are in the ground model, collapses some cardinal $\leq 2^{\kappa }$. The dotted arrow denotes the relative consistency, while others are logical implications.Appendices. Appendix A includes merely the above diagram. Appendix B presents a proof of the Mapping Reflection Principle with finite conditions under $\mathrm {PFA}$. Appendix C contains open problems. Finally, the thesis’s bibliography consists of 42 items.Abstract prepared by Rahman MohammadpourE-mail: [email protected]: https://theses.hal.science/tel-03209264. (shrink)

RésuméDans cet article, nous analysons en détail les deux mémoires de Legendre, Sur les intégrations par arcs d’ellipse (1786a, 1786b), en comparant les deux démonstrations qu’il donne de la rectification de l’hyperbole au moyen de deux arcs d’ellipse. Entre le premier et le second mémoire, Legendre prend connaissance d’un théorème analogue de Landen, qu’il cherche à incorporer à son projet de constitution d’un calcul des arcs d’ellipse et dont il propose une interprétation originale en le déduisant de ses propres principes. (...) En retraçant la préhistoire de la transformation de Landen, des premières méthodes d’intégration par arcs de sections coniques chez Maclaurin, d’Alembert et Landen jusqu’à l’élaboration par Legendre des échelles de modules, nous cherchons à mettre en lumière les conditions de son identification. Nous montrons comment Legendre fut amené à discerner dans le théorème de Landen ce qui entre ses mains allait devenir l’instrument privilégié de la mise en ordre systématique des transcendantes elliptiques, grâce à une lecture orientée par les exigences spécifiques liées à une méthode d’approximation fondée sur la variation continue des paramètres et à la constitution de tables numériques d’arcs d’ellipse. (shrink)

Jacopo Zabarella’s two treatises On Methods and On Regressus (1578) are among the most important Renaissance discussions of how scientific knowledge should be acquired, arranged, and transmitted. They belong to a lively debate about the order in which sciences should be taught and the method to be followed in scientific demonstration that roiled the Late Renaissance world for decades. In these famous works Zabarella rejected the views of Ramists and modern Galenists in favor of the pure doctrine of (...) Aristotle, freed from misunderstandings foisted upon it by medieval interpreters. The influence of these works on Galileo’s scientific method and Descartes’ famous Discourse on Method (1637) has long been debated. They are here translated into English for the first time, along with a new Latin text based on the corrected 1586 edition. -/- Volume 1 contains On Methods, Books I-II. (shrink)

Jacopo Zabarella’s two treatises On Methods and On Regressus (1578) are among the most important Renaissance discussions of how scientific knowledge should be acquired, arranged, and transmitted. They belong to a lively debate about the order in which sciences should be taught and the method to be followed in scientific demonstration that roiled the Late Renaissance world for decades. In these famous works Zabarella rejected the views of Ramists and modern Galenists in favor of the pure doctrine of (...) Aristotle, freed from misunderstandings foisted upon it by medieval interpreters. The influence of these works on Galileo’s scientific method and Descartes’ famous Discourse on Method (1637) has long been debated. They are here translated into English for the first time, along with a new Latin text based on the corrected 1586 edition. Volume 1 contains On Methods, Books I-II. Volume 2 contains On Methods, Books III-IV, and On Regressus. (shrink)

We live in a world where it is impossible to exist without, and beyond, technologies. Despite this omnipresence, we tend to overlook their influence on us. The vigorously developing approach of postphenomenology, combining insights from phenomenology and pragmatism, focuses on the so-called technological mediation, i.e., on how technologies as mediators of human-world relations influence the appearing of both the world and the human beings in it. My analysis aims at demonstrating both the methodological weaknesses and open possibilities of postphenomenology. After (...) summarizing its essentials, I will scrutinize, first, its ability to turn to the technological things themselves and, second, the so-called empirical turn as realized by postphenomenology. By assessing its conceptual framework from the phenomenological perspective, I hope to demonstrate that postphenomenology needs philosophical clarification and strengthening. In short, it needs a more phenomenological, and less pragmatic, approach to technology in its influence on human experience. (shrink)

Since the financial crisis, the malfeasance of business leaders has been a recurring theme in the news, along with calls for increased regulation and oversight. This focus on the ethics of the business community raises a concern about the ethics of those in business or going into business. The ethics of business people and business students has been explored by a number of researchers using survey techniques. We propose and report the results of an alternative method for investigating unethical (...) behavior by students. In a motivated economic experiment with introductory level students, we find that business students were almost twice as likely to lie for a monetary reward as students in other disciplines, demonstrating the need for effective business ethics. (shrink)

Both sides in controversies tend to argue they have logic on their side. This book proposes that the interminable nature of these controversies suggests there is a problem with the main tool of logic, the syllogism. Drawing on contemporary developments in social theory and philosophy, Stanley Raffel argues that metaphors are not just aesthetic tools; they can also be used to judge phenomena. Featuring case studies drawn from both literary material and current controversial debates, _The Method of Metaphor_ ultimately (...) demonstrates the value of this neglected potential of metaphoric reasoning and shows its far-reaching implications in both moral behavior and moral education. (shrink)

“Artworks are not being but a process of becoming” —Theodor W. Adorno, Aesthetic Theory In the everyday use of the concept, saying that something is grotesque rarely implies anything other than saying that something is a bit outside of the normal structure of language or meaning – that something is a peculiarity. But in its historical use the concept has often had more far reaching connotations. In different phases of history the grotesque has manifested its forms as a means of (...) subversive resistance against society’s prevailing notions of form and power. What aids this impact and distinguishes two of its basic stylistic features is the grotesque’s dissolution of form and its hyperbole. Such grotesqueries, however, soon solidify into new forms, new structures of meaning, hierarchy and practice, and in this sense the history of the grotesque is, on one hand, a continual opposition and transgression of the prevailing notions of art as well as of God and humanity, while on the other hand it offers continual resistance to its own solidifying process. As such the grotesque will not and cannot be contained in form without it losing the very thing that makes it grotesque. Even though it is somewhat easy to point out certain stylistic features of the grotesque, the sum of those features tell us very little about what is at play within it. Definitions concerned with the grotesque’s content rather than its form faces similar difficulties. Throughout history, expressions relating to the grotesque have been used in defense of a whole host of different social and cultural discourse including, for instance, Catholicism (See Erhard Schön’s Der Teufel mit der Sackpfeife , 1536), Protestantism (See Lucas Cranach’s Der Papstesel , 1523), a material folk culture (see Mikhail Bakhtin’s Rabelais and his World , 1984) and an idealistic romantic structure of meaning (see Wolfgang Kayser’s The Grotesque in Art and Literature , 1957). Thus though the grotesque cannot be reduced to the expression of certain forms or meanings, in order to examine what the grotesque is about one has to try to see how it’s relationship to flow and process and how, by maintaining this relationship, it attempts to avoid solidifying into form and meaning. The process of the grotesque alluded to here revolves around a play between periphery and center, the marginalized and the dominant. Most often this is expressed as a direct negation of the center of power. In the medieval grotesque tradition of the carnival, for example, it is expressed by its emphasis on the nether regions of the body as the center of creation of meaning. Spirit does not come from above, but from the belly, buttocks and genitals, and there is, expressed in this manner, a mockery of the predominant Christian notion of truth and meaning. Such inversions of the sites of meaning most often explicitly express an increased interest in materiality instead of ideal content which comes to the fore through the play between periphery and center. Even in early grotesque Renaissance art (for example in the works of Raphael) the depiction of the mythological or ideal reveals an exploration of the possibilities of the material. The works of art thus explore their own boundaries rather than act as vessels of the divine and in this way the grotesque explores the limits of form and materiality. This in turn brings to the fore a metaphysical dimension in the workings of the grotesque: It is an immanent exploration of its own boundaries. Materiality and metaphysics are joined together, because it is through the awareness of itself as a structuring (dis)order that it places itself in opposition to the prevailing notions of form and power. This way the grotesque expresses an awareness of the division of sign and reality and a search for this reality. It implicitly expresses the awareness that meaning is not something God-given and static, but fluctuating and man-made. In modern explorations of the history of the grotesque it is commonly seen as a form of realism that manifests a shift from the ideal towards the material, freeing art from representing some hidden higher order and instead making the work of art the very site of creation and meaning. Going even further, the grotesque actively opposes the notions of the ideal by marking a shift from an ahistorical view of the world towards the historical. However, this also makes clear why the grotesque has a tendency to solidify into new static forms of meaning, for by establishing itself as a subversive counterforce there is an idea of transgression and emancipation. That is why the grotesque often historicizes and relativizes only to repeat the mistakes of that which it negates: putting itself in the king’s chair. The exploration of the material seems to create new forms and notions of the ideal. The representation of an otherness outside the prevailing notions of meaning and truth becomes a positive manifestation of this otherness as truth itself. Thus the historical “truths” of the grotesque are superseded by history itself. When the expressions of the grotesque solidify into static form and meaning, they become mere objects like anything else in the world. Instead of being this elusive thing of process and flow, it becomes tangible to the existing hierarchy of power as well as history itself. In this way the grotesque can be expunged, included or simply revealed as yet another false notion of truth, which is precisely what has happened with the grotesque throughout the course of history. If from the beginning the expression of the grotesque has not already been in the service of some structure of meaning and truth, it has quickly been included or has quickly included itself in such a structure. But by doing so it rejects its own basis: the tension between periphery and center is replaced by the attempt to create a new center, a new structure of meaning and truth. The doubleness, ambiguity and flow of the grotesque are then rejected by the grotesque itself. THE NON-FORM OF FORM In the critical thinking of Theodor W. Adorno (1903-69) the problem of art, caught between a reductive and prevalent notion of truth and meaning and a peripheral and alienated otherness, is reexamined and reformulated. For Adorno, the instrumental rationality of Enlightenment itself reverts into a new form of mythology which is every bit as static and exclusive as the hierarchies of religion it supersedes. All is excluded that is non-identical to the instrumental mastery of the objects of the world, "For the Enlightenment, anything which cannot be resolved into numbers, and ultimately into one, is illusion; modern positivism consigns it to poetry." 1 As such the non-identical has been banished from the realm of thought and action, and banished specifically to the realm of art. But the realm of art is not able to provide a decent home for it because even modern art is not something entirely autonomous. While it is excluded from the notions of truth and meaning provided by instrumental rationality, it still originates from society. Just like instrumental rationality art is about mastery, structuring and exclusion. Therefore, the problem for art is that it cannot directly provide a space for the non-identical because its mode of operation is similar to that of instrumental rationality. Even worse, art has very few possibilities to free itself from this. If it becomes l’art pour l’art it is at the same time reduced to the very thing instrumental rationality claims it to be: a subjective judgment of taste.expressionism also stands as an example of this. Conversely, art cannot work within the framework of the identity-thinking of society, because any notion of freedom or emancipation would reproduce the exclusive practices of instrumental rationality. For example: Explicit socialist literature may establish itself in opposition to instrumental rationality while at the same time reproducing it. Its language may seem different, but in reality it merely provides a different set of reductive schematics for human life and experience. The problem for the art of the grotesque was, as I mentioned earlier, that far too often it was merely a symbolic manifestation of a notion of otherness—not otherness itself. Because of this the subversive character of the grotesque ends up shaping and containing otherness instead of providing a space for it. According to Adorno the only way to avoid this is to radicalize the grotesque. In order to avoid solidifying into form the work of art has to be an object which cannot be contained in thought or form—a non-form of form. The work of art has to work in a way that it strives for autonomy but without entirely leaving a discernible reality. In other words, it has to pull in two directions at once. Thus the work of art is a paradox. It is autonomous in the sense that it closes itself off from everything outside of the work of art, trying to shy away from the contaminating influence of the identity thinking of instrumental rationality. At the same time though the work of art is heteronomous in the sense that it originates from a specific historical context and is bound to be what society is not. Autonomy and heteronomy are inseparably intertwined. Unable to display otherness itself, but still trying to be a refuge for it, there is only one option for art: It has to turn against itself and destroy its own logic of form, thereby demonstrating how any representation of otherness is impossible. Art becomes a lamentation of the victims of the identity thinking of instrumental rationality and shows the traces of the otherness that is unable to appear. Adorno’s pessimistic theory of art and history stages art as a negative dialectical process where the work of art closes itself off and rejects everything outside, while the individual elements in the work of art destroys its very own logic of form from within: Artworks synthetize ununifiable, nonidentical elements that grind away at each other; they truly seek the identity of the identical and nonidentical processually because even their unity is only an element and not the magical formula of the whole […]. The resistance to them of otherness, on which they are nevertheless dependent compels them to articulate their own formal language, to leave not the smallest unformed particle as remnant. This reciprocity constitutes art’s dynamic; it is an irresolvable antithesis that is never brought to rest in the state of being. 2 Relative to a traditional understanding of the grotesque, Adorno radicalizes the tension between center and periphery, autonomy and heteronomy. In the traditional understanding of the grotesque, as we find it for example in the writings of Mikhail Bakhtin, the grotesque establishes the display of otherness as a new center of meaning and truth. However Adorno rejects such notions and argues instead for a modernism of the grotesque in which both center and periphery are included in a negative dialectical process and continually synthesizing and destabilizing each other’s positions. A modernism of the grotesque works on the inside of the sign or the artwork, continually outlining and questioning the boundaries between materiality and form. This moves the focus away from the relation between the sign or work of art as a conceptual manifestation on one side and the object it refers to on the other side. Instead it implicitly points to the amorphous mass from which the signs and thereby meaning have been carved, the remnants that have been left behind. Modernism of the grotesque does not imply that it is emancipatory or that it reconciles man with nature, and does not represent a new position or a new ideology. It merely remembers and insists on the double nature of man and art: to write or paint yourself or an artwork whole by inscribing meaning in life or by applying form on a canvas is at the same time both creation and destruction. The very signs we use to center meaning in our lives carry its own alienation in them. Meaning surfaces only when process and flow comes to a halt—solidifying, but at the same time excluding parts that do not fit into that particular structure of meaning. NOTHING DONE AND NOTHING UNDONE It has always been difficult for art historians to find a suitable category for the works of the Danish artist Leif Lage (b. 1933). In his paintings the sensitive figuration seems so fragile that it is on the verge of turning into abstraction. Or conversely: the figurative emerges cautiously and hesitantly out of abstraction. As an art critic once wrote, he can almost paint things away. 3 Working in some undefinable space between abstraction and figuration, the Lage’s works shy away from the realm of words, and as a result few critics have been able to write anything meaningful about his works. In fact even fewer have been able to write more than one or two pages. The Danish author and art critic Leif Hjernøe is one of those few, but even he starts off by saying how impossible it is to write about Lage, confessing that his works exist both as process and in a field of in-between which words cannot reach. He writes: Always you find yourself in a place where nothing is done and nothing left undone, and where the elements of the work of art rest in a continuous motion. Always there is the open wound, where infection rather than surgical intervention is considered as an opportunity. And the conflict between matter and antimatter makes all diagnoses uncertain and allows conditions of uncertainty to spread in a place of raw presence. 4 The art works against the diagnosis and the certainty. Words are being eaten up by what is outside the realm of words: tension, process and doubleness. An approach to an understanding of the work of Lage could be to follow his connection to Samuel Beckett (1906-89). One can note, therefore, that Lage has illustrated several of the Danish translations of Beckett’s works. Though one is an author and the other a painter both seek a place where figuration, where the word, erodes. For both this entails an attempt to question and examine and so move in behind the façade of the surface in an exploration of that something or nothing that may be behind representation. At the same time even in the vanishing point of figuration or words, the meaningless words or the disjointed lines still stand as signs of human activity—signs of movement in emptiness. With very few exceptions Lage’s artworks revolve around one motif: Man—most often “en face.” But unlike traditional portraitures Lage’s people are found within. The artworks do not sense the reality of appearances, but rather the existential dimensions within man. As a seismograph they are sensitive to the utmost subjectivity in order to display an objective, sensuous depiction of the very problem of subjectivity. Instead of a static façade of a man, Lage’s “en face” shows the process-character of man. The people in Lage’s paintings are always in process—in the midst of becoming or dissolving. I will take a closer look in the following at the ways in which Lage establishes this sense of being in constant process, of being in-between modes or categories. THE DOUBLENESS OF THE STROKE Lage’s etchings attract attention in particular for the tension conveyed there between the material and the form. The material physically opposes the violence of the needle. But instead of embracing the violence of the needle and the victory over matter—instead of making the artistic creation and figuration express a heroic mastery of the background it is made out of—Lage uses the stroke to express the very tension between stroke and material, figuration and background. In the drypoint etching Untitled from 1983, which illustrated the Danish translation of Beckett’s Ill Seen, Ill Said , the needle tears up the material in long rough lines: Together, the primarily horizontal and vertical lines form a face. Thus the force needed to etch a line in the metal-plate draws attention to itself: It is there in the absence of curves and nuances. Man emerges on the metal-plate after great exertion and in a very simplistic form. This way Lage enhances the nature of the material, as the material’s resistance is not something to overcome. On the contrary the figuration is smitten by its very resistance and as such expresses the violence of its own becoming. Even more pronounced is the fact that the lines do not just show the violence of creation—it actively erases figuration in the same process that creates it. For example the mouth consists of 8-10 horizontal strokes, of which some seem to be connected to each other as if the mouth has been quickly scratched out. The mouth speaks of the inability to speak. In the same way, the eyes are black holes due to a large amount of criss-cross cuts, which together form a dark middle. Those lines, at the same time, form the eyes of the figuration and scratch out the eyes of the figuration. The extroverted aspects of the face—connected to speech and sight—are portrayed as introverted as well. Just as the etchings down into the metal-plate makes something appear. Leif Lage, Untitled , 1983 (etching) The figuration of the etching is connected to creation. It expresses that something is wrought into existence out of nothing by sheer artistic force. However, this force is at the same time presented as a violence of creation, which makes it impossible for form to truly emerge. Herein lies one of the basic principles of Lage’s art, namely that art cannot be that nothing or something behind the realm of words or signs. Without form, art would lose its ability to express anything at all. Form is a necessity if art is to avoid becoming as devoid of expression as the reality is that we cannot reach behind the appearance of things. On the other hand, art cannot raise itself above its own material in joyous celebration of the beauty of form. This would use the material in the manner of an instrument and thus would suppress the otherness it attempts to rescue. When art becomes mere form, any traces of otherness will have dissolved. Then art would be a question of technique, in no way different from the instrumental rationality of society. Therefore art works in a particular space between form and non-form. As Hjernøe says of the works of Lage, it is in the center of the event, in the in-between where things neither are nor are not, "And everything takes place just before it changes character. As the blood just before it coagulates, as the milk just before it separates, as fried egg just before it turns white […]." 5 The precise emphasis on the in-between of Lage’s art points in particular to the work of art as both outside of and in time. The work of art is a singular point in time, but at the same time it is continually in process. In the borderland between form and non-form, between creation and destruction, it shimmers like a fata morgana . The work is done but at the same time undone. It is only there as a cry in response to the inability to come into being. Akin to the etching is the drawing, but while both, of course, use the stroke or line as their main instrument, the paper does not resist the line in the same sense as the metal-plate of the etching. As a result in Lage’s drawings the stroke frolics in a space with almost no tension at all. There is nothing there to keep the pencil stroke at bay, but at the same time this means that there is nothing there to keep it together. One of the more expressive examples of this is found in an untitled drawing from Tegninger og Text ( Drawings and Text ) from 1999. The drawing consists of one unbroken pencil stroke. It is as if the stroke is confused—it darts around on the paper making doodles on the way or gathers itself in more straight lines in the center of the paper. It is in this manner that the semblance of a body is established. A couple of small circles serve as eyes and are the reason that the rest can be read as both face and body instead of pure abstraction. In fact the unbroken stroke serves as both abstraction and figuration as on the one hand it is the stroke that seemingly outlines the shape of a figure, while on the other hand the unbroken stroke dissolves any truly recognizable figuration by continuously, without end or aim, overflowing the boundaries of the figure. Seen again here is a doubleness to the stroke and the act of creation. In the etching it was all about the tension between the resistance of the material which created the doubleness. Here it is the opposite. It is the lack of tension. The stroke is free to do anything, but has no aim: without some kind of resistance, there is nothing to hold figuration together. It threatens to dissolve into nothingness. Conversely, the drawing can also be seen as a process of becoming. Like a form of automatic writing, the pencil darts around until it finds a point of densification. But even in such an interpretation of the drawing, the figuration appears artificial—it points to itself as the result of the artistic act of creation. The stroke is primarily stroke and only secondarily figuration. With its wild movement it calls attention to itself as stroke. Thus the figuration never becomes something in its own right. It points to the basic principle of creation: Someone has drawn me, I am the result of artistic endeavors, and therefore I am not for myself but always overflowing the boundaries that contain me. It is the stroke that in the very same movement creates figuration and dissolves it. Leif Lage, Untitled , 1999 (drawing) THE LIGHTNESS OF COLOR, THE DENSITY OF PAPER Often the watercolor is used as a precursor for larger paintings, because it has an immediacy in which one can quickly paint the main lines of a composition. However, Lage’s watercolors are not temporary points in a process leading to another final painting. They are not sketches, later to be filled with details in another material. For him watercolor is an end in itself. This also implies that he doesn’t try to work against the paper’s absorption of the water color and its tendency to absorb detail. On the contrary, he examines the possibilities inherent in this blurring of the line and absorption of color. As in the previous examples, there are of course recognizable shapes in Lage’s water colors. But these shapes are rarely separable from color, line or even paper. In other words: the figurative and the abstract more or less become one. One of the reasons for this is that Lage often works on wetted paper which means that the paper hungrily absorbs color into its fabric instead of it being on top of the paper. The paper becomes line because it is the absorption of the color which, together with the brush stroke itself, separates the colors from each other. The line is also color and the color is also line, because there is no separation between the different colors other than the colors themselves. At times this results in almost complete abstraction. In such cases Lage add lines with a pencil as if he wants to hold some sort of figuration together. At other times it is the other way around: the strokes of the pencil are a being dissolved by the water color blurring out the figuration. Untitled 1 from 1999 displays various tones of green. The contour of the colors appears unusually rough. Most of all it is reminiscent of a shoreline which has found its form through the work of thousands of years between water and land. Pockets of resistance surface as islands not yet drowned in color—as paper or color not yet consumed by the dominant color. The shape of the colors does not seem created by the hand of the artist, but rather by the inner workings of the watercolor: color against color over time has resulted in this very image, as if it is all a part of a natural process of change and decay. Despite the fact that there are no strong differences in color there seems to be a struggle taking place in the watercolor. For example, inexplicable holes in the dark color, which cover most of the right side of the watercolor, appear as if the underlying color is eating away the dark color, or that the dark color is in the process of covering up the underlying color. The small pockets of resistance demonstrate a process and development that, almost as a happy accident, evokes a couple of small eyes and a large mouth. Behind the colors a few slanted lines can be discerned, but the hand of the artist has long ago disappeared behind the life of the colors. Thus the watercolor seems to be held at precisely the point in time where figuration randomly appears. The small eyes and wide mouth seemingly express the realization of the figuration’s temporality. It is just a moment in time, soon to be consumed again in the life of the colors. The nature, the background it stems from and is part of, moves on undeterred, continuing its everlasting process of creation and decay. In this sense, the watercolor provides an experience of how neither artist nor man is able to transcend the materiality they consist of. The colors of man, the materials man consists of are “becoming” and “progress” but also “decay” and “disappearance”. The artist’s pencil strokes have been eaten up long ago, and the figuration is living on borrowed time. Human or artistic activity is about creating form, transcending mere matter by shaping and applying meaning to it. But Untitled 1 shows the doubleness of such creation: the transience and fragility of human life. Should the figuration come into being, should it rise and transcend the material, which binds it to its temporal existence, it would become nothing because its very existence is conditioned by the life and work of the colors. In the same sense man cannot escape his own temporality. He too, for better or worse, must accept a life in the volatility of sensation. Leif Lage, Untitled 1 , 1999 (watercolor) In most of Lage’s watercolors there seem to be a stronger artistic control than in Untitled 1 . Most often both the arrangement of colors and the technique in which they are painted express the hand of the artist. An example of this is Untitled 2 from 1999. While figuration in Untitled 1 seemed to appear as a happy accident, the figuration is much more “created” in Untitled 2 . Here the most important parts of the figuration, the eyes, the mouth and part of the skull, are colored black and painted on top of the background’s play of colors. The background primarily consists of blue and yellow tones. Only parts of the paper are covered in color, however, which yet again stresses the act of painting: There is a surface which is being filled by color by an artist. The blue tones are concentrated in the figuration, while the yellow tones surround it. All this means that the figuration stands out more clearly in this watercolor. This is also underlined by the fact that the blue and dark tones cover part of the yellow tones as spots here and there. Thus it is not a background which is in the process of consuming figuration, but rather the emerging figuration which blots out the background. Such an understanding is even suggested by how the mouth and eyes are placed in the larger blue color field. The eyes and mouth are in the center of the watercolor, while the blue color field is placed from center out towards the left side. This gives the impression of a face turned slightly to the right and slightly upwards, which again makes the mouth appear to emerge from the paper. It also helps that the mouth cuts the center axis of the watercolor. In other words, the arrangement of the blue and black colors create some depth and perspective which gives the illusion of a figuration, seen partially in profile, emerging from the background. Seen in profile, the eyes and mouth seem extroverted—they almost seem as if they are put on top of the face. But at the same time they are painted as black holes, sucking in the gaze of the onlooker. The watercolor is even more challenging if one follows what may be the faint outline of the skull, which, on the right side of the watercolor, no longer works together with the blue color, but rather alone postulates the outline of the skull. If not the blue color field, but this line, is the outline of the skull, then all of a sudden the face is not in profile but “en face”—staring directly towards the onlooker. Outline and color seemingly work against each other and establish two different expressions. Without the slightly upward tilted expression of the profile, the eyes and mouth do not seem to emerge from the paper. On the contrary, seen “en face,” the eyes and mouth are really gaping pits of darkness. In this sense Untitled 2 is at the same time surface and depth of perspective. The line gives form but at the same time it dissolves the form created by the colors, and vice versa. Leif Lage, Untitled 2 , 1999 (watercolor) As the last example of Lage’s artistic method, I have chosen another untitled work (as indeed nearly all of Lage’s artworks are)—this time from 2000. This is perhaps one of the most figurative watercolors Lage has created, though that doesn’t tell us too much. The painting depicts a human face in blue and green tones on a yellow toned background. The colors create a clear demarcation between the figure and the background, which compensate for the watercolor’s lack of outline. Beneath the face darker tones imply the beginning of the torso, and nuances of color even hint at something which could be a collar. The hair is in even darker tones and its structure is emphasized using pencil strokes on top of the water color. One eye is marked by a brown spot with a darker spot in the middle, while the other eye is added by pencil. The mouth is a round, red dot. In Untitled from 2000 the work between abstraction and figuration is much less pronounced than in the previous examples cited here. Nonetheless the watercolor has a delicacy to it which almost makes the figuration disappear, even as it appears. This has something to do with the fact that all the individual brush strokes have dissolved. The only outlines are those created by the clash of colors. Even the red mouth seems to be more paint than mouth—unable to be formed truly as anything other than a speck of color with some small semblance to a mouth. In contrast to the other watercolors, there is no movement, no progress or decay, just a vibrating standstill. The figure is not emerging or disappearing but embedded in and as surface, and as such it makes the figure seem stuck in its condition rather than freed by the act of giving form: mouth open as a wound. Pencil strokes add detail and life to the hair as an attempt to help the figure emerge. But all this does is create two levels in the watercolor: The pencil strokes are put on top of the figuration rather than being part of it. Thus they end up highlighting the endless distance between the movement and form-giving of the pencil strokes and the static and stuck figure behind these strokes. Leif Lage, Untitled , 2000 (watercolor) MAN AND THE VIEW OF THE ONLOOKER Lage’s works seem at the same time to be an examination of tensions between form and material in art and a display of an image of man full of the same tensions. This is because the people who are emerging in Lage’s images are not just in his works, They are his works. This means that man is not something emerging from a background but is part of this background and vice versa. The art of Lage inscribes man in its surroundings and background. Man is not the ruler of nature. Man does not rise above matter; there is no truly transcendent position for man to occupy in the art of Lage. Instead man is a part of the very matter, it, at the same time, tries to distance itself from in order to distinguish itself from its surroundings. Man emerges in an attempt not to be line, stroke, color. In an attempt to free itself of matter. Should it succeed in this, however, it would turn into nothing. On the other hand, if man fully accepted itself as mere matter it would disappear in it—in instincts, urges and lack of reflection. The appearance of man is thus subject to a state of being in-between. Only in the tension between material and its negation can the outlines of man be traced. However this also means that in the art of Lage man is never something in itself but always in process—on the way to its freedom and its loss. However, Lage’s art is not just about showing the tensions inherent in man but also about showing such tension on the verge of breaking point. In the moment before everything is done, or when nothing yet has been done, the delicate tension between form and material has been stretched to its utmost in such a way that man’s character of process emerges and is contained on the paper or canvas. Therefore, Lage’s art contain traces of human life. Not only is it an autonomous unity of tensions where man is stretched out between its singularity and the surroundings it is a part of. It is also this pulsation between figuration and material which brings about the traces of human endeavor and activity. Even when man almost seems to have disappeared into the material, strokes and lines are still there as a reminder of human activity and potential creative power—as a reminder that hope is still possible and that man is still there. The view of the onlooker seeks out forms and meaning. It seeks outlines and edges. But first and foremost it is the eyes in Lage’s works of art that allow the onlooker to decode the figuration at play. This creates a distinctive relationship between the onlooker and the artwork. The onlooker tries to wrest the enigma from the artwork, tries to reduce it to solid, meaningful form. But the very same moment that hints at such a possibility sees the view of the onlooker confronted with a gaze of its own. The eyes of the figure in the work of art are most often dark pits, as if they were an illustration of the violence committed against the eyes of the onlookers and their search for meaning. Or as if they were a dark reflection of the onlooker’s failed attempts to delineate the traces of life in the artwork to a solid meaningful form. Therefore, the gaze of the figuration speaks not only of its own powerlessness but also of the powerlessness of the onlooker. When the view or sight has trouble finding solid meaningful forms, it has something to do with the fact that the precondition for sight, light, no longer stems from something transcendent. In Lage’s art there is nothing outside the works of art, nothing outside of human life, and as such nothing to shed light on the works of art or human life and reveal solid meaningful forms. All light comes from within. In a western context, light as a medium for sight is central to the understanding of meaning. People speak of the clarity of thought, while knowledge is tied together with enlightenment, and so forth. But the light no longer originates from a divine point of view. It originates from man, who has created himself in the image of God. The problem with this is that light always covers up its own base. Light illuminates something but at the same time it hides itself. 6 While it was previously God who was unknowable, now it is man. It is also problematic that sight and the medium of sight stem from the same place. Following this thought one can posit two final problems. Firstly, the immediacy and presence established by light by making forms and objects accessible to sight is fake. Light is not some independent entity which present things in a neutral manner for the onlooker. It is inextricably tied together with the gaze’s desire after meaning. In other words: Light perverts the appearance of things because it doesn’t originate from some objective entity which allows them to appear as they are. Instead light is based upon and originates from the subject and its conquering gaze, seeking out meaning and form constantly. Secondly, the joining of sight and light makes introspection within human life impossible. Everything can be illuminated by its use value for the subject but only as long as it is separated from the subject, as long as it is an object. But the subject itself cannot be illuminated. Lage’s art tears down such a dividing line between subject and matter, but it does so without reestablishing a divine position from where the light emanates. Therefore, the light in Lage’s art may not illuminate very well. It may not have the certainty presented by modern science or the religions of yesterday. But it does show what such light tries to hide, namely, the subject as it is in its material reality—inscribed in time and death, which are the basic conditions of materiality, but at the same time also full of life in its joy and will to create. For the onlooker the meeting of the gaze in Lage’s works of art is thus also a destruction of the view of the onlooker. The ability to see is challenged in a radical way. Those outlines will not solidify into static form, as if the light was too dim to see. Just as in Lage’s figurations, the view of the onlooker turns to black: turns towards the onlooker in recognition and becoming—or disappearance. NOTES Max Horkheimer and Theodor W. Adorno. Dialectic of Enlightenment . (Palo Alto: Stanford University Press, 2002): 4-5. Theodor W. Adorno. Aesthetic Theory . (London & New York, 2002): 176. Carsten Bach-Nielsen. “Mere glæde end gru.” Kristeligt Dagblad . September 24, 2002. Leif Hjernøe. “Den yderliggående inderlighed.” LEIF LAGE—Retrospektiv udstilling 1983 . (Copenhagen: Brøndum, 1983): 18. Ibid. Maurice Blanchot. The Infinite Conversation . (Minneapolis: University of Minnesota Press, 1993): 162-163. (shrink)

The debate on the possibility of attaining metaphysical knowledge by the method of reasoning began with the ancient Greek philosophers and continues to this day. This article aims to examine how Râzî argues for the possibility of attaining metaphysical knowledge through the method of reasoning. He first argues that existence has two parts, the sensed and the thought, in order to demonstrate that metaphysical knowledge can be obtained through the method of reasoning. Then he tries to prove (...) that existence is not limited to the material. After presenting evidence for the existence of things other than the sensible in existence that can be perceived with the intellect, he tries to discuss our devices to relate to this sphere of existence in a comparative manner. In this comparison, two possible devices for attaining metaphysical knowledge emerge: the theoretical intellect and the purified soul. After revealing the positive and negative aspects of both in this comparison, he argues that the most reliable device is the theoretical intellect and the technique is the method of reasoning Râzî gives various answers to those who object to the possibility of obtaining metaphysical knowledge through the method of reasoning. Râzî tries to put forward the grounds on which the groups who object to the method of reasoning are based. He then evaluates their justifications in terms of accuracy and consistency. Thus, he tests both the relevance of each group's objection to the subject and its consistency with the group's other beliefs. He then presents the justifications for his own opinion on the method of reasoning and the consistency of this method with his other beliefs. Following this method, Râzî first divides those who object to the method of reasoning into two categories according to whether or not they accept a metaphysical sphere of existence. According to this division, those who object to the method because they do not accept a metaphysical sphere of existence are the Sophists, Sumeniyya, Mujasimah, Dhahriyya, and Hashawiyya. Although this group does not accept a metaphysical sphere of existence, they are divided into two classes: those who believe in God and those who do not. According to Râzî, the group that accepts the metaphysical sphere of existence but objects to the method of reasoning is the Talimiyya. They claim that metaphysical knowledge can only be attained through the teaching of an innocent instructor, not by the method of reasoning. The different approaches of these groups are the reason why Râzî sometimes emphasizes accuracy, sometimes consistency, and sometimes proving the metaphysical domain of existence in his answers to those who object to the method of reasoning. (shrink)

Stojnić et al. (2013, 2017) argue that the reference of demonstratives is fixed without any contribution from the extra-linguistic context. On their `prominence/coherence' theory, the reference of a demonstrative expression depends only on its context-independent linguistic meaning. Here, we argue that Stojnić et al.’s striking claims can be maintained in only the thinnest technical sense. Instead of eliminating appeals to the extra-linguistic context, we show how the prominence/coherence theory merely suppresses them. Then we ask why one might be tempted to (...) try and offer such a view. Since we are rather sympathetic to the motivations we find, we close by sketching a more plausible alternative. (shrink)

Few interpreters of Aristotle have denied that both empirical, inductive methods and some kind of systematic deduction played a role in the philosophy of the biologist who expounded the West's first formal logic. But it has usually been the fashion to focus on one side of this polarity. In recent decades the focus has been on the empirical Aristotle. But some of the latest studies emphasize that Aristotle varied his methods according to context. G. E. L. Owen, for example, although (...) he feels that Aristotle took little care to separate inductive and deductive methods in the treatises, does allow that he uses deduction at times, and mentions book 6 of the Physics among them. (shrink)