Online research in philosophy

This paper explores the distinction between perceiving an object as extended in time, and experiencing a sequence of perceptions. I argue that this distinction cannot be adequately described by any present theory of time-consciousness and that in order to solve the puzzle, we need to consider perceptual content as having three distinct constituents: Explicit content, which has a particular phenomenal character, modal content, or the kind of content that is contributed by the psychological mode, and implicit content, which lacks phenomenal (...) character. These notions are then further clarified and related to each other. (shrink)

Abstract I develop the idea that there exists a special dimension of depth, or of scale. The depth dimension is physically real and extends from the bottom micro-level to the ultimate macro-level of the Universe. The depth dimension, or the scales axis, complements the standard three spatial dimensions. I discuss the tentative qualities of the depth dimension and the universal arrangement of matter along this dimension. I suggest that all matter in the Universe, at least in the present cosmological epoch, (...) is in joint downward motion along the depth dimension. The joint downward motion manifests itself in the universal contraction of matter. The opposite direction of motion, upward the dimension, would cause the expansion of matter. The contraction of matter is a primary factor, whereas the shrinking of space in the vicinity of matter is a derivative phenomenon. The observed expansion of the Universe is explained by the fact that celestial bodies become smaller due to matter contraction, while the overall space remains predominantly intact. Thus, relative to the contracting material bodies, the total span of cosmic space appears to be becoming vaster. I attempt to explain how the contraction of matter engenders the effect of universal gravity. I use over thirty animated and graphical color visualizations in the text to make the explanation of the proposed ideas more lucid. Content Type Journal Article Category Original Paper Pages 1-39 DOI 10.1007/s10516-011-9178-4 Authors A. Alyushin, Department of Philosophy, The Higher School of Economics, 20 Myasnitskaya Street, 101000 Moscow, Russia Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

Abstract Since modernity, the concept of subject supposes both an anthropocentric and a dualistic view of life and reality. In this study, we carry out an analytic interpretation of the Descartes’ notion of subject, in order to build a different dimension of the concept of subject. We discuss the activity of computing, as the manner by which the living subject relates with and in-forms the world. We further examine computing in the aging yeast as an example of living subject and (...) we try to comprehend the maturity of the subjectivity in Descartes’ res cogitans and in our proposed res computans . Content Type Journal Article Category Original Paper Pages 1-12 DOI 10.1007/s10516-011-9177-5 Authors María Belén Campero, Center of Philosophical Investigations, CONICET, Buenos Aires, Argentina Cristián Favre, Institute of Experimental Physiology, CONICET, School of Biochemical Sciences, University of Rosario, Suipacha 570, S2002LRL Rosario, Argentina Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

Contingencies in Nature may be explained, but such explanations refer to other contingencies (pt. I). Is there a way to “explain away” all contingencies? The first physical theory of modern times, Newton’s theory of gravitation, was received in a way that leaves this question open (pt. II), while Kepler’s theory of cosmological harmony arrived at a positive solution (pt. III). However, later developments in science outdated Kepler’s approach (pt. IV).

This paper is an extended discussion of Robert Ulanowicz’s critique of mechanistic and reductionistic metaphysics of science. He proposes “process ecology” as an alternative. In this paper I discuss four sets of question coming out of Ulanowicz’s proposal. First, I argue that universality remains one of the hallmarks of the scientific enterprise even with his new process metaphysics. I then discuss the Second Law of Thermodynamics in the interpretation of the history of the universe. I question Ulanowicz’s use of the (...) terms “random” and “chance” in his definition of process. Finally, I discuss what difference a relational and process metaphysics might make in addressing the political and practical problems in the twenty-first century. (shrink)

In this article I intend to show that certain aspects of the axiomatical structure of mathematical theories can be, by a phenomenologically motivated approach, reduced to two distinct types of idealization, the first-level idealization associated with the concrete intuition of the objects of mathematical theories as discrete, finite sign-configurations and the second-level idealization associated with the intuition of infinite mathematical objects as extensions over constituted temporality. This is the main standpoint from which I review Cantor’s conception of infinite cardinalities and (...) also the metatheoretical content of some later well-known theorems of mathematical foundations. These are, the Skolem-Löwenheim Theorem which, except for its importance as such, it is also chosen for an interpretation of the associated metatheoretical paradox (Skolem Paradox), and Gödel’s (first) incompleteness result which, notwithstanding its obvious influence in the mathematical foundations, is still open to philosophical inquiry. On the phenomenological level, first-level and second-level idealizations, as above, are associated respectively with intentional acts carried out in actual present and with certain modes of a temporal constitution process. (shrink)

This article is composed of three sections that investigate the epistemological foundations of Husserl’s idea of logic from the Logical Investigations . First, it shows the general structure of this logic. Husserl conceives of logic as a comprehensive, multi-layered theory of possible theories that has its most fundamental level in a doctrine of meaning. This doctrine aims to determine the elementary categories that constitute every possible meaning (meaning-categories). The second section presents the main idea of Husserl’s search for an epistemological (...) foundation for knowledge, science and logic. Their epistemological clarification can only be reached through a detailed analysis of the structure of those intentions that give us what is meant in our intentions. To reveal the intuitive giveness of logical forms is the ultimate aim of Husserl’s epistemology of logic. Logical forms and meaning-categories can only be given in a certain higher-order intuition that Husserl calls categorical intuition. The third section of this article distinguishes different kinds of categorical intuition and shows how the most basic logical categories and concepts are given to us in a categorical abstraction. (shrink)

In this paper I provide a framework—what I refer to as ‘development theory’—for Ulanowicz’s ascendency theory of ecosystem development. Development theory is based in thermodynamics and information theory. A prominent feature of development theory is an understanding of senescence.

I argue that Amie Thomasson’s recent theory of the methodology to be applied to find the truth-conditions for claims of existence faces serious objections. Her account is based on Devitt and Sterelny’s solution to the qua problem for theories of reference fixing; however, such a solution cannot be also applied to analyze existential claims.

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical (...) geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl’s ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl. (shrink)

After a “very personal” introduction, and a reference to how accurate indeed is the use of the “new window” metaphor by Ulanowicz and about what “can be seen through it”, the article dwells into the evolution of our understanding about the most general sources—material and/or non-material—of change and transformation; in order to examine further the item about the ways through which “information” can be a source of change and transformation also in pre-biotic processes, where commonly it is not taken into (...) account. Thus, the article argues the convergence between Ulanowicz’s and the Author’s treatments of—non only biotic—networks of configuration of processes (a central theme in Ulanowicz’s book). Finally, the article pays attention to how Ulanowicz’s vision through his “new Third Window”, can indeed help us transcend the non desirable division of contemporary culture into two isolated compartments (science and technology versus the humanities and ethics), which has contributed not only to the globalization of communications, transactions, knowledge and so on, but also to the globalization of multiple crisis of different sort that need to be solved if we want “a better world to be possible”. (shrink)

This work speaks about very special solution of the mind–body problem. This solution based on the so-called Principle of Co - existence stands out as one of the most interesting attempts at solving the mind–body problem. It states that substances can only exert a mutual influence on one another if they have something in common. This does not have to be a common property but rather, a binding relationship. Thus, substances co-exist when they remain bound by a common relationship, for (...) instance, to an external subject. The Principle of Co - existence played an extremely important role in Kant’s philosophy, not only since it provided a framework for solving the mind–body problem, but since it captured the very basis of its existence. The Principle found also reflection in the works of Kant’s successors, such as Fichte, Schelling, Hegel or Feuerbach. It had significant—though often hidden—repercussions on later philosophy of mind. The notion of force and the principle of its operation became key concepts in resolving the mind–body problem. As a result, philosophy of mind concentrated on the search for a principle explaining the occurrence of two complementary types of phenomena. This established a tradition which, to a greater or lesser extent, has survived to our day. (shrink)

The respondent agrees with William Grassie that many windows on nature are possible; that emphasis must remain on the generation of order; that “chance” would better be recast as “contingency”; and that the ecological metaphysic has wide implications for a “politics of nature”. He accepts the challenge by Pedro Sotolongo to extend his metaphysic into the realm of pan-semiotics and agrees that an ecological perspective offers the best hope for solving the world’s inequities. He replies to Stanley Salthe that he (...) now agrees that the second law of thermodynamics is the overarching law of nature, but only when the duality inherent in of the concept of entropy is widely recognized. The respondent is enthusiastic over Jeffrey Lockwood’s extrapolation of process ecology to include the concept of “species” and over John Haught’s description of how the construct paves the way for a “theology of evolution” by recasting evolution as an unfolding “drama”. (shrink)

This paper asks whether persistence can be a matter of convention. It argues that in a rather unexciting de dicto sense persistence is indeed a matter of convention, but it rejects the notion that persistence can be a matter of convention in a more substantial de re sense. However, scenarios can be imagined that appear to involve conventional persistence of the latter kind. Since there are strong reasons for thinking that such conventionality is impossible, it is desirable that our metaphysical-cum-semantic (...) theories of persistence be able to account for such scenarios in terms of conventions of the first kind. Later parts of the article therefore investigate whether three of the currently most influential metaphysical-cum-semantic theories of persistence—the endurance theory, the stage theory, and the perdurance theory—can do this. Fortunately, for them, it turns out that all can, though some philosophers have disputed this. However, when we ask how they account for a typical case of “conventional persistence” some problematic features of the theories —having to do with reference, persistence conditions, how they relate, and the epistemology of persistence — are revealed. (shrink)

Exemplification can be found in ontologies from the ancient world, such as those of Plato and Aristotle, and more recent ontologies, in particular those that take what exists to be determined by the empiricist’s Principle of Acquaintance. This study examines some of the ways in which exemplification takes different forms in these different ontologies. Exemplification has also been criticized as an ontological category. This paper examines a number of these criticisms, to see the extent to which they are viable.

My goal is to conceive how the reality would look like for hypothetical creatures that supposedly perceive on time scales much faster or much slower than that of us humans. To attain the goal, I propose modelling in two steps. At step one, we have to single out a unified parameter that sets time scale of perception. Changing substantially the value of the parameter would mean changing scale. I argue that the required parameter is duration of discrete perceptive frames, or (...) snapshots, whose sequencing constitutes perceptive process. I show that different standard durations of perceptive frames is the ground for differences in perceptive time scales of various animals. Abnormally changed duration of perceptive frames is the cause of the effect of distorted subjective time observed by humans under some conditions. Now comes step two of the modelling. By inserting some arbitrary duration of a perceptive frame, we set a hypothetical scale and thus emulate a viewpoint for virtual observation of the reality in a wider or narrower angle of embracing events in time. Like changing lenses of a microscope, viewing reality in different temporal scales makes certain features of reality manifested, others veiled. These are, in particular, features of life. If we observe an object in an inappropriate interval, we may not notice the very essence of a process it is undergoing. (shrink)

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the first (...) two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered. (shrink)

A widely accepted thesis in the philosophy of language is that natural language proper names are rigid designators, and that they are so de jure, or as a matter of the “semantic rules of the language.” This paper questions this claim, arguing that rigidity cannot be plausibly construed as a property of name types and that the alternative, rigidity construed as a property of tokens, means that they cannot be considered rigid de jure; rigidity in this case must be viewed (...) as a pragmatic and not a semantic property. (shrink)

This paper focuses on the relation between logic and ontology. In particular, it demonstrates how classical logical theory can clarify the ontological part of Ludwig Wittgenstein’s Tractatus Logico-Philosophicus. To this end, the work examines the adequacy of a formal system that was devised by the Polish logician, mathematician and philosopher Roman Suszko (1919–1979) as a model for the Tractatus. Following a brief explanation of the Tractarian ontology, the main ideas of Suszko’s system and its philosophical significance will be considered. The (...) latter will be illustrated in the context of central Tractarian concepts. Finally, two implications for a better understanding of the Tractarian ontology will be pointed out. (shrink)

Abstract In the year 1894, Husserl had not been already contaminated by Bolzano’s realism. It was then that he conceived a theory of assumptions in order to “save an existence” for mathematical objects. Here we would like to explore this theory and show in what way it represented a convincing alternative to realistic ontology and its counterpart: the correspondence theory of truth. However, as soon as he designed it, Husserl shoved away all the implications for his theory of assumptions, and (...) merely abandoned it. We would also like to consider the wrong reasons for this renouncement, which undoubtedly have to do with the dichotomy between signification and perception in his elaboration of phenomenology. Content Type Journal Article Category Invited paper Pages 1-15 DOI 10.1007/s10516-011-9158-8 Authors Robert Brisart, Facultés universitaires Saint-Louis, Bruxelles, Belgium Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

Second-order logic has a number of attractive features, in particular the strong expressive resources it offers, and the possibility of articulating categorical mathematical theories (such as arithmetic and analysis). But it also has its costs. Five major charges have been launched against second-order logic: (1) It is not axiomatizable; as opposed to first-order logic, it is inherently incomplete. (2) It also has several semantics, and there is no criterion to choose between them (Putnam, J Symbol Logic 45:464–482, 1980 ). Therefore, (...) it is not clear how this logic should be interpreted. (3) Second-order logic also has strong ontological commitments: (a) it is ontologically committed to classes (Resnik, J Phil 85:75–87, 1988 ), and (b) according to Quine (Philosophy of logic, Prentice-Hall: Englewood Cliffs, 1970 ), it is nothing more than “set theory in sheep’s clothing”. (4) It is also not better than its first-order counterpart, in the following sense: if first-order logic does not characterize adequately mathematical systems, given the existence of non - isomorphic first-order interpretations, second-order logic does not characterize them either, given the existence of different interpretations of second-order theories (Melia, Analysis 55:127–134, 1995 ). (5) Finally, as opposed to what is claimed by defenders of second-order logic [such as Shapiro (J Symbol Logic 50:714–742, 1985 )], this logic does not solve the problem of referential access to mathematical objects (Azzouni, Metaphysical myths, mathematical practice: the logic and epistemology of the exact sciences, Cambridge University Press, Cambridge, 1994 ). In this paper, I argue that the second-order theorist can solve each of these difficulties. As a result, second-order logic provides the benefits of a rich framework without the associated costs. (shrink)

The present paper is intended to analyse from a theoretical point of view the relationships between natural language and idiolects in the context of communication by means of the Davidson–Dummett controversy on the nature of language. I will explore from a pragmatic point of view the reliability of an alternative position inspired by the recent literalism/contextualism debate in philosophy of language in order to overcome some limitations of Dummett’s and Davidson’s perspectives on language, idiolects and communication.

Conceptual realism begins with a conceptualist theory of the nexus of predication in our speech and mental acts, a theory that explains the unity of those acts in terms of their referential and predicable aspects. This theory also contains as an integral part an intensional realism based on predicate nominalization and a reflexive abstraction in which the intensional contents of our concepts are object -ified, and by which an analysis of predication with intensional verbs can be given. Through a second (...) nominalization of the common names that are part of conceptual realism’s theory of reference (via quantifier phrases), the theory also accounts for both plural reference and predication and mass noun reference and predication. Finally, a separate nexus of predication based on natural kinds and the natural properties and relations nomologically related to those natural kinds, is also an integral part of the framework of conceptual realism. (shrink)

Abstract Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of (...) physical geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl’s ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl. Content Type Journal Article Category Invited paper Pages 1-26 DOI 10.1007/s10516-011-9161-0 Authors Jairo José da Silva, Unesp-Rio Claro, Rio Claro, Brazil Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

Relations occur on all levels of systems. Following a major assumption of generalized quantum theory, namely that the principles of quantum mechanics will occur on higher system levels as well, it was investigated in an a posteriori analysis of pre-existing data whether relational patterns found for two-photon experiments are similarly performed by two cell-populations. In particular, the typical pattern in outcomes of two-photon entanglement experiments was extrapolated to discover similar patterns of relationships in the cellular biological system of the Ciliate (...) Paramecium caudatum. In the former case we find one photon assuming a particular state when being measured and the other assuming a correlated state with regard to the first particle. From a perspective of degrees of freedom (df) the author interprets this outcome as follows: Each particle has only one df for assuming a particular state (e.g. its spin). When measured this is leading to a pattern: They use their two degrees of freedom for establishing a relation among them (particle-to-particle) and for a relation with the environment (particle-to-measurement). If this pattern is unique then we should find it also in cell-to-cell relationships. It was suggested to consider causations in cell-to-cell relations as the analogue to the relationship between the quantum particles (see above) and the dependence of repeating the experiments as the analogue to the measurement event in the quantum experiment. It was hypothesized that in a relational system of two cell populations only one should be sensitive to the repetition of the experiment. The other population, however, should establish a relation with the first one. Since the author had successfully performed experiments with pairs of cell populations that were separated with glass barriers from each other but having effects on each other (Fels in PLoS One 4:e5086, 2009), the system was perfectly well suited for testing the hypothesis. The assessed cell variable was cell division. An a posteriori analysis of three similar experiments confirmed that when populations were in a relation with each other, only one of them stood in relation with the repetition of the experiment. (shrink)

Abstract How do we reconcile Husserl’s repeated criticism of Mach’s phenomenalism almost everywhere in his work with the leading role that Husserl seems to attribute to Mach in the genesis of his own phenomenology? To answer this question, we shall examine, first, the narrow relation that Husserl establishes between his phenomenological method and Mach’s descriptivism. Second, we shall examine two aspects of Husserl’s criticism of Mach: the first concerns phenomenalism and Mach’s doctrine of elements, while the second concerns the principle (...) of economy of thought, which Husserl closely associates with a form of psychologism in his Logical Investigations . Our working hypothesis is that the apparent contradictory comments of Husserl regarding Mach’s positivism can be partially explained by the double status he confers to his own phenomenology—as a philosophical program radically opposed to positivism, and as a method akin to Mach’s descriptivism. Content Type Journal Article Category Invited Paper Pages 1-22 DOI 10.1007/s10516-011-9159-7 Authors Denis Fisette, Université du Québec à Montréal, Montreal, Canada Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

In most computational ontologies, information inheritance is based on the taxonomic relation is_a. A given type inherits from other type only if the latter subsumes the former. We assume, however, that inheritance can be related, not only to the taxonomic relation, but also to the meronymic relationship between parts and wholes. The main aim of this paper is to organise upper-level ontologies associated with lexical information by taking into account part-whole subsumption. As we consider that parts may subsume wholes under (...) specific conditions, ontologies can be defined in terms of systems in which wholes inherit information from its parts. In this article, we describe how part-whole subsumption and, then, meronymic inheritance can be used to deal with type mismatch and metonymic interpretation of polysemous nouns. For this purpose, we attempt to merge old assumptions from both formal ontology and lexical semantics into a homogeneous framework. (shrink)

The paper relates the basic ontological categories defined by Roman Ingarden to an engineering model of function known by the name of Functional Basis. The intended aim of this exercise in applied philosophy is to make this model more consistent and outline some possible extensions thereof.

Attempts to explicate the substance-property nexus are legion in the philosophical literature both historical and contemporary. In this paper, I shall attempt to impose some structure into the discussion by exploring ways to combine two unlikely bedfellows—Platonic properties and Aristotelian substances. Special attention is paid to the logical structure of substances and the metaphysics of property exemplification. I shall argue that an Aristotelian-Platonic account of the substance-property nexus is possible and has been ably defended by contemporary philosophers.

This paper is concerned with the use of logic to solve philosophical problems. Such use of logic goes counter to the prevailing empiricist tradition in analytic circles. Specifically, model-theoretic tools are applied to three fundamental issues in the philosophy of logic and mathematics, namely, to the issue of the existence of mathematical entities, to the dispute between first- and second-order logic and to the definition of analyticity.

How are philosophical questions about what kinds of things there are to be understood and how are they to be answered? This paper defends broadly Fregean answers to these questions. Ontological categories—such as object , property , and relation —are explained in terms of a prior logical categorization of expressions, as singular terms, predicates of varying degree and level, etc. Questions about what kinds of object, property, etc., there are are, on this approach, reduce to questions about truth and logical (...) form: for example, the question whether there are numbers is the question whether there are true atomic statements in which expressions function as singular terms which, if they have reference at all, stand for numbers, and the question whether there are properties of a given type is a question about whether there are meaningful predicates of an appropriate degree and level. This approach is defended against the objection that it must be wrong because makes what there depend on us or our language. Some problems confronting the Fregean approach—including Frege’s notorious paradox of the concept horse—are addressed. It is argued that the approach results in a modest and sober deflationary understanding of ontological commitments. (shrink)

There are, broadly, three sorts of account of intrinsicality: ‘self-sufficiency’, ‘essentiality’ and ‘pure qualitativeness’. I argue for the last of these, and urge that we take intrinsic properties of concrete objects to be all and only those shared by actual or possible duplicates, which only differ extrinsically. This approach gains support from Francescotti’s approach: defining ‘intrinsic’ in contradistinction to extrinsic properties which ‘consist in’ relations which rule out intrinsicality. I answer Weatherson’s criticisms of Francescotti, but, to answer criticisms of my (...) own, I amend his account, proposing that possession of an extrinsic property consists in a relation to one or more actual or possible distinct concrete objects. Finally I indicate ways to avoid some apparent objections to this account. (shrink)

In his 1896 lecture course on logic–reportedly a blueprint for the Prolegomena to Pure Logic–Husserl develops an explicit account of logic as an independent and purely theoretical discipline. According to Husserl, such a theory is needed for the foundations of logic (in a more general sense) to avoid psychologism in logic. The present paper shows that Husserl’s conception of logic (in a strict sense) belongs to the algebra of logic tradition. Husserl’s conception is modeled after arithmetic, and respectively logical inferences (...) are viewed as analogical to arithmetical calculation. The paper ends with an examination of Husserl’s involvement with the key characters of the algebra of logic tradition. It is concluded that Ernst Schröder, but presumably also Hermann and Robert Grassmann influenced Husserl most in his turn away from psychologism. (shrink)

In A Third Window Robert Ulanowicz exposes the explanatory weaknesses of both classical and statistical methods in scientific inquiry. His book, however, does much more than that. While being completely grounded in empirical science, it also outlines a worldview, or a metaphysics, that renders intelligible the fact of chance and emergent novelty. Ulanowicz establishes his position by comparing his third window onto nature with two others conventional scientific approaches. The purpose of this essay is to point out the value of (...) Ulanowicz’s approach for improving the quality of conversation between science and theology. (shrink)

Anna-TeresaTymieniecka writes of a dynamic skeleton for future fusions of sense rising from the seemingly disjointed situation of philosophy and details how her phenomenology of life can put flesh on it. Examined here are her efforts to: uncover the deep-lying intelligibility of life by emphasizing the role of the logos of life in connection with meaning structures developed by Husserl; undertake a critique of phenomenological reason; delineate life’s path, not from cognition in isolation, but from within the fullness of human (...) functioning in all its complexity; give Husserl’s phenomenology a metaphysico-existential foundation; analyze the human creative process penetrating the very individualized meanderings of life; show how the creative logos reaches into communal/societal life and opens the way to spiritual and sacral horizons of experience. (shrink)

In “Function and Concept” and “On Concept and Object”, Frege argued that certain differences between dependent and independent meanings were inviolable and “founded deep in the nature of things” but, in those articles, he was not explicit about the actual consequences of violating such differences. However, since by creating a law that permitted one to pass from a concept to its extension, he himself mixed dependent and independent meanings, we are in a position to study some of the actual consequences (...) of his having done so. To make certain of Frege’s ideas about the inviolability of logical form more tangible, I describe a string of very interrelated consequences that his attempt to transform dependent meanings into independent meanings actually brought in its wake. (shrink)

The article considers, in a historical setting, the links between varieties of nominalism—the extreme nominalism of the Quine-Goodman variety and the trope nominalism current today—and types of idealism. In so doing arguments of various twentieth century figures, including Husserl, Bradley, Russell, and Sartre, as well as a contemporary attack on relations by Peter Simons are critically examined. The paper seeks to link the rejection of realism about universals with the rejection of a mind-independent world —in short, linking nominalism with idealism.

The question whether qualities are metaphysically more fundamental than or mere limiting cases of relations can be addressed in an applied symbolic logic. There exists a logical equivalence between qualitative and relational predications, in which qualities are represented as one-argument-place property predicates, and relations as more-than-one-argument-place predicates. An interpretation is first considered, according to which the logical equivalence of qualitative and relational predications logically permits us ontically to eliminate qualities in favor of relations, or relations in favor of qualities. If (...) metaphysics is understood at least in part as an exercise in ontic economy, then we may be encouraged to adopt a property ontology of qualities without quality-irreducible relations, or relations without relation-irreducible qualities. If either strategy is followed, the choice of reducing qualities to relations or relations to qualities will need to be justified on extra-logical grounds. These might include a perceived greater intuitiveness, explanatory fecundity, compatibility with cognitive ontogeny or developmental psychology, expressive or explanatory elegance or cumbersomeness, and an open-ended list of philosophical motivations that could reasonably favor the ontic prioritization of qualities over relations or relations over qualities. Despite its intuitive appeal, the thesis that logical equivalence together with extra-logical preferences justifies unidirectional ontic reduction of relations to qualities or qualities to relations is rejected in light of the more defensible proposition that the logical equivalence of qualitative and relational predications actually supports the opposite conclusion, that both qualities and relations are logically indispensable to a complete ontology of properties. The logical equivalence of qualitative and relational predications, insofar as we continue to observe the distinction, makes it logically necessary ontically for both qualities and relations to exist whenever either one exists. That logically equivalent qualitative and relational predications have as their truth-makers the exemplification by objects of both qualities and relations as equi-foundational properties further suggests that there is no deeper logical distinction between qualities and relations, but only two convenient lexical-grammatical designations for property predications involving one- versus more-than-one-argument-place. (shrink)

Can there be relational universals? If so, how can they be exemplified? A monadic universal is by definition capable of having a scattered spatiotemporal localization of its different exemplifications, but the problem of relational universals is that one single exemplification seems to have to be scattered in the many places where the relata are. The paper argues that it is possible to bite this bullet, and to accept a hitherto un-discussed kind of exemplification relation called ‘scattered exemplification’. It has no (...) immediate symbolic counterpart in any Indo-European natural language or in any so far constructed logical language. In order to remedy this, a notion called ‘many-place copula’ is introduced, too. (shrink)

The paper undertakes three interdisciplinary tasks. The first one consists in constructing a formal model of the basic arithmetic competence, that is, the competence sufficient for solving simple arithmetic story-tasks which do not require any mathematical mastery knowledge about laws, definitions and theorems. The second task is to present a generalized arithmetic theory, called the arithmetic of indexed numbers (INA). All models of the development of counting abilities presuppose the common assumption that our simple, folk arithmetic encoded linguistically in the (...) mind is based on the linear number representation. This classical conception is rejected and a competitive hypothesis is formulated according to which the basic mature representational system of cognitive arithmetic is a structure composed of many numerical axes which possess a common constituent, namely, the numeral zero. Arithmetic of indexed numbers is just a formal tool for modelling the basic mature arithmetic competence. The third task is to develop a standpoint called temporal pluralism, which is motivated by neo-Kantian philosophy of arithmetic. (shrink)

We develop a general method for applying functional models to natural systems and cite recent progress in protein modeling that demonstrates the power of this approach. Functional modeling constrains the range of acceptable structural models of a system, reduces the difficulty of finding them, and improves their fidelity. However, functional models are distinctly different from the structural models that are more commonly applied in science. In particular, structural and functional models ask different questions and provide different kinds of answers. As (...) we clarify these differences and articulate how to use these models jointly, we extend our ability to do science and gain insight into the proper use of the terms organization , order , and emergence when describing systems in nature. (shrink)

Abstract In this article I deal with the notion of observation, from a phenomenologically motivated point of view, and its representation mainly by means of the formal language of quantum mechanics. In doing so, I have taken the notion of observation in two diverse contexts. In one context as a notion related with objects of a logical-mathematical theory taken as registered facts of phenomenological perception ( Wahrnehmung ) inasmuch as this phenomenological idea can also be linked with a process of (...) measurement on the quantum-mechanical level. In another context I have taken it as connected with a notion of temporal constitution basically as it is described in E. Husserl’s texts on the phenomenology of temporal consciousness. Given that mathematical objects as formal-ontological objects can be thought of as abstractions of perceptual objects by means of categorial intuition, the question is whether and under what theoretical assumptions we can, in principle, include quantum objects in abstraction in the class of formal-ontological objects and thus inquire on the limits of their description within a formal-axiomatical theory. On the one hand, I derive an irreducibility on the level of individuals taken in formal representation as syntactical atoms-substrates without any further content and on the other hand a transcendental subjectivity of consciousness objectified as a self-constituted temporal unity upon which it is ultimately grounded the possibility of generation of an abstract predicative universe of discourse. Content Type Journal Article Category Invited paper Pages 1-23 DOI 10.1007/s10516-011-9168-6 Authors Stathis Livadas, Messologgiou 66, Patras, 26222 Greece Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

Abstract The ‘species problem’ in the philosophy of biology concerns the nature of species. Various solutions have been proposed, including arguments that species are sets, classes, natural kinds, individuals, and homeostatic property clusters. These proposals parallel debates in ecology as to the ontology and metaphysics of populations, communities and ecosystems. A new solution—that species are processes—is proposed and defended, based on Robert Ulanowicz’s metaphysics of process ecology. As with ecological systems, species can be understood as emergent, autocatalytic systems with propensities (...) for centripetality and mutuality in the course of dynamically balancing ascendency (order and persistence) and overhead (randomness and change). The species-as-processes perspective accords with the Ulanowicz’s postulates of process ecology and it can be accommodated by existing theories of species—particularly in a reframing of Richard Boyd’s metaphysics such that species are homeostatic process clusters. Rather than contending that process-based metaphysics is the only, best or true account of species, a pluralist-realist approach is advocated based on the pragmatic principles that are reflected in modern view of species and ecology. If species are understood to be comprised of processes and to be emergent processes themselves, there are important implications for the life sciences, including: animal models in medical and environmental studies, conservation biology, extinction, biodiversity, restoration ecology, and evolutionary biology. Content Type Journal Article Category Invited Paper Pages 1-30 DOI 10.1007/s10516-011-9169-5 Authors Jeffrey A. Lockwood, Department of Philosophy, University of Wyoming, Laramie, WY 82071, USA Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

Abstract After a brief outline of the topic of non-language thinking in mathematics the central phenomenological tool in this concern is established, i.e. the eidetic method. The special form of eidetic method in mathematical proving is implicit variation and this procedure entails three rules that are established in a simple geometrical example. Then the difficulties and the merits of analogical thinking in mathematics are discussed in different aspects. On the background of a new phenomenological understanding of the performance of non-language (...) thinking in mathematics the well-known theses of B. L. van der Waerden that mathematical thinking to a great extent proceeds without the use of language is discussed in a new light. Content Type Journal Article Category Invited paper Pages 1-12 DOI 10.1007/s10516-011-9164-x Authors Dieter Lohmar, Universität zu Köln, Cologne, Germany Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

Algebraic/topological descriptions of living processes are indispensable to the understanding of both biological and cognitive functions. This paper presents a fundamental algebraic description of living/cognitive processes and exposes its inherent ambiguity. Since ambiguity is forbidden to computation, no computational description can lend insight to inherently ambiguous processes. The impredicativity of these models is not a flaw, but is, rather, their strength. It enables us to reason with ambiguous mathematical representations of ambiguous natural processes. The noncomputability of these structures means computerized (...) simulacra of them are uninformative of their key properties. This leads to the question of how we should reason about them. That question is answered in this paper by presenting an example of such reasoning, the demonstration of a topological strategy for understanding how the fundamental structure can form itself from within itself. (shrink)

Abstract In this paper I critically investigate an unorthodox attempt to metaphysically explain in virtue of what there are states of affairs. This is a suggestion according to which states of affairs exist thanks to, rather than, as is the common view, in spite of, the infinite regress their metaphysical explanation seems to engender. I argue that, no matter in which form it is defended, or in which theoretical framework it is set, this suggestion cannot provide us with the explanation (...) we crave. Content Type Journal Article Category Original Paper Pages 1-17 DOI 10.1007/s10516-011-9174-8 Authors Anna-Sofia Maurin, Lund University, Lund, Sweden Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

In this article I present and (modestly) defend a hybrid position which we may call a Platonist constituent ontology. More specifically, I present a version of exemplification which entails (1) a certain form of Platonism, (2) a constituent ontology of ordinary objects, (3) a view of exemplification as a tiedto nexus, and (4) a view of properties as abstract objects that are non-spatially in ordinary objects. I clarify two sets of preliminary issues, present my hybrid analysis of exemplification, raise and (...) seek to undercut an argument against my constituent realism, and surface some of the costs and benefits relevant to assessing the relative merits of relational versus constituent realism. (shrink)

In spite of the ‘experimental turn’ now fashionable in the philosophy of science, the question of the structure and identity criteria of scientific theories continues to be a central issue for the philosophical analysis of empirical science. We need a precise metatheory of empirical theories to deal with this issue. Metatheoretical structuralism appears to offer the most adequate approach in this sense so far. First, some basic intuitions about what empirical theories are, and how they are structured, are laid out. (...) Then, the main notions used by metatheoretical structuralism to analyze theories are explained, and they are illustrated by applying them to an example of a simple physical theory. Finally, it is argued that the picture of the structure and identity of empirical theories coming out of structuralistic analysis adequately corresponds to the basic intuitions stated at the beginning. (shrink)

The aim of this paper is to present and discuss the philosophical views concerning mathematics of the founders of the so called Warsaw Mathematical School, i.e., Wacław Sierpiński, Zygmunt Janiszewski and Stefan Mazurkiewicz. Their interest in the philosophy of mathematics and their philosophical papers will be considered. We shall try to answer the question whether their philosophical views influenced their proper mathematical investigations. Their views towards set theory and its rôle in mathematics will be emphasized.

The conceptualisation of movement has always been problematical for Western thought, ever since Parmenides declared our incapacity to conceptualise the plurality of change because our self-identical thought can only know an identical being. Exploiting this peculiar feature and constraint on our thought, Zeno of Elea devised his famous paradoxes of movement in which he shows that the passage from a position to movement cannot be conceptualised. In this paper, I argue that this same constraint is at the root of our (...) incapacity to conceptualise the unseen movement at the micro-level and that the aporetic idea of super-position far from opening the gate on a deeper reality is a symptomatic word for this lack of understanding. (shrink)

Abstract This paper discusses Husserl’s views on physical theories in the first volume of his Logical Investigations , and compares them with those of his contemporaries Pierre Duhem and Henri Poincaré. Poincaré’s views serve as a bridge to a discussion of Husserl’s almost unknown views on physical geometry from about 1890 on, which in comparison even with Poincaré’s—not to say Frege’s—or almost any other philosopher of his time, represented a rupture with the philosophical tradition and were much more in tune (...) with the physical geometry underlying the Einstein-Hilbert general theory of relativity developed more than two decades later. Content Type Journal Article Category Invited paper Pages 1-23 DOI 10.1007/s10516-011-9165-9 Authors Guillermo E. Rosado Haddock, University of Puerto Rico at Río Piedras, San Juan, Puerto Rico Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

Introduction: The Other Husserl Content Type Journal Article Pages 1-4 DOI 10.1007/s10516-011-9160-1 Authors Guillermo E. Rosado Haddock, San Juan, Puerto Rico Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151.

I present the realist conception of logic supported by Oswaldo Chateaubriand which integrates ontological and epistemological aspects, opposing it to mathematical and linguistic conceptions. I give special attention to the peculiarities of his hierarchy of types in which some properties accumulate and others have a multiple degree. I explain such deviations of the traditional conception, showing the underlying purpose in each of these peculiarities. I compare the ideas of Chateaubriand to the similar ideas of Frege, Tarski and Gödel. I suggest (...) a view of the logical properties in terms of the Aristotelian notion of focal meaning and I give a formal expression to the type of the entities in the hierarchy proposed by Chateaubriand. (shrink)

Extensionalism, as I understand it here, is the view that physical reality consists exclusively of extensional entities. On this view, intensional entitities must either be eliminated in favor of an ontology of extensional entities, or be reduced to such an ontology, or otherwise be admitted as non-physical. In this paper I argue that extensionalism is a misguided philosophical doctrine. First, I argue that intensional phenomena are not confined to the realm of language and thought. Rather, the ontology of such phenomena (...) is intimately entwined with the ontology of properties. After providing some evidence to the popularity of extensionalism in contemporary analytic philosophy, I investigate the motivating reasons behind it. Considering several explanations, I argue that the main motivating reason is rooted in the identification of matter with extension, an identification which is one of the hallmarks of the mechanistic conception of nature inherited from the founding fathers of our modern scientific outlook. I then argue that such a conception is not only at odds with a robust ontology of properties but is also at odds with our best contemporary physics. Rather than vindicating extensionalism contemporary science undermines the position, and the lesson to be drawn from this surprising fact is that extensionalism needs no longer be espoused as a regulative ideal of naturalistic philosophy. I conclude by showing that the ontological approach to intensional phenomena advocated throughout the paper also gains support from an examination of the historical context within which ‘intension’ was first introduced as a semantic notion. (shrink)

In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.

The game of life is an excellent framework for metaphysical modelling. It can be used to study ontological categories like space, time, causality, persistence, substance, emergence, and supervenience. It is often said that there are many levels of existence in the game of life. Objects like the glider are said to exist on higher levels. Our goal here is to work out a precise formalization of the thesis that there are various levels of existence in the game of life. To (...) formalize this thesis, we develop a set-theoretic construction of the glider. The method of this construction generalizes to other patterns in the game of life. And it can be extended to more realistic physical systems. The result is a highly general method for the set-theoretical construction of substances. (shrink)

Abstract This work speaks about very special solution of the mind–body problem. This solution based on the so-called Principle of Co - existence stands out as one of the most interesting attempts at solving the mind–body problem. It states that substances can only exert a mutual influence on one another if they have something in common. This does not have to be a common property but rather, a binding relationship. Thus, substances co-exist when they remain bound by a common relationship, (...) for instance, to an external subject. The Principle of Co - existence played an extremely important role in Kant’s philosophy, not only since it provided a framework for solving the mind–body problem, but since it captured the very basis of its existence. The Principle found also reflection in the works of Kant’s successors, such as Fichte, Schelling, Hegel or Feuerbach. It had significant—though often hidden—repercussions on later philosophy of mind. The notion of force and the principle of its operation became key concepts in resolving the mind–body problem. As a result, philosophy of mind concentrated on the search for a principle explaining the occurrence of two complementary types of phenomena. This established a tradition which, to a greater or lesser extent, has survived to our day. Content Type Journal Article Category Original Paper Pages 1-11 DOI 10.1007/s10516-011-9171-y Authors Janusz Sytnik-Czetwertyński, The Jan Kochanowski University, 25–029 Kielce, ul. Krakowska 11, Kielce, Poland Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

In this paper the reader is asked to engage in some simple problem-solving in classical pure number theory and to then describe, on the basis of a series of questions, what it is like to solve the problems. In the recent philosophy of mind this “what is it like” question is one way of signaling a turn to phenomenological description. The description of what it is like to solve the problems in this paper, it is argued, leads to several morals (...) about the epistemology and ontology of classical pure mathematical practice. Instead of simply making philosophical judgments about the subject matter in advance, the exercise asks the reader to briefly engage in a mathematical practice and to then reflect on the practice. (shrink)

In 1928 Edmund Husserl wrote that The ideal of the future is essentially that of phenomenologically based ( philosophical ) sciences, in unitary relation to an absolute theory of monads ( Phenomenology , Encyclopedia Britannica draft) There are references to phenomenological monadology in various writings of Husserl. Kurt Gödel began to study Husserl’s work in 1959. On the basis of his later discussions with Gödel, Hao Wang tells us that Gödel’s own main aim in philosophy was to develop metaphysics—specifically, something (...) like the monadology of Leibniz transformed into exact theory—with the help of phenomenology. (A Logical Journey: From Gödel to Philosophy, p. 166) In the Cartesian Meditations and other works Husserl identifies ‘monads’ (in his sense) with ‘transcendental egos in their full concreteness’. In this paper I explore some prospects for a Gödelian monadology that result from this identification, with reference to texts of Gödel and to aspects of Leibniz’s original monadology. (shrink)

This paper investigates relations between truth and consistency. The basic intuition is that truth implies consistency, but the reverse dependence fails. However, this simple account leads to some troubles, due to some metalogical results, in particular the Gödel-Malcev completeness theorem. Thus, a more advanced analysis is required. This is done by employing the concept of ω-consistency and ω-inconsistency. Both concepts motivate that the concept of the standard truth should be introduced as well. The results are illustrated by an interpretation of (...) the well-known logical square and its generalization. (shrink)