Online research in philosophy

The Weak Principle of the Identity of Indiscernibles (weak PII), states that numerically distinct items must be discernible by a symmetrical and irreflexive relation. Recently, some authors have proposed that weak PII holds in non relativistic quantum mechanics, contradicting a long tradition claiming PII to be simply false in that theory. The question that arises then is: are relations allowed in the scope of PII? In this paper, we propose that quantum mechanics does not help us in deciding matters concerning (...) that problem, since that is a metaphysical problem rather than a quantum mechanical one. We argue further that weak PII is unmotivated on metaphysical grounds. We examine three metaphysical theses (bundle theory, counting, empiricism) that may provide reasons for one to sustain PII, and we conclude that weak PII gets no independent motivation from them. (shrink)

Different interpretations of Bradley’s regress argument are considered. On the basis of textual evidences, it is argued that the most persuasive is the one that sees the argument as primarily addressing the general issue of unity or connectedness.

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 However, later developments in science outdated Kepler’s approach (pt.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).

It is standardly assumed in discussions of quantum theory that physical systems can be regarded as having well-defined Hilbert spaces. It is shown here that a Hilbert space can be consistently partitioned only if its components are assumed not to interact. The assumption that physical systems have well-defined Hilbert spaces is, therefore, physically unwarranted.

If it is possible to think that human life is temporal as a whole, and we can make sense of Wittgenstein’s claim that the psychological phenomena called ‘dispositions’ do not have genuine temporal duration on the basis of a distinction between dispositions and other mental processes, we need a compelling account of how time applies to these dispositions. I undertake this here by examining the concept of expectation, a disposition with a clear nexus to time by the temporal point at (...) which the expectation is satisfied. However, it seems that we cannot always identify the beginning of an expectation, and in a few cases, its end. If so, the reduction of expectations to neural events or accompanying feelings which spread over time in the usual way seems a hard enterprise, because these processes, much as other physical processes, have a definite and largely measurable time span. Only at a higher level, that is, as part of human life, expectation can be said to be temporal. (shrink)

Our conscious minds exist in the Universe, therefore they should be identified with physical states that are subject to physical laws. In classical theories of mind, the mental states are identified with brain states that satisfy the deterministic laws of classical mechanics. This approach, however, leads to insurmountable paradoxes such as epiphenomenal minds and illusionary free will. Alternatively, one may identify mental states with quantum states realized within the brain and try to resolve the above paradoxes using the standard Hilbert (...) space formalism of quantum mechanics. In this essay, we first show that identification of mind states with quantum states within the brain is biologically feasible, and then elaborating on the mathematical proofs of two quantum mechanical no-go theorems, we explain why quantum theory might have profound implications for the scientific understanding of one’s mental states, self identity, beliefs and free will. (shrink)

The empirical literature on phenomenal causality (the notion that causality can be perceived) is reviewed. Different potential types of phenomenal causality and variables that influence phenomenal causality were considered in Part I (Hubbard 2012b ) of this two-part series. In Part II, broader questions regarding properties of phenomenal causality and connections of phenomenal causality to other perceptual or cognitive phenomena (different types of phenomenal causality, effects of spatial and temporal variance, phenomenal causality in infancy, effects of object properties, naïve physics, (...) spatial localization, other illusions, amodal completion, Gestalt principles of perceptual grouping, effects of context, differences between physical and social causality, effects of learning and experience, individual differences, effects of predictability, asymmetry in phenomenal causality, differences between perceived causality and perceived force, phenomenal causality in nonhuman animals) are considered. Potential mechanisms of phenomenal causality (inference from contiguity, a priori understanding, ampliation, perceptual learning, stimulus activity, beliefs regarding kinematics, haptic experience, beliefs regarding impetus, postdiction, innateness, modularity, specific neural structures) are also considered. (shrink)

Displacements in the remembered location of stimuli in displays based on Michotte’s (1946/ 1963 ) launching effect and entraining effect were examined. A moving object contacted an initially stationary target, and the target began moving. After contacting the target, the mover became stationary (launching trials) or continued moving in the same direction and remained adjacent to the target (entraining trials). In launching trials, forward displacement was smaller for targets than for movers; in entraining trials, forward displacement was smaller for movers (...) than for targets. Also, forward displacement was smaller for targets in launching trials than for targets in entraining trials. Data are consistent with a hypothesis that the launching effect involves an attribution that the mover imparted to the target a dissipating impetus that was responsible for target motion. Introspective experience of a perception of physical causality in the launching effect might result because behavior of movers and targets is consistent with that predicted by an impetus heuristic. (shrink)

On the one hand, Pavel Tichý has shown in his Transparent Intensional Logic (TIL) that the best way of explicating meaning of the expressions of a natural language consists in identification of meanings with abstract procedures. TIL explicates objective abstract procedures as so-called constructions. Constructions that do not contain free variables and are in a well-defined sense ´normalized´ are called concepts in TIL. On the second hand, Kolmogorov in (Mathematische Zeitschrift 35: 58–65, 1932 ) formulated a theory of problems, using (...) NL expressions. He explicitly avoids presenting a definition of problems. In the present paper an attempt at such a definition (explication)—independent of but in harmony with Medvedev´s explication—is given together with the claim that every concept defines a problem. The paper treats just mathematical concepts, and so mathematical problems, and tries to show that this view makes it possible to take into account some links between conceptual systems and the ways how to replace a noneffective formulation of a problem by an effective one. To show this in concreto a wellknown Kleene’s idea from his (Introduction to metamathematics. D. van Nostrand, New York, 1952 ) is exemplified and explained in terms of conceptual systems so that a threatening inconsistence is avoided. (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)

I defend a physicalistic version of ontological emergence; qualia emerge from the brain, but are physical properties nevertheless. First, I address the following questions: what are the central tenets of physicalistic ontological emergentism; what are the relationships between these tenets; what is the relationship between physicalistic ontological emergentism and non-reductive physicalism; and can there even be a physicalistic version of ontological emergentism? This discussion is merely an attempt to clarify exactly what a physicalistic version of ontological emergentism must claim, and (...) to show that the view is at least coherent. I then defend the view from objections, for example, Kim’s (Philos Stud 95:3–36, 1999 ) attempt to apply a version of his exclusion argument to ontological emergentism. I conclude by offering a positive argument for the view: given certain empirical evidence concerning the organization of the brain, physicalism might have to endorse ontological emergentism to avoid epiphenomenalism. (shrink)

In celebration of the centenary of the Italian philosopher Cornelio Fabro’s birth (1911–1995), this paper investigates the essential theoretical traits that undergird the framework of Fabro’s 1941 texts, by comparing them with Franz Brentano’s (1838–1817) project of renewing Thomism through a new understanding of Aristotle. The secondary literature concerning the comparison of both these authors is almost nonexistent. Our goal is to clarify some of the central issues regarding the relation between Fabro and Brentano through direct textual analysis of unpublished (...) letters exchanged between Fabro and Agostino Gemelli about Brentano and his pupil Carl Stumpf. (shrink)

This paper compares the two known logical forms of hierarchy, both of which have been used in models of natural phenomena, including the biological. I contrast their general properties, internal formal relations, modes of growth (emergence) in applications to the natural world, criteria for applying them, the complexities that they embody, their dynamical relations in applied models, and their informational relations and semiotic aspects.

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.

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)

Abstract The relation between universal and particular is considered to be the Achilles’ heel of universal realism. However, modern universal realism with facts does not have the difficulties which traditional Platonic universal realism had. Its exemplification relation connecting particulars and universals in atomic facts is very different from Platonic participation. Bradley’s regress argument against the exemplification relation can be refuted in two different ways. Nevertheless, there are good reasons to avoid the assumption of an exemplification relation and thus to go (...) without the Achilles’ heel altogether. Content Type Journal Article Category Invited Paper Pages 1-7 DOI 10.1007/s10516-012-9191-2 Authors Erwin Tegtmeier, University of Mannheim, Heinrich-Delp-Str. 214, Darmstadt, 64297 Germany Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)

Quantum logic is only applicable to microscopic phenomena while classical logic is exclusively used for everyday reasoning, including mathematics. It is shown that both logics are unified in the framework of modal interpretation. This proposed method deals with classical propositions as latently modalized propositions in the sense that they exhibit manifest modalities to form quantum logic only when interacting with other classical subsystems.

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.

Besides presenting a phenomenological-experimental analysis of consciousness, Meinong challenged one of the major indisputable axioms of current scientific research, i.e. that perception in awareness has to be veridical on the stimulus. Meinong’s analysis of consciousness, which he conducted through a kind of dissection of its structures from a systematic and an experimental viewpoint, offers relevant insights to contemporary consciousness studies.

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)

One of the advantages of my account in the essay “Instantiation as Partial Identity” was capturing the contingency of instantiation—something David Armstrong gave up in his experiment with a similar view. What made the contingency possible for me was my own non-standard account of identity, complete with the apparatus of counts and aspects. The need remains to lift some obscurity from the account in order to display its virtues to greater advantage. To that end, I propose to respond to those (...) who have grappled with it in print. There are various criticisms by commentators: that it is rendered absurd by the transitivity of identity, that it makes instantiation necessary instead of contingent, that it is unclear what counts are, that aspects are simply tropes, that my view does not capture multiple location, that I make an unclear reference to a theory of composition as identity, that the account suffers from problems with polyadicity, and that it is not a realist account of universals after all. I give responses to these objections. (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)

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)

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)

Consider the things that exist—the entities—and let us suppose they are mereologically structured, that is, some are parts of others. The project of ontology within the bounds of bare mereology use this structure to say which of these entities belong to various ontological kinds, such as properties and particulars. My purpose in this paper is to defend the most radical section of the project, the mereological theory of the exemplification of universals. Along the way I help myself to several hypotheses: (...) the existence of merely possible worlds; that particulars have thisnesses; and that mereology is far from classical. Moreover, the way I characterize instantiation might be judged too complicated to be plausible. At the end of the paper, I reply to these objections based on complexity. (shrink)

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)

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)

Most philosophical accounts of emergence are based on supervenience, with supervenience being an ontologically synchronic relation of determination. This conception of emergence as a relation of supervenience, I will argue, is unable to make sense of the kinds of emergence that are widespread in self-organizing and nonlinear dynamical systems, including distributed cognitive systems. In these dynamical systems, an emergent property is ontological (i.e., the causal capacities of P, where P is an emergent feature, are not reducible to causal capacities of (...) the parts, and may exert a top-down causal influence on the parts of the system) and diachronic (i.e., the relata of emergence are temporally extended, and P emerges as a result of some dynamical lower-level processes that unfold in real time). (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)

Radical non-dispositionalism is the view according to which the actual causal/nomic roles of natural properties are totally irrelevant to their de re modal representation. The major difficulty besetting all forms of radical non-dispositionalism is that the latter allegedly allows the metaphysical possibility of two natural properties swapping their actual causal/nomic roles. The aim of this paper is to provide a plausible solution to that problem. To this end, I describe the necessary steps that a proponent of the view may take (...) to respond to it. I argue that those steps include the rejection of the transworld existence of natural properties and the adoption of a counterpart-theoretic framework for their de re modal representation. I, finally, present two versions of the property-counterpart framework which are consistent with the radical non-dispositionalism. (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)

We argue that the set of humanly known mathematical truths (at any given moment in human history) is finite and so recursive. But if so, then given various fundamental results in mathematical logic and the theory of computation (such as Craig’s in J Symb Log 18(1): 30–32(1953) theorem), the set of humanly known mathematical truths is axiomatizable. Furthermore, given Godel’s (Monash Math Phys 38: 173–198, 1931) First Incompleteness Theorem, then (at any given moment in human history) humanly known mathematics must (...) be either inconsistent or incomplete. Moreover, since humanly known mathematics is axiomatizable, it can be the output of a Turing machine. We then argue that any given mathematical claim that we could possibly know could be the output of a Turing machine, at least in principle. So the Lucas-Penrose (Lucas in Philosophy 36:112–127, 1961; Penrose, in The Emperor’s new mind. Oxford University Press, Oxford (1994)) argument cannot be sound. (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)

A topological inevitability of early developmental events through the use of classical topological concepts is discussed. Topological dynamics of forms and maps in embryo development are presented. Forms of a developing organism such as cell sets and closed surfaces are topological objects. Maps (or mathematical functions) are additional topological constructions in these objects and include polarization, singularities and curvature. Topological visualization allows us to analyze relationships that link local morphogenetic processes and integral developmental structures and also to find stable spatio-temporal (...) topological characteristics that are invariant for a taxonomic group. The application of topological principles reveals a topological imperative: certain topological rules define and direct embryogenesis. A topological stability of embryonic morphogenesis is proposed and a topological scenario of developmental and evolutionary transformations is presented. (shrink)

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)

Cognitive science depends on abstractions made from the complex reality of human behaviour. Cognitive scientists typically wish the abstractions in their theories to be universals, but seldom attend to the ontology of universals. Two sorts of universal, resulting from Galilean abstraction and materialist abstraction respectively, are available in the philosophical literature: the abstract universal—the one-over-many universal—is the universal conventionally employed by cognitive scientists; in contrast, a concrete universal is a material entity that can appear within the set of entities it (...) describes, of which it represents the essential, paradigmatic case. The potential role of concrete universals in cognitive science is discussed. (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.

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)

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)