Abstract: Abstract
In this article I respond to Heathcote’s “On the Exhaustion of Mathematical Entities by Structures”. I show that his ontic exhaustion issue is not a problem for ante rem structuralists. First, I show that it is unlikely that mathematical objects can occur across structures. Second, I show that the properties that Heathcote suggests are underdetermined by structuralism are not so underdetermined. Finally, I suggest that even if Heathcote’s ontic exhaustion issue if thought of as a problem of reference, the structuralist has a readily available solution. PubDate: 2014-06-27

Abstract: Abstract
The arrow paradox is an argument purported to show that objects do not really move. The two main metaphysics of motion, the At–At theory of motion and velocity primitivism, solve the paradox differently. It is argued that neither solution is completely satisfactory. In particular it is contended that there are no decisive arguments in favor of the claim that velocity as it is constructed in the At–At theory is a truly instantaneous property, which is a crucial assumption to solve the paradox. If so the At–At theory faces the threat that most of our physical theories turn out to be non-Markovian. Finally it is considered whether all those threats and paradoxes are dispelled if only a new metaphysics of persistence is taken into account, namely four-dimensionalism. PubDate: 2014-06-03

Abstract: Neo-logicism is, not least in the light of Frege’s logicist programme, an important topic in the current philosophy of mathematics. In this essay, I critically discuss a number of issues that I consider to be relevant for both Frege’s logicism and neo-logicism. I begin with a brief introduction into Wright’s neo-Fregean project and mention the main objections that he faces. In Sect. 2, I discuss the Julius Caesar problem and its possible Fregean and neo-Fregean solution. In Sect. 3, I raise what I take to be a central objection to the position of neo-logicism. In Sect. 4, I attempt to clarify how we should understand Frege’s stipulation that the two sides of an abstraction principle qua contextual definition of a term-forming operator shall be “gleichbedeutend”. In Sect. 5, I consider the options that Frege might have had to establish the analyticity of Hume’s Principle: The number that belongs to the concept F is equal to the number that belongs to the concept G if and only if F and G are equinumerous. Section 6 is devoted to Frege’s two criteria of thought identity. In Sects. 7 and 8, I defend the position of the neo-logicist against an alleged “knock-down argument”. In Sect. 9, I comment on Frege’s description of abstraction in Grundlagen, §64 and the use of the terms “recarving” and “reconceptualization” in the relevant literature on Fregean abstraction and neo-logicism. I argue that Fregean abstraction has nothing to do with the recarving of a sentence content or its decomposition in different ways. I conclude with remarks on global logicism versus local logicisms. PubDate: 2014-06-01

Abstract: Abstract
Psychological Sequentialism holds that no causal constraint is necessary for the preservation of what matters in survival; rather, it is sufficient for preservation if two groups of mental states are similar enough and temporally close enough. Suppose that one’s body is instantaneously dematerialized and subsequently, by an amazing coincidence, a collection of molecules is configured to form a qualitatively identical human body. According to Psychological Sequentialism, these events preserve what matters in survival. In this article, I examine some of the main arguments for the view and argue that they fail to establish that no causal constraint is necessary. I also argue that Psychological Sequentialism yields implausible consequences that render it hard to accept the view. PubDate: 2014-06-01

Abstract: Abstract
There has been considerable discussion in the literature of one kind of identity problem that mathematical structuralism faces: the automorphism problem, in which the structure is unable to individuate the mathematical entities in its domain. Shapiro (Philos Math 16(3):285–309, 2008) has partly responded to these concerns. But I argue here that the theory faces an even more serious kind of identity problem, which the theory can’t overcome staying within its remit. I give two examples to make the point. PubDate: 2014-06-01

Abstract: Abstract
The “memory of water” was a major international controversy that remains unresolved. Taken seriously or not, this hypothesis leads to logical contradictions in both cases. Indeed, if this hypothesis is held as wrong, then we have to explain how a physiological signal emerged from the background and we have to elucidate a bulk of coherent results. If this hypothesis is held as true, we must explain why these experiments were difficult to reproduce by other teams and why some blind experiments were so disturbing for the expected outcomes. In this article, a third way is proposed by modeling these experiments in a quantum-like probabilistic model. It is interesting to note that this model does not need the hypothesis of the “memory of water” and, nevertheless, all the features of Benveniste’s experiments are taken into account (emergence of a signal from the background, difficulties faced by other teams in terms of reproducibility, disturbances during blind experiments, and apparent “jumps of activity” between samples). In conclusion, it is proposed that the cognitive states of the experimenter exhibited quantum-like properties during Benveniste’s experiments. PubDate: 2014-06-01

Abstract: Abstract
Van Fraassen (The scientific image, Oxford University Press, Oxford, 1980) claims that successful theories exist today because successful theories survive and unsuccessful ones die. Wray (Erkenntnis 67:81–89, 2007; Erkenntnis 72:365–377, 2010) appeals to Stanford’s new pessimistic induction (Exceeding our grasp: science, history, and the problem of unconceived alternatives, Oxford University Press, Oxford, 2006), arguing that van Fraassen’s selectionist explanation is better than the realist explanation that successful theories exist because they are approximately true. I argue that if the pessimistic induction is correct, then the evolutionary explanation is neither true nor empirically adequate, and that realism is better than selectionism because realism explains more phenomena in science than selectionism. PubDate: 2014-06-01

Abstract: Abstract
Since the discovery of incommensurability in ancient Greece, arithmeticism and geometricism constantly switched roles. After ninetieth century arithmeticism Frege eventually returned to the view that mathematics is really entirely geometry. Yet Poincaré, Brouwer, Weyl and Bernays are mathematicians opposed to the explication of the continuum purely in terms of the discrete. At the beginning of the twenty-first century ‘continuum theorists’ in France (Longo, Thom and others) believe that the continuum precedes the discrete. In addition the last 50 years witnessed the revival of infinitesimals (Laugwitz and Robinson—non-standard analysis) and—based upon category theory—the rise of smooth infinitesimal analysis and differential geometry. The spatial whole-parts relation is irreducible (Russell) and correlated with the spatial order of simultaneity. The human imaginative capacities are connected to the characterization of points and lines (Euclid) and to the views of Aristotle (the irreducibility of the continuity of a line to its points), which remained in force until the ninetieth century. Although Bolzano once more launched an attempt to arithmetize continuity, it appears as if Weierstrass, Cantor and Dedekind finally succeeded in bringing this ideal to its completion. Their views are assessed by analyzing the contradiction present in Grünbaum’s attempt to explain the continuum as an aggregate of unextended elements (degenerate intervals). Alternatively a line-stretch is characterized as a one-dimensional spatial subject, given at once in its totality (as a whole) and delimited by two points—but it is neither a breadthless length nor the (shortest) distance between two points. The overall aim of this analysis is to account for the uniqueness of discreteness and continuity by highlighting their mutual interconnections exemplified in the nature of a line as a one-dimensional spatial subject, while acknowledging that points are merely spatial objects which are always dependent upon an extended spatial subject. Instead of attempting to reduce continuity to discreteness or discreteness to continuity, a third alternative is explored: accept the irreducibility of number and space and then proceed by analyzing their unbreakable coherence. The argument may be seen as exploring some implications of the view of John Bell, namely that the “continuous is an autonomous notion, not explicable in terms of the discrete.” Bell points out that initially Brouwer, in his dissertation of 1907, “regards continuity and discreteness as complementary notions, neither of which is reducible to each other.” PubDate: 2014-06-01

Abstract: Abstract
Aspectual shape is widely recognized property of intentionality. This means that subject’s access to reality is necessarily conditioned by applied concepts, perspective, modes of sensation, etc. I argue against representational and indirect-realist account of this phenomenon. My own proposition—presentational and direct realist—is based on the recognition of historical contexts, in which the phenomenon of aspectuality should be reconsidered; on the other hand—it is based on Ludwig Wittgenstein’s conception of aspectual perception. Moreover I apply some results from the area of logicophilosophical investigations called qua theory. PubDate: 2014-05-21

Abstract: Abstract
According to no-futurism, past and present entities are real, but future ones are not. This view faces a skeptical challenge (Bourne in Australas J Philos 80(3):359–371 2002; A future for presentism, Clarendon Press, Oxford 2006; Braddon-Mitchell in Analysis 64(283):199–203 2004): if no-futurism is true, how do you know you are present' I shall propose a new skeptical argument based on the physical possibility of Gödelian worlds (Albert Einstein: philosopher-scientist, Open Court, La Salle, pp. 555–562, 1949). This argument shows that a no-futurist has to endorse a metaphysical contingentist reading of no-futurism, the view that no-futurism is contingently true. But then, the no-futurist has to face a new skeptical challenge: how do you know that you are in a no-futurist world' PubDate: 2014-05-13

Abstract: Abstract
From antiquity several philosophers have claimed that the goal of natural science is truth. In particular, this is a basic tenet of contemporary scientific realism. However, all concepts of truth that have been put forward are inadequate to modern science because they do not provide a criterion of truth. This means that we will generally be unable to recognize a scientific truth when we reach it. As an alternative, this paper argues that the goal of natural science is plausibility and considers some characters of plausibility. PubDate: 2014-05-13

Abstract: Abstract
The aim of this paper is to present and discuss main philosophical ideas concerning logic and mathematics of a significant but forgotten Polish philosopher Benedykt Bornstein. He received his doctoral degree with Kazimierz Twardowski but is not included into the Lvov–Warsaw School of Philosophy founded by the latter. His philosophical views were unique and quite different from the views of main representatives of Lvov–Warsaw School. We shall discuss Bornstein’s considerations on the philosophy of geometry, on the infinity, on the foundations of set theory and his polemics with Stanisław Leśniewski as well as his conception of a geometrization of logic, of the categorial logic and of the mathematics of quality. PubDate: 2014-05-13

Abstract: Abstract
The Ollivier–Poulin–Zurek definition of objectivity provides a philosophical basis for the environment as witness formulation of decoherence theory and hence for quantum Darwinism. It is shown that no account of the reference of the key terms in this definition can be given that does not render the definition inapplicable within quantum theory. It is argued that this is not the fault of the language used, but of the assumption that the laws of physics are independent of Hilbert-space decomposition. All evidence suggests that this latter assumption is true. If it is, decoherence cannot explain the emergence of classicality. PubDate: 2014-03-01

Abstract: Abstract
The representational nature of human cognition and thought in general has been a source of controversies. This is particularly so in the context of studies of unconscious cognition, in which representations tend to be ontologically and structurally segregated with regard to their conscious status. However, it appears evolutionarily and developmentally unwarranted to posit such segregations, as, otherwise, artifact structures and ontologies must be concocted to explain them from the viewpoint of the human cognitive architecture. Here, from a by-and-large Classical cognitivist viewpoint, I show why this segregation is wrong, and elaborate on the need to postulate an ontological and structural continuity between unconscious and conscious representations. Specifically, I hypothesize that this continuity is to be found in the symbolic-based interplay between the syntax and the semantics of thought, and I propose a model of human information processing characterized by the integration of syntactic and semantic representations. PubDate: 2014-03-01

Abstract: Abstract
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. PubDate: 2014-03-01

Abstract: Abstract
The view that mathematics deals with ideal objects to which we have epistemic access by a kind of perception (’intuition’) has troubled many thinkers. Using ideas from Husserl’s phenomenology, I will take a different look at these matters. The upshot of this approach is that there are non-material objects and that they can be recognized in a process very closely related to sense perception. In fact, the perception of physical objects may be regarded as a special case of this more universal way of recognizing objects of any kind. PubDate: 2014-03-01

Abstract: Abstract
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. PubDate: 2014-03-01

Abstract: Abstract
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. PubDate: 2014-03-01

Abstract: Abstract
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. PubDate: 2014-03-01