Are Mathematical Theories Reducible to Non-analytic Foundations?

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.     

Paranormal Experience in a Medico-Swimming Rescue: A Case Study

This study looks at the case of a 20-year-old fisherman, who was speared in the head, the spear entering at his jaw and protruding from the top of his scull, while he was swimming unaccompanied; he was rescued, admitted to the intensive care unit for an operation, remained in a coma for a few days and then had a full recovery. About 10 days before the rescue, he had visited a monk who, intuited and functioning as channel of the divine spirit, had told him that he ‘should not be afraid of anything’, rubbing the top of his scull and his jaw exactly at the points through which the 40-inch spear passed. After the incident, the monk prescience again the exact day on which he would recover from the coma. It is concluded that the survival of the fisherman can be attributed to a paranormal event. The monk’s prescience permit the assumption that a divine spirit was pervasive throughout the universe and present in this life-threatening situation, endeavouring to assist the lifeguard, the neurosurgeons and the young fisherman.     

SCIENTIFIC REALISM AND METAPHYSICS

The tendency to take scientific realism to be a richer metaphysical view than it ought to be stems from the fact that there are two ways in which we can conceive of reality. The first is to conceive of reality as comprising all facts and the other is to conceive of it as comprising all and only fundamental facts. I argue that scientific realism should be committed to the factualist view of reality and not, in the first instance, to the fundamentalist. An anti‐fundamentalist conception of reality acts as a constraint on scientific realism, but it is a further and (conceptually) separate issue whether or not a scientific realist should come to adopt a fundamentalist view of reality. I argue that scientific realism is independent of physicalism and non‐Humeanism and that the concept of truth is required for a sensible understanding of the metaphysical commitments of scientific realism.     

What Do Powers Do When They Are Not Manifested?*

In the present paper, I offer a conceptual argument against the view that all properties are pure powers. I claim that thinking of all properties as pure powers leads to a regress. The regress, I argue, can be solved only if non‐powers are admitted. The kernel of my thesis is that any attempt to answer the title question in an informative way will undermine a pure‐power view of properties. In particular, I focus my critique on recent arguments in favour of pure powers by the Late George Molnar and Jennifer McKitrick. The lines of defence of the friends of powers converge on what I call ‘the ultimate argument for powers’, viz., that current physics entails (or supports) the view that the fundamental properties (spin, mass, charge) are ungrounded powers. I take issue with this argument and make a modest suggestion: that the evidence from current physics is inconclusive.     

Agnostic empiricism versus scientific realism: Belief in truth matters

This paper aims to defend scientific realism against two versions of agnostic empiricism: a naive agnostic position, which suggests that the only rational option is to remain agnostic as to the truth of theoretical assertions, and van Fraassen's more sophisticated agnostic empiricism - which may be called "Hypercritical Empiricism". It first argues that given semantic realism, naive agnostic empiricism cannot be maintained: there is no relevant epistemic difference between theoretical assertions and observational ones. It then focuses on van Fraassen's more sophisticated alternative to scientific realism and suggests that an attitude towards science which involves less than aiming at theoretical truth and believing in theories would be, in some concrete respect that empiricists should recognize, worse off than the recommended realist attitude. To this end, the paper develops the so-called conjunction argument into a diachronic argument for scientific realism.     

The Transcendental Source of Logic by Way of Phenomenology

In this article I am going to argue for the possibility of a transcendental source of logic based on a phenomenologically motivated approach. My aim will be essentially carried out in two succeeding steps of reduction: the first one will be the indication of existence of an inherent temporal factor conditioning formal predicative discourse and the second one, based on a supplementary reduction of objective temporality, will be a recourse to a time-constituting origin which has to be assumed as a non-temporal, transcendental subjectivity and for that reason as possibly the ultimate transcendental root of pure logic. In the development of the argumentation and taking into account W.V. Quine’s views in his well-known Word and Object, a special emphasis will be given to the fundamentally temporal character of universal and existential predicative forms, to their status in logical theories in general, and to their underlying role in generating an inherently non-finitistic character reflected, for instance, in the undecidability of certain infinity statements in formal mathematical theories. This is shown also to concern metatheorems of such vital importance as Gödel’s incompleteness theorems in mathematical foundations. Moreover in the course of the discussion the quest for the ultimate limits of predication will lead to the notions of separation and intentional correlation between an ‘observing’ subject and the object of ‘observation’ as well as to the notion of syntactical individuals taken as the irreducible non-analytic nuclei-forms within analytical discourse.