Responding to the myth of a purely sensuous “given”, we turn to phenomenology, to the structure of consciousness in an everyday perception of an everyday object. We first consider Brentano’s model of an act of consciousness: featuring the presentation of an object “intentionally” contained “in” the act, joined by the presentation of that object-presentation in “inner consciousness”. We then dig into Husserl’s intricate “semantic” theory of intentionality: featuring “noematic” meaning within a “horizon” of implicated meaning regarding the object of perceptual (...) consciousness. Brentanian inner consciousness morphs into “inner time consciousness” for Husserl, where noematic sense shapes more basic sensory elements of temporal experience. Drawing on these Brentanian and Husserlian analyses, we develop an enhanced account of how an object is “given” in perceptual acquaintance or “intuition”: by virtue of a structure of meaning entertained in the experience. This account we develop further in a “modal” model of the structure of consciousness in everyday perception: distinguishing fundamental factors of phenomenal intentional experience, including inner awareness, phenomenality, and spatiotemporal awareness. Within this model, we specify how the external object of perception is “constituted” in consciousness by virtue of ideal meaning, all within the real world wherein an intentional relation of acquaintance links the perceptual experience with its object. What is “given” in a familiar type of perceptual acquaintance turns out to be quite complex, embracing: the object perceived, the visual experience, its subject, the spatiotemporal context including consciousness and object, and the manifold of meaning shaping the “constitution” of the given object. Where we refer to historical figures, including Husserl, the aim is theoretical rather than exegetical, seeking to develop a contemporary theory of “the given” with roots in classical philosophical views. The resulting theory develops in a series of explorations of increasing complexity in the phenomenology and attendant ontology of “the given”. (shrink)

This article deals with a question of a most general, comprehensive and profound content as it is the nature of mathematical–logical objects insofar as these are considered objects of knowledge and more specifically objects of formal mathematical theories. As objects of formal theories they are dealt with in the sense they have acquired primarily from the beginnings of the systematic study of mathematical foundations in connection with logic dating from the works of G. Cantor and G. Frege in the last (...) decades of the nineteenth century. Largely motivated by a phenomenologically founded view of mathematical objects/states-of-affairs, I try to consistently argue for their character as objects shaped to a certain extent by intentional forms exhibited by consciousness and the modes of constitution of inner temporality and at the same time as constrained in the form of immanent ‘appearances’ by what stands as their non-eliminable reference, that is, the world as primitive soil of experience and the mathematical intuitions developed in relations of reciprocity within-the-world. In this perspective and relative to my intentions I enter, in the last section, into a brief review of certain positions of G. Sher’s foundational holism and R. Tieszen’s constituted platonism, among others, respectively presented in Sher and Tieszen. (shrink)

In this article I try to articulate a defensible argumentation against the idea of an ontology of infinity. My position is phenomenologically motivated and in this virtue strongly influenced by the Husserlian reduction of the ontological being to a process of subjective constitution within the immanence of consciousness. However taking into account the historical charge and the depth of the question of infinity over the centuries I also include a brief review of the platonic and aristotelian views and also those (...) of Locke and Hume on the concept to the extent that they are relevant to my own discussion of infinity both in a purely philosophical and epistemological context. Concerning the latter context, I argue against Kanamori’s position, in The Infinite as Method in Set Theory and Mathematics, that the mathematical infinite can be accounted for solely in terms of epistemological articulation, that is, in the way it is approached, assimilated, and applied in the course of the construction of mathematical hierarchies. Instead I point to a subjectively constituted immanent ‘infinity’ in virtue of the a priori as well as factual characteristics of subjective constitution, underlying and conditioning any talk of infinity in an epistemological sense. From this viewpoint I also address some other positions on the question of a possible ontology of the mathematical infinite. My whole approach to the question of the infinite in an epistemological sense hinges on the assumption that the mathematical infinite subsumes the infinite of physical theories to the extent that physics and science in general deal with the infinite in terms of the corresponding mathematical language and the specific techniques involved. (shrink)

This is an article whose intended scope is to deal with the question of infinity in formal mathematics, mainly in the context of the theory of large cardinals as it has developed over time since Cantor’s introduction of the theory of transfinite numbers in the late nineteenth century. A special focus has been given to this theory’s interrelation with the forcing theory, introduced by P. Cohen in his lectures of 1963 and further extended and deepened since then, which leads to (...) a development and further refinement of the theory of large cardinals ultimately touching, especially in view of the discussion in the last section, on the metatheoretical nature of infinity. The whole undertaking, which takes into account major stages of the research in large cardinals theory, tries to present a defensible argumentation against an ontology of infinity actually rooted in the notion of subjectivity within the world. This means that rather than talking of a general ontology of infinity in the ideal platonic or in the aristotelian sense of potentiality, even in the alternative sense of an ontology of the event in A. Badiou’s sense, one can argue from a subjective point of view about the impossibility of defining cardinalities greater than the first uncountable one \ that would correspond to a distinct existence in real world terms or would be supported by a mathematical intuition in terms of reciprocity with experience. The argumentation from the particular standpoint includes also certain comments on the delimitative character of Gödel’s constructive universe L and the influence of the constructive approach in narrowing the breadth of an ‘ontology’ of infinity. (shrink)

A debated issue in the mathematical foundations in at least the last two decades is whether one can plausibly argue for the merits of treating undecidable questions of mathematics, e.g., the Continuum Hypothesis, by relying on the existence of a plurality of set-theoretical universes except for a single one, i.e., the well-known set-theoretical universe V associated with the cumulative hierarchy of sets. The multiverse approach has some varying versions of the general concept of multiverse yet my intention is to primarily (...) address ontological multiversism as advocated, for instance, by Hamkins or Väätänen, precisely for the reason that they proclaim, to the one or the other extent, ontological preoccupations for the introduction of respective multiverse theories. Taking also into account Woodin’s and Steel’s multiverse versions, I take up an argumentation against multiversism, and in a certain sense against platonism in mathematical foundations, mainly on subjectively founded grounds, while keeping an eye on Clarke-Doane’s concern with Benacerraf’s challenge. I note that even though the paper is rather technically constructed in arguing against multiversism, the non-negligible philosophical part is influenced to a certain extent by a phenomenologically motivated view of the matter. (shrink)

European Journal of Philosophy, Volume 30, Issue 3, Page 1010-1027, September 2022.

Husserl claims that his phenomenological–epistemological system amounts to a “universal” form of empiricism. The present paper shows that this universal moment of Husserl’s empiricism is why his empiricism qualifies as a rationalism. What is empiricist about Husserl’s phenomenological–epistemological system is that he takes experiences to be an autonomous source of immediate justification. On top of that, Husserl takes experiences to be the ultimate source of justification. For Husserl, every justified belief ultimately depends epistemically on the subject’s experiences. These are paradigms (...) of empiricist claims and thus Husserl seems to subscribe to empiricism. However, what is universal about Husserl’s “empiricism” is that he does not limit the concept of experiences to sensory experiences or sensory experiences plus introspective intuitions but broadens the concept of experience such that also a priori intuitions are included. Husserl insists that logical, mathematical, and phenomenological intuitions such as ~, 2 + 2 = 4, and “Experiences necessarily bear the mark of intentionality” provide non-inferential justification analogous to how sensory experiences can non-inferentially justify beliefs such as “There is a table in front of me.” Importantly, Husserl makes clear that such a priori intuitions are not about our concepts but about reality. This is why Husserl’s universal empiricism is a rationalism. Husserl differs from traditional rationalism as he allows that a priori intuitions can be fallible and empirically underminable. This distinguishes Husserl’s rationalism from Descartes’ and makes him a proponent of moderate rationalism as currently championed by Laurence BonJour. (shrink)

Phenomenology is the study of structures of consciousness as experienced from the first-person point of view. The central structure of an experience is its intentionality, its being directed toward something, as it is an experience of or about some object. An experience is directed toward an object by virtue of its content or meaning (which represents the object) together with appropriate enabling conditions.

Although there is no consensus on what distinguishes analytic from Continental philosophy, I focus in this paper on one source of disagreement that seems to run fairly deep in dividing these traditions in recent times, namely, disagreement about the relation of natural science to philosophy. I consider some of the exchanges about science that have taken place between analytic and Continental philosophers, especially in connection with the philosophy of mind. In discussing the relation of natural science to philosophy I employ (...) an analysis of the origins of natural science that has been developed by a number of Continental philosophers. Awareness and investigation of interactions between analytic and Continental philosophers on science, it is argued, might help to foster further constructive engagement between the traditions. In the last section of the paper I briefly discuss the place of natural science in relation to global philosophy on the basis of what we can learn from analytic/Continental exchanges. (shrink)

Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...) be crucial, and show how one may provide responses to Maddy's concerns based on a careful analysis of 'multiverse practice'. (shrink)