Platonism in Lotze and Frege Between Psyschologism and Hypostasis

In the section “Validity and Existence in Logik, Book III,” I explain Lotze’s famous distinction between existence and validity in Book III of Logik. In the following section, “Lotze’s Platonism,” I put this famous distinction in the context of Lotze’s attempt to distinguish his own position from hypostatic Platonism and consider one way of drawing the distinction: the hypostatic Platonist accepts that there are propositions, whereas Lotze rejects this. In the section “Two Perspectives on Frege’s Platonism,” I argue that this is an unsatisfactory way of reading Lotze’s Platonism and that the Ricketts-Reck reading of Frege is in fact the correct way of thinking about Lotze’s Platonism

Prioritizing platonism

Discussion of atomistic and monistic theses about abstract reality

Platonism and Christian Thought in Late Antiquity

Platonism and Christian Thought in Late Antiquity examines the various ways in which Christian intellectuals engaged with Platonism both as a pagan competitor and as a source of philosophical material useful to the Christian faith. The chapters are united in their goal to explore transformations that took place in the reception and interaction process between Platonism and Christianity in this period. The contributions in this volume explore the reception of Platonic material in Christian thought, showing that the transmission of cultural content is always mediated, and ought to be studied as a transformative process by way of selection and interpretation. Some chapters also deal with various aspects of the wider discussion on how Platonic, and Hellenic, philosophy and early Christian thought related to each other, examining the differences and common ground between these traditions. Platonism and Christian Thought in Late Antiquity offers an insightful and broad ranging study on the subject, which will be of interest to students of both philosophy and theology in the Late Antique period, as well as anyone working on the reception and history of Platonic thought, and the development of Christian thought

Indispensability Without Platonism

According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage

A Dilemma for Mathematical Constructivism

In this paper I argue that constructivism in mathematics faces a dilemma. In particular, I maintain that constructivism is unable to explain (i) the application of mathematics to nature and (ii) the intersubjectivity of mathematics unless (iii) it is conjoined with two theses that reduce it to a form of mathematical Platonism. The paper is divided into five sections. In the first section of the paper, I explain the difference between mathematical constructivism and mathematical Platonism and I outline my argument. In the second, I argue that the best explanation of how mathematics applies to nature for a constructivist is a thesis I call Copernicanism. In the third, I argue that the best explanation of how mathematics can be intersubjective for a constructivist is a thesis I call Ideality. In the fourth, I argue that once constructivism is conjoined with these two theses, it collapses into a form of mathematical Platonism. In the fifth, I confront some objections

Dummett’s Criticism of the Context Principle

This paper was written during my AHRC research leave on Frege's Platonism and Platonism today.This paper was written during my AHRC research leave on Frege's Platonism and Platonism toda

Introduction

This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book explores, inter alia, the strategy employed by Augustine in using Plato as a pseudo-prophet against later Platonists and explores Eusebius’ reception of Porphyry’s daemonology. It examines Plotinus’ claim that matter is absolute badness and focuses on Maximus the Confessor’s doctrine of creation and asks whether one may detect any influence on Maximus from Philoponus. The book addresses Christian receptions of Platonic metaphysics and also examines the philosophy of number in Augustine’s early works. It argues that the aspect of Augustine’s philosophy must be read in context with the intellectual problems that occupied him at the beginning of his career as a writer. It draws on a number of sources to investigate the development of the doctrine and the various intellectual issues it confronted, including Plato’s Timaeus, Philo of Alexandria, Clement of Alexandria, Origen, Plotinus and, finally, Athanasius

Kripkenstein from the mathematical point of view: a preliminary survey

This paper deals with the problem of the impact of Kripke’s skeptical paradox on the philosophy of mathematics. By perceiving mathematics as a huge rule-following discipline, one could argue that the Kripkean nonfactualist thesis should be adopted within the philosophy of mathematics en bloc to imply a refutation of objectivity and an enforcement of a particular view on the nature of mathematics. In this paper I will discuss this claim. According to Kripke’s skeptical solution we should reject the notion of fact and adopt the use theory of meaning that could be stated as follows: ’One understands the concepts embodied in a language to the extent that one knows how to use the language correctly.’ [Shapiro 1991, 211] [Kripke 1982]. Focusing on mathematical discourse, we should ask: what are the implications of the use theory of meaning for the philosophy of mathematics? Furthermore, is the answer to the skeptical paradox consistent with selected views in philosophy of mathematics? The supposed answer to the first question is that it demands the view that mathematics should be perceived as a strictly pragmatic discipline and the rules of mathematical discourse are mere conventions. But this is too simplistic a view and the matter at hand is far more complicated.This paper is a part of a research project financed by National Centre of Science (Poland) on the basis of the decision no. UMO-2016/20/T/HS5/00232