Online research in philosophy

This article is an extended critical study of Kit Fine’s The limits of abstraction, which is a sustained attempt to take the measure of the neo-logicist program in the philosophy and foundations of mathematics, founded on abstraction principles like Hume’s principle. The present article covers the philosophical and technical aspects of Fine’s deep and penetrating study.

The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those difficulties while still being able to put abstraction principles to a foundational use.

This article is composed of three sections that investigate the epistemological foundations of Husserl’s idea of logic from the Logical Investigations . First, it shows the general structure of this logic. Husserl conceives of logic as a comprehensive, multi-layered theory of possible theories that has its most fundamental level in a doctrine of meaning. This doctrine aims to determine the elementary categories that constitute every possible meaning (meaning-categories). The second section presents the main idea of Husserl’s search for an epistemological foundation for knowledge, science and logic. Their epistemological clarification can only be reached through a detailed analysis of the structure of those intentions that give us what is meant in our intentions. To reveal the intuitive giveness of logical forms is the ultimate aim of Husserl’s epistemology of logic. Logical forms and meaning-categories can only be given in a certain higher-order intuition that Husserl calls categorical intuition. The third section of this article distinguishes different kinds of categorical intuition and shows how the most basic logical categories and concepts are given to us in a categorical abstraction.

Edmund Husserl is the founder of phenomenology. The Logical Investigations is Edmund Husserl's most famous work and has had a decisive impact on the direction of twentieth century philosophy. This is the first time both volumes of this classic work, translated by J.N. Findlay, have been available in paperback. They include a new introduction by Dermot Moran, placing the Logical Investigations in historical context and bringing out its importance for contemporary philosophy.

Frege, G. Review of Dr. E. Husserl's Philosophy of arithmetic.--Mohanty, J. N. Husserl and Frege.--Husserl, E. A Reply to a critic of my refutation of logical psychologism.--Willard, D. The Paradox of logical psychologism.--Natorp, P. On the question of logical method.--Næss, A. Husserl on the apodictic evidence of ideal laws.--Mohanty, J. N. Husserl's thesis of the ideality of meanings.--Atwell, J. E. Husserl on signification and object.--Sokolowski, R. The logic of parts and wholes in Husserl's Investigations.--Gurwitsch, A. Outlines of a theory of essentially occasional expressions.--Bar-Hillel, Y. Husserl's conception of a purely logical grammar.--Edie, J. M. Husserl's conception of the grammatical and contemporary linguistics.--Downes, C. On Husserl's approach to necessary truth.--Patzig, G. Husserl on truth and evidence.--Husserl, E. The task and the significance of the Logical investigations.

Berkeley and Hume object to Locke's account of abstraction. Abstraction is separating in the mind what cannot be separated in reality. Their objection is that if a is inseparable in reality from b, then the idea of a is inseparable from the idea of b. The former inseparability is the reason for the latter. In most interpretations, however, commentators leave the former unexplained in explaining the latter. This article assumes that Berkeley and Hume present a unified front against Locke. Hume supplements Berkeley's argument just where there are gaps. In particular, Hume makes explicit something Berkeley leaves implicit: The argument against Locke depends on the principle that things are inseparable if and only if they are identical. Abstraction is thinking of one of an inseparable pair while not thinking of the other. But doing so entails thinking of something while not thinking of it. This is the fundamental objection.

The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently availeble tool for explicating a notion’s logical character—permutation invariance—has not received a lot of attention in this debate. This paper aims to fill this gap. After characterizing abstraction principles as particular mappings from the subsets of a domain into that domain and exploring some of their properties, the paper introduces several distinct notions of permutation invariance for such principles, assessing the philosophical significance of each.

The twelve original studies collected in this volume examine different aspects of Edmund Husserl's Logical Investigations. They are authored by scholars and specialists internationally recognized for their expertise in the fields of phenomenology, logic, history of philosophy and philosophy of mind. They approach Husserl's groundwork from different angles and perspectives and shed new light on a number of issues such as meaning, intentionality, ontology, logic, etc. They also explore questions such as the place of the Logical Investigations within the whole of Husserl's work, its sources in 19th century philosophy and in particular in the philosophical work of Franz Brentano and Bernard Bolzano, its reception amongst the so-called members of the Munich Circle and its influence on contemporary philosophy. In short, this volume constitutes a "companion" to Husserl's Logical Investigations.

Both Alexius Meinong and Edmund Husserl wrote about relations in their early works, in periods in which they were still influenced by Franz Brentano. However, besides the split between Brentano and Meinong, the latter also accused Husserl of plagiarism with respect to the theory of relations. Examining Meinong’s and Husserl’s early works and the Brentanist framework they were written in, we will try to assess their similarities and differences. As they shared other sources besides Brentano, we will consider very carefully whether we should speak at all of influence or plagiarism. Despite Meinong’s accusations it seems that both he and Husserl took over some elements from Brentano and, partially through him, from John Stuart Mill, who appears to be the most probable source on relations.

While Hermann Lotze's philosophy was widely received all over the world, his views on abstraction and Platonic ideas are of particular interest because they were to a large extent adopted by one of the most eminent philosophers of the twentieth century, namely Edmund Husserl. In this paper these views are examined in three distinct aspects. The first of these aspects is to be found in Lotze's thesis that there is a mental process, prior to abstraction, whereby "first universals" are apprehended. The second one lies in his view that there is yet a higher level of apprehension, as found in the process of abstraction itself. According to Lotze, abstraction is not to be identified with the mere removal of particular features, but rather the replacement of these with first universals, resulting in "general images" and ultimately concepts. In addition to Lotze's analysis of the cognition of universals, there is finally a third thesis (an ontological one) which is examined in this paper, namely that the universals are Platonic Ideas in the sense that they have "validity" (Geltung) independently of their corresponding particulars and also of the mind which grasps them. The three claims in question are examined here in detail. Also, an attempt is made to point out some of the connections between Lotze and Husserl on the topic under discussion.