Publisher’s Note: Hannah Arendt’s last philosophical work was an intended three-part project entitled The Life of the Mind. Unfortunately, Arendt lived to complete only the first two parts, Thinking and Willing. Of the third, Judging, only the title page, with epigraphs from Cato and Goethe, was found after her death. As the titles suggest, Arendt conceived of her work as roughly parallel to the three Critiques of Immanuel Kant. In fact, while she began work on The Life of the Mind, Arendt lectured on “Kant’s Political Philosophy,” using the Critique of Judgment as her main text. The present volume brings Arendt’s notes for these lectures together with other of her texts on the topic of judging and provides important clues to the likely direction of Arendt’s thinking in this area.
Classical Logic
Summary: This article provides the basics of a typical logic, sometimes called ‘classical elementary logic’ or ‘classical first-order logic’, in a rigorous yet accessible manner. Section 2 develops a formal language, with a syntax and grammar. Section 3 sets up a deductive system for the language, in the spirit of natural deduction. Section 4 provides a model-theoretic semantics. Section 5 turns to the relationships between the deductive system and the semantics, and in particular, the relationship between derivability and validity. The authors show that an argument is derivable only if it is valid (soundness). Then they establish a converse: that an argument is valid only if it is derivable (completeness). They also briefly indicate other features of the logic, some of which are corollaries to soundness and completeness. The final section, Section 6, is devoted to a brief examination of the philosophical position that classical logic is ‘the one right logic’.
Proof Theory: Sequent Calculi and Related Formalisms
Publisher’s Note: Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other non-classical logics and meta-logical results, including decidability results obtained specifically using sequent calculus formalizations of logics.
Primitive Ontology in a Nutshell
Abstract: The aim of this paper is to summarize a particular approach of doing metaphysics through physics – the primitive ontology approach. The idea is that any fundamental physical theory has a well-defined architecture, to the foundation of which there is the primitive ontology, which represents matter. According to the framework provided by this approach when applied to quantum mechanics, the wave function is not suitable to represent matter. Rather, the wave function has a nomological character, given that its role in the theory is to implement the law of evolution for the primitive ontology.
Platonism and Anti-Platonism: Why Worry?
Abstract: This paper argues that it is scientific realists who should be most concerned about the issue of Platonism and anti-Platonism in mathematics. If one is merely interested in accounting for the practice of pure mathematics, it is unlikely that a story about the ontology of mathematical theories will be essential to such an account. The question of mathematical ontology comes to the fore, however, once one considers our scientific theories. Given that those theories include amongst their laws assertions that imply the existence of mathematical objects, scientific realism, when construed as a claim about the truth or approximate truth of our scientific theories, implies mathematical Platonism. However, a standard argument for scientific realism, the ‘no miracles’ argument, falls short of establishing mathematical Platonism. As a result, this argument cannot establish scientific realism as it is usually defined, but only some weaker position. Scientific ‘realists’ should therefore either redefine their position as a claim about the existence of unobservable physical objects, or alternatively look for an argument for their position that does establish mathematical Platonism.
Medieval Christian and Islamic Mysticism and the Problem of a “Mystical Ethics”
Abstract: In this chapter, we examine a few potential problems when inquiring into the ethics of medieval Christian and Islamic mystical traditions: First, there are terminological and methodological worries about defining mysticism and doing comparative philosophy in general. Second, assuming that the Divine represents the highest Good in such traditions, and given the apophaticism on the part of many mystics in both religions, there is a question of whether or not such traditions can provide a coherent theory of value. Finally, the antinomian tendencies and emphasis on passivity of some mystics might lead one to wonder whether their prescriptive exhortations can constitute a coherent theory of right action. We tackle each of these concerns in turn and discuss how they might be addressed, in an attempt to show how medieval mysticism, as a fundamentally practical enterprise, deserves more attention from practical and moral philosophy than it has thus far received.
Stoic Syllogistic
Abstract: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules which establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out.
Women in Philosophy: What Needs to Change?
Publisher’s Note: Despite its place in the humanities, the career prospects and numbers of women in philosophy much more closely resemble those found in the sciences and engineering. This book collects a series of critical essays by female philosophers pursuing the question of why philosophy continues to be inhospitable to women and what can be done to change it. By examining the social and institutional conditions of contemporary academic philosophy in the Anglophone world as well as its methods, culture, and characteristic commitments, the volume provides a case study in interpretation of one academic discipline in which women’s progress seems to have stalled since initial gains made in the 1980s. Some contributors make use of concepts developed in other contexts to explain women’s under-representation, including the effects of unconscious biases, stereotype threat, and micro-inequities. Other chapters draw on the resources of feminist philosophy to challenge everyday understandings of time, communication, authority and merit, as these shape effective but often unrecognized forms of discrimination and exclusion. Often it is assumed that women need to change to fit existing institutions. This book instead offers concrete reflections on the way in which philosophy needs to change, in order to accommodate and benefit from the important contribution women’s full participation makes to the discipline.
Extensionalism and Scientific Theory in Quine’s Philosophy
Abstract: In this article, I analyze Quine’s conception of science, which is a radical defence of extensionalism on the grounds that first?order logic is the most adequate logic for science. I examine some criticisms addressed to it, which show the role of modalities and probabilities in science and argue that Quine’s treatment of probability minimizes the intensional character of scientific language and methods by considering that probability is extensionalizable. But this extensionalizing leads to untenable results in some cases and is not consistent with the fact that Quine himself admits confirmation which includes probability. Quine’s extensionalism does not account for this fact and then seems unrealistic, even if science ought to be extensional in so far as it is descriptive and mathematically expressible.
Avicenna on Possibility and Necessity
Abstract: In this paper, I raise the following problem: How does Avicenna define modalities? What oppositional relations are there between modal propositions, whether quantified or not? After giving Avicenna’s definitions of possibility, necessity and impossibility, I analyze the modal oppositions as they are stated by him. This leads to the following results:
1. The relations between the singular modal propositions may be represented by means of a hexagon. Those between the quantified propositions may be represented by means of two hexagons that one could relate to each other.
2. This is so because the exact negation of the bilateral possible, i.e. ‘necessary or impossible’ is given and applied to the quantified possible propositions.
3. Avicenna distinguishes between the scopes of modality which can be either external (de dicto) or internal (de re). His formulations are external unlike al-F̄ar̄ab̄
;’s ones.
However his treatment of modal oppositions remains incomplete because not all the relations between the modal propositions are stated explicitly. A complete analysis is provided in this paper that fills the gaps of the theory and represents the relations by means of a complex figure containing 12 vertices and several squares and hexagons.