Introduction: From a logical point of view the measurement problem of quantum mechanics, can be described as a characteristic question of ‘semantical closure’ of a theory: to what extent can a consistent theory (in this case 2R) be closed with respect to the objects and the concepfs which are described and expressed in its metatheory?
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.
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.
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.
Continental Feminism Reader
Publisher’s Note: Ann J. Cahill and Jennifer Hansen collect the most groundbreaking recent work in Continental feminist theory, introducing and explaining pieces that are often mystifying to those outside the field and outside academia. With these essays, Continental Feminism Reader begins the process of reanimating feminist politics through the critical tools of its contributors.
Hegel’s Moral Philosophy
Abstract: Hegel’s criticism of morality, or Moralität, has had a decisive influence in the reception of his thought. By general acknowledgment, while his writings support a broadly neo-Aristotelian ethics of self-actualization, his views on moral philosophy are exhausted by his criticisms of Kant, whom he treats as paradigmatic exponent of the standpoint of morality. The aim of this chapter is to correct this received view and show that Hegel offers a positive conception of moral willing. The main argument is presented in two parts: (a) an interpretation of the ‘Morality’ section of the Philosophy of Right that shows Hegel defending a guise of the good version of willing; and (b) an examination of problems raised by this view of willing, some of which are anticipated by Hegel in in his treatment of the ‘Idea of the Good’ in the Logic, and of the interpretative options available to deal with these problems.
Hegel’s Philosophy of Art
Abstract: Despite Hegel’s effusive praise for art as one of the ways humans express truth, art by his description is both essentially limited and at perpetual risk of ending. This hybrid assessment is apparent first in Hegel’s account of art’s development, which shows art culminating in classical sculpture’s perfect unity, but then, unable to depict Christianity’s interiority, evolving into religion, surrendering to division, or dissipating into prose. It is also evident in his ranking of artistic genres from architecture to poetry according to their ability to help humans produce themselves both individually and collectively: the more adequately art depicts human self-understanding, the more it risks ceasing to be art. Nevertheless, art’s myriad endings do not exhaust its potential. Art that makes humans alive to the unity and interdependence at the heart of reality continues to express the Idea and so achieves Hegel’s ambitions for its role in human life.
The Art and Philosophy of George Eliot
Abstract: Much remains to be said about Eliot as a philosopher. I argue that her novels should be understood as attempts to practice philosophy in an alternative key. Her decision to write novels rather than conventional philosophy reflects her desire to actively engage the imaginative and affective, as well as the cognitive, powers of her readers. On her view the imagination grounds our disposition to feel sympathy for our fellow human beings. It is this disposition and its potential for refinement as moral knowledge that she sought to realize in her novels. An appreciation of her philosophical commitments is necessary in order to understand her efforts to construct an immanent ground for moral life. The parts played by the imagination, reason and emotion in the attainment of moral knowledge were of prime concern to both Spinoza and Feuerbach. Each philosopher offered an account of the relations between these capacities and argued for their reformation. This reformative task is one that Eliot attempted in her novels. The radical holism of Spinoza and Feuerbach resonates throughout her work. She had a deep suspicion of dualistic philosophies that separate reason and imagination. Like Spinoza and Feuerbach, she understood these ruptures within our capacities, indeed within our very being, to derive in large part from religion, especially Christianity. The reform of our habitual ways of understanding the world must therefore begin with critical reflection on religion.
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.
Do Experiences Have Contents?
Summary: This paper argues that despite the differences between perception and belief, perception involves states that are importantly similar to beliefs: conscious visual experiences. According to the Content View, these experiences have contents in the form of accuracy conditions. The paper develops and defends the Content View, discusses its significance, and argues that contrary to what is often supposed, the Content View is compatible with Naive Realist disjunctivism.