Ioannis G. Ntagkas

We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving. The intended audience ranges from students interested in logic over historians to logicians. Besides the well-known correction of Herbrand’s False Lemma by Goedel and Dreben, we also present the hardly known unpublished correction of Heijenoort and its consequences on Herbrand’s Modus Ponens Elimination. Besides Herbrand’s Fundamental Theorem and its relation to the Loewenheim-Skolem-Theorem, we carefully investigate Herbrand’s notion of intuitionism in connection with his notion of falsehood in an infinite domain. We sketch Herbrand’s two proofs of the consistency of arithmetic and his notion of a recursive function, and last but not least, present the correct original text of his unification algorithm with a new translation.

In this article, we canvass a few of the interesting topics that philosophers can pursue as part of the simultaneous study of logic and metaphysics. To keep the discussion to a manageable length, we limit our survey to deductive, as opposed to inductive, logic. Though most of this article will focus on the ways in which logic can be deployed in the study of metaphysics, we begin with a few remarks about how metaphysics might be needed to understand what logic is. When we ask the question, “What is logic and what is its subject matter?”, there is no obvious answer. There have been so many di erent kinds of studies that have gone by the name ‘logic’ that it is di cult to give an answer that applies to them all. But there are some basic commonalities. Most philosophers would agree that logic presupposes (1) the existence of a language for expressing thoughts or meanings, (2) certain analytic connections between the thoughts that ground and legitimize the inferential relations among them, and (3) that the analytic connections and inferential relations can be studied systematically by investigating (often formally) the logical words and sentences used to express the thoughts so connected and related. For example, analytic connections give rise to various patterns of inferences expressed by certain logical words and phrases..

This paper reconstructs what I take to be the central evolutionary debunking argument that underlies recent critiques of moral realism. The argument claims that given the extent of evolutionary influence on our moral faculties, and assuming the truth of moral realism, it would be a massive coincidence were our moral faculties reliable ones. Given this coincidence, any presumptive warrant enjoyed by our moral beliefs is defeated. So if moral realism is true, then we can have no warranted moral beliefs, and hence no moral knowledge. In response, I first develop what is perhaps the most natural reply on behalf of realism namely, that many of our highly presumptively warranted moral beliefs are immune to evolutionary influence and so can be used to assess and eventually resuscitate the epistemic merits of those that have been subject to such influence. I then identify five distinct ways in which the charge of massive coincidence has been understood and defended. I argue that each interpretation is subject to serious worries. If I am right, these putative defeaters are themselves subject to defeat. Thus many of our moral beliefs continue to be highly warranted, even if moral realism is true

This paper addresses skepticism about progress in philosophy. After distinguishing four problems regarding philosophical progress ('existential,' 'comparative,' 'practical,' and 'theoretical'), the authors propose that the deep question is methodological: is there a method whose proper execution facilitates the realization of theoretical understanding about philosophical topics? The paper develops a method designed to answer this question affirmatively, and then shows how the method helps to resolve all four problems of progress.

We offer a reconstruction of Richard Price’s intuition-based epistemology of normative essences, highlighting its key elements and showing how it differs from the approaches taken by other intuitionists such as Thomas Reid and G. E. Moore, as well as sentimentalists such as Francis Hutcheson and David Hume. While our analysis aims to shed light on Price’s moral epistemology, it also seeks to contribute to contemporary debates about the epistemology of essence, advancing a general intuition-based theory. These two goals are related, for the former operates in the service of the latter. In this way, our discussion illustrates the role that historical research might play in contemporary inquiries into intuition.

This is a new volume of original essays on the metaphysics of quantum mechanics. The essays address questions such as: What fundamental metaphysics is best motivated by quantum mechanics? What is the ontological status of the wave function? Does quantum mechanics support the existence of any other fundamental entities, e.g. particles? What is the nature of the fundamental space of quantum mechanics? What is the relationship between the fundamental ontology of quantum mechanics and ordinary, macroscopic objects like tables, chairs, and persons? This collection includes a comprehensive introduction with a history of quantum mechanics and the debate over its metaphysical interpretation focusing especially on the main realist alternatives.

The quantum theory of decoherence plays an important role in a pragmatist interpretation of quantum theory. It governs the descriptive content of claims about values of physical magnitudes and offers advice on when to use quantum probabilities as a guide to their truth. The content of a claim is to be understood in terms of its role in inferences. This promises a better treatment of meaning than that offered by Bohr. Quantum theory models physical systems with no mention of measurement: it is decoherence, not measurement, that licenses application of Born’s probability rule. So quantum theory also offers advice on its own application. I show how this works in a simple model of decoherence, and then in applications to both laboratory experiments and natural systems. Applications to quantum field theory and the measurement problem will be discussed elsewhere

A quantum state represents neither properties of a physical system nor anyone’s knowledge of its properties. The important question is not what quantum states represent but how they are used—as informational bridges. Knowing about some physical situations, an agent may assign a quantum state to form expectations about other possible physical situations. Quantum states are objective: only expectations based on correct state assignments are generally reliable. If a quantum state represents anything, it is the objective probabilistic relations between its backing conditions and its advice conditions. This paper offers an account of quantum states and their function as informational bridges, in quantum teleportation and elsewhere.

Quantum theory is a fundamental part of contemporary science. But some recent arguments have been taken to show that if this theory is universally applicable then the outcome of a quantum measurement is not an objective fact. They motivate the more general reappraisal of the notions of fact and objectivity that I offer here. I argue that if quantum theory is universally applicable the facts about the physical world include a fact about each quantum measurement outcome. The physical facts may lack an ideal kind of objectivity, but their more modest objectivity is all that science needs.

The contributors to this 1981 volume are all concerned with scientific realism, but each author questions or rejects aspects of the way it has traditionally been discussed. There are three main foci of attention - reduction, time and modality - and the analyses bring out complexities and difficulties obscured in the standard accounts of scientific realism. The papers are powerful and original, representing some of the best in modern philosophy of science, and each were specifically commissioned for the volume. It is an excellent source book for courses on realism or the philosophy of science. The book therefore takes its place in the informal series of volumes arising from meetings sponsored by the Thyssen Foundation, which already includes C. Hookway and P. Pettit Action and Interpretation and R. Harrison Rational Action.

The role of probability is one of the most contested issues in the interpretation of contemporary physics. In this paper, I’ll be reevaluating some widely held assumptions about where and how probabilities arise. Larry Sklar voices the conventional wisdom about probability in classical physics in a piece in the Stanford Online Encyclopedia of Philosophy, when he writes that “Statistical mechanics was the first foundational physical theory in which probabilistic concepts and probabilistic explanation played a fundamental role.” And the conventional wisdom about quantum probabilities is that they are basic, not reducible to the types of probabilities we see in statistical mechanics. In the first section of this paper, I’ll argue that in fact classical physics was steeped in probability long before statistical mechanics came on the scene, specifically, that an objective measure over phase space is an indispensable component of any informative physical theory. In the next section, I’ll argue that this objective measure is the fundamental form of physical probability and that quantum probabilities can be defined in terms of it. In the last, I’ll raise some questions about the metaphysical status of the fundamental measure

This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low probability, their very existence implies that the no-signaling principle used in proofs of randomness of outcomes of quantum-mechanical measurements should be reinterpreted statistically, like the second law of thermodynamics. In three appendices I discuss the Born rule and its status in both single and repeated experiments, review the notion of 1-randomness that in various guises was investigated by Kolmogorov and others and treat Bell’s Theorem and the Free Will Theorem with their implications for randomness.

What are the main debates in philosophy of biology today? The present book (part of the series Contemporary Debates in Philosophy) attempts to identify and discuss some of the most important of these. The endeavour is, I think, successful; the collection is a valuable contribution to the literature of philosophy of biology. Before discussing some particular lines of thought in the book, some brief remarks on its structure and organization: the book consists of ten parts, each of which is centred around an important issue in philosophy of biology. Like other collections in this series, each part includes two papers arguing for opposing views concerning the central issue, together with postscripts where the authors have the opportunity to directly confront the arguments of the opposition. There is also considerable interaction between the authors in the main body of their papers, short introductions by the editors and lists with suggestions for further reading. This arrangement is the mai ...