Ioannis G. Ntagkas

In Der logische Aufbau der Welt, first published in 1928, Carnap aims to rationally reconstruct all objects of cognition by logico-definitional means. As a result, he intends to obtain a fully objective framework in which scientific discourse can take place. This is made possible by the novel method of ‘purely structural definite description’ of all scientifically relevant objects, which is first introduced in the Aufbau. Key to the attainment of this goal is the notion of ‘foundedness’, which Carnap presents as a new basic notion of logic, in order to establish a link between the purely conventional world of logical and mathematical knowledge and the empirical world of knowledge of scientific objects. This idea experienced major criticism by Friedman (1999a,b) since he considers it to lead to the demolition of the boundary between those two worlds. In this essay, we want to defend foundedness against Friedman’s critique by arguing that its introduction is necessary within Carnap’s logicist world of thought to deal with a more fundamental problem: the demarcation of the empirical parts of the Aufbau. In the last section, we will give an outlook on the actual cause for the failure of the Aufbau, the lack of a principle to determine the truth of the instances of the basic relation in the Aufbau, and we will show how this can contribute to the explanation of Carnap’s future philosophical development and retrospective self-evaluation. This essay serves as a dense informal sketch for a later extensive formal treatment of this reading of foundedness and focuses on its implications for the interpretation of Carnap’s post-Aufbau development.

A. J. Ayer’s empiricist criterion of meaning was supposed to have sorted all statements into nonsense on the one hand, and tautologies or genuinely factual statements on the other. Unfortunately for Ayer, it follows from classical logic that his criterion is trivial—it classifies all statements as either tautologies or genuinely factual, but none as nonsense. However, in this paper, I argue that Ayer’s criterion of meaning can be defended from classical proofs of its triviality by the adoption of a relevant logic—an idea which is motivated because, according to Ayer, the genuinely factual statements are those which observation is relevant to.

Scientific realists claim that the best of successful rival theories is (approximately) true. Relative realists object that we cannot make the absolute judgment that a theory is successful, and that we can only make the relative judgment that it is more successful than its competitor. I argue that this objection is undermined by the cases in which empirical equivalents are successful. Relative realists invoke the argument from a bad lot to undermine scientific realism and to support relative realism. In response, I construct the argument from double spaces. It is similar to the argument from a bad lot, but threatens many philosophical inferences, including relative realists’ inference from comparative success to comparative truth.

There is a standard way of interpreting physicalism. This is as a completeness thesis of some kind. Completeness physicalists believe there is or in principle could be some future physics that provides a complete explanatory or ontological basis for our universe. And this provides a sense in which physics is special among the sciences, the sense in which it is fundamental. This paper contrasts this standard completeness physicalism with what is a more plausible maximality physicalism. Maximality physicalists believe physics is special only in its providing an epistemic framework that is ontologically or explanatorily superior in some respect. This paper shows how completeness physicalists cannot, while maximality physicalists can, provide an adequate explanation of the empirical support for and the pragmatic usefulness of physicalism. It also shows how maximality physicalism is better supported in light of several developments from late twentieth century philosophy of science.

This paper attends to two main tasks. First, I introduce the notion of perspectival disagreement in science. Second, I relate perspectival disagreement in science to the broader issue of realism about science: how to maintain realist ontological commitments in the face of perspectival disagreement among scientists? I argue that often enough perspectival disagreement is not at the level of the scientific knowledge claims but rather of the methodological and justificatory principles. I introduce and clarify the notion of ‘agreeing-whilst-perspectivally-disagreeing’ with an episode from the history of modern physics: namely, how we came to agree about the electric charge as a minimal natural unit despite different scientific perspectives and associated data-to-phenomena inferences available for it in the period 1897–1906.

This book offers a novel account of the relationship of experience to knowledge. The account builds on the intuitive idea that our ordinary perceptual judgments are not autonomous, that an interdependence obtains between our view of the world and our perceptual judgments. Anil Gupta shows in this important study that this interdependence is the key to a satisfactory account of experience. He uses tools from logic and the philosophy of language to argue that his account of experience makes available an attractive and feasible empiricism.

This book aims to offer an account of conscious experience and of concepts that help us understand empirical reasoning and empirical dialectic. The account offered possesses, it is claimed, two virtues. First, it provides great theoretical freedom. It allows the theoretician freedom to radically reconceive the world. The theoretician may, for example, begin with the conception that colors are genuine qualities of physical bodies and may, in light of empirical findings, shift to the conception that colors are not genuine qualities at all. Second, the account grants empirical reason a great power to constrain: empirical reason can force a particular conception of the self and the world on the rational inquirer. These seemingly contrary virtues are reconciled through a novel treatment of presentation and appearances in the account offered of conscious experience and a novel treatment of ostensive definitions in the account offered of concepts. The argument of the book is buttressed by a critical study of the principal approaches to experience and reason found in the philosophical literature.--

It is commonly supposed that a certain kind of belief is necessary for religious experience. Yet it is not clear that this must be so. In this article, I defend the possibility that a subject could have a genuine emotional religious experience without thereby necessarily believing that the purported object of her experience corresponds to reality and/or is the cause of her experience. Imaginative engagement, I argue, may evoke emotional religious experiences that may be said to be both genuine and appropriate, despite not necessarily including beliefs of the aforementioned kind.I go on to maintain that such religious engagement is compatible not only with non-belief but also with disbelief.

Reprinted in Philosophy of Religion: An Anthology, Wadsworth 2015, 6th edition, eds Michael Rea and Louis Pojman. What is propositional faith? At a first approximation, we might answer that it is the psychological attitude picked out by standard uses of the English locution “S has faith that p,” where p takes declarative sentences as instances, as in “He has faith that they’ll win”. Although correct, this answer is not nearly as informative as we might like. Many people say that there is a more informative answer. They say that, at the very least, propositional faith requires propositional belief. More precisely, they say that faith that p requires belief that p or that it must be partly constituted by belief that p. This view is common enough; call it the Common View. I have two main aims in this paper: (i) to exhibit the falsity of the Common View and the paucity of reasons for it, and (ii) to sketch a more accurate and comprehensive account of what propositional faith is.

Fixing Frege is one of the most important investigations to date of Fregean approaches to the foundations of mathematics. In addition to providing an unrivalled survey of the technical program to which Frege's writings have given rise, the book makes a large number of improvements and clarifications. Anyone with an interest in the philosophy of mathematics will enjoy and benefit from the careful and well-informed overview provided by the first of its three chapters. Specialists will find the book an indispensable reference and an invaluable source of insights and new results. Although Frege is widely regarded as the father of analytic philosophy, his work on the foundations of mathematics was for a long time rather peripheral to ongoing research. The main reason for this is no doubt Russell's discovery in 1901 that the paradox now bearing his name can be derived in Frege's logical system. But recent decades have seen a huge surge of interest in Fregean approaches to the foundations of mathematics. A variety of consistent theories have been discovered that can be salvaged from Frege's inconsistent system, and foundational and philosophical claims have been made on behalf of many of these theories. Burgess claims quite plausibly that the significance of any such modified Fregean theory will in large part depend on how much of ordinary mathematics it enables us to develop. His book is accordingly 'a survey of various modified Fregean systems, attempting to determine the scope and limits of each'. The book's agenda is thus predominantly technical, and its spirit open-minded and experimental.

Platonism about mathematics (or mathematical platonism) isthe metaphysical view that there are abstract mathematical objectswhose existence is independent of us and our language, thought, andpractices. Just as electrons and planets exist independently of us, sodo numbers and sets. And just as statements about electrons and planetsare made true or false by the objects with which they are concerned andthese objects' perfectly objective properties, so are statements aboutnumbers and sets. Mathematical truths are therefore discovered, notinvented., Existence. There are mathematical objects

We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and Löwe [14], including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism, Grothendieck–Zermelo potentialism, transitive-set potentialism, forcing potentialism, countable-transitive-model potentialism, countable-model potentialism, and others. In each case, we identify lower bounds for the modal validities, which are generally either S4.2 or S4.3, and an upper bound of S5, proving in each case that these bounds are optimal. The validity of S5 in a world is a potentialist maximality principle, an interesting set-theoretic principle of its own. The results can be viewed as providing an analysis of the modal commitments of the various set-theoretic multiverse conceptions corresponding to each potentialist account.

Thirteen up-and-coming researchers in the philosophy of mathematics have been invited to write on what they take to be the right philosophical account of mathematics, examining along the way where they think the philosophy of mathematics is and ought to be going. A rich and diverse picture emerges. Some broader tendencies can nevertheless be detected: there is increasing attention to the practice, language and psychology of mathematics, a move to reassess the orthodoxy, as well as inspiration from philosophical logic.

Mathematics is one of the most successful human endeavors—a paradigm of precision and objectivity. It is also one of our most puzzling endeavors, as it seems to deliver non-experiential knowledge of a non-physical reality consisting of numbers, sets, and functions. How can the success and objectivity of mathematics be reconciled with its puzzling features, which seem to set it apart from all the usual empirical sciences? This book offers a short but systematic introduction to the philosophy of mathematics. Readers are introduced to all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. The book also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The exposition is always closely informed by ongoing research in the field and sometimes draws on the author’s own contributions to this research. This means that Gottlob Frege—a German mathematician and philosopher widely recognized as one of the founders of analytic philosophy—figures prominently in the book, both through his own views and his criticism of other thinkers.

This paper defends an interventionist account of causation by construing this account as a contribution to methodology, rather than as a set of theses about the ontology or metaphysics of causation. It also uses the topic of causation to raise some more general issues about the relation between, on the one hand, methodology, and, on the other hand, ontology and metaphysics, as these are understood in contemporary philosophical discussion, particularly among so-called analytic metaphysicians. It concludes with the suggestion that issues about the ontology of causation often can be fruitfully reconstrued as methodological proposals

This article discusses some philosophical theories of causation and their application to several areas of science. Topics addressed include regularity, counterfactual, and causal process theories of causation; the causal interpretation of structural equation models and directed graphs; independence assumptions in causal reasoning; and the role of causal concepts in physics. In connection with this last topic, this article focuses on the relationship between causal asymmetries, the time-reversal invariance of most fundamental physical laws, and the significance of differences among varieties of differential equations in causal interpretation. It concludes with some remarks about “grounding” special science causal generalizations in physics.