Ioannis G. Ntagkas

In ‘Induction and Natural Kinds’, I proposed a solution to the problem of induction according to which our use of inductive inference is reliable because it is grounded in the natural kind structure of the world. When we infer that unobserved members of a kind will have the same properties as observed members of the kind, we are right because all members of the kind possess the same essential properties. The claim that the existence of natural kinds is what grounds reliable use of induction is based on an inference to the best explanation of the success of our inductive practices. As such, the argument for the existence of natural kinds employs a form of ampliative inference. But induction is likewise a form of ampliative inference. Given both of these facts, my account of the reliability of induction is subject to the objection that it provides a circular justification of induction, since it employs an ampliative inference to justify an ampliative inference. In this paper, I respond to the objection of circularity by arguing that what justifies induction is not the inference to the best explanation of its reliability. The ground of induction is the natural kinds themselves.

At its strongest, Hume's problem of induction denies the existence of any well justified assumptionless inductive inference rule. At the weakest, it challenges our ability to articulate and apply good inductive inference rules. This paper examines an analysis that is closer to the latter camp. It reviews one answer to this problem drawn from the VC theorem in statistical learning theory and argues for its inadequacy. In particular, I show that it cannot be computed, in general, whether we are in a situation where the VC theorem can be applied for the purpose we want it to.

I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act as if one has substantive information about the world when one does not. I sketch the outlines of a solution in part I, showing how it differs from others, with full details to follow in subsequent parts. The solution is pragmatic in sentiment (though differs in specifics to arguments from, for example, William James); the conceptions we use to guide our actions are and should be at least partly determined by preferences. This is cashed out in a reformulation of decision theory motivated by a non-reductive formulation of hypotheses and logic. A distinction emerges between initial assumptions--that can be non-dogmatic--and effective assumptions that can simultaneously be substantive. An explanation is provided for the plausibility arguments used to explain assigned probabilities in BCT. In subsequent parts, logic is constructed from principles independent of language and mind. In particular, propositions are defined to not have form. Probabilities are logical and uniquely determined by assumptions. The problems considered fatal to logical probabilities--Goodman's `grue' problem and the uniqueness of priors problem are dissolved due to the particular formulation of logic used. Other problems such as the zero-prior problem are also solved. A universal theory of (non-linguistic) meaning is developed. Problems with counterfactual conditionals are solved by developing concepts of abstractions and corresponding pictures that make up hypotheses. Spaces of hypotheses and the version of Bayes' theorem that utilises them emerge from first principles. Theoretical virtues for hypotheses emerge from the theory. Explanatory force is explicated. The significance of effective assumptions is partly determined by combinatoric factors relating to the structure of hypotheses. I conjecture that this is the origin of simplicity.

This paper reports (in section 1 “Introduction”) some quotes from Nelson Goodman which clarify that, contrary to a common misunderstanding, Goodman always denied that “grue” requires temporal information and “green” does not require temporal information; and, more in general, that Goodman always denied that grue-like predicates require additional information compared to what green-like predicates require. One of the quotations is the following, taken from the first page of the Foreword to chapter 8 “Induction” of the Goodman’s book “Problems and Projects”: “Nevertheless, we may by now confidently conclude that no general distinction between projectible and non- projectible predicates can be drawn on syntactic or even on semantic grounds. Attempts to distinguish projectible predicates as purely qualitative, or non-projectible ones as time-dependent, for example, have plainly failed”. Barker and Achinstein in their famous paper of 1960 tried to demonstrate that the grue-speaker (named Mr. Grue in their paper) needs temporal information to be able to determine whether an object is grue, but Goodman replied (in “Positionality and Pictures”, contained in his book “Problems and Projects”, chapter 8, section 6b) that they failed to prove that Mr. Grue needs temporal information to determine whether an object is grue. According to Goodman, since the predicates “blue” and “green” are interdefinable with the predicates “grue” and “bleen”, “if we can tell which objects are blue and which objects are green, we can tell which ones are grue and which ones are bleen” [pages 12-13 of “Reconceptions in Philosophy and Other Arts and Sciences”]. But this paper points out that an example of interdefinability is also that one about the predicate “gruet”, which is a predicate that applies to an object if the object either is green and examined before time t, or is non-green and not examined before time t. The three predicates “green”, “gruet”, “examined before time t” are interdefinable: and even though the predicates “green” and “examined before time t” are interdefinable, being able to tell if an object is green does not imply being able to tell if an object is examined before time t (the interdefinability among three elements is a type of interdefinability present, for example, also among the logical connectives). Thus, it is wrong the Goodman’s thesis according to which if it is possible to determine without having temporal information whether the predicate “green” has to be applied to an object, then it is also possible to determine without having temporal information whether a predicate interdefinable with “green” has to be applied to an object. Another example of interdefinability is that one about a decidable predicate PD, which is interdefinable with an undecidable predicate PU: therefore even though we can tell whether an object is PD and whether an object is non-PD, we cannot tell whether an object is PU (since PU is an undecidable predicate) and whether an object is non-PU. Although the predicates PD and PU are interdefinable, the possibility to determine whether an object is PD does not imply the possibility to determine whether an object is PU (since PU is an undecidable predicate). Similarly, although the predicates “green” and “grue” are interdefinable, the possibility to determine whether an object is “green” even in absence of temporal information does not imply the possibility to determine whether an object is “grue” even in absence of temporal information. These and other examples about “grue” and “bleen” point out that even in case two predicates are interdefinable, the possibility to apply a predicate P does not imply the possibility to apply a predicate interdefinable with P. And that the possibility to apply the predicate “green” without having temporal information does not imply the possibility to apply the predicate “grue” without having temporal information. Furthermore, knowing that an object is both green and grue implies temporal information: in fact, we know by definition that a grue object can only be: 1) either green (in case the object is examined before time t); 2) or blue (in case the object is not examined before time t). Thus, knowing that an object is both grue and green, we know that we are faced with case 1, the case of a grue object that is green and examined before time t. Then the paper points out why the Goodman-Kripke paradox is a paradox about meaning that cannot have repercussions on induction. Finally the paper points out why Hume’s problem is a problem different from Goodman’s paradox and requires a specific treatment.

John D. Norton is responsible for a number of influential views in contemporary philosophy of science. This paper will discuss two of them. The material theory of induction claims that inductive arguments are ultimately justified by their material features, not their formal features. Thus, while a deductive argument can be valid irrespective of the content of the propositions that make up the argument, an inductive argument about, say, apples, will be justified (or not) depending on facts about apples. The argument view of thought experiments claims that thought experiments are arguments, and that they function epistemically however arguments do. These two views have generated a great deal of discussion, although there hasn’t been much written about their combination. I argue that despite some interesting harmonies, there is a serious tension between them. I consider several options for easing this tension, before suggesting a set of changes to the argument view that I take to be consistent with Norton’s fundamental philosophical commitments, and which retain what seems intuitively correct about the argument view. These changes require that we move away from a unitary epistemology of thought experiments and towards a more pluralist position.

This article argues for the thesis that the distinction between propositional and doxastic justification should be extended to knowledge. A consequence of this thesis is that there is a type of knowledge that requires belief and a type that does not. A familiar example strikingly similar to the sort of example used to introduce the propositional/doxastic justification makes a prima facie case. Additional theoretical advantages are revealed when the distinction is applied within the context of some recent epistemological debates. These include debates over the knowledge account of assertion, testimonial knowledge, self-deception, and the question of whether knowledge can be essentially based on falsehood. It is contended that the sort of distinction offered here provides a way to settle these debates and, at the same time, acknowledge what is correct in the opposing positions

This article aims to present how paper-folding activities were integrated into recreational mathematics during the 17th and the 18th centuries. Recreational mathematics was conceived during these centuries as a way not only to pique one’s curiosity, but also to communicate mathematical knowledge to the literate classes of the population. Starting with Leurechon’s 1624 Récréation mathématique, which did not contain any exercise concerning paper folding, we show how two other traditions—Dürer’s folded nets on the one hand and napkin folding on the other hand—prompted and influenced the integration of folding within subsequent books and manuscripts, especially those of Georg Philipp Harsdörffer and Daniel Schwenter. In Germany, but also to a lesser extent in France, folding was henceforth re-conceptualised within recreational mathematics as a way to transmit geometrical knowledge. Following Harsdörffer, the paper will claim that practising folding activities enabled the acquiring of a geometrical knowledge, which was haptic rather than symbolical or merely visual. This tactility reflects the Baconian conception of science and scientific experiment; and the paper will try to illuminate how folding, by advancing practice and tactility via experiments, was representing these traditions and conceptions.

Rudolf Carnap is increasingly regarded as one of the most important philosophers of the twentieth century. He was one of the leading figures of the logical empiricist movement associated with the Vienna Circle and a central figure in the analytic tradition more generally. He made major contributions to philosophy of science and philosophy of logic, and, perhaps most importantly, to our understanding of the nature of philosophy as a discipline. In this volume a team of contributors explores the major themes of his philosophy and discusses his relationship with the Vienna Circle and with philosophers such as Frege, Husserl, Russell, and Quine. New readers will find this the most convenient and accessible guide to Carnap currently available. Advanced students and specialists will find a conspectus of recent developments in the interpretation of Carnap.

Kant was centrally concerned with issues in the philosophy of natural science throughout his career. The Metaphysical Foundations of Natural Science presents his most mature reflections on these themes in the context of both his 'critical' philosophy, presented in the Critique of Pure Reason, and the natural science of his time. This volume presents a translation by Michael Friedman which is especially clear and accurate. There are explanatory notes indicating some of the main connections between the argument of the Metaphysical Foundations and the first Critique - as well as parallel connections to Newton's Principia. The volume is completed by an historical and philosophical introduction and a guide to further reading.

Kant's Metaphysical Foundations of Natural Science is one of the most difficult but also most important of Kant's works. Published in 1786 between the first and second editions of the Critique of Pure Reason, the Metaphysical Foundations occupies a central place in the development of Kant's philosophy, but has so far attracted relatively little attention compared with other works of Kant's critical period. Michael Friedman's book develops a new and complete reading of this work and reconstructs Kant's main argument clearly and in great detail, explaining its relationship to both Newton's Principia and eighteenth-century scientific thinkers such as Euler and Lambert. By situating Kant's text relative to his pre-critical writings on metaphysics and natural philosophy and, in particular, to the changes Kant made in the second edition of the Critique, Friedman articulates a radically new perspective on the meaning and development of the critical philosophy as a whole.

Sextus Empiricus offers an underappreciated and under-discussed version of dream-based skepticism. Most philosophers interested in dreams and skepticism focus on the question of how you know you are not currently dreaming. Sextus points out that our waking experiences and dreams often conflict. And, the challenge goes, what reason do you have to trust the one over the other? This question presupposes that dreams and waking experiences are distinguishable. Thus the kinds of responses typically offered against dream-based skepticism do not apply. And if we accept an idea upheld by one camp in the contemporary debate over the epistemology of disagreement, Sextus’ challenge is difficult to answer. A G.E. Moore-inspired response to the problem is also proposed and explored. It is argued that Sextus’ version of the problem reveals a certain limitation in that sort of approach to skeptical problems.

In my book Understanding Scientific Progress, I argue that fundamental philosophical problems about scientific progress, above all the problem of induction, cannot be solved granted standard empiricism (SE), a doctrine which most scientists and philosophers of science take for granted. A key tenet of SE is that no permanent thesis about the world can be accepted as a part of scientific knowledge independent of evidence. For a number of reasons, we need to adopt a rather different conception of science which I call aim-oriented empiricism (AOE). This holds that we need to construe physics as accepting, as a part of theoretical scientific knowledge, a hierarchy of metaphysical theses about the comprehensibility and knowability of the universe, these theses becoming increasingly insubstantial as we go up the hierarchy. Fundamental philosophical problems about scientific progress, including the problems of induction, theory unity, verisimilitude and scientific discovery, which cannot be solved granted SE, can be solved granted AOE. In his review of Understanding Scientific Progress, Moti Mizrahi makes a number of criticisms, almost all of which are invalid in quite elementary ways.

The world faces grave global problems. These have been made possible by modern science and technology. We have put knowledge-inquiry into academic practice – a seriously irrational kind of inquiry that seeks knowledge and technological know-how dissociated from a more fundamental concern to seek and promote wisdom. We urgently need to bring about a revolution in academic inquiry, so that knowledge-inquiry becomes wisdom-inquiry – a kind of inquiry rationally designed and devoted to helping humanity make progress towards a wiser world. In this paper I indicate what needs to change if knowledge-inquiry is to become wisdom-inquiry, and I indicate a number of recent developments, mainly in universities in the UK, that can be regarded as first steps towards wisdom-inquiry.

Humanity faces two fundamental problems of learning: learning about the universe, and learning to become civilized. We have solved the first problem, but not the second one, and that puts us in a situation of great danger. Almost all of our global problems have arisen as a result. It has become a matter of extreme urgency to solve the second problem. The key to this is to learn from our solution to the first problem how to solve the second one. This was the basic idea of the 18th century Enlightenment, but in implementing this idea, the Enlightenment blundered. Their mistakes are still built into academia today. In order to le arn how to create a civilized, enlightened world, the key thing we need to do is to cure academia of the structural blunders we have inherited from the Enlightenment. We need to bring about a revolution in science, and in academia more broadly so that the basic aim becomes wisdom, and not just knowledge.

The purpose of this document is to outline why and how universities must both transform and mobilise to avert the worst impacts of the global crises faced by humanity. The first section addresses the justification for transformation and how academia can and must transform. In the second section, the document highlights the need for a peaceful mobilisation of student and staff bodies to make effective the transformation advocated for. The document then outlines a blueprint as to action that must be taken in order to initiate the required transformation and mobilisation. (2020)

A kind of academic inquiry rationally devoted to helping to promote human welfare would give intellectual priority to the tasks of (1) articulating, and improving the articulating of, problems of living, and (2) proposing and critically assessing possible solutions - possible actions, policies, political programmes, ways of living. The pursuit of knowledge and technological know-how would be important but secondary. If such a genuinely rigorous kind of academic inquiry had been in place in our universities at the beginning of the year, many nations would have dealt with Covid-19 far better than they have, and thousands of lives would have been saved.

Imre Lakatos and Paul Feyerabend initially both accepted Popper's philosophy of science, but then reacted against it, and developed it in different directions. Lakatos sought to reconcile Kuhn and Popper by characterizing science as a process of competing research programmes, competing fragments of Kuhn's normal science. Feyerabend emphasized the need to develop rival theories to facilitate severe empirical testing of accepted theories, but then, as a result of a disastrous mistake, came to hold that theories that are incompatible with one another cannot be compared empirically. He ended up rejecting method in science. All four philosophers, Popper, Kuhn, Lakatos and Feyerabend missed the decisive defect in Popper's philosophy of science: persistent acceptance of unified theories only when endlessly many empirically more successful disunified rivals are available means that physics makes a big, highly problematic metaphysical assumption about the nature of the universe: it is such that some kind of underlying unity exists in nature. We need to adopt a new conception of science. In order to subject this implicit metaphysical conjecture to sustained critical assessment in an attempt to improve it, we need to see science as making a hierarchy of metaphysical assumptions about the knowability and comprehensibility of the universe, these assumptions becoming less substantial and more likely to be true as we ascend the hierarchy. Elements of Popper, Kuhn and Lakatos are to be found in this picture, but it also differs radically from all three. It more closely resembles Einstein's mature views about the nature of science.