We investigate how nonstandard reals can be established constructively as arbitrary infinite sequences of rationals, following the classical approach due to Schmieden and Laugwitz. In particular, a total standard part map into Richman's generalised Dedekind reals is constructed without countable choice.

Should weak forms of the axiom of choice really be accepted within constructive mathematics? A critical view of the Brouwer-Heyting-Kolmogorov interpretation, accompanied by the intention to include nondeterministic algorithms, leads us to subscribe to Richman's appeal for dropping countable choice. As an alternative interpretation of intuitionistic logic, we propose to renew dialogue semantics.

Even after yet another grand conjecture has been proved or refuted, any omniscience principle that had trivially settled this question is just as little acceptable as before. The significance of the constructive enterprise is therefore not affected by any gain of knowledge. In particular, there is no need to adapt weak counterexamples to mathematical progress.

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be (...) extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students. (shrink)

In a fragment entitled Elementa Nova Matheseos Universalis Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is (...) possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects”. It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” of others, and the latter are “consequences” of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification. (shrink)

These new studies of Wittgenstein's Tractatus represent a significant step beyond recent polemical debate.

Critical Thinking : A Methodology for Interpreting Information 'deconstructs' common errors in thinking and teaches students to become smarter consumers of research results. Written to complement a textbook or a collection of readings, this brief methods book strengthens students' ability to interpret information whenever and wherever data are used. It includes a wide range of examples along with end of chapter exercises for further discussion. This book will be a coursebook for the undergraduate social science courses where critical thinking, numeracy, (...) and data literacy are common learning objectives"--Provided by publisher. (shrink)

This chapter contains sections titled: Two‐Wheeled Sensations The “Bicycling Method” Lessons from the Saddle Finding the Words Notes.

Although the relationship of part to whole is one of the most fundamental there is, this is the first full-length study of this key concept. Showing that mereology, or the formal theory of part and whole, is essential to ontology, Simons surveys and critiques previous theories--especially the standard extensional view--and proposes a new account that encompasses both temporal and modal considerations. Simons's revised theory not only allows him to offer fresh solutions to long-standing problems, but also has far-reaching consequences for (...) our understanding of a host of classical philosophical concepts. (shrink)

This book present research in ethics with topics including a step-by-step guide to students; wellbeing and disadvantage; ethical disposition of accounting and business management students; collegiality of journals and self-citation on annual bibliometric scorings; trends of tainted publications and their authors' publication profiles; from bioethics to biopolitics and the limits of liberalism.

The seventeenth century marked a critical phase in the emergence of modern science. But we misunderstand this process, if we assume that seventeenth-century modes of natural inquiry were identical to the highly specialised, professionalised and ever proliferating family of modern sciences practised today.

Coleman states that social phenomena cannot be directly accounted for by their social antecedents without analyzing three intervening steps: what motives the antecedents create, how these affect individual behavior, and the transition from the acts of interdependent individuals to social phenomena. The last is most important. I agree, but Foundations has its causal link upside down. Reanalyzing some of his cases, I try to show that macrostructures are not the product of microfoundations but the existential conditions that circumscribe individuals’ choices.

This paper is a review of work on Newman's objection to epistemic structural realism (ESR). In Section 2, a brief statement of ESR is provided. In Section 3, Newman's objection and its recent variants are outlined. In Section 4, two responses that argue that the objection can be evaded by abandoning the Ramsey-sentence approach to ESR are considered. In Section 5, three responses that have been put forward specifically to rescue the Ramsey-sentence approach to ESR from the modern versions of (...) the objection are discussed. Finally, in Section 6, three responses are considered that are neutral with respect to one's approach to ESR and all argue (in different ways) that the objection can be evaded by introducing the notion that some relations/structures are privileged over others. It is concluded that none of these suggestions is an adequate response to Newman's objection, which therefore remains a serious problem for ESRists. Introduction Epistemic Structural Realism 2.1 Ramsey-sentences and ESR 2.2 WESR and SESR The Objection 3.1 Newman's version 3.2 Demopoulos and Friedman's and Ketland's versions Replies that Abandon the Ramsey-Sentence Approach to ESR 4.1 Redhead's reply 4.2 French and Ladyman's reply Replies Designed to Rescue the Ramsey-Sentence Approach 5.1 Zahar's reply 5.2 Cruse's reply 5.3 Melia and Saatsi's reply Replies that Argue that Some Structures/Relations are Privileged 6.1 A Carnapian reply 6.2 Votsis' reply 6.3 The Merrill/Lewis/Psillos reply Summary CiteULike Connotea Del.icio.us What's this? (shrink)

There are at least three things we might mean by "ethics in robotics": the ethical systems built into robots, the ethics of people who design and use robots, and the ethics of how people treat robots. This paper argues that the best approach to robot ethics is one which addresses all three of these, and to do this it ought to consider robots as socio-technical systems. By so doing, it is possible to think of a continuum of agency that lies (...) between amoral and fully autonomous moral agents. Thus, robots might move gradually along this continuum as they acquire greater capabilities and ethical sophistication. It also argues that many of the issues regarding the distribution of responsibility in complex socio-technical systems might best be addressed by looking to legal theory, rather than moral theory. This is because our overarching interest in robot ethics ought to be the practical one of preventing robots from doing harm, as well as preventing humans from unjustly avoiding responsibility for their actions. (shrink)

This book with an introduction by Witold Marciszewski, views the history of philosophy and logic from 1837 to 1939 from the perspective of the cradle of modern exact philosophy - Central Europe. In a series of case studies, it illuminates the developments in this region, most notably in Austria and Poland, examining thinkers such as Bolzano, Brentano, Meinong, Husserl, Twardowski, Lesniewski, and Tarski, as well as the logicians like Frege and Russell with whom they bore a close resemblance. The book (...) challenges established views about the history of philosophy and logic in Europe, and shows the vitality of the Central European tradition. (shrink)

How can anyone be rational in a world where knowledge is limited, time is pressing, and deep thought is often an unattainable luxury? Traditional models of unbounded rationality and optimization in cognitive science, economics, and animal behavior have tended to view decision-makers as possessing supernatural powers of reason, limitless knowledge, and endless time. But understanding decisions in the real world requires a more psychologically plausible notion of bounded rationality. In Simple heuristics that make us smart (Gigerenzer et al. 1999), we (...) explore fast and frugal heuristics – simple rules in the mind's adaptive toolbox for making decisions with realistic mental resources. These heuristics can enable both living organisms and artificial systems to make smart choices quickly and with a minimum of information by exploiting the way that information is structured in particular environments. In this précis, we show how simple building blocks that control information search, stop search, and make decisions can be put together to form classes of heuristics, including: ignorance-based and one-reason decision making for choice, elimination models for categorization, and satisficing heuristics for sequential search. These simple heuristics perform comparably to more complex algorithms, particularly when generalizing to new data – that is, simplicity leads to robustness. We present evidence regarding when people use simple heuristics and describe the challenges to be addressed by this research program. Key Words: adaptive toolbox; bounded rationality; decision making; elimination models; environment structure; heuristics; ignorance-based reasoning; limited information search; robustness; satisficing; simplicity. (shrink)

The paper is concerned with the idea that the world is the totality of facts, not of things – with what is involved in thinking of the world in that way, and why one might do so. It approaches this issue through a comparison between Wittgenstein’s Tractatus and the identity theory of truth proposed by Hornsby and McDowell.The paper’s positive conclusion is that there is a genuine affinity between these two. A negative contention is that the modern identity theory is (...) vulnerable to a complaint of idealism that the Tractatus can deflect. (shrink)

A way of reading the Tractatus has been proposed which, according to its advocates, is importantly novel and essentially distinct from anything to be found in the work of such previously influential students of the book as Anscombe, Stenius, Hacker or Pears. The point of difference is differently described, but the currently most used description seems to be Goldfarb’s term ‘resolution’ – hence one speaks of ‘the resolute reading’. I’ll shortly ask what resolution is. For now, it is enough that (...) it aims to give full weight to the penultimate section of the Tractatus in which Wittgenstein declares his propositions to be nonsense, where giving full weight to that declaration involves not hearing it as allowing that those ‘nonsensical’ propositions might have another kind of ‘sense’. In that same section Wittgenstein explains that these nonsense propositions, while devoid of meaning, have a use: to make the kind of use of them that their author intends – and so to understand him – requires recognizing that they are nonsense; and through that recognition one ‘surmounts’ these propositions, and is led ‘to see the world aright’. So there is a point to all this nonsense. What point? (shrink)

Moving beyond the traditional, and unproductive, rivalry between the fields of motivation and cognition, this book integrates the two domains to shed new light ...

Traditional views of rationality posit general-purpose decision mechanisms based on logic or optimization. The study of ecological rationality focuses on uncovering the “adaptive toolbox” of domain-specific simple heuristics that real, computationally bounded minds employ, and explaining how these heuristics produce accurate decisions by exploiting the structures of information in the environments in which they are applied. Knowing when and how people use particular heuristics can facilitate the shaping of environments to engender better decisions.

For most of the history of metaphysics, the subject has been dominated by the concept of substance. There is an everyday commonsense notion of substance which is perfectly harmless and which I shall defend against attempts to remove it or revise it away. But I deny that substance has to be construed as a primitive even in everyday terms. Borrowing Strawson’s distinction between descriptive and revisionary metaphysics, I press the legitimate claims of revisionary metaphysics and argue that there is no (...) place for a fundamental concept of substance within it, although aspects of the concept are likely to find their place therein. (shrink)

While theories of rationality and decision making typically adopt either a single-powertool perspective or a bag-of-tricks mentality, the research program of ecological rationality bridges these with a theoretically-driven account of when different heuristic decision mechanisms will work well. Here we described two ways to study how heuristics match their ecological setting: The bottom-up approach starts with psychologically plausible building blocks that are combined to create simple heuristics that fit specific environments. The top-down approach starts from the statistical problem facing the (...) organism and a set of principles, such as the bias– variance tradeoff, that can explain when and why heuristics work in uncertain environments, and then shows how effective heuristics can be built by biasing and simplifying more complex models. We conclude with challenges these approaches face in developing a psychologically realistic perspective on human rationality. (shrink)

0. My aims in this paper are largely expository: I am more interested in presenting the picture theory than deciding its truth. Even so, I hope that the arguments by which I develop the theory will do something to support it, since I believe that what I will present as Wittgenstein's view is indeed the truth. This is not an admission of insanity, though some things that have been thought intrinsic to the picture theory are things it would be insane (...) to believe. So clearly the view I will present, when compared to the most embracing interpretations, is a partial and selective one. It would be another kind of madness, one I am just as eagre to disown, to suppose that my own favoured selection is the only possible one. That is pretty well the last remark in this paper about other commentators. I trust my reticence entitles me to be presumed catholic until proven nonconformist. (shrink)

Wittgenstein presents in the Tractatus a variable purporting to capture the general form of proposition. One understanding of what Wittgenstein is doing there, an understanding in line with the ‘new’ reading of his work championed by Diamond, Conant and others, sees it as a deflationary or even an implosive move—a move by which a concept sometimes put by philosophers to distinctively metaphysical use is replaced, in a perspicuous notation, by an innocent device of generalization, thereby dispersing the clouds of philosophy (...) that formerly surrounded the concept. By asking how Wittgenstein supposed his variable to work, and what work he imagined it was fit for, the paper questions the adequacy of that understanding. (shrink)

Wittgenstein, in the Tractatus, conceives the world as ‘the totality of facts’. Type-stratification threatens that conception : the totality of facts is an obvious example of an illegitimate totality. Wittgenstein’s notion of truthoperation evidently has some role to play in avoiding that threat, allowing propositions, and so facts, to constitute a single type. The paper seeks to explain that role in a way that integrates the ‘philosophical’ and ‘technical’ pressures on the notion of an operation.

It is sometimes argued that Wittgenstein's conception of grammar and the role he allocated to grammar (in his sense of the term) in philosophy changed between the Big Typescript and the Philosophical Investigations. It is also held that some of the grammatical propositions Wittgenstein asserted prior to his writing of the Philosophical Investigations are theses, doctrines, opinions or dogmatism, which he abandoned by 1936/37. The purpose of this paper is to show these claims to be misunderstandings and misinterpretations. On all (...) important matters, his conception of grammar and of grammatical investigations, of grammatical statements or propositions and of grammatical clarification did not change between the Big Typescript and the Investigations. Grammatical propositions (e.g. the meaning of a word is its use; a sample in an ostensive definition belongs to the means of representation; belief is not a mental state) are no more theses, doctrines or opinions than is “a bachelor is an unmarried man.” Nor are they in any way dogmatic. (shrink)

In this paper we articulate and diagnose a previously unrecognized problem for theories of entitlement, what we call the Claims Conundrum. It applies to all entitlements that are originally generated by some claim-generating action, such as laboring, promising, or contract-signing. The Conundrum is spurred by the very plausible thought that a later claim to the object to which one is entitled is a function of whether that original claim-generating action is attributable to one. This is further assumed to depend on (...) one’s being identical to the person who performed the claim-generating action. But the right theory of personal identity for grounding these later claims proves quite elusive. In demonstrating both the Claims Conundrum and diagnosing its source, we begin with its instantiation in John Locke’s theories of personal identity and initial acquisition, and then we gradually expand its net to include both Lockean and non-Lockean theories of both, moving ultimately to show that this is a problem for most entitlements generally. We then diagnose the source of the trouble, showing that a basic assumption about the link between attributability and identity that most people take to be obvious is in fact false, clearing a path for future investigation into this overlooked but serious problem’s resolution. (shrink)

The paper is concerned with the idea that the world is the totality of facts, not of things – with what is involved in thinking of the world in that way, and why one might do so. It approaches this issue through a comparison between Wittgenstein's Tractatus and the identity theory of truth proposed by Hornsby and McDowell. The paper's positive conclusion is that there is a genuine affinity between these two. A negative contention is that the modern identity theory (...) is vulnerable to a complaint of idealism that the Tractatus can deflect. (shrink)

Introduction Max Horkheimer was born on February in Stuttgart. By the time he died, on 7 July in Nuremberg, he had played a decisive role in launching and ...

Introduction By the late fifth century BCE Panini had composed the Astadhyayi, consisting of nearly 4000 rules giving a precise and fairly complete ...

rené descartes famously and explicitly rejects appeals to final causes in natural philosophy, suggesting that such appeals depend on knowledge of God’s inscrutable ends.For since I now know that my own nature is very weak and limited, whereas the nature of God is immense, incomprehensible and infinite, I also know without more ado that he is capable of countless things whose causes are beyond my knowledge. And for this reason alone I consider the whole kind of causes, customarily sought from (...) an end, to be totally useless in physics; there is considerable rashness in thinking myself capable of investigating God’s ends.1This rejection did not go unnoticed nor without controversy. In the Fifth.. (shrink)