Shepherdson [14] showed that for a discrete ordered ring I, I is a model of IOpen iff I is an integer part of a real closed ordered field. In this paper, we consider integer parts satisfying PA. We show that if a real closed ordered field R has an integer part I that is a nonstandard model of PA (or even IΣ₄), then R must be recursively saturated. In particular, the real closure of I, RC (I), is recursively saturated. We (...) also show that if R is a countable recursively saturated real closed ordered field, then there is an integer part I such that R = RC(I) and I is a nonstandard model of PA. (shrink)

In [4] the authors studied the residue field of a model M of IΔ0 + Ω1 for the principal ideal generated by a prime p. One of the main results is that M/ has a unique extension of each finite degree. In this paper we are interested in understanding the structure of any quotient field of M, i.e. we will study the quotient M/I for I a maximal ideal of M. We prove that any quotient field of M satisfies the (...) property of having a unique extension of each finite degree. We will use some of Cherlin's ideas from [3], where he studies the ideal theory of non standard algebraic integers. (shrink)

S. Tommaso occupa un posto di enorme importanza nella Storia della Metafisica. Ma la sua è una dottrina originale, o una rielaborazione della metafisica aristotelica e di quella neoplatonica? Per rispondere a questa domanda il P. Battista Mondin, con il suo solito stile chiaro ed essenziale, nella Prima Parte del volume presenta le principali interpretazioni della metafisica di S. Tommaso; nella seconda espone approfonditamente le caratteristiche e le grandi ricchezze della concezione metafisica dell'Aquinate, nei suoi vari aspetti: Tommaso e la (...) metafisica aristotelica; le proprietà della metafisica; la conoscenza dell'essere; il linguaggio antologico di Tommaso; la metafisica dell'essere e la sua struttura ontologica; l'analisi delle cinque vie per conoscere l'esistenza di Dio; i nomi divini e il problema dell'analogia, i trascendentali, la creazione e la provvidenza. (shrink)

We consider the theory and its weak fragments in the language of arithmetic expanded with the functional symbol . We prove that and its weak fragments, down to and , are subject to the Tennenbaum phenomenon with respect to , , and . For the last two theories it is still unknown if they may have nonstandard recursive models in the usual language of arithmetic.

We study the relative strength of the two axioms Every Pell equation has a nontrivial solution Exponentiation is total over weak fragments, and we show they are equivalent over IE1. We then define the graph of the exponential function using only existentially bounded quantifiers in the language of arithmetic expanded with the symbol #, where # = x[log2y]. We prove the recursion laws of exponentiation in the corresponding fragment.

In [4] it is shown that only using exponentiation can one prove the existence of non trivial solutions of Pell equations in IΔ 0 . However, in this paper we will prove that any Pell equation has a non trivial solution modulo m for every m in IΔ 0.

We give a valuation theoretic characterization for a real closed field to be recursively saturated. This builds on work in [9], where the authors gave such a characterization forκ-saturation, for a cardinal$\kappa \ge \aleph _0 $. Our result extends the characterization of Harnik and Ressayre [7] for a divisible ordered abelian group to be recursively saturated.

A generalization is given of McAloon's result on initial segments ofmodels of GlΔ0, the fragment of Peano Arithmetic where the induction scheme is restricted to formulas with bounded quantifiers.

Gauss used quadratic forms in his second proof of quadratic reciprocity. In this paper we begin to develop a theory of binary quadratic forms over weak fragments of Peano Arithmetic, with a view to reproducing Gauss’ proof in this setting.

In this paper we prove, modulo Schanuel's Conjecture, that there are algorithms which decide if two exponential polynomials in π are equal in ℝ and if two exponential polynomials in π and i coincide in ℂ.

In this second paper of the series we do a local analysis of quadratic forms over completions of a non-standard model of IΔ0+Ω1.

The Argument from Inductive Risk (AIR) is taken to show that values are inevitably involved in making judgements or forming beliefs. After reviewing this conclusion, I pose cases which are prima facie counterexamples: the unreflective application of conventions, use of black-boxed instruments, reliance on opaque algorithms, and unskilled observation reports. These cases are counterexamples to the AIR posed in ethical terms as a matter of personal values. Nevertheless, it need not be understood in those terms. The values which load a (...) theory choice may be those of institutions or past actors. This means that the challenge of responsibly handling inductive risk is not merely an ethical issue, but is also social, political, and historical. (shrink)

Given the fact that many people use Wikipedia, we should ask: Can we trust it? The empirical evidence suggests that Wikipedia articles are sometimes quite good but that they vary a great deal. As such, it is wrong to ask for a monolithic verdict on Wikipedia. Interacting with Wikipedia involves assessing where it is likely to be reliable and where not. I identify five strategies that we use to assess claims from other sources and argue that, to a greater of (...) lesser degree, Wikipedia frustrates all of them. Interacting responsibly with something like Wikipedia requires new epistemic methods and strategies. (shrink)

Let R be a real closed field. An integer part I for R is a discretely ordered subring such that for every \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r \in R}$$\end{document}, there exists an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${i \in I}$$\end{document} so that i ≤ r < i + 1. Mourgues and Ressayre (J Symb Logic 58:641–647, 1993) showed that every real closed field has an integer part. The procedure of Mourgues and (...) Ressayre appears to be quite complicated. We would like to know whether there is a simple procedure, yielding an integer part that is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^0_2(R)}$$\end{document} —limit computable relative to R. We show that there is a maximal Z-ring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${I \subseteq R}$$\end{document} which is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^0_2(R)}$$\end{document}. However, this I may not be an integer part for R. By a result of Wilkie (Logic Colloquium ’77), any Z-ring can be extended to an integer part for some real closed field. Using Wilkie’s ideas, we produce a real closed field R with a Z-ring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${I \subseteq R}$$\end{document} such that I does not extend to an integer part for R. For a computable real closed field, we do not know whether there must be an integer part in the class \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^0_2}$$\end{document}. We know that certain subclasses of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^0_2}$$\end{document} are not sufficient. We show that for each \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n \in \omega}$$\end{document}, there is a computable real closed field with no n-c.e. integer part. In fact, there is a computable real closed field with no n-c.e. integer part for any n. (shrink)

Cover songs are a familiar feature of contemporary popular music. Musicians describe their own performances as covers, and audiences use the category to organize their listening and appreciation. However, until now philosophers have not had much to say about them. This book explores how to think about covers, appreciating covers, and the metaphysics of covers and songs. Along the way, it explores a range of issues raised by covers, from the question of what precisely constitutes a cover, to the history (...) and taxonomy of the category, the various relationships that hold between songs, performances, and tracks, and the appreciation and evaluation of covers. (shrink)

When we ask what natural kinds are, there are two different things we might have in mind. The first, which I’ll call the taxonomy question, is what distinguishes a category which is a natural kind from an arbitrary class. The second, which I’ll call the ontology question, is what manner of stuff there is that realizes the category. Many philosophers have systematically conflated the two questions. The confusion is exhibited both by essentialists and by philosophers who pose their accounts in (...) terms of similarity. It also leads to misreading philosophers who do make the distinction. Distinguishing the questions allows for a more subtle understanding of both natural kinds and their underlying metaphysics. (shrink)

The accepted narrative treats John Stuart Mill’s Kinds as the historical prototype for our natural kinds, but Mill actually employs two separate notions: Kinds and natural groups. Considering these, along with the accounts of Mill’s nineteenth-century interlocutors, forces us to recognize two distinct questions. First, what marks a natural kind as worthy of inclusion in taxonomy? Second, what exists in the world that makes a category meet that criterion? Mill’s two notions offer separate answers to the two questions: natural groups (...) for taxonomy and Kinds for ontology. This distinction is ignored in many contemporary debates about natural kinds and is obscured by the standard narrative that treats our natural kinds just as a development of Mill’s Kinds. (shrink)

Although some authors hold that natural kinds are necessarily relative to disciplinary domains, many authors presume that natural kinds must be absolute, categorical features of the reality —often assuming that without even mentioning the alternative. Recognizing both possibilities, one may ask whether the difference especially matters. I argue that it does. Looking at recent arguments about natural kind realism, I argue that we can best make sense of the realism question by thinking of natural kindness as a relation that holds (...) between a category and a domain. (shrink)

This discussion note addresses Caleb Hazelwood’s ‘Practice-Centered Pluralism and a Disjunctive Theory of Art’. Hazelwood advances a disjunctive definition of art on the basis of an analogy with species concept pluralism in the philosophy of biology. We recognize the analogy between species and art, we applaud attention to practice, and we are bullish on pluralism—but it is a mistake to take these as the basis for a disjunctive definition.

Kyle Stanford has recently claimed to offer a new challenge to scientific realism. Taking his inspiration from the familiar Pessimistic Induction (PI), Stanford proposes a New Induction (NI). Contra Anjan Chakravartty’s suggestion that the NI is a ‘red herring’, I argue that it reveals something deep and important about science. The Problem of Unconceived Alternatives, which lies at the heart of the NI, yields a richer anti-realism than the PI. It explains why science falls short when it falls short, and (...) so it might figure in the most coherent account of scientific practice. However, this best account will be antirealist in some respects and about some theories. It will not be a sweeping antirealism about all or most of science. (shrink)

Some philosophers understand natural kinds to be the categories which are constraints on enquiry. In order to elaborate the metaphysics appropriate to such an account, I consider the complicated history of scurvy, citrus, and vitamin C. It may be tempting to understand these categories in a shallow way (as mere property clusters) or in a deep way (as fundamental properties). Neither approach is adequate, and the case instead calls for middle-range ontology: starting from categories which we identify in the world (...) and elaborating their structure, but not pretending to jump ahead to a complete story about fundamental being. (shrink)

It is now commonly held that values play a role in scientific judgment, but many arguments for that conclusion are limited. First, many arguments do not show that values are, strictly speaking, indispensable. The role of values could in principle be filled by a random or arbitrary decision. Second, many arguments concern scientific theories and concepts which have obvious practical consequences, thus suggesting or at least leaving open the possibility that abstruse sciences without such a connection could be value-free. Third, (...) many arguments concern the role values play in inferring from evidence, thus taking evidence as given. This paper argues that these limitations do not hold in general. There are values involved in every scientific judgment. They cannot even conceivably be replaced by a coin toss, they arise as much for exotic as for practical sciences, and they are at issue as much for observation as for explicit inference. (shrink)

There is a history of thinking that photographs provide a special kind of access to the objects depicted in them, beyond the access that would be provided by a painting or drawing. What is included in the photograph does not depend on the photographer’s beliefs about what is in front of the camera. This feature leads Kendall Walton to argue that photographs literally allow us to see the objects which appear in them. Current generative algorithms produce images in response to (...) users’ text prompts. Depending on the parameters, the output can resemble specific people or things which are named in the prompt. This resemblance does not depend on the user’s beliefs, so generated images are in this sense like photographs. Given this parallel, how should we think about AI-generated images? (shrink)

1. Etica e coscienza. Etica, scienza e tecnica -- 2. Etica e cultura. Etica e politica -- 3. Etica ed economia. Problemi de etica.

Introduction 1 P. D. Magnus and Jacob Busch 1. Form-driven vs. Content-driven Arguments for Realism 8 Juha Saatsi 2. Optimism about the Pessimistic Induction 29 Sherrilyn Roush 3. Metaphysics between the Sciences and Philosophies of Science 59 Anjan Chakravartty 4. Nominalism and Inductive Generalizations 78 Jessica Pfeifer 5. Models and Scientific Representations 94 Otávio Bueno 6. The Identical Rivals Response to Underdetermination 112 Gregory Frost-Arnold and P. D. Magnus 7. Scientific Representation and the Semiotics of Pictures 131 Laura Perini 8. (...) Philosophy of the Environmental Sciences 155 Jay Odenbaugh 9. Value Judgements and the Estimation of Uncertainty in Climate Modeling 172 Justin Biddle and Eric Winsberg 10. Feminist Standpoint Empiricism: Rethinking the Terrain in Feminist Philosophy of Science 198 Kristen Intemann 11. Naturalism and the Enlightenment Ideal: Rethinking a Central Debate in the Philosophy of Social Science 226 Daniel Steel 12. New Approaches to the Division of Cognitive Labor 250 Michael Weisberg. (shrink)