According to the new family of theories that emerged around the second half of the nineteenth century, time is more similar to space than it had been construed to be under the previous family of theories. These new theories of time treat time as being a “fourth dimension” that is much more like the three spatial dimensions than it was imagined to be under the older rival theories. Over the two centuries following Newton, the key concepts of graphs and the (...) differential and integral calculus, trickled out into a wide intellectual community. Mc Taggart's theorem purports to be a disproof of all the old theories of time – on the grounds that they are logically inconsistent. It also purports to be a disproof of all the new theories of time – on the grounds that what they describe as “time” is simply not time, properly so‐called. (shrink)

McTaggart famously argued that time is unreal. Today, almost no one agrees with his conclusion.1 But his argument remains thelocus classicusfor both the A–theory and the B-theory of time. I want to show how McTaggart's argument provided the impetus for both of these opposing views of the nature of time. I will also present and defend what I take to be the correct view of the nature of time.

Carnap gives a definition for a comparative concept of confirmation. For it he uses the notation “MC.” His defined notation is intended to be an explicatum for the explicandum: “the hypothesis h is confirmed by the evidence e equally strongly or more strongly than h′ by e′”.

Following Hartry Field in distinguishing disquotational truth from a conception that grounds truth conditions in a community's usage, it is argued that the notions are materially inequivalent (since the latter allows truth-value gaps) and that both are needed. In addition to allowing blanket endorsements ("Everything the Pope says is true"), disquotational truth facilitates mathematical discovery, as when we establish the Gödel sentence by noting that the theorems are all disquotationally true and the disquotational truths are consistent. We require a more (...) substantial notion, however, if we intend to use truth values and truth conditions in explaining communication by language. (shrink)

Mc Taggart's celebrated proof of the unreality of time is a chain of implications whose final step asserts that the A-series (i.e. the classification of events as past, present or future) is intrinsically contradictory. This is widely believed to be the heart of the argument, and it is where most attempted refutations have been addressed; yet, it is also the only part of the proof which may be generalised to other contexts, since none of the notions involved in it (...) is specifically temporal. In fact, as I show in the first part of the paper, McTaggart's refutation of the A-series can be easily interpreted in mathematical terms; subsequently, in order to strengthen my claim, I apply the same framework by analogy to the cases of space, modality, and personal identity. Therefore, either McTaggart's proof as a whole may be extended to each of these notions, or it must embed some distinctly temporal element in one of the steps leading up to the contradiction of the A-series. I conclude by suggesting where this element might lay, and by hinting at what I believe to be the true logical fallacy of the proof. (shrink)

The original Specker–Blatter theorem (1983) was formulated for classes of structures $\mathcal {C}$ of one or several binary relations definable in Monadic Second Order Logic MSOL. It states that the number of such structures on the set $[n]$ is modularly C-finite (MC-finite). In previous work we extended this to structures definable in CMSOL, MSOL extended with modular counting quantifiers. The first author also showed that the Specker–Blatter theorem does not hold for one quaternary relation (2003).If the vocabulary allows (...) a constant symbol c, there are n possible interpretations on $[n]$ for c. We say that a constant c is hard-wired if c is always interpreted by the same element $j \in [n]$. In this paper we show: (i)The Specker–Blatter theorem also holds for CMSOL when hard-wired constants are allowed. The proof method of Specker and Blatter does not work in this case.(ii)The Specker–Blatter theorem does not hold already for $\mathcal {C}$ with one ternary relation definable in First Order Logic FOL. This was left open since 1983.Using hard-wired constants allows us to show MC-finiteness of counting functions of various restricted partition functions which were not known to be MC-finite till now. Among them we have the restricted Bell numbers $B_{r,A}$, restricted Stirling numbers of the second kind $S_{r,A}$ or restricted Lah-numbers $L_{r,A}$. Here r is a non-negative integer and A is an ultimately periodic set of non-negative integers. (shrink)

We first consider the entailment logic MC, based on meaning containment, which contains neither the Law of Excluded Middle (LEM) nor the Disjunctive Syllogism (DS). We then argue that the DS may be assumed at least on a similar basis as the assumption of the LEM, which is then justified over a finite domain or for a recursive property over an infinite domain. In the latter case, use is made of Mathematical Induction. We then show that an instance of the (...) LEM is intrumental in the proof of Cantor's Theorem, and we then argue that this is based on a more general form than can be reasonably justified. We briefly consider the impact of our approach on arithmetic and naive set theory, and compare it with intuitionist mathematics and briefly with recursive mathematics. Our "Four Basic Logical Issues" paper would provide useful background, the current paper being an application of the some of the ideas in it. (shrink)

Bilimin ne olduğunun belirlenmesi ve bu bağlamda bilimin sözde bilim ya da bilimsel olmayan alanlara ilişkin sınırının nasıl çizileceği tartışması, bilim felsefesinde sınır çizme problemi olarak ele alınmaktadır. Çalışmanın ana konusunu oluşturan bu problem, özellikle yirminci yüzyıldan itibaren, bilim felsefecileri tarafından birçok ölçüt ortaya konularak çözümlenmeye çalışılmıştır. Bu ölçütler genellikle, bilim ile sözde bilim arasındaki sınırı belirlemek amacıyla, bilimi mantık ve mantıksal önermeler üzerinden değerlendirmektedir. Şu ana kadar Viyana Çevresi, Popper, Kuhn, Lakatos gibi filozoflarca ortaya konulan ölçütler, nihai olarak problemi (...) mantıksal açıdan ele almıştır. Sınır çizme sorununun mantıksal açıdan ya da mantıksal ifadeler aracılığıyla ele alınması demek; sorunu içeriği yerine daha çok biçimsel açıdan ele almak anlamına gelmektedir. Ayrıca, ifade, kuram, araştırma programı gibi bilim öğelerinin bilimsellik durumunu tespit edebilmek amacıyla önerilen ölçütün, tek tek gerekli ve hep birlikte yeterli olan uygun sınır çizme ölçütünü karşılaması anlamına da gelmektedir. Bu çalışma, gerek ve yeter koşul arayışının, bilimin değişken ve çeşitli yapısını tam olarak yakalayamayacağını ve bilimin belirlenmesinin ve sınırının çizilmesinin bu yöntemle mümkün olmayacağını vurgulamaktadır. Bu konunun mutlaka sosyolojik açıdan da ele alınması gerekmektedir. Bilimin sosyal yapısına, değerler sistemine de bakmamız gerekir. Sonuç olarak, sınır çizme probleminin gerek ve yeter koşulun ortaya koyduğu katı ve ortak özellikler üzerinden sonuçlandırılamayacağı, bunun yerine bilimin “aile benzerliği yaklaşımı” çerçevesinde ele alınması gerektiği vurgulanacaktır. Aile benzerliği yaklaşımının temel oluşturduğu çok boyutlu ölçüt, bu sorunun çözümünde sosyal etkenleri dâhil etmesi, bilimin çeşitliliğini kapsayabilecek ölçüde çoklu ve esnek yapıda olması ile katkıda bulunacaktır. (shrink)

Moses transmits to Israel the call of a God of incomparable power, and his intimate access to that power without being destroyed by it makes him not only mediator but model for the formation of a people set apart, holy to Yahweh.

Bell’s theorem admits several interpretations or ‘solutions’, the standard interpretation being ‘indeterminism’, a next one ‘nonlocality’. In this article two further solutions are investigated, termed here ‘superdeterminism’ and ‘supercorrelation’. The former is especially interesting for philosophical reasons, if only because it is always rejected on the basis of extra-physical arguments. The latter, supercorrelation, will be studied here by investigating model systems that can mimic it, namely spin lattices. It is shown that in these systems the Bell inequality can be (...) violated, even if they are local according to usual definitions. Violation of the Bell inequality is retraced to violation of ‘measurement independence’. These results emphasize the importance of studying the premises of the Bell inequality in realistic systems. (shrink)

A sustained account of Taggart's (English, Shippensburg U.) personal and poetic experience of A Woman in the Sun by American painter Edward Hopper (1882-1967).

Historically, Ehrenfest’s theorem is the first one which shows that classical physics can emerge from quantum physics as a kind of approximation. We recall the theorem in its original form, and we highlight its generalizations to the relativistic Dirac particle and to a particle with spin and izospin. We argue that apparent classicality of the macroscopic world can probably be explained within the framework of standard quantum mechanics.

The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell’s theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for (...) the derivation of Bell’s theorem. Determinism as such does not undermine that independence . Only entanglement could do so. However, generic entanglement without collapse on the level of the universal wave-function can go together with effective wave-functions for subsystems of the universe, as in Bohmian mechanics. The paper argues that such effective wave-functions are sufficient for the mentioned independence premise to hold. (shrink)

Formulas of n variables of Łukasiewicz sentential calculus can be represented, via McNaughton’s theorem, by piecewise linear functions, with integer coefficients, from hypercube [0,1] n to [0,1], called McNaughton functions. As a consequence of the McNaughton representation of a formula it is obtained a canonical form of a formula. Indeed, up to logical equivalence, any formula can be written as an infimum of finite suprema of formulas associated to McNaughton functions which are truncated functions to $[0,1]$ of the restriction (...) to [0,1] n of single hyperplanes, for short, called simple McNaughton functions. In the present paper we will concern with the problem of presenting formulas of Lukasiewicz sentential calculus in normal form. Here we list the main results we obtained: a) we give an axiomatic description of some classes of formulas having the property to be canonically mapped one-to-one onto the class of simple Mc Naughton functions; b) we provide normal forms for Lukasiewicz sentential calculus, making use of formulas defined in a); c) we prove the polynomial complexity of formulas, in normal form, coming from a certain class described as in a); d) we extend the results described in a), b) and c) to Rational Lukasiewicz logic. (shrink)

Hindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated into second order arithmetic.

Haag’s theorem has been interpreted as establishing that quantum field theory cannot consistently represent interacting fields. Earman and Fraser have clarified how it is possible to give mathematically consistent calculations in scattering theory despite the theorem. However, their analysis does not fully address the worry raised by the result. In particular, I argue that their approach fails to be a complete explanation of why Haag’s theorem does not undermine claims about the empirical adequacy of particular quantum field (...) theories. I then show that such empirical adequacy claims are protected from Haag’s result by the techniques that are required to obtain theoretical predictions for realistic experimental observables. I conclude by showing how Haag’s theorem is illustrative of a general tension between the foundational significance of results that can be obtained in perturbation theory and non-perturbative characterizations of the content of quantum field theory. 1 Introduction2 Haag’s Theorem and the Interaction Picture3 Earman and Fraser on the Success of Scattering Theory4 Haag’s Theorem and Empirical Adequacy5 Conclusion. (shrink)

Diogenes of Sinope, bilinen adıyla Diogenes ya da Sinoplu Diyojen’e yönelik yapılan bu çalışmada amacım, Dioegenes’in yaşamının, felsefi duruşunun ve benimsediği etik kuralların kapsamlı ve belgelenmiş bir şekilde sunulmasıdır. Diogenes’in hayatını ve öğretilerini güvenilir bir şekilde aktarmak aşırı derecede zordur, çünkü diğer antik filozoflardan ayrı olarak, onun yaşamına ilişkin güvenilir kaynaklar bulmak oldukça sınırlıdır. Ayrıca, fıçının içinde yaşayan bir Kinikli’ye yönelik ortaya konulmuş birçok kurmaca anekdot ile uğraşılması gerekmektedir. Güvenilir bilginin azlığı ve belgesiz atıfların yarattığı zorluklara rağmen, yine de birçok (...) kişinin hayalinde hayatta kalmayı başaran ünlü filozofun portresini ölümünden yirmi üç yüzyıl sonra yeniden inşa etmek mümkün gözükmektedir. Bu bağlamda, Diogenes’in yaşam tarzı ve felsefesine yönelik bilgiler verilecek, ardından temsil ettiği akım olan kinizmin temel öğretileri çeşitli kaynaklardan gösterilerek aktarılacaktır. Son olarak da, Diogenes’in Sinop kültürünün ve kültürel mirasımızın bir parçası olarak kabul edilmesinin mümkün olup olmadığı tartışılacaktır. (shrink)

Paul Goodman, 1960’larda modern Amerikan toplumunun organize sistemi içerisinde dönemin gençliğinin sorunlarını ön plana çıkaran ‘Growing Up Absurd: Problems of Youth in the Organized System’ (Saçmayı Büyütmek: Organize Sistemde Gençliğin Problemleri, 1960) eseri ile sosyal bir eleştirmen olarak ön plana çıkmıştır. Amerikalı bir düşünür olan Paul Goodman’ın kısa öyküler, romanlar, şiirler ve makalelerden oluşan çalışmaları, siyaset, sosyal teori, eğitim, kentsel tasarım, edebi eleştiri, hatta psikoterapi gibi geniş bir yelpazeye dağılmıştır. Onun temel argümanı (1960: 9-10) tek bir merkez etrafında örgütlenen teknoloji (...) toplumunun başarısızlıklarını eleştirerek, mevcut düzenin insanın doğasına uygun bir biçimde yeniden inşasını vurgulamaktadır. Goodman’ın yeniden inşa süreci içerisinde insan doğasına önem veren faaliyete dayalı anarşist ideolojisi, sorumluluk duygusunun homojen bir şekilde bireyler arasında paylaşılması gerektiğini vurgular. Goodman merkeziyetçi olmayan siyaset anlayışı ile kendisini Amerikan siyasetinin ve kültürünün karşısında yer alan bir pozisyonda konumlandırmaktadır (Honeywell, 2011: 1). Diğer bir deyişle Goodman (1960: 36), anarşist geleneği formüle etmek amacıyla yirminci yüzyıl Amerikası’nın içinde bulunmuş olduğu mevcut durumdan yola çıkarak eleştirilerini ademi merkeziyetçilik, katılımcı demokrasi, özerk toplum temaları üzerine temellendirmiştir. -/- Goodman’a göre, sosyal, kültürel, ahlâk ve eğitim gibi alanlarda uygulanan kurallar günümüz devletlerini etkisi altına alan kapitalist düzen tarafından belirlenmektedir (Bakır, 2016: 110). Bu durum Goodman’ın da içerisinde bulunduğu anarşist düşünürler tarafından kabul edilebilecek bir husus değildir, çünkü anarşistler mevcut düzenin ve sosyal yaşamın otorite ve itaat yapılarıyla güçlendirilen belirli yaklaşımlar ile kontrol altına alınmasını, insanların fikirlerini özgürce ifade edemeyeceği, bir nevi entelektüel bir hapishane içerisinde yaşaması anlamına geleceğinden dolayı karşı çıkmaktadırlar (Sheean, 2003: 122). Aynı nedenlerden dolayı Goodman, modern liberalizm ve Marksizm gibi alternatif radikal ideolojileri yerinden yönetim düşüncesi ve sosyal mühendislik konusundaki eğilimleri dolayısıyla reddetmektedir. Goodman için anarşizm, özgürlük ve toplumsal değişime yeterli düzeyde arka çıkabilecek tek ideolojik çerçeve olarak görülmektedir. Ona göre (2010: 143), “anarşizm ya da daha iyisi, anarko-pasifizm (toplumsal değişim hareketleri içerisinde örgütlü şiddete ve kurumlara karşı çıkan anarşist anlayış) günümüzün gelişmiş toplumlarının bürokrasilerini, karar verme konusunda aşırı merkezîleşmelerini ve sosyal mühendislik gibi problematik durumlarını ve tehlikelerini tutarlı bir şekilde öngörmüştür”. -/- Siyaset, sosyoloji ve felsefe gibi çeşitli alanlar içerisinde etkili olan anarşist kuramlar, radikal bir söylem olarak eğitimcileri ve araştırmacıları yeni öğretilere ve uygulamalara teşvik etme konusunda itici bir güç oluşturabilmektedirler. Anarşist yaklaşımlardan eğitim kuramı ve araştırmalara yönelik daha belirleyici bir rol alması beklenmektedir, ancak bu yaklaşımlar mevcut radikal akademik görüşü büyük ölçüde etkisi altına alan Marksizm’in eğitim alanında göstermiş olduğu aynı etkiyi gösterememiştir. Anarşist düşünceleri eğitim alanı içerisinde daha etkili ve görünür kılabilmek amacıyla Paul Goodman, Francisco Ferrer ve Alexander Neill’ın ileri sürmüş olduğu çeşitli düşünceler, girişimler ve uygulamalar ortaya çıkmıştır. Bu doğrultuda Goodman’ın anarşizme ilişkin düşünceleri ile bu çalışma sıkı bir anarşizm tahlili, eleştirisi ve felsefesinden öte anarşist anlayışın eğitimdeki uygulanabilirliğine yönelik bir soruşturma içerisine girmekte ve anarşist yaklaşımın mevcut eğitim sistemlerinden hangi yönleriyle farklılaştığını, sonucunda etkili bir eğitim anlayışı ortaya koyup koyamadığını tartışmaktadır. (shrink)

We prove the following version of Hechler's classical theorem: For each partially ordered set (Q, ≤) with the property that every countable subset of Q has a strict upper bound in Q, there is a ccc forcing notion such that in the generic extension for each tall analytic P-ideal J (coded in the ground model) a cofinal subset of (J, ⊆*) is order isomorphic to (Q, ≤).

Fen eğitimi ve öğretiminin anahtar unsurlarından bir tanesi bilimin doğasının ve özelliklerinin doğru bir şekilde tespit edilmesidir. Bilimin doğasına yönelik tespitler fen eğitimi yöntemlerini birçok açıdan etkilemektedir. Fen eğitimi ve fen öğretimi ile ilgili olan kişiler bilimin doğasının açık bir şekilde öğretilmesi gerektiğini kabul etmektedir. Thomas Kuhn’un bilim tarihi, bilim felsefesi ve bilim sosyolojisi alanlarını içeren incelemeleri neticesinde ileri sürdüğü bilimin yapısına, işleyişine ve doğasına yönelik tezleri (paradigma, olağan bilim, bilimsel devrimler, eşölçülemezlik, bulmaca çözme, kuram seçimi, keşif ve gerekçelendirme ayrımı) (...) fen eğitimi ve öğretimi alanında sıklıkla başvurulan kaynaklar olmuştur. Bu doğrultuda makalede mantıkçı pozitivist bilim anlayışının bilimin nesnel, evrensel, kesin gerçekleri ortaya çıkaran, sosyal-kültürel değerlerden ve ön yargılardan bağımsız, bilimsel bilginin birikimsel bir şekilde ilerlediği yönündeki iddiası bilimin gerçek doğasını yansıtamadığı düşüncesiyle Kuhn’un görüşleri çerçevesinde tartışılmaktadır. Makalenin temel savı Kuhn’un bilime ve bilimin doğasına yönelik tespitlerinin bilimin gelişen, dönüşen ve değişen yapıdaki gerçek doğasına vurgu yaptığı ve böylece fen eğitiminde sıklıkla başvurulan bilimin doğasına yönelik kavrayışı dönüştürdüğüdür. (shrink)

In his 1967 paper Vaught used an ingenious argument to show that every recursively enumerable first order theory that directly interprets the weak system VS of set theory is axiomatizable by a scheme. In this paper we establish a strengthening of Vaught's theorem by weakening the hypothesis of direct interpretability of VS to direct interpretability of the finitely axiomatized fragment VS2 of VS. This improvement significantly increases the scope of the original result, since VS is essentially undecidable, but VS2 (...) has decidable extensions. We also explore the ramifications of our work on finite axiomatizability of schemes in the presence of suitable comprehension principles. (shrink)

In a recent paper (Okasha, Mind 120:83–115, 2011), Samir Okasha uses Arrow’s theorem to raise a challenge for the rationality of theory choice. He argues that, as soon as one accepts the plausibility of the assumptions leading to Arrow’s theorem, one is compelled to conclude that there are no adequate theory choice algorithms. Okasha offers a partial way out of this predicament by diagnosing the source of Arrow’s theorem and using his diagnosis to deploy an approach that (...) circumvents it. In this paper I explain why, although Okasha is right to emphasise that Arrow’s result is the effect of an informational problem, he is not right to locate this problem at the level of the informational input of a theory choice rule. Once the informational problem is correctly located, Arrow’s theorem may be dismissed as a problem. (shrink)

In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the radically (...) impure (ergodic) proof due to Furstenberg (Section 3). Furstenberg’s ergodic proof is striking because it utilizes intuitively foreign and infinitary resources to prove a finitary combinatorial result and does so in a perspicuous fashion. I claim that Furstenberg’s proof is explanatory in light of its clear expression of a crucial structural result, which provides the “reason why” Szemerédi’s theorem is true. This is, however, rather surprising: how can such intuitively different conceptual resources “get a grip on” the theorem to be proved? I account for this phenomenon by articulating a new construal of the content of a mathematical statement, which I call structural content (Section 4). I argue that the availability of structural content saves intuitive epistemic distinctions made in mathematical practice and simultaneously explicates the intervention of surprising and explanatorily rich conceptual resources. Structural content also disarms general arguments for thinking that impurity and explanatory power might come apart. Finally, I sketch a proposal that, once structural content is in hand, impure resources lead to explanatory proofs via suitably understood varieties of simplification and unification (Section 5). (shrink)

It was shown by Cholak, Jockusch, and Slaman that every computable 2-coloring of pairs admits an infinite low₂ homogeneous set H. We answer a question of the same authors by showing that H may be chosen to satisfy in addition $C\,\not \leqslant _T \,H$, where C is a given noncomputable set. This is shown by analyzing a new and simplified proof of Seetapun's cone avoidance theorem for Ramsey's theorem. We then extend the result to show that every computable (...) 2-coloring of pairs admits a pair of low₂ infinite homogeneous sets whose degrees form a minimal pair. (shrink)

Gleason's theorem for ������³ says that if f is a nonnegative function on the unit sphere with the property that f(x) + f(y) + f(z) is a fixed constant for each triple x, y, z of mutually orthogonal unit vectors, then f is a quadratic form. We examine the issues raised by discussions in this journal regarding the possibility of a constructive proof of Gleason's theorem in light of the recent publication of such a proof.

Herbrand’s theorem is a central fact about classical logic, [9, 10]. It provides a constructive method for associating, with each first-order formula X, a sequence of formulas X1, X2, X3, . . . , so that X has a first-order proof if and only if some Xi is a tautology. Herbrand’s theorem serves as a constructive alternative to..

A partition is finitary if all its members are finite. For a set A, $\mathscr {B}(A)$ denotes the set of all finitary partitions of A. It is shown consistent with $\mathsf {ZF}$ (without the axiom of choice) that there exist an infinite set A and a surjection from A onto $\mathscr {B}(A)$. On the other hand, we prove in $\mathsf {ZF}$ some theorems concerning $\mathscr {B}(A)$ for infinite sets A, among which are the following: (1) If there is a finitary (...) partition of A without singleton blocks, then there are no surjections from A onto $\mathscr {B}(A)$ and no finite-to-one functions from $\mathscr {B}(A)$ to A. (2) For all $n\in \omega $, $|A^n|<|\mathscr {B}(A)|$. (3) $|\mathscr {B}(A)|\neq |\mathrm {seq}(A)|$, where $\mathrm {seq}(A)$ is the set of all finite sequences of elements of A. (shrink)

Because an agent’s constitutive luck may seem to preclude free will, it may seem to preclude moral responsibility. An agent is basically morally responsible for performing actionAat timetonly if there is another possible world with the same past up totand the same laws of nature in which the agent does not performAatt. A compatibilist can solve the constitutive luck problem for moral responsibility without worrying about basic moral responsibility. According to compatibilism, if determinism is true, then agents can be morally (...) responsible for performing actions without being basically morally responsible for performing them. But a libertarian who thinks agents can be basically morally responsible for what they do must explain how basic moral responsibility is possible. ACT-endorsing libertarianism can both solve the constitutive luck problem for moral responsibility and explain how agents can be basically morally responsible for what they do. (shrink)

Bayes's theorem is a tool for assessing how probable evidence makes some hypothesis. The papers in this volume consider the worth and applicability of the theorem. Richard Swinburne sets out the philosophical issues. Elliott Sober argues that there are other criteria for assessing hypotheses. Colin Howson, Philip Dawid and John Earman consider how the theorem can be used in statistical science, in weighing evidence in criminal trials, and in assessing evidence for the occurrence of miracles. David Miller (...) argues for the worth of the probability calculus as a tool for measuring propensities in nature rather than the strength of evidence. The volume ends with the original paper containing the theorem, presented to the Royal Society in 1763. (shrink)

Arrow’s axiomatic foundation of social choice theory can be understood as an application of Tarski’s methodology of the deductive sciences—which is closely related to the latter’s foundational contribution to model theory. In this note we show in a model-theoretic framework how Arrow’s use of von Neumann and Morgenstern’s concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation; this approach entails an alternative indirect ultrafilter proof for Arrow’s dictatorship result. This link also connects Arrow’s seminal result (...) to key developments and concepts in the history of model theory, notably ultraproducts and preservation results. (shrink)

Derk Pereboom has posed an empirical objection to agent-causal libertarianism: The best empirically confirmed scientific theories feature physical laws predicting no long-run deviations from fixed conditional frequencies that govern events. If agent-causal libertarianism were true, however, then it would be virtually certain, absent ‘wild coincidences’, that such long-run deviations would occur. So, current empirical evidence makes agent-causal libertarianism unlikely. This paper formulates Pereboom’s ‘Problem of Wild Coincidences’ as a five-step argument and considers two recent responses. Then, it offers a different (...) response: The Problem of Wild Coincidences does not show that current empirical evidence makes agent-causal libertarianism unlikely, even if all events are governed by physical laws featuring fixed long-run conditional frequencies and even if agents can ‘overrule’ normal physical laws. (shrink)