We study some aspects of the emergence of _lógos_ from _xáos_ on a basal model of the universe using methods and techniques from algorithmic information and Ramsey theories. Thereby an intrinsic and unusual mixture of meaningful and spurious, emerging laws surfaces. The spurious, emergent laws abound, they can be found almost everywhere. In accord with the ancient Greek theogony one could say that _lógos_, the Gods and the laws of the universe, originate from “the void,„ or from _xáos_, a picture (...) which supports the unresolvable/irreducible lawless hypothesis. The analysis presented in this paper suggests that the “laws„ discovered in science correspond merely to syntactical correlations, are local and not universal. (shrink)

Very large databases are a major opportunity for science and data analytics is a remarkable new field of investigation in computer science. The effectiveness of these tools is used to support a “philosophy” against the scientific method as developed throughout history. According to this view, computer-discovered correlations should replace understanding and guide prediction and action. Consequently, there will be no need to give scientific meaning to phenomena, by proposing, say, causal relations, since regularities in very large databases are enough: “with (...) enough data, the numbers speak for themselves”. The “end of science” is proclaimed. Using classical results from ergodic theory, Ramsey theory and algorithmic information theory, we show that this “philosophy” is wrong. For example, we prove that very large databases have to contain arbitrary correlations. These correlations appear only due to the size, not the nature, of data. They can be found in “randomly” generated, large enough databases, which—as we will prove—implies that most correlations are spurious. Too much information tends to behave like very little information. The scientific method can be enriched by computer mining in immense databases, but not replaced by it. (shrink)

If is a random sequence, then the sequence is clearly not random; however, seems to be “about half random”. L. Staiger [Kolmogorov complexity and Hausdorff dimension, Inform. and Comput. 103 159–194 and A tight upper bound on Kolmogorov complexity and uniformly optimal prediction, Theory Comput. Syst. 31 215–229] and K. Tadaki [A generalisation of Chaitin’s halting probability Ω and halting self-similar sets, Hokkaido Math. J. 31 219–253] have studied the degree of randomness of sequences or reals by measuring their “degree (...) of compression”. This line of study leads to various definitions of partial randomness. In this paper we explore some relations between these definitions. Among other results we obtain a characterisation of Σ1-dimension in terms of strong Martin-Löf ε-tests , and we show that ε-randomness for ε is different than the classical 1-randomness. (shrink)

A real is computable if it is the limit of a computable, increasing, computably converging sequence of rational...

Do the partial order and ortholattice operations of a quantum logic correspond to the logical implication and connectives of classical logic? Rephrased, How far might a classical understanding of quantum mechanics be, in principle, possible? A celebrated result of Kochen and Specker answers the above question in the negative. However, this answer is just one among various possible ones, not all negative. It is our aim to discuss the above question in terms of mappings of quantum worlds into classical ones, (...) more specifically, in terms of embeddings of quantum logics into classical logics; depending upon the type of restrictions imposed on embeddings, the question may get negative or positive answers. (shrink)

Turing’s famous 1936 paper “On computable numbers, with an application to the Entscheidungsproblem” defines a computable real number and uses Cantor’s diagonal argument to exhibit an uncomputable real. Roughly speaking, a computable real is one that one can calculate digit by digit, that there is an algorithm for approximating as closely as one may wish. All the reals one normally encounters in analysis are computable, like π, √2 and e. But they are much scarcer than the uncomputable reals because, as (...) Turing points out, the computable reals are countable, whilst the uncomputable reals have the power of the continuum. Furthermore, any countable set of reals has measure zero, so the computable reals have measure zero. In other words, if one picks a real at random in the unit interval with uniform probability distribution, the probability of obtaining an uncomputable real is unity. One may obtain a computable real, but that is in- finitely improbable. But how about individual examples of uncomputable reals? We will show two: H and the halting probability Ω, both contained in the unit interval. Their construction was anticipated in.. (shrink)

Recently, G. ASSER has obtained two interesting characterizations of the class of unary primitive recursive string-functions over a fixed alphabet as Robinson algebras. Both characterizations use a somewhat artificial string-function, namely the string-function lexicographically associated with the number-theoretical excess-over-a-square function. Our aim is to offer two new and natural Robinson algebras which are equivalent to ASSER’S algebras.

We present an abstract framework in which we give simple proofs for Gödel’s First and Second Incompleteness Theorems and obtain, as consequences, Davis’, Chaitin’s and Kritchman-Raz’s Theorems.

Gödel's Incompleteness Theorems have the same scientific status as Einstein's principle of relativity, Heisenberg's uncertainty principle, and Watson and Crick's double helix model of DNA. Our aim is to discuss some new faces of the incompleteness phenomenon unveiled by an information-theoretic approach to randomness and recent developments in quantum computing.

The present paper proposes a generalisation of the notion of disjunctive sequence, that is, of an infinite sequence of letters having each finite sequence as a subword. Our aim is to give a reasonable notion of disjunctiveness relative to a given set of sequences F. We show that a definition like “every subword which occurs at infinitely many different positions in sequences in F has to occur infinitely often in the sequence” fulfils properties similar to the original unrelativised notion of (...) disjunctiveness. Finally, we investigate our concept of generalised disjunctiveness in spaces of Cantor expansions of reals. (shrink)

Penrose [40] has discussed a new point of view concerning the nature of physics that might underline conscious thought processes. He has argued that it might be the case that some physical laws are not computable, i.e. they cannot be properly simulated by computer; such laws can most probably arise on the “no-man’s-land” between classical and quantum physics. Furthermore, conscious thinking is a non-algorithmic activity. He is opposing both strong AI , and Searle’s [47] contrary viewpoint mathematical “laws”).

In this paper we consider the possibility of a Quantum Molinism : such a view applies an analogue of the Molinistic account of free will‘s compatibility with God’s foreknowledge to God’s knowledge of (supposedly) indeterministic events at a quantum level. W e ask how (and why) a providential God could care for and know about a world with this kind of indeterminacy. We consider various formulations of such a Quantum Molinism, and after rejecting a number of options arrive at one (...) seemingly coherent formulation. (shrink)

We prove that every computably enumerable random real is provable in Peano Arithmetic to be c.e. random. A major step in the proof is to show that the theorem stating that “a real is c.e. and random iff it is the halting probability of a universal prefix-free Turing machine” can be proven in PA. Our proof, which is simpler than the standard one, can also be used for the original theorem. Our positive result can be contrasted with the case of (...) computable functions, where not every computable function is provably computable in PA, or even more interestingly, with the fact that almost all random finite strings are not provably random in PA. We also prove two negative results: a) there exists a universal machine whose universality cannot be proved in PA, b) there exists a universal machine U such that, based on U, PA cannot prove the randomness of its halting probability. The paper also includes a sharper form of the Kraft-Chaitin Theorem, as well as a formal proof of this theorem written with the proof assistant Isabelle. (shrink)

The development of neuropsychological assessment methods using virtual reality (VR) is a valid and promising option for the detection of cognitive impairment in the older people, focusing on activities composed of tasks of multiple demands. This study verified the association of age, schooling, and general cognitive status on the performance of neurologically healthy older adults in ECO-VR, a virtual reality task of multiple demands for neuropsychological assessment. A total of 111 older adults answered a sociodemographic questionnaire, the Mini Mental State (...) Examination, the Vocabulary subtest of the Wechsler Intelligence Scale for Adults (third edition), and the ECO-VR. Correlation analyses, multiple linear regression, and comparisons between groups (effects by age and schooling groups) were used to evaluate the results. The ECO-VR total score was significantly associated with age, years of education, MMSE, and Vocabulary subtest. The linear regression models identified that age was the main predictor for total score and rule breaking of ECO-VR. According to the univariate analysis, it was identified the main effect of age group and schooling group in the total ECO-VR score, but there was no interaction effect. The results are discussed in order to understand the role of sociodemographic characteristics in the performance of older adults in a virtual reality task of multiple demands. It was also verified the possibility use of virtual reality for neuropsychological assessment of older adults. (shrink)

Finite automata have been recently used as alternative, discrete models in theoretical physics, especially in problems related to the dichotomy between endophysical/intrinsic and exophysical/ extrinsic perception . These studies deal with Moore experiments; the main result states that it is impossible to determine the initial state of an automaton, and, consequently, a discrete model of Heisenberg uncertainty has been suggested. For this aim the classical theory of finite automata — which considers automata with initial states — is not adequate, and (...) a new approach is necessary. A study of finite deterministic automata without initial states is exactly the aim of this paper. We will define and investigate the complexity of various types of simulations between automata. Minimal automata will be constructed and proven to be unique up to an isomorphism. We will build our results on an extension of Myhill-Nerode technique; all constructions will make use of “automata responses” to simple experiments only, i.e., no information about the internal machinery will be considered available. (shrink)

Suppose that persons A and B give us a sequence of 32 bits each, saying that they were obtained from independent coin flips. If A gives the stringu = 01001110100111101001101001110101and B gives the stringv = 00000000000000000000000000000000,then we would tend to believe A and would not believe B: the string u seems to be random, but the string v does not. Further on, if we change the value of a bit in a “random” string, then the result is still a “random” (...) string. If we keep making such changes in a “random” string, then we will eventually complete destroy randomness. (shrink)

IntroductionTranscranial magnetic stimulation is a consolidated procedure for the treatment of depression, with several meta-analyses demonstrating its efficacy. Theta-burst stimulation is a modification of TMS with similar efficacy and shorter session duration. The geriatric population has many comorbidities and a high prevalence of depression, but few clinical trials are conducted specifically for this age group. TBS could be an option in this population, offering the advantages of few side effects and no pharmacological interactions. Therefore, our aim is to investigate the (...) efficacy of TBS in geriatric depression.Clinical trial registration[https://clinicaltrials.gov/ct2/], identifier [NCT04842929]. (shrink)

In a famous lecture in 1900, David Hilbert listed 23 difficult problems he felt deserved the attention of mathematicians in the coming century. His conviction of the solvability of every mathematical problem was a powerful incentive to future generations: ``Wir müssen wissen. Wir werden wissen.'' (We must know. We will know.) Some of these problems were solved quickly, others might never be completed, but all have influenced mathematics. Later, Hilbert highlighted the need to clarify the methods of mathematical reasoning, using (...) a formal system of explicit assumptions, or axioms. Hilbert's vision was the culmination of 2,000 years of mathematics going back to Euclidean geometry. He stipulated that such a formal axiomatic system should be both `consistent' (free of contradictions) and `complete' (in that it represents all the truth). Hilbert also argued that any wellposed mathematical problem should be `decidable', in the sense that there exists a mechanical procedure, a computer program, for deciding whether something is true or not. Of course, the only problem with this inspiring project is that it turned out to be impossible. (shrink)

The Homeric epics are among the greatest masterpieces of literature, but when they were produced is not known with certainty. Here we apply evolutionary-linguistic phylogenetic statistical methods to differences in Homeric, Modern Greek and ancient Hittite vocabulary items to estimate a date of approximately 710–760 BCE for these great works. Our analysis compared a common set of vocabulary items among the three pairs of languages, recording for each item whether the words in the two languages were cognate – derived from (...) a shared ancestral word – or not. We then used a likelihood-based Markov chain Monte Carlo procedure to estimate the most probable times in years separating these languages given the percentage of words they shared, combined with knowledge of the rates at which different words change. Our date for the epics is in close agreement with historians' and classicists' beliefs derived from historical and archaeological sources. (shrink)

Journal Name: Cognitive Linguistics Issue: Ahead of print.

Intitulé Lectures de Jean-Luc Marion et composé d'une vingtaine d'articles, le volume assume l'équivocité d'une mise en abîme : lire Marion dans sa propre lecture de la philosophie. Montrer à l'oeuvre le dialogue du philosophe avec l'histoire de la philosophie constitue en effet le pari de ce livre, pari qui fait fond sur l'idée que tel est le chemin même de la philosophie et que ceci est en outre l'accès le plus respectueux que nous pouvons avoir à une oeuvre s'accomplissant (...) sous nos yeux. De Grégoire de Nysse et Denys l'Aréopagite à Derrida, en passant par Descartes, Kant, Nietzsche, Husserl et Heidegger, la pensée de Marion embrasse, approfondit, reprend et réfute les thèmes fondateurs de la métaphysique et de la phénoménologie. L'oeuvre entière de Marion est traversée par sa lecture personnelle et novatrice de la philosophie. Elle se construit en dialogue avec les textes classiques et rend en même temps compte des grands débats théoriques de l'époque qu'elle traverse. Le dialogue est d'ailleurs privilégié aussi dans ce volume, Jean-Luc Marion répondant aux auteurs des études qui lui sont consacrées."--Page 4 of cover. (shrink)

The forfeiture thesis is posed as an independent thesis in moral philosophy according to which agents forfeit (or lose) rights if they perform certain act-types. According to many, this thesis plays a crucial role in the justification of (legal) punishment. In this paper, I argue that the forfeiture thesis is unnecessary – we can simply dismiss it without any substantive loss. Echoing an aspect of the specificationist approach to rights, the reason is that we may replace the forfeiture thesis with (...) an exception clause in the very content of the right not to be subjected to hard treatment: P has no right not to be subjected to hard treatment simpliciter, but a right not to be subjected to hard treatment unless P performs an act-type φ – e.g., murdering an innocent person. This alternative has substantive advantages over the forfeiture thesis, which, in turn, shows that the former cannot be reduced to the latter. (shrink)

Kitcher has proposed an ideal-theory account—well-ordered science (WOS)— of the collective good that science’s research agenda should promote. Against criticism regarding WOS’s action-guidance, Kitcher has advised critics not to confuse substantive ideals and the ways to arrive at them, and he has defended WOS as a necessary and useful ideal for science policy. I provide a distinction between two types of ideal-theories that helps clarifying WOS’s elusive nature. I use this distinction to argue that the action-guidance problem that WOS faces (...) remains even under the aims/means distinction, because the WOS’s failure is more basic than critics have suggested. (shrink)

The debate about how neurotechnologies impact authenticity has focused on two inter-related dimensions: self-discovery and self-creation. In this paper, we develop a broader framework that includes the experimental and relational dimensions of authenticity, both understood as decisive for shaping one’s narrative identity. In our view, neurointerventions that alter someone’s personality traits will also impact her very own self-understanding across time. We argue that experimental authenticity only needs a minimum conception of narrative coherence of the self and that reversibility should remain (...) a key feature in the ethical assessment of neurotechnologies. The relational dimension of authenticity derives from the fact that a process of self-constitution is never a solitary business. The significant others act not just as subsequent judges of one’s life decisions, but as real co-authors of one’s self. We discuss relevant cases in which others are actively contributing to the meaning-making process, as to the direction one’s life is taking. We also claim that the experimental and the relational dimensions of authenticity should aim to correct each other. The relational dimension introduces socially approved standards as well as limitations to the array of available possibilities of self-fashioning or human enhancement. The experimental side enables us to avoid confusing one’s personal identity with a social and narrative construct that only bears the mark of social pressure and conformism. (shrink)

Dans cet article, je propose une exploration du phénomène du témoignage. Mon but est de montrer que la perspective phénoménologique rend possible une approche intégrative du témoignage, compris comme un phénomène qui engage la structure existentielle du sujet, articulant les relations entre langage, présence, mémoire, vérité et temporalité. Le témoin n’est pas seulement celui qui témoigne, mais d’abord celui qui affronte, dans sa présence expérientielle, un événement dont le sens est bouleversant et institue ainsi le sujet comme témoin : soit (...) comme « témoin endurant » si l’enjeu est d’abord le soi le plus propre du témoin, ou comme « témoin oculaire»s’il s’agit principalement de l’autre. Le témoignage trouve sa signification particulière dans la tension qui se creuse entre le pôle ontologique, où le témoin est compris comme « être là » en présence de l’événement sur le plan expérientiel, et le pôle herméneutique, où le témoin est convoqué devant les autres au niveau du langage. Une autre différence doit être tracée entre le « témoin-confessant », lorsque le témoignage porte précisément sur ce que le témoin a enduré soi-même, et le « témoin-tiers », dont le témoignage porte sur ce que l’on a principalement observé sans le subir soi-même. (shrink)

Is it justified to hold that an agent S has a (moral) right to P if the duty-bearer is not specified? There is an intense ongoing debate on this question. There are two positions in the literature. On the one hand, O´Neill´s much-discussed account of rights holds that it is justified to say that an agent S has a right to P if and only if the duty-bearer is sufficiently determined – i.e. if and only if it is clear against (...) whom S may claim her right to P (O’Neill 1986, 1988, 1996, 2000, 2005, 2016). Call this, the ‘claimability condition’. On the other hand, interest-based theorists argue that it can be justified to say that an agent S has a right to P even if the duty-bearer is not sufficiently determined (Caney 2007; Griffin, 2008; Raz 1988; Tasioulas 2007; see also: Etinson, 2013; Ypi 2010). Who (if anyone) is correct in this fundamental discussion about the very nature of rights? In this paper, I provide an answer to this crucial question. Neither O´Neill nor interest-based theorists provide good reasons to justify their positions. However, I argue, the claimability condition is an existence condition of rights justified on the basis of their action-guiding character. The reason is that if the duty-bearer is not specified, the content of the right (its correlative obligation) does not sufficiently guide what the agent should do because it is indeterminate who is required to act (or refrain from acting). (shrink)

The much-discussed “claimability objection” holds that it is unjustified to believe that all individuals have a human right to subsistence because the bearers of the correlative duties are not sufficiently determined. This argument is based on the so-called “claimability-condition”: S has a right to P if and only if the duty-bearer is sufficiently determined. Practice-based theorists defend the human right to subsistence by arguing that if we take the existing human rights practice seriously, there is no indeterminacy about the allocation (...) of duties. In this paper, I challenge this (apparently compelling) defense of the human right to subsistence with a dilemma. If the claimability condition is true, the practice-based defense fails to undermine the claimability objection because the duty-bearer is determined in some, but not all, cases. If practice-based theorists reject the claimability condition, they generate an account of human rights that is problematic from the practical perspective because it may contain duties that are unable to guide action. (shrink)

Barnes (2014) has argued in this journal for the following conditional: If there is any metaphysical indeterminacy, this must be at the most fundamental level of reality. To argue for this claim, Barnes relies on two principles that I shall call bivalent completeness and determinate link. According to the former, a complete description is a bivalent assignment of truth values to every sentence. The determinate link, instead, establishes that the determination relation between levels of reality preserves determinacy from one level (...) to another. In response to Barnes’ conclusion, Eva (2018) has recently pointed out that bivalent completeness is question begging. In this paper, I will first show why Eva's line of reasoning can be resisted. My aim will then be to present a stronger case against Barnes’ argument by challenging the determinate link. In the presence of metaphysical indeterminacy, the link between fundamental and derivative facts might itself be the locus of indeterminacy. I will conclude by showing that Barnes and Eva make many unwarranted assumptions regarding both indeterminacy and fundamentality. The logical space around the connection between these two notions appears to be much wider than what they seem to be aware of, or so I will argue. (shrink)

Wodak (2019) persuasively argues that we are not justified in believing that well-being measurements are linear. From this, he infers grave consequences for both political philosophy thought experiments and empirical psychological research. Here I argue that these consequences do not follow. Wodak’s challenges to the status of well-being measurements do not affect thought experiments, and well-being empirical researchers may be justified in making average comparisons even if their measurements are not linear.

Mercier and Sperber (2011a, 2011b; Mercier, 2011a, 2011b, 2011c, and 2011d) have presented a stimulating and provocative new theory of reasoning: the argumentative theory of reasoning. They maintain that argumentation is a meta-representational module. In their evolutionary view of argumentation, the function of this module would be to regulate the flow of information between interlocutors through persuasiveness on the side of the communicator and epistemic vigilance on the side of the audience. The aim of this paper is to discuss the (...) perspective of the authors in which they conceive this competence as the natural scenario of reflective reasoning. (shrink)

We reply to Artiga and Martinez’s claim according to which the organizational account of cross-generation functions implies a backward looking interpretation of etiology, just as standard etiological theories of function do. We argue that Artiga and Martinez’s claim stems from a fundamental misunderstanding about the notion of “closure”, on which the organizational account relies. In particular, they incorrectly assume that the system, which is relevant for ascribing cross-generation organizational function, is the lineage. In contrast, we recall that organizational closure refers (...) to a relational description of a network of mutual dependencies, abstracted from time, in which production relations are irrelevant. From an organizational perspective, ascribing a function to an entity means locating it in the abstract system that realizes closure. In particular, the position of each entity within the relational system conveys an etiological explanation of its existence, because of its dependence on the effects exerted by other entities subject to closure. Because of the abstract relational nature of closure, we maintain that the organizational account of functions does not endorse a backward looking interpretation of etiology. As a consequence, it does not fall prey of epiphenomenalism. (shrink)

Agostinho de Hipona recebeu uma formação intelectual nos moldes da cultura clássica, tendo sido educado segundo o ciclo disciplinar varroniano. Provém dessa educação sua apreciação da dialética como arte que instrui argumentar corretamente e que permite discernir, nos discursos, os elementos que geram a falsidade da conclusão. É a dialética que permite conectar proposições verdadeiras para alcançar conclusões também verdadeiras e é elaa ciência que deflagra a falsidade e a dissimulação nos argumentos. Ora, na obra Contra Crescônio, gramático e donatista, (...) Agostinho defende-se da acusação descabida de ser ele um homo dialecticus que, por sua habilidade de argumentar, falsearia o verdadeiro e tornaria o verdadeiro falso. Crescônio, para acusar Agostinho, acusa a dialética. Em sua réplica, Agostinho defenderá a eminência e importância dessa ciência para, a partir desse fundamento, atacar o donatismo e, finalmente, liquidar Crescônio. É precisamente essa apreciação positiva da dialética que este artigo pretende destacar, ressaltando assim a importância do estudo de Contra Crescônio para o estudo da dialética agostiniana. Abstract:Augustine of Hippo received an intellectual formation in the molds of the classical culture, having been educated according to Varro’s disciplinary cycle. This educational background provided him an appreciation of Dialectics as the liberal art which instructs to reason correctly, and allows discerning, in discourses, the elements that generate false conclusions. It is Dialectics that allows connecting true propositions to reach true conclusions, and it is the science that deflagrates falsehood and dissimulation in arguments. In his work, Against Cresconius, grammarian and Donatist, Augustine defends himself against the unreasonable charge of being a homo dialecticus, who, by his ability to argue, would falsify the truth and turn it false. Cresconius, to accuse Augustine, charges dialectics. In his reply, Augustine will defend the eminence and importance of this science to, from this foundation, attack Donatism and, finally, liquidate Cresconius. It is precisely this positive appreciation of Dialectics that this article intends to highlight, thus highlighting the importance of studying Contra Cresconius for the study Augustinian Dialectics. (shrink)

In order to grasp the true ethical meaning of Foucault's aesthetics of existence, I begin by explaining in what sense he was an anti-normativist, arguing that the most important thing about the "final" Foucault is his strong emphasis on the idea of human freedom. I go on with a brief discussion about Foucault's sources of inspiration and a criticism of Rorty's kindred plea for "aesthetic life". I strongly reject the interpretation of Foucault's aesthetics of existence in terms of narcissistic individualism, (...) arguing, on the contrary, that it has a definite communitarian dimension. I also claim that it is rooted in the Socratic and Stoic understanding of "care of the self," at the same time allowing new challenging developments fitted for our "post-duty" historical age, by way of analogy with the process of artistic making. I conclude with some short answers to a few questions regarding the status of this aesthetics of living. (shrink)

It has been argued that measurement-induced collapses in Orthodox Quantum Mechanics generates an intrinsic (or built-in) quantum arrow of time. In this paper, I critically assess this proposal. I begin by distinguishing between an intrinsic and non-intrinsic arrow of time. After presenting the proposal of a collapse-based arrow of time in some detail, I argue, first, that any quantum arrow of time in Orthodox Quantum Mechanics is non-intrinsic since it depends on external information about the measurement context, and second, that (...) it cannot be global, but just local. I complement these arguments by assessing some criticisms and considerations about the implementation of time reversal in contexts wherein measurement-induced collapses work. I conclude that the quantum arrow of time delivered by Orthodox Quantum Mechanics is much weaker than usually thought. (shrink)

En este artículo se discute la visión de la teoría de la argumentación como una forma de epistemología aplicada. El punto de partida es la descripción de cuatro perspectivas que se consideran fundadoras de la teoría moderna de la argumentación, para desde allí observar si en ellas hubo un concepto s..

This volume collects previously unpublished contributions to the philosophy of science. What brings them together is a twofold goal: first and foremost, celebrating the name of Roberto Torretti, whose works in this and other areas have had –and continue to have– a significant impact on the international philosophy of science community; and second, the desire of advancing novel perspectives on various issues in the philosophy of science broadly construed. Roberto Torretti has made substantial contributions to current debates in the history (...) and philosophy of science, the general philosophy of science, and the philosophy of physics and geometry. Among his landmark contributions, we find his investigations in the history and philosophy of geometry, as well as his systematic studies of Einstein's relativity theory. This volume convenes leading philosophers and early-career scholars compiling a fine collection of chapters addressing recent debates on Kantian philosophy of science, the general philosophy of science, and the history and philosophy of physics and mathematics. (shrink)