We investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol for S. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.

We investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol for S. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.

In the 1970s Codd introduced the relational algebra, with operators selection, projection, union, difference and product, and showed that it is equivalent to first-order logic. In this paper, we show that if we replace in Codd’s relational algebra the product operator by the “semijoin” operator, then the resulting “semijoin algebra” is equivalent to the guarded fragment of first-order logic. We also define a fixed point extension of the semijoin algebra that corresponds to μGF.

In the 1970s Codd introduced the relational algebra, with operators selection, projection, union, difference and product, and showed that it is equivalent to first-order logic. In this paper, we show that if we replace in Codd’s relational algebra the product operator by the “semijoin” operator, then the resulting “semijoin algebra” is equivalent to the guarded fragment of first-order logic. We also define a fixed point extension of the semijoin algebra that corresponds to μGF.

6 and 14 recently proposed taxonomies that distinguish between four processing states, based on bottom-up stimulus strength and top-down attentional amplification. The aim of the present study was to empirically test these processing states using the priming paradigm. Our results showed that attention and stimulus strength significantly modulated priming effects: either receiving top-down attention or possessing sufficient bottom-up strength was a prerequisite for a stimulus to elicit priming. When both top-down attention and sufficient bottom-up strength were present, the priming effect (...) was boosted. The origins of the observed priming effects also varied between different processing states. We can conclude that our empirical study using the priming paradigm confirmed the presence of four processing states, which displayed a differential pattern of response priming effects and differential origins of the response priming effects. (shrink)

'What is real?' has been one of the key questions of philosophy since its beginning in antiquity. But it is not just a question that philosophers ask. This Very Short Introduction discusses what reality is by looking at a variety of arguments, theories, and thought-experiments from philosophy, physics, and cognitive science.

This paper briefly discusses the relations between logic and metalogic in history. Metalogic is understood as a reflection on logic in its various senses, particularly sensu stricto (formal, mathematical) and sensu largo (formal logic plus semantic plus methodology of science). It is shown that metalogic in its contemporary understanding arose after mathematical logic had become a mature discipline. Special passage is devoted to metalogic in Poland. The last part of the paper discussed so-called logocentric predicament.

This paper investigates the basis arguments of so-called legal logic and their relation to logic in its standard meaning. There is no doubt that legal arguments belong to logic in the wide sense (sensu largo), but their reduction to schemes of formal logic (logica sensu stricto) is a controversial issue. It can be demonstrated that only some legal arguments fall under explicit rules of formal logic, that is, having a deductive character. Most such reasoning is fallible, and its correctness depends (...) on appealing to extra-logical principles taken from legal norms. For instance, if we say, “If it is permitted more, then it is permitted less” (argumentum a maiori ad minus), we assume that the concepts expressed by the words “more” and “less” are already defined. (shrink)

1. Die erste Hälfte des Kommentars, mit Ausnahme der Kapitel über die Weltseele.

The relevance of metamathematical researches for philosophy of math- ematics is an indubitable matter. In the paper I shall speak about impli- cations of metamathematics for general philosophy, especially for classical epistemological problems. Let us start with a historical observation con- cerning Hilbert's programme, the rst research programme in metamathe- matics as a separate study of formal systems. This programme was strongly in uence by epistemological considerations. In fact, Hilbert wanted to se- cure all classical mathematics against inconsistencies and this (...) aim had be achieved with the help of nitary consistency proof. Hilbert's claim is like the Cartesian project of reduction of all concepts to clarae et distinctae ideae. The epistemological commitment of original Hilbert's programme may be treated as a prelim- inary heuristic motivation for looking for epistemological implications of metamathematical results. It seems reasonable to examine in this respect three so-called limitative theorems: the rst Godel's incompleteness theo- rem , the second Godel's incom- pleteness theorem consistency of S, cannot be proved in S, providing that S is consistent) and Tarski's undenability theorem ; \S" stands for formal system containing elementary number theory. From the above-mentioned theorems we obtain an important, from philosophical point of view, conclusion: semantics of S cannot be expressed in S. Now, I shall present three applications of limitative theorems to the analysis of classical epistemological problems. (shrink)

El presente estudio tiene por objetivo demostrar lo siguiente: que no es posible comprender suficientemente, al menos en un aspecto, el método de ejecución(Methode der Ausführung) de la Fenomenología del espíritu como “la exposición del saber que aparece” (die Darstellung des erscheinenden Wissens), si es que no se comprende la relación que tiene dicho método de ejecución con la temática del auto-engaño. Este objetivo se lleva a cabo de la siguiente manera: 1) se propone el tipo de relación que se (...) busca establecer entre el concepto de “auto-engaño” y el método de ejecución, 2) se presentan las notas que les corresponden a ambos y 3) se argumenta en orden a demostrar que el método de ejecución no se puede comprender rectamente sino en relación con la temática del auto-engaño. (shrink)

Stephenson (2022) has argued that Kant’s thesis that all transcendental truths are transcendentally a priori knowable leads to omniscience of all transcendental truths. His arguments depend on luminosity principles and closure principles for transcendental knowability. We will argue that one pair of a luminosity and a closure principle should not be used, because the closure principle is too strong, while the other pair of a luminosity and a closure principle should not be used, because the luminosity principle is too strong. (...) Stephenson’s argument also depends on a factivity principle for transcendental knowability, which we will argue to be false. (shrink)

The Natural Philosophy of Jan Bayer The main focus of this study is a reconstruction of the natural philosophy of the early modern Prešov's scholar Jan (Johannes) Bayer (1630–1674), with special regard to its Mosaic profile. After a critical reading of the research done on Bayer up to this point, the author concludes that Bayer’s natural-philosophical work, as such, has not yet been satisfactorily analyzed, nor has its connection to its supposedly two most important sources, Francis Bacon and Jan Amos (...) Comenius, been sufficiently explored. The study therefore concentrates on a critical analysis of Bayer’s interpretation of creation and his natural history, which are then both situated in the philosophical context of their time. The author then notes that although Bayer’s project of erecting an original and on the (especially Aristotelian) tradition independent Mosaic natural philosophy ended in failure, the thinker’s work can be assessed as a valuable attempt to synthesize Baconian and Comenian motifs while at the same time reflecting broader intellectual contexts of the period. (shrink)

Cílem této studie je představit základní rámec filozofického díla anglického volnomyšlenkáře Anthonyho Collinse (1676–1729) v kontextu britského osvícenského myšlení konce 17. a první poloviny 18. století. Prostřednictvím analýzy jednotlivých spisů je vyloženo Collinsovo chápání rozumu jako nástroje nepostradatelného nejen v oblasti poznání profánního, ale také divinálního. Studie dále sleduje Collinsovu obhajobu naprosté volnosti myšlení i formy jeho vyjádření. Významný prostor je věnován rovněž autorově filozofii náboženství. Studie dokládá, že Collins nebyl izolovaným myslitelem, ale že ve svém díle těžil jak z (...) předcházející (Spinoza, Herbert z Cherbury a především John Locke), tak i současné filozofické diskuze (zejména John Toland). (shrink)

Some early modern scholars believed that Scripture provided more certain knowledge than all secular authorities – even Aristotle – or investigating nature as such. In this paper, I analyse one such attempt to establish the most reliable knowledge of nature: the so-called Mosaic physics proposed by the Reformed encyclopaedist Johann Heinrich Alsted. Although in his early works on Physica Mosaica Alsted declares that his primary aim is proving the harmony that exists between various traditions of natural philosophy, namely between the (...) Mosaic and the Peripatetic approaches, and despite the fact that his biblical encyclopaedia of 1625 was intended to be based on a literal reading of the Bible, he never truly abandoned the Aristotelian framework of physics. What is more, in his mature encyclopaedia of 1630, he eventually openly preferred Aristotle to other natural-philosophical traditions. I argue, therefore, that Alsted’s bold vision of Mosaic physics remained unfulfilled and should be assessed as an unsuccessful project of early modern natural philosophy. (shrink)

This paper reviews some of the ethical issues associated with the administration of long and intrusive questionnaires and interview schedules, particularly to people whose mental health is compromized. The author argues that this approach to research is potentially abusive and challenges its acceptance as the best method of obtaining relevant data. Recommendations focus on collaboration between the National Research Ethics Service, patient representatives and the research community in order to develop more humane approaches to help understand the needs of vulnerable (...) patients. (shrink)

This is a collection of essays about logic and its applications to various philosophical problems. In general, it is argued that logic constitutes an important device of philosophical analysis. Concerning the nature of logic the author defends the thesis that first-order logic is the logic. Among the philosophical problems to which logic is applied in the essays are: truth, consistency, realism, foundations of semantics, psychologism, undetermination of theories by empirical data, modalities, value concepts, identity, vagueness, God's existence, transcendentals, legal reasoning, (...) category mistakes, bivalence, the cognitive relation, and meaningfulness. (shrink)

Summary This article focuses on the Tacitist thought shared by Justus Lipsius and Hugo Grotius. Contrary to what his later works might suggest, in the years before the Dutch political crisis of 1618, Grotius appears willing to look at history and contemporary politics in terms of the Tacitist and reason-of-state-based categories defined in Lipsius's political works. A specific Lipsian inspiration seems present in Grotius's Amsterdam address of 1616, and his analysis of the early Dutch Revolt in the Annales et Historiae (...) is determined by categories of thought which at the time were identified with Lipsius's intellectual legacy. (shrink)

The recent progress in the development of autonomous cars has seen ethical questions come to the forefront. In particular, life and death decisions regarding the behavior of self-driving cars in trolley dilemma situations are attracting widespread interest in the recent debate. In this essay we want to ask whether we should implement a mandatory ethics setting for the whole of society or, whether every driver should have the choice to select his own personal ethics setting. While the consensus view seems (...) to be that people would not be willing to use an automated car that might sacrifice themselves in a dilemma situation, we will defend the somewhat contra-intuitive claim that this would be nevertheless in their best interest. The reason is, simply put, that a PES regime would most likely result in a prisoner’s dilemma. (shrink)

Modern societies are characterized by a division of epistemic labor between laypeople and epistemic authorities. Authorities are often far more competent than laypeople and can thus, ideally, inform their beliefs. But how should laypeople rationally respond to an authority’s beliefs if they already have beliefs and reasons of their own concerning some subject matter? According to the standard view, the beliefs of epistemic authorities are just further, albeit weighty, pieces of evidence. In contrast, the Preemption View claims that, when one (...) discovers what an authority believes, it is not permissible to rely on any of one’s own reasons concerning the subject matter. The original version of this view, as proposed by Linda Zagzebski, has recently been severely criticized for recommending blind trust and for abandoning even minimal standards for critical thinking. In our paper, we defend a new version of the Preemption View—Defeatist Preemptionism—in a way that differs radically from Zagzebski’s. We argue that our view can be derived from certain widely accepted general epistemic principles. In particular, we claim that preemption can be identified as a special case of source sensitive defeat. Moreover, we argue that Defeatist Preemptionism does not lead to the undesirable consequences that critics ascribe to the Preemption View. The paper thus articulates the foundations and refinements of the Preemption View, such that it adequately captures the phenomenon of epistemic authority and the rational requirements related to it. (shrink)

It is a frequent assumption that—via superluminal information transfers—superluminal signals capable of enabling communication are necessarily exchanged in any quantum theory that posits hidden superluminal influences. However, does the presence of hidden superluminal influences automatically imply superluminal signalling and communication? The non-signalling theorem mediates the apparent conflict between quantum mechanics and the theory of special relativity. However, as a ‘no-go’ theorem there exist two opposing interpretations of the non-signalling constraint: foundational and operational. Concerning Bell’s theorem, we argue that Bell employed (...) both interpretations, and that he finally adopted the operational position which is associated often with ontological quantum theory, e.g., de Broglie–Bohm theory. This position we refer to as “effective non-signalling”. By contrast, associated with orthodox quantum mechanics is the foundational position referred to here as “axiomatic non-signalling”. In search of a decisive communication-theoretic criterion for differentiating between “axiomatic” and “effective” non-signalling, we employ the operational framework offered by Shannon’s mathematical theory of communication, whereby we distinguish between Shannon signals and non-Shannon signals. We find that an effective non-signalling theorem represents two sub-theorems: Non-transfer-control theorem, and Non-signification-control theorem. Employing NTC and NSC theorems, we report that effective, instead of axiomatic, non-signalling is entirely sufficient for prohibiting nonlocal communication. Effective non-signalling prevents the instantaneous, i.e., superluminal, transfer of message-encoded information through the controlled use—by a sender-receiver pair —of informationally-correlated detection events, e.g., in EPR-type experiments. An effective non-signalling theorem allows for nonlocal quantum information transfer yet—at the same time—effectively denies superluminal signalling and communication. (shrink)

The aim of this article is to look at an early 17th-century analysis of a prince’s management of an ‘agglomerate polity’ in order to obtain a view of its chief focuses, concerns, and terms of analysis. Four main types of issues appear (apart from Grotius’ general analysis of Philip’s person and policies, which are also discussed): 1. Acceptation and legitimacy of a prince who was perceived to ignore local customs, rights and interests of his various territories; 2. The king’s representatives (...) and intermediaries, their (mis)management of their task, or the King’s (mis)management of them; 3. The conflicting demands of international politics; 4. Controlling armies and the connected issue of financial resources. The ‘Tacitean’ mode of writing history was regarded as the most ‘true’ and ‘revealing’ historiography in Grotius’ time. However Tacitean perceptiveness and analysis were not about what historians today regard as deeper historical processes and causation (like those associated with the ‘philosophic’ histories from the Enlightenment onwards, e.g. in Edward Gibbon), but about understanding personal motives and (hidden) immediate causes and intentions behind particular events and decisions. This historic differences in historical explanation should be taken into account when judging the value of Grotius’ history of his own time. (shrink)

The purpose of this article is to show, by the example of Hugo Grotius's Annales et Historiae de rebus Belgicis (AH), that the nature and content of the concept of Tacitism (Tacitist, Tacitean) in the period around 1600 was markedly different from modern perceptions of the style and political purport of Tacitus's works. This gap between current and early-modern conceptions of Tacitus is important to bear in mind for intellectual historians dealing with early-modern intellectual currents such as Reason of State, (...) Neo-Stoicism, Tacitism, and others. This article first describes how the Tacitean style is characterised in literary criticism around 1600; then it explores the qualities of Hugo Grotius's imitation of Tacitus from the 17th-century perspective and from that of some main aspects of the present-day view of Tacitus. It concludes that Grotius's imitation shows Tacitus's style in a characteristically 17th-century mirror, in that it puts emphasis on Tacitean syntax, brevity and choice of words (the stylistic micro-level), as well as on political iudicium and Reason of State, but omits imitation of the narrative and structural qualities of Tacitus's composition, and their implications, which are central to modern interpretations. ☆ This article is part of the outcome of a research project on Grotius's Annales et Historiae conducted at the Radboud University Nijmegen in 2004–2008 with a VENI-grant from the Dutch research organisation NWO. I thank Corinna Vermeulen, Marc van der Poel, Hans Blom and HEI's anonymous referees for their comments on this piece. (shrink)

This book compiles and reviews the most prominent linguistic theories into a single source that serves as an essential reference for future solutions to one of the most important challenges of our age.

Students of Thomas Aquinas have so far lacked a comprehensive study of his doctrine of the transcendentals. This volume fills this lacuna, showing the fundamental character of the notions of being, one, true and good for his thought. The book inquires into the beginnings of the doctrine in the thirteenth century and explains the relation of the transcendental way of thought to Aquinas's conception of metaphysics. It analyzes 'Being', 'One', 'True', 'Good' and 'Beautiful' individually and discusses their importance for the (...) philosophical knowledge of God. Medieval Philosophy and the Transcendentals: The Case of Thomas Aquinas is intended as a contribution to the question 'What is philosophy in the Middle Ages?' It argues that the doctrine of the transcendentals is essential for understanding medieval philosophy. (shrink)