The issue of human nature is very complex and elusive, and mankind has been trying to unveil its elements since the beginnings of any philosophical reasoning. Whether they were questions of ontology, gnoseology, or ethics, it has been an uneasy task to uncover the complexity of the term. This article concentrates on finding ideas that support the existence of human nature and consequently searches for its possible ethical implications. I focused on the traditional issues of good vs evil, especially in (...) terms of dichotomy between committing violent acts and waging wars in contradiction to creation of conditions for peaceful and just societies. In the article, I compare various ideas on human nature and analyse their potential in unveiling its ethical implications. I also comment on the possibility of war and peace being consequences of human nature and its connection to our disposition of being moral subjects. (shrink)

The article deals with the newly discussed set of principles that focus on various issues concerning the end of a war and the establishment of peaceful conditions for the society after a war ends. It also reveals some drawbacks of the jus post bellum principles and searches for its possible modifications into a more complex and applicable set of rules that should govern any post-war activities on both sides of the conflict. The aim is to reach its plausibility in a (...) dynamic global society and thus argue that global peace is an attainable goal only when it becomes the goal of the global community. (shrink)

The aim of this paper is to study and analyse the Charlie Hebdo attacks from a methodological and an ethical perspective, concentrating generally, though in some cases indirectly, on the consequences of our actions and the motives behind them. The analysis examines the issues of liberties, freedoms and responsibilities in general and further applies these values to the phenomenon of terrorism in contemporary society. The primary goal of this study is to use the Thomas Aquinas doctrine of double effect and (...) Michael Ignatieff’s lesser evil theory to appraise specific acts of terrorism. The article suggests that certain freedoms should be limited in democratic societies and thus ensure safety. (shrink)

This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

The article deals with ethics of social consequences as a modern ethical theory and proposes some critical remarks based on various elaborations of the theory presented in the newly published edited volume Ethics of social consequences: Philosophical, applied and professional challenges. It confronts and challenges several of the presented concepts and ideas and tries to find a solution for the theory to become even more elaborated but still remain within the boundaries of its ontological framework.

The post-war generation of Marxist Slovak intelligentsia was formed from people who had experience with the war and this experience in the fight against fascism, together with the pre-war social situation, were the main reasons of their inclinations towards the theory of socialism and at the same time caused their sharp criticism of the Church and its ideas. Jaroslav Čelko can also be included in the generation of these authors, and this paper describes and explores his ideas and their influence (...) on the development of secular humanism during the existence of the Czechoslovak Socialist Republic and after its disintegration. At the same time, the aim of the paper is to evaluate the influences and connections between the ideas of scientific atheism (including examples of the works of Jaroslav Čelko) and secular humanism in Slovakia. (shrink)

Ethics in business and economics is often attacked for being too superficial. By elaborating the conclusions of two such critics of business ethics and welfare economics respectively, this article will draw the attention to the ethics behind these apparently well-intended, but not always convincing constructions, by help of the fundamental ethics of Emmanuel Levinas. To Levinas, responsibility is more basic than language, and thus also more basic than all social constructions. Co-operation relations in organizations, markets and value networks are generated (...) from personal relations and personal responsibilities. It is not sufficient to integrate ethics in an impersonal, rational system, neither in business organizations nor in the world economy. Ethics has its source not in rationality, but in the personal. (shrink)

By a valid inference is here understood an inference that succeeds in its aim to justify its conclusion given that its premisses are already justified. For an inference to be valid it is thus not enough that the sentence asserted in the conclusion is a logical consequence of the sentences asserted in the premisses. A proof is understood as a succession of valid inferences that is closed (i.e. all its assumptions are discharged and all its free variables are bound by (...) some of the inferences). On the other hand, in mathematics the justification of an assertion has traditionally been taken to consist in a proof of it, which gives rise to an explanatory circle.In an attempt to avoid this circle, I have in previous works tried to explain the notion of ground for an assertion without referring to valid inferences. However, it turns out that the resulting notion of ground has unwanted consequences like the notion of proof in the so-called BHK-interpretation of intuitionistic logic. For instance, one is guaranteed a ground or a proof of an implication A → B as soon as there is in fact no ground or proof of A, regardless of whether one really knows this fact, and hence without having a real justification of the assertion of the implication.In the absence of a non-circular explanation of the notions of valid inference and proof, I suggest that we should try to formulate a number of principles of how these two epistemic notions depend on each other. A more careful explanation of the validity of an inference results in what I call a heuristic idea about the validity of inference, which is used as a guide to formulate precise principles. One such principle generalizes Gentzen’s idea that his introduction rules define the meaning of the logical constants. Another principle generalizes a previously noted property of Gentzen’s elimination rules that I have called that of satisfying the inversion principle. It results in a notion that I call non-creativity, which implies validity. (shrink)

The paper elaborates two points: i) There is no principal opposition between predicate logic and adherence to subject-predicate form, ii) Aristotle's treatment of quantifiers fits well into a modern study of generalized quantifiers.

According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to introduction form. One main part of the paper is devoted to the exact development of (...) this notion. Another main part of the paper is concerned with a modification of this notion as it occurs in Michael Dummett’s book The Logical Basis of Metaphysics. The two notions are compared and there is a discussion of how they fare as a foundation for a theory of meaning. It is noted that Dummett’s notion has a simpler structure, but it is argued that it is less appropriate for the foundation of a theory of meaning, because the possession of a valid argument for a sentence in Dummett’s sense is not enough to be warranted to assert the sentence. (shrink)

This article points out problems in current dynamic treatments of anaphora and provides a new account that solves these by grafting Muskens' Compositional Discourse Representation Theory onto a partial theory of types. Partiality is exploited to keep track of which discourse referents have been introduced in the text (thus avoiding the overwrite problem) and to account for cases of anaphoric failure. Another key assumption is that the set of discourse referents is well-ordered, so that we can keep track of the (...) order in which they have been introduced, allowing a semantic characterization of anaphoric accessibility across stretches of discourse. Unlike other dynamic approaches, the system defines semantic values for unresolved anaphors. This leads to a clear separation of monotonic and non-monotonic content (in this case anaphoric resolution) and arguably provides a sound basis for a non-monotonic theory of anaphoric resolution. (shrink)

Levinas did not present any new ethical theories; he did not even give any normative recommendations. But his phenomenological investigations help us to understand how the idea of ethics emerges and how we try to cope with it. The purpose of this paper is to suggest some implications from a reading of Levinas on how ethical challenges are handled within a management perspective. The paper claims that management, both in theory and in practice, is necessarily egocentric and thus ethically biased. (...) Therefore, ethics, defined as the idea that it is possible to do otherwise than pursue one's own interest, must have its source outside the scope of management. Levinas identifies this source as the call for responsibility from the Other, beyond the reach of managerial control. He also suggests how this idea of ethics is put into practice, especially in economic life: the existence of money makes it both possible and necessary to compare unique and incomparable others. Management tools may be used in the service of always more justice, as it also may be used for the opposite purpose. Instead of trying to draw a normative conclusion from Levinas, we may distinguish between two ways of experiencing reality: one through language and knowledge, covering both descriptive and normative knowledge, including business ethics, and the other through the particular events of encounters, from where this knowledge is continuously questioned through the call for responsibility, and thereby may provide possibilities for continuous improvements towards always more justice. (shrink)

I attempt an explication of what it means for an operation across domains to be the same on all domains, an issue that ) took to be central for a successful delimitation of the logical operations. Some properties that seem strongly related to sameness are examined, notably isomorphism invariance, and sameness under extensions of the domain. The conclusion is that although no precise criterion can satisfy all intuitions about sameness, combining the two properties just mentioned yields a reasonably robust and (...) useful explication of sameness across domains. (shrink)

We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a locally bounded function is bounded on certain domains, i.e. one of the first ‘local-to-global’ principles. It is well-known that such principles in analysis are intimately connected to (open-cover) compactness, but we nonetheless exhibit fundamental differences between compactness and Pincherle's theorem. For instance, the main question of Reverse Mathematics, namely which set existence axioms are necessary to (...) prove Pincherle's theorem, does not have an unique or unambiguous answer, in contrast to compactness. We establish similar differences for the computational properties of compactness and Pincherle's theorem. We establish the same differences for other local-to-global principles, even going back to Weierstrass. We also greatly sharpen the known computational power of compactness, for the most shared with Pincherle's theorem however. Finally, countable choice plays an important role in the previous, we therefore study this axiom together with the intimately related Lindelöf lemma. (shrink)

There are two main routes to a concept of (generalized) quantifier. The first starts from first‐order logic, FO, and generalizes from the familiar ∀ and ∃ occurring there. The second route begins with real languages, and notes that many so‐called noun phrases, a kind of phrase which occurs abundantly in most languages, can be interpreted in a natural and uniform way using quantifiers.

In this paper I reflect critically on the concept of pragmatism as it is used in Ottoman historiography. Pragmatism has gained increasing currency over the last ten to fifteen years as one of the defining features of the Ottoman polity. I argue that unless it is properly defined from a theoretical-philosophical perspective, and carefully contextualized from a historical perspective, pragmatism cannot be used as an explanatory or comparative category. When used as a framework of explanation for historical change, pragmatism blurs (...) more than it clarifies an essential aspect of the Ottoman polity that it seeks to define, namely, the political. It is essential to reflect on the difference between the political and politics because whereas the political refers to the configuration of the power relations that organize a society as a legitimate entity, politics refers to the strategies, practices, institutions, or discourses whose purpose is to construct and retain hegemony within a polity. Through an analysis of the concept of pragmatism in Ottoman historiography, I show that for most proponents of Ottoman pragmatism, pragmatism pertains to politics rather than to the political. From a perspective rigorously confined to political theory, I argue that much like the discourse of modern tolerance, pragmatism in Ottoman historiography posits a problematic periodization, relegates the political to the background, and depoliticizes essential power relations. (shrink)

In terms of Arabic philology, the concept of reason performs the function of bonding and is a key to terms such as wisdom, goodness, duty, and autonomy. By using the reason in its proper place, morality that regulates the self (nafs) emerges. The reason, which is seen as the source of spiritual values, has given human beings the quality of being the subject of trust (amana). In Islamic Wisdom, human beings are distinguished from animals by the characteristics of carrying the (...) Trust and having morality. Morality is not a factual but a spiritual value produced by the self. Thus, having reason also requires being moral. Reason, which is related to both matter and meaning, must move in parallel like a clock with morality, which is related to ideas and deeds. The unity of reason and morality is like the two boat oars that must be pulled in order to navigate the boat at the sea. The disruption of this balance leads to the disruption of the order. Islamic wisdom emphasizes that when this dual plane is well established, order and dynamism arise, and when it is disrupted, chaos and stagnation occur. In this paper, the unity of reason and morality relationship in Islamic wisdom is discussed. (shrink)

This article examines the metaphysical and moral foundations of Spinoza’s account of suicide. Spinoza’s treatment of suicide is brought into question by his conatus doctrine, which posits the striving to preserve one’s own being as the very essence of existence. Accordingly, suicide, or the termination of life, as the destruction of one’s own being, represents the exhaustion of this striving. The analysis of the causes that lead to self-destruction has sparked significant debate in Spinoza’s literature, raising the question of whether (...) suicide is a passive and irrational decision or a free and rational choice. This article, which engages with prominent scholars of this literature, notably Matson, Bennett, LeBuffe and Nadler, aims to alleviate this controversy by offering alternative readings and arguments. It concludes that free and rational suicide does not exist in Spinoza’s thought; instead, the “suicide of reason or rationality” forms the basis for bodily suicide. (shrink)

A semantics may be compositional and yet partial, in the sense that not all well-formed expressions are assigned meanings by it. Examples come from both natural and formal languages. When can such a semantics be extended to a total one, preserving compositionality? This sort of extension problem was formulated by Hodges, and solved there in a particular case, in which the total extension respects a precise version of the fregean dictum that the meaning of an expression is the contribution it (...) makes to the meanings of complex phrases of which it is a part. Hodges' result presupposes the so-called Husserl property, which says roughly that synonymous expressions must have the same category. Here I solve a different version of the compositional extension problem, corresponding to another type of linguistic situation in which we only have a partial semantics, and without assuming the Husserl property. I also briefly compare Hodges' framework for grammars in terms of partial algebras with more familiar ones, going back to Montague, which use many-sorted algebras instead. (shrink)

The traditional picture of logic takes it for granted that "valid arguments have a fundamental epistemic significance", but neither model theory nor traditional proof theory dealing with formal system has been able to give an account of this significance. Since valid arguments as usually understood do not in general have any epistemic significance, the problem is to explain how and why we can nevertheless use them sometimes to acquire knowledge. It is suggested that we should distinguish between arguments and acts (...) of inferences and that we have to reconsider the latter notion to arrive at the desired explanation. More precisely, the notions should be developed so that the following relationship holds: one gets in possession of a ground for a conclusion by inferring it from premisses for which one already has grounds, provided that the inference in question is valid. The paper proposes explications of the concepts of ground and deductively valid inference so that this relationship holds as a conceptual truth. Logical validity of inference is seen as a special case of deductive validity, but does not add anything as far as epistemic significance is concerned—it resides already in the deductively valid inferences. (shrink)

This is a reply to H. Ben-Yami, 'Generalized quantifiers, and beyond' (this journal, 2009), where he argues that standard GQ theory does not explain why natural language quantifiers have a restricted domain of quantification. I argue, on the other hand, that although GQ theory gives no deep explanation of this fact, it does give a sort of explanation, whereas Ben-Yami's suggested alternative is no improvement.

The main question addressed in this chapter is how to analyze the modal ingredient in the concept of logical consequence or logical validity of an inference, here expressed by saying that the truth of the conclusion of a logically valid inference should follow by necessity of thought from the truth of the premisses. It is claimed that this modal ingredient is not taken care of by Tarski’s requirement, later developed in model theory, that for all interpretations of the non-logical terms (...) of the sentences, the conclusion is true if the premisses are. Instead we must bring in reasoning or the notion of proof in the analysis, and it is shown how one may develop a notion of proof or validity of an argument based on the constructive meaning of the logical constants. It is proposed that from a constructive point of view, a sentence is a consequence of a set of premisses if and only if there is a proof in the sense explained of the sentence from the set of premisses. Knowledge of such a proof compels us to hold the conclusion true given that we hold the premisses true. (shrink)

We study the logical and computational properties of basic theorems of uncountable mathematics, including the Cousin and Lindelöf lemma published in 1895 and 1903. Historically, these lemmas were among the first formulations of open-cover compactness and the Lindelöf property, respectively. These notions are of great conceptual importance: the former is commonly viewed as a way of treating uncountable sets like e.g. [Formula: see text] as “almost finite”, while the latter allows one to treat uncountable sets like e.g. [Formula: see text] (...) as “almost countable”. This reduction of the uncountable to the finite/countable turns out to have a considerable logical and computational cost: we show that the aforementioned lemmas, and many related theorems, are extremely hard to prove, while the associated sub-covers are extremely hard to compute. Indeed, in terms of the standard scale (based on comprehension axioms), a proof of these lemmas requires at least the full extent of second-order arithmetic, a system originating from Hilbert–Bernays’ Grundlagen der Mathematik. This observation has far-reaching implications for the Grundlagen’s spiritual successor, the program of Reverse Mathematics, and the associated Gödel hierarchy. We also show that the Cousin lemma is essential for the development of the gauge integral, a generalization of the Lebesgue and improper Riemann integrals that also uniquely provides a direct formalization of Feynman’s path integral. (shrink)

Cantor’s first set theory paper (1874) establishes the uncountability of ${\mathbb R}$. We study this most basic mathematical fact formulated in the language of higher-order arithmetic. In particular, we investigate the logical and computational properties of ${\mathsf {NIN}}$ (resp. ${\mathsf {NBI}}$ ), i.e., the third-order statement there is no injection resp. bijection from $[0,1]$ to ${\mathbb N}$. Working in Kohlenbach’s higher-order Reverse Mathematics, we show that ${\mathsf {NIN}}$ and ${\mathsf {NBI}}$ are hard to prove in terms of (conventional) comprehension axioms, (...) while many basic theorems, like Arzelà’s convergence theorem for the Riemann integral (1885), are shown to imply ${\mathsf {NIN}}$ and/or ${\mathsf {NBI}}$. Working in Kleene’s higher-order computability theory based on S1–S9, we show that the following fourth-order process based on ${\mathsf {NIN}}$ is similarly hard to compute: for a given $[0,1]\rightarrow {\mathbb N}$ -function, find reals in the unit interval that map to the same natural number. (shrink)

Reviewed Works:Gaisi Takeuti, Proof Theory.Georg Kreisel, Proof Theory: Some Personal Recollections.Wolfram Pohlers, Contributions of the Schutte School in Munich to Proof Theory.Stephen G. Simpson, Subsystems of $\mathbf{Z}_2$ and Reverse Mathematics.Solomon Feferman, Proof Theory: A Personal Report.

We investigate the connections between computability theory and Nonstandard Analysis. In particular, we investigate the two following topics and show that they are intimately related. A basic property of Cantor space$2^ $ is Heine–Borel compactness: for any open covering of $2^ $, there is a finite subcovering. A natural question is: How hard is it to compute such a finite subcovering? We make this precise by analysing the complexity of so-called fan functionals that given any $G:2^ \to $, output a (...) finite sequence $\langle f_0, \ldots,f_n \rangle $ in $2^ $ such that the neighbourhoods defined from $\overline {f_i } G\left$ for $i \le n$ form a covering of $2^ $. A basic property of Cantor space in Nonstandard Analysis is Abraham Robinson’s nonstandard compactness, i.e., that every binary sequence is “infinitely close” to a standard binary sequence. We analyse the strength of this nonstandard compactness property of Cantor space, compared to the other axioms of Nonstandard Analysis and usual mathematics.Our study of yields exotic objects in computability theory, while leads to surprising results in Reverse Mathematics. We stress that and are highly intertwined, i.e., our study is holistic in nature in that results in computability theory yield results in Nonstandard Analysis and vice versa. (shrink)

In the analysis of the ethicalproblems of online research, there is much tobe learned from the work that has already beendone on research ethics in the socialsciences and the humanities. I discuss thestructure of norms in the Norwegian ethicalguidelines for research in the social scienceswith respect to their relevance for the ethicalissues of Internet research. A four-stepprocedure for the ethical evaluation ofresearch is suggested. I argue that eventhough, at one level, the problems of onlineresearch are very similar to those we (...) find intraditional areas of social scientificresearch, there still are some issues that areunique to research online. A general model forthe analysis of privacy and data protection issuggested. This model is then used tocharacterize the special problems pertaining tothe protection of privacy in online contexts,and to argue that one cannot assume a simpledistinction between the private and the publicwhen researching in such contexts. (shrink)

We characterize the generalized quantifiers Q which satisfy the scheme $QxQy\phi \leftrightarrow QyQx\phi$ , the so-called self-commuting quantifiers, or quantifiers with the Fubini property.

I see the question what it is that makes an inference valid and thereby gives a proof its epistemic power as the most fundamental problem of general proof theory. It has been surprisingly neglected in logic and philosophy of mathematics with two exceptions: Gentzen’s remarks about what justifies the rules of his system of natural deduction and proposals in the intuitionistic tradition about what a proof is. They are reviewed in the paper and I discuss to what extent they succeed (...) in answering what a proof is. Gentzen’s ideas are shown to give rise to a new notion of valid argument. At the end of the paper I summarize and briefly discuss an approach to the problem that I have proposed earlier. (shrink)