We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L–tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L*∅ is of degree 0’. We show that the same holds also for some weaker logics like L ∅(Hω) and L ∅(Eω). We show that each logic of the form (...) L ∅ (k)(Q), with the number of variables restricted to k, is decidable. Nevertheless – following the argument of M. Mostowski from [Mos89] – for each reasonable set theory no concrete algorithm can provably decide L (k) (Q), for some (Q). We improve also some results related to undecidability and expressibility for logics L(H4) and L(F2) of Krynicki and M. Mostowski from [KM92]. (shrink)

We examine second order intuitionistic propositional logic, IPC². Let $F_\exists $ be the set of formulas with no universal quantification. We prove Glivenko's theorem for formulas in $F_\exists $ that is, for φ € $F_\exists $ φ is a classical tautology if and only if ¬¬φ is a tautology of IPC². We show that for each sentence φ € $F_\exists $ (without free variables), φ is a classical tautology if and only if φ is an intuitionistic tautology. As a corollary (...) we obtain a semantic argument that the quantifier V is not definable in IPC² from ⊥, V, ^, →. (shrink)

We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ₂—theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ₁—theory of multiplication and order is decidable in finite models as well (...) as in the standard model. We show also that the exponentiation function is definable in finite models by a formula of arithmetic with multiplication and that one can define in finite models the arithmetic of addition and multiplication with the concatenation operation. We consider also the spectrum problem. We show that the spectrum of arithmetic with multiplication and arithmetic with exponentiation is strictly contained in the spectrum of arithmetic with addition and multiplication. (shrink)

It is known that various complexity-theoretical problems can be translated into some special spectra problems. Thus, questions about complexity classes are translated into questions about the expressive power of some languages. In this paper we investigate the spectra of some logics with Henkin quantifiers in the empty vocabulary.

It is known that various complexity-theoretical problems can be translated into some special spectra problems (see e.g. Fagin [Fa74] or Blass and Gurevich, [Bl-Gu86]). So questions about complexity classes are translated into questions about the expressive power of some languages. In this paper we investigate the spectra of some logics with Henkin quanti fiers in the empty vocabulary. This problem has been investigated fi rstly by Krynicki and Mostowski in [Kr-Mo 92] and [Kr- Mo 95]. All presented results can be (...) also treated as results about the expressive power of certain languages in fi nite models. (shrink)

We prove that for each β, γ < ε0 there existsα < ε0 such that whenever A ⊆ ω is α ‐large and G: A → β is such that (∀a ∈ A)(psn(G (a)) ≤ a), then there exists a γ ‐large C ⊆ A on which G is nondecreasing. Moreover, we give upper bounds for α for small ordinals β ≤ ω (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

Building on our diverse research traditions in the study of reasoning, language and communication, the Polish School of Argumentation integrates various disciplines and institutions across Poland in which scholars are dedicated to understanding the phenomenon of the force of argument. Our primary goal is to craft a methodological programme and establish organisational infrastructure: this is the first key step in facilitating and fostering our research movement, which joins people with a common research focus, complementary skills and an enthusiasm to work (...) together. This statement—the Manifesto—lays the foundations for the research programme of the Polish School of Argumentation. (shrink)

Festschrift volume to K. Ramakrishna Rao, Indian psychologist, philosopher and educationist; contributed articles.

Constitutional and judicial law-making is increasingly beginning to find its reflection not only in the Anglo-Saxon, but also in the Romano-Germanic legal family. However, the prerequisites for the use of this legal instrument are different, which determines the relevance of conducting a comparative analysis regarding the provision of such a mechanism in the USA and Kazakhstan. The purpose of the research is to identify common and distinctive features in the process of implementation of constitutional and judicial law-making in countries belonging (...) to different legal systems. The article uses the methods of analysis, synthesis, comparison, deduction and generalization. As a result, the specificity of ensuring the mechanism of constitutional law-making in the USA was expressed, taking into account various forms of law-making activity. It has been established that the development of constitutional provisions in the United States takes place with the help of the constitutional doctrines of the Supreme Court of the United States, which provide for the introduction of amendments to constitutional provisions without a formal procedure. As a result of the study of the experience of Kazakhstan, it was established that special priority was given to the role of precedent, in particular, the decision of the Supreme Court of the Republic of Kazakhstan. This is explained by the integrative nature of the Romano-Germanic legal system, which allows effective development of national legislation as a whole and its provisions. The obtained results can be used during the professional training of judges in the Republic of Kazakhstan. (shrink)

K. Satchidananda Murty (1924-2011) was a vociferous writer and an iconoclast. This volume is a collection of his unpublished writings. It includes Murty's views on the Veda, its meaning, relevance, and study, and shows the significance of the Vedāntic vision to the modern world. Murty elucidates the basic tenets of Advaita Vedānta and expounds the Advaitic doctrine of the relationships between Brahman and God, Brahman and the individual self, as well as between God and the world. In his writings, Murty (...) contrasts empirical knowledge with transcendental wisdom and surveys the history of Indian science and scientific views in ancient times. The book also includes Murty's musings on the scholar Śankara's philosophy, authorship and religious life. An important contribution to Indian philosophy, the volume will be of great interest to scholars, teachers and students of Hindu philosophy, Vedāntic philosophy, Advaita Vedanta, comparative philosophy, religious studies, and South Asian studies. (shrink)

This monograph aims to mathematically codify the notion of "moral systems" and define a sensible distance between them. It consists of three parts, aimed at an audience with varying interests and mathematical backgrounds. The first part steers philosophical, formally defining moral systems and several related concepts. The second part studies black box algorithms, including questions of inference and metric construction. The third part explores the technical construction of metrics amongst conditional probability distributions.

PART The Early Wittgenstein Half of what I say is meaningless. I say it so that the other half may reach you. Kahlil Gibran My work consists of two parts ...

Principles of justice, David Estlund argues, cannot be falsified by people’s unwillingness to satisfy them. In his Utopophobia, Estlund rejects the view that justice must bend to human motivation to deliver practical implications for how institutions ought to function. In this paper, I argue that a substantive argument against such bending of justice principles must challenge the reasons for making these principles sensitive to motivational limitations. Estlund, however, provides no such challenge. His dispute with benders of justice is therefore a (...) verbal one over the true meaning of justice, which need not worry those with the intuition that justice should perform a function that requires bending. By focusing on John Rawls’s reasons for bending his justice principles, I point towards a substantive critique of bent justice. (shrink)

The provability problem in intuitionistic propositional second-order logic with existential quantifier and implication (∃,→) is proved to be undecidable in presence of free type variables (constants). This contrasts with the result that inutitionistic propositional second-order logic with existential quantifier, conjunction and negation is decidable.

What is interest and how has it been conceptualized and studied? -- What explains the power of interest? : Why are students who have an interest for content more likely to continue to reengage and develop more conceptual sophistication? -- What is known about assessing existing interest? How do new interests develop? How can the phase of a person's interest be identified and measured? -- What is the relation between the development of interest and other motivational variables? -- Is it (...) a paradox that interest declines as subject matter gets more developed? What is "interest driven learning"? Does it matter if interests are taken up in rather than out of school? How different is an interest in one versus another subject matter, or domain? -- What we can now say about interest, its generation and development? What are the implications of knowing that interest can be developed? What could further research help us to understand? (shrink)

Recent research in the cognitive science of religion suggests that humans intuitively believe that others survive death. In response to this finding, three cognitive theories have been offered to explain this: the simulation constraint theory (Bering, Citation2002); the imaginative obstacle theory (Nichols, Citation2007); and terror management theory (Pyszczynski, Rothschild, & Abdollahi, 2008). First, I provide a critical analysis of each of these theories. Second, I argue that these theories, while perhaps explaining why one would believe in his own personal immortality, (...) leave an explanatory gap in that they do not explain why one would intuitively attribute survival of death to others. To fill in the gap, I offer a cognitive theory based on offline social reasoning and social embodiment which provides for the belief in an eternal social realm in which the deceased survive—the afterlife. (shrink)