Anti-tank hyper-hedgehog in N-dimensional space of unsolvable problems or How to measure genius?

With a narrow specialization of scientists, the development of science leads to the rapid growth of the space of unsolvable tasks, that grows faster than the of existing scientific knowledge. The practical development of the field of unsolvable tasks is possible only by the forces of niversalscientists of the future, who must have a high level of scientific knowledge in several general scientific disciplines.

Mutual Influence between Different Views of Probability and Statistical Inference

In this paper, we analyse the various meanings of probability and its different applications, and we focus especially on the classical, the frequentist, and the subjectivist view. We describe the different problems of how probability can be measured in each of the approaches, and how each of them can be well justified by a mathematical theory. We analyse the foundations of probability, where the scientific analysis of the theory that allows for a frequentist interpretation leads to unsolvable problems. Kolmogorov’s axiomatic theory does not suffice to establish statistical inference without further definitions and principles. Finally, we show how statistical inference essentially determines the meaning of probability and a shift emerges from purely objectivist views to a complementary conception of probability with frequentist and subjectivist constituents. For didactical purpose, the result of the present analyses explains basic problems of teaching, originating from a biased focus on frequentist aspects of probability. It also indicates a high priority for the design of suitable learning paths to a complementary conception of probability. In the applications, modellers use information in a pragmatic way processing this information regardless of its connotation into formal mathematical models, which are always thought as essentially wrong but useful.

Unsolvable economic problems. Existence in contradictions

V. B. Sirotkin considers causes that underlie the existence of unsolvable problems in the society, i.e. corruption, low labor efficiency, etc., and shows that uncontrollable contradictions in human behavior and mentality serve as sources for the existence of such problems. The author suggests a transdisciplinary approach to studying behavior management of individuals and groups.

Literatur und Problemdenken

With the term ›problem thinking‹ Nicolai Hartmann points to a core idea - not only of modern philosophy: In addition to paradoxes and aporias, there are many unsolvable problems that need to be described precisely, because they can make the limits of possible knowledge or the finding of consent in discourses visible. A literary history of problems can identify such unsolved problems in literary texts and attempt to reconstruct the historical context. This essay demonstrates this technique through the example of two of Brecht's Geschichten von Herrn Keuner.

Epistemic predicates in the arithmetical context

In this paper, we investigate epistemic predicates in extensions of arithmetic. We use as our case study Kurt Gödel’s 1951 thesis that either the power of the human mind surpasses that of any finite machine or there are absolutely unsolvable problems. Because Gödel also claimed that his disjunction was a mathematically established fact, we must ask the following: what sort of syntactical object should formalize human reason? In this paper, we lay the foundations for a predicate treatment of this epistemic feature. We begin with a very general examination of the Gödel sentence in the arithmetical context. We then discuss two systems of modal predicates over arithmetic. The first, called coreflective arithmetic or ${\textsf{CoPA}}$, extends ${\textsf{PA}}$ with a coreflective modal predicate but does not contain a consistency statement. The second, called doxastic arithmetic or ${\textsf{DA}}$, has as its characteristic feature the consistency statement but does not contain coreflection or its instance, the ${\textsf{4}}$ axiom. We examine the logical properties of, motivations for and criticisms of both systems. We close with a brief comparison of the systems in the context of Gödel’s disjunction.

On Absolutely Unsolvable Problems

It was not Alan Turing or Kurt Gödel, but Emil Post, who reflected most deeply on issues of absolutely unsolvable problems. He proposed an open-ended research program that was abandoned upon his death.

Hard Law or Soft Law—Does it Matter?

The European Court of Human Rights takes both hard law and soft law seriously, especially when it is necessary to adapt the wording of the European Convention on Human Rights to changed conditions in European societies and to explore what is called the ‘European consensus’. Nevertheless, the Court does not treat hard law and soft law in the same way. When clashes occur, it takes hard law more seriously than soft law. This finding can be linked to the acceptability and legitimacy of the Court’s jurisprudence. An interpretation of the Convention creating irreconcilable treaty obligations is generally not acceptable. An interpretation of the Convention going less far or further than rules of soft law might be criticized, but does not create unsolvable problems for member States. Thus, while there is no black-and-white scenario, the difference between hard law and soft law still matters in the Court’s jurisprudence.

Nagel, Thomas (1937–)

The comprehensiveness of Thomas Nagel’s approach to philosophy sets him apart among late-twentieth-century analytic philosophers. Nagel develops a compelling analysis of the fundamental philosophical problems, showing how they result from our capacity to take up increasingly objective viewpoints that detach us from our individual subjective viewpoints as well as from the viewpoints of our community, nation and species. Our essentially dual nature, which allows us to occupy objective as well as subjective viewpoints, poses unsolvable problems for us because subjective and objective viewpoints reveal conflicting facts and values. Our ability to undertake increasingly detached viewpoints from which objective facts come into view indicates that we are contained in a world that transcends our minds; similarly, our ability to examine our values and reasons from a detached or impartial objective viewpoint implies that moral values are real in the sense that they transcend our personal motives and inclinations. Yet Nagel also holds that our capacity for objective thought is limited by the fact that we cannot detach ourselves completely from our own natures in our attempts either to know our world or to act morally. Subjective facts are equally a part of reality and our moral outlook is essentially the outlook of individual agents with personal and communal ties. Consequently, Nagel argues against any form of reductionism which holds that only objective facts and values are real or which attempts to explain subjective facts and values in terms of objective ones.