What the Tortoise Said to Achilles: Lewis Carroll’s Paradox in Terms of Hilbert Arithmetic

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems).

What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmetic

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure

What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmetic

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achillesand the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox thereforenaturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems).

Mechanisms adopted by social enterprises for effective volunteer-based operations

Purpose This paper aims to describe an exploratory study aiming to identify the mechanisms adopted by social enterprises for effective operations based on volunteer work. Design/methodology/approach An inductive multiple case study method was used addressing three social enterprises whose operations rely on a volunteer workforce. Findings Volunteer-based operations benefit from the establishment of a formal structure, involving different levels of volunteering complemented with other mechanisms, namely, educate and train, empower and connect. Special attention must be given to first-level volunteers, reinforcing the range of practices to motivate and engage them, as they serve as intermediaries between the paid employees and lower-level volunteers. Practical implications The study provides valuable insights for managers for the implementation of effective operations, building on volunteer work, aiming at the generation of social and economic value. Social implications Due to their innovative character, social enterprises are well-positioned to mobilize more and more qualified volunteers for a significant change in their communities. Adopting a more strategic and structured approach to volunteer management can enable these organizations to take advantage of it. Originality/value This study contributes to the literature on social enterprise by identifying a set of mechanisms adopted for effective volunteer-based operations. It also contributes to the literature on volunteer management by addressing an underexplored context.

Debatable aspects of constructing construction of corpus delicti in the sphere of economic activity (Chapter 22 of the Criminal Code of the Russian Federation)

The article analyzes the features of the regulation of crimes in the field of economic activity with formal, material and truncated structures of the compositions in the 1996 Criminal Code of the Russian Federation. The author notes that the presence in Chapter 22 of the Criminal Code of the Russian Federation of a significant number of criminal-legal prohibitions containing a formal type of structure of a crime is criticized in the doctrine of criminal law and does not always meet the rules of criminalization of a socially dangerous act and the needs of law enforcement practice. The absence of signs characterizing the economic consequences (damage, avoidance of losses, etc.) in many dispositions with a formal structure does not allow us to speak of the presence of the level of social danger necessary for criminalization of the illegal behavior of economic entities. A number of crimes, in our opinion, should be legally transferred to the category of administrative offenses. The author notes that when designing complex alternative compositions, one should carefully select the necessary features with a homogeneous nature and level of public danger. Such alternative signs should be used in a situation where it is impossible to use abstract linguistic terms covering all the signs listed in the disposition. You should also avoid including false signs in alternative constructions of dispositions: repetitive, unreasonable criminologically, intersecting with other elements of crime, etc.

New Remarks on the Concept in Logical Use

The main thesis of this paper is directed against the traditional (cognitivetheoretical) definition of the concept which claims that the concept is the '' thought about the essence of the object being thought'', i.e. that it is “a set of essential features or essential characteristics of an object''. But the '' set of essential features or essential characteristics of an object of thought'' is a '' content’’ of the thought. The thought about the essence of an object is definition and the concept is not definition but the part of definition! Besides as the part of formal structure of thought, the concept possesses calculative logical properties that in formal logic (be it syllogistics, or the logic of propositions, or the logic of predicates) come to the front place of formal logical computation. Without the calculative properties of the concept, there would be no calculative properties of propositions which express the thought (thought structures). The calculative properties of a concept include the (1) degree of its logical generality (degree of variability), the (2) logical relations it can establish within the whole of the conceptual content, the (3) operability of the concept in structure of affirmation and negation, the (4) deducibility of either axiomatic or probabilistic systems. Therefore, I believe that, from the logical point of view, the definition of a concept should be applied in favor of its calculative properties that it possesses.

Author Profiling in Informal and Formal Language Scenarios Via Transfer Learning

The interest in author profiling tasks has increased in the research community because computer applications have shown success in different sectors such as security, marketing, healthcare, and others. Recognition and identification of traits such as gender, age or location based on text data can help to improve different marketing strategies. This type of technology has been widely discussed regarding documents taken from social media. However, its methods have been poorly studied using data with a more formal structure, where there is no access to emoticons, mentions, and other linguistic phenomena that are only present in social media. This paper proposes the use of recurrent and convolutional neural networks and a transfer learning strategy to recognize two demographic traits, i.e., gender and language variety, in documents written in informal and formal language. The models were tested in two different databases consisting of tweets (informal) and call-center conversations (formal). Accuracies of up to 75 % and 68 % were achieved in the recognition of gender in documents with informal and formal language, respectively. Moreover, regarding language variety recognition, accuracies of 92 % and 72 % were obtained in informal and formal text scenarios, respectively. The results indicate that, in relation to the traits considered in this paper, it is possible to transfer the knowledge from a system trained on a specific type of expressions to another one where the structure is completely different and data are scarcer.

Inter-subject Correlation While Listening to Minimalist Music: A Study of Electrophysiological and Behavioral Responses to Steve Reich's Piano Phase

Musical minimalism utilizes the temporal manipulation of restricted collections of rhythmic, melodic, and/or harmonic materials. One example, Steve Reich's Piano Phase, offers listeners readily audible formal structure with unpredictable events at the local level. For example, pattern recurrences may generate strong expectations which are violated by small temporal and pitch deviations. A hyper-detailed listening strategy prompted by these minute deviations stands in contrast to the type of listening engagement typically cultivated around functional tonal Western music. Recent research has suggested that the inter-subject correlation (ISC) of electroencephalographic (EEG) responses to natural audio-visual stimuli objectively indexes a state of “engagement,” demonstrating the potential of this approach for analyzing music listening. But can ISCs capture engagement with minimalist music, which features less obvious expectation formation and has historically received a wide range of reactions? To approach this question, we collected EEG and continuous behavioral (CB) data while 30 adults listened to an excerpt from Steve Reich's Piano Phase, as well as three controlled manipulations and a popular-music remix of the work. Our analyses reveal that EEG and CB ISC are highest for the remix stimulus and lowest for our most repetitive manipulation, no statistical differences in overall EEG ISC between our most musically meaningful manipulations and Reich's original piece, and evidence that compositional features drove engagement in time-resolved ISC analyses. We also found that aesthetic evaluations corresponded well with overall EEG ISC. Finally we highlight co-occurrences between stimulus events and time-resolved EEG and CB ISC. We offer the CB paradigm as a useful analysis measure and note the value of minimalist compositions as a limit case for the neuroscientific study of music listening. Overall, our participants' neural, continuous behavioral, and question responses showed strong similarities that may help refine our understanding of the type of engagement indexed by ISC for musical stimuli.

Testing Grounds and Launching Pads: Situating the Artist-Run Space Today

<p>My research is concerned with the formation of artists as creative subjects in an increasingly neoliberalised art world. This study examines to what extent does the artist-run space offer alternatives to current neoliberal orthodoxy in the art world. There has been little research to understand the lived experiences of emerging visual artists within neoliberalism. The thesis is located in museum studies but stretches beyond this field in an interdisciplinary approach to explore the complexity of what it means to both make art and self-organise. The thesis presents multiple case-study research into three New Zealand artist-run spaces; RM, Enjoy Contemporary Art Space and Meanwhile. Qualitative research brings the experiences of artist-run space participants to the fore through interviews, examining how they understand and articulate their involvement, negotiate tensions over power, and position themselves in an art world that seeks to enfold them in its own narratives. I analyse and discuss the findings through a series of connecting theoretical frameworks—assemblage theory, creative labour and governmentality—which together map the distinct practices that shape, and reshape, the artist-run space. My research contributes to literature on creative workers within neoliberalism, providing new knowledge about tactics and strategies deployed by emerging visual artists to carve space for their activities on their own terms. The thesis argues that while artist-run spaces are embedded in the mainstream through both networks of strategic reciprocity and funding imperatives, the nuances which define an individual artist-run space are both broader and messier than their increasingly formal structure suggests. The identity formation of the artists and creative workers whose hard work and passion keep artist-run spaces going is similarly compromised, confounding simplistic readings. I propose that the notion of ‘alternative’ is too binary an understanding to describe artist-run spaces within a time of neoliberalism, instead, this thesis seeks to complicate and problematise the term.</p>

Testing Grounds and Launching Pads: Situating the Artist-Run Space Today

<p>My research is concerned with the formation of artists as creative subjects in an increasingly neoliberalised art world. This study examines to what extent does the artist-run space offer alternatives to current neoliberal orthodoxy in the art world. There has been little research to understand the lived experiences of emerging visual artists within neoliberalism. The thesis is located in museum studies but stretches beyond this field in an interdisciplinary approach to explore the complexity of what it means to both make art and self-organise. The thesis presents multiple case-study research into three New Zealand artist-run spaces; RM, Enjoy Contemporary Art Space and Meanwhile. Qualitative research brings the experiences of artist-run space participants to the fore through interviews, examining how they understand and articulate their involvement, negotiate tensions over power, and position themselves in an art world that seeks to enfold them in its own narratives. I analyse and discuss the findings through a series of connecting theoretical frameworks—assemblage theory, creative labour and governmentality—which together map the distinct practices that shape, and reshape, the artist-run space. My research contributes to literature on creative workers within neoliberalism, providing new knowledge about tactics and strategies deployed by emerging visual artists to carve space for their activities on their own terms. The thesis argues that while artist-run spaces are embedded in the mainstream through both networks of strategic reciprocity and funding imperatives, the nuances which define an individual artist-run space are both broader and messier than their increasingly formal structure suggests. The identity formation of the artists and creative workers whose hard work and passion keep artist-run spaces going is similarly compromised, confounding simplistic readings. I propose that the notion of ‘alternative’ is too binary an understanding to describe artist-run spaces within a time of neoliberalism, instead, this thesis seeks to complicate and problematise the term.</p>