Aristotle axiomatically divides the 28 syllogisms of necessity of Anal, prior. I 9-11 into two classes: those with a necessary conclusion and those with a non-necessary conclusion. The fact that Aristotle axiomatically comprehends only 24 syllogisms of necessity, however, raises two questions: 1. What method does he use to decide about the remaining four syllogisms? 2. Is this method consistent with the initial one? This essay pursues the answers to these questions first by means of semantic analysis, showing that Aristotle (...) ultimately considers assertoric propositions to be possible and therewith non-necessary propositions. Aristotle employs this approach, developed within the axiomatic, to the four syllogisms in question, thereby integrating them into the axiomatic. Finally, this essay answers the question of consistency by way of a formalization of the syllogisms of necessity. (shrink)

Aristotle axiomatically divides the 28 syllogisms of necessity of Anal, prior. I 9-11 into two classes: those with a necessary conclusion and those with a non-necessary conclusion. The fact that Aristotle axiomatically comprehends only 24 syllogisms of necessity, however, raises two questions: 1. What method does he use to decide about the remaining four syllogisms? 2. Is this method consistent with the initial one? This essay pursues the answers to these questions first by means of semantic analysis, showing that Aristotle (...) ultimately considers assertoric propositions to be possible and therewith non-necessary propositions. Aristotle employs this approach, developed within the axiomatic, to the four syllogisms in question, thereby integrating them into the axiomatic. Finally, this essay answers the question of consistency by way of a formalization of the syllogisms of necessity. (shrink)

This study gives an arithmetic calculus to determine tautologies, contradictions and satisfiable formulas of the first order logic. The presented calculus may easily be extended on modal and deontic logic. The mathematical foundation of this arithmetic calculus is a Boolean ring.

Summary This study continues in calculating formulas of the first order logic. Whereas the preceding part delt with monadic predicates, the present part treats polyadic predicates. The presumptions were supplied analogously.

The goal of this paper is an interpretation of Aristotle's modal syllogistics closely oriented on the text using the resources of modern modal predicate logic. Modern predicate logic was successfully able to interpret Aristotle's assertoric syllogistics uniformly , that is, with one formula for universal premises. A corresponding uniform interpretation of modal syllogistics by means of modal predicate logic is not possible. This thesis does not imply that a uniform view is abandoned. However, it replaces the simple unity of the (...) assertoric by the complex unity of the modal. The complexity results from the fact that though one formula for universal premises is used as the basis, it must be moderated if the text requires . Aristotle introduces his modal syllogistics by expanding his assertoric syllogistics with an axiom that links two apodictic premises to yield a single apodictic sentence . He thus defines a regular modern modal logic. By means of the regular modal logic that is thus defined, he is able to reduce the purely apodictic syllogistics to assertoric syllogistics. However, he goes beyond this simple structure when he looks at complicated inferences. In order to be able to link not only premises of the same modality, but also premises with different modalities, he introduces a second axiom, the T-axiom, which infers from necessity to reality or - equivalently - from reality to possibility. Together, the two axioms, the axiom of regularity and the T-axiom, define a regular T-logic. It plays an important role in modern logic. In order to be able to account for modal syllogistics adequately as a whole, another modern axiom is also required, the so-called B-axiom. It is very difficult to decide whether Aristotle had the B-axiom. The two last named axioms are sufficient to achieve the required contextual moderation of the basic formula for universal propositions. (shrink)

On the unity of modal syllogistics in Aristotle. The goal of this paper is an interpretation of Aristotle’s modal syllogistics closely oriented on the text using the resources of modern modal predicate logic. Modern predicate logic was successfully able to interpret Aristotle’s assertoric syllogistics uniformly, that is, with one formula for universal premises. A corresponding uniform interpretation of modal syllogistics by means of modal predicate logic is not possible. This thesis does not imply that a uniform view is abandoned. However, (...) it replaces the simple unity of the assertoric by the complex unity of the modal. The complexity results from the fact that though one formula for universal premises is used as the basis, it must be moderated if the text requires.Aristotle introduces his modal syllogistics by expanding his assertoric syllogistics with an axiom that links two apodictic premises to yield a single apodictic sentence. He thus defines a regular modern modal logic. By means of the regular modal logic that is thus defined, he is able to reduce the purely apodictic syllogistics to assertoric syllogistics. However, he goes beyond this simple structure when he looks at complicated inferences.In order to be able to link not only premises of the same modality, but also premises with different modalities, he introduces a second axiom, the T-axiom, which infers from necessity to reality or – equivalently – from reality to possibility. Together, the two axioms, the axiom of regularity and the T-axiom, define a regular T-logic. It plays an important role in modern logic. In order to be able to account for modal syllogistics adequately as a whole, another modern axiom is also required, the so-called B-axiom. It is very difficult to decide whether Aristotle had the B-axiom. Each of the two last named axioms is sufficient to achieve the required contextual moderation of the basic formula for universal propositions. (shrink)

Critical reasoning (CR) when confronted with contradictory information from multiple sources is a crucial ability in a knowledge-based society and digital world. Using information without critically reflecting on the content and its quality may lead to the acceptance of information based on unwarranted claims. Previous personal beliefs are assumed to play a decisive role when it comes to critically differentiating between assertions and claims and warranted knowledge and facts. The role of generic epistemic beliefs on critical stance and attitude in (...) reflectively dealing with information is well researched. Relatively few studies have been conducted on the influence of domain-specific beliefs, i.e. beliefs in relation to specific content encountered in a piece of information or task, on the reasoning process, and on how these beliefs may affect the information-processing and decision-making processes. This study focuses on students’ task- and topic-related beliefs that may influence their reasoning when dealing with multiple and partly contradictory sources of information. To validly assess CR among university students, we used a newly developed computer-based performance assessment in which the students were confronted with an authentic task which contains theoretically defined psychological stimuli for measuring CR. To investigate the particular role of task- and topic-related beliefs on CR, a purposeful sample of 30 university students took part in a performance assessment and then were interviewed immediately afterwards. In the semi-structured cognitive interviews, the participants’ task-related beliefs were assessed. Based on qualitative analyses of the interview transcripts, three distinct profiles of decision-making among students have been identified. More specifically, the different types of students’ beliefs and attitudes derived from the cognitive interview data suggest their influence on information processing, reasoning approaches and decision-making. The results indicated that the students’ beliefs had an influence on their selection, critical evaluation and use of information as well as on their reasoning processes and final decisions. (shrink)

The pull to coordinate with other individuals is fundamental, serving as the basis for our social connectedness to others. Discussed is a dynamical and ecological perspective to joint action, an approach that embeds the individual’s mind in a body and the body in a niche, a physical and social environment. Research on uninstructed coordination of simple incidental rhythmic movement, along with research on goal‐directed, embodied cooperation, is reviewed. Finally, recent research is discussed that extends the coordination and cooperation studies, examining (...) how synchronizing with another, and how emergent social units of perceiving and acting are reflected in people’s feelings of connection to others. (shrink)

Faces are complex stimuli that can be described via intuitive facial features like the eyes, nose, and mouth, “configural” features like the distances between facial landmarks, and features that correspond to computations performed in the early visual system (e.g. oriented edges). With regard to this latter category of descriptors, adult face recognition relies disproportionately on information in specific spatial frequency and orientation bands: Many recognition tasks are performed more accurately when adults have access to mid-range spatial frequencies (8-16 cycles/face) and (...) horizontal orientations (Dakin & Watt, 2009). In the current study, we examined how this information bias develops in middle childhood. We recruited children between the ages of 5-10 years old to participate in a simple categorization task that required them to label images according to whether they depicted a face or a house. Critically, children were presented with face and house images comprised either of primarily horizontal orientation energy, primarily vertical orientation energy, or both horizontal and vertical orientation energy. We predicted that any bias favoring horizontal information over vertical should be more evident in faces than in houses, and also that older children would be more likely to show such a bias than younger children. We designed our categorization task to be sufficiently easy that children would perform at near-ceiling accuracy levels, but with variation in response times that would reflect how they rely on different orientations as a function of age and object category. We found that horizontal bias for face detection (but not house detection) correlated significantly with age, suggesting an emergent category-specific bias for horizontal orientation energy that develops during middle childhood. These results thus suggest that the tuning of high-level recognition to specific low-level visual features takes take place over several years of visual development. (shrink)