This article considers distinct ways of understanding the world, referred to in psychology as functions of consciousness or as cognitive modes, having as the scope of interest epistemology and natural sciences. Inspired by C.G. Jung’s simile of the spectrum, we consider three basic cognitive modes associated to: (R) embodied instinct, experience, and action; (G) reality perception and learning; and (B) concept abstraction, rational thinking, and language. RGB stand for the primary colors: red, green, and blue. Accordingly, a conceptual map between (...) cognitive modes and primary and secondary colors is built based on the physics and physiology of color perception and epistemological characteristics of the aforementioned cognitive modes, leading to logical relations structured as an hexagon of opposition. Finally, this model of cognitive modes is applied to the analysis and interpretation of some important episodes in the historical development of physics and technology. (shrink)

This article considers distinct ways of understanding the world, referred to in psychology as Functions of Consciousness or as Cognitive Modes, having as the scope of interest epistemology and natural sciences. Inspired by C.G. Jung's Simile of the Spectrum, we consider three basic cognitive modes associated to: (R) embodied instinct, experience, and action; (G) reality perception and learning; and (B) concept abstraction, rational thinking, and language. RGB stand for the primary colors: red, green, and blue. Accordingly, a conceptual map between (...) cognitive modes and primary and secondary colors is built based on the physics and physiology of color perception and epistemological characteristics of the aforementioned cognitive modes, leading to logical relations structured as an Hexagon of Opposition. Finally, this model of cognitive modes is applied to the analysis and interpretation of some important episodes in the historical development of physics and technology. (shrink)

Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for these modalities to be logically (...) consistent. Prisms composed of hexagons of oppositions show how the credal modalities obtained from two agnostic tests vary according to their threshold values. Nested hexagons of oppositions summarize logical relations between the credal modalities in these tests and prove new relations. (shrink)

This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise hypotheses. These pragmatic (...) versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais. (shrink)

Following the speech act theory, we take hypotheses and assertions as linguistic acts with different illocutionary forces. We assume that a hypothesis is justified if there is at least a scintilla of evidence for the truth of its propositional content, while an assertion is justified when there is conclusive evidence that its propositional content is true. Here we extend the logical treatment for assertions given by Dalla Pozza and Garola by outlining a pragmatic logic for assertions and hypotheses. On the (...) basis of this extension we analyse the standard logical opposition relations for assertions and hypotheses. We formulate a pragmatic square of oppositions for assertions and a hexagon of oppositions for hypotheses. Finally, we give a mixed hexagon of oppositions to point out the opposition relations for assertions and hypotheses. (shrink)

The paper proposes two logical analyses of (the norms of) justification. In a first, realist-minded case, truth is logically independent from justification and leads to a pragmatic logic LP including two epistemic and pragmatic operators, namely, assertion and hypothesis. In a second, antirealist-minded case, truth is not logically independent from justification and results in two logical systems of information and justification: AR4 and AR4¢, respectively, provided with a question-answer semantics. The latter proposes many more epistemic agents, each corresponding to a (...) wide variety of epistemic norms. After comparing the different norms of justification involved in these logical systems, two hexagons expressing Aristotelian relations of opposition will be gathered in order to clarify how (a fragment of) pragmatic formulas can be interpreted in a fuzzy-based question-answer semantics. (shrink)

We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds of (...) import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle’s system appears then as a fragment of a broader system which can be developed by using FOL. (shrink)

Nanoparticles can also be used as catalysts due to their high surface area. Of course, catalytic properties also occur in certain dimensions like magnetic properties. In other words, nanoparticles usually have catalytic properties if their specific surface is between 100 and 400 square meters per gram. Therefore, among nanoparticles with a specific volume, a nanoparticle with a larger surface area shows better catalytic properties. An example of nanoparticles that act as catalysts where various substances are placed on their surface and (...) chemical reactions are carried out. Apart from the mentioned cases, nanoparticles have many other applications in various medical industries (drug delivery, etc.), automobiles (anti-fogging windows, lightening the body, strengthening tires), electronics (making transistors), etc. The strength of carbon-carbon bonds gives carbon nanotubes amazing electronic properties. No previous material exhibits the extraordinary combination of mechanical, thermal and electronic properties attributed to them . However, their conductivity is what sets them apart. Multi-layered carbon nanotubes are the strongest materials that mankind has discovered so far in terms of electronic conductivity. The highest tensile strength or breaking strain for a carbon nanotube was up to 63 GPa, which is about 50 times more than the strongest conductors. Even the weakest types of multi-layered carbon nanotubes have multifold power in electronic conduction. These properties, along with the lightness of carbon nanotubes, give them great potential in applications such as aerospace. The electronic properties of the wall of carbon nanotubes are also extraordinary. It has high electrical conductivity (comparable to copper). It is particularly noteworthy that nanotubes can be metallic or semiconducting. The rolling action breaks the symmetry of the planar system and imposes a specific direction with respect to the hexagonal grid and the axial direction. Depending on the relationship between these axial directions and the unit vectors that describe the hexagonal lattice, nanotubes may behave electrically like metals or semiconductors , with some nanotubes having higher conductivity than copper, while Others behave more like silicon . And there are possibilities of making nano electronic devices from multi-layer nanotubes of CNTs. (shrink)

The gender spectrum, a continuum ranging from “male” to “female,” is a huge improvement over the traditional binary model, according to which one can be either one or the other, and no degrees are allowed. However, the model still suffers from some inadequacies, most notably the inability to represent other genders and agender identities. This is accounted for in the new “spectral” models of gender, which use independent scales to measure the degree to which a person identifies with a given (...) gender category. However, by conceiving the amounts on gender dimensions to be mutually independent, these models invite other difficulties, most notably the inability to account for agender identities in a straightforward fashion. In this paper, I argue that a way to solve the problems with the new models (and not to have the old problems re-appear) is to take a step back, of sorts, towards the initial gender spectrum. I explore from a perspective of philosophical logic the types of relations among gender categories in the spectral models of gender and argue that the initial spectrum construes gender categories to be in the logical opposition of “fuzzy contradiction,” while the models with more than one spectrum do not construe gender categories to be in any kind of logical opposition. I propose a weaker opposition (namely, “fuzzy contrariety”) between gender categories, as well as the “fuzzy gender hexagon”—an application of a particular abstract logical diagram to gender terms—as a model of gender identity. (shrink)

The aim of this paper is to elucidate the relationship between Aristotelian conceptual oppositions, commutative diagrams of relational structures, and Galois connections.This is done by investigating in detail some examples of Aristotelian conceptual oppositions arising from topological spaces and similarity structures. The main technical device for this endeavor is the notion of Galois connections of order structures.