Dialectical monism in Aztec philosophy

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It is worth mentioning a form of dialectical monism in the ancient Aztec philosophy and especially in the concept of ” Teotl “, which is at the center of Aztec metaphysics and cosmology. Teotl is the expression of an endless alternation of continuous and cyclical oscillation between opposite poles. Teotl is thus characterized by a dual prominent structure, which results from the union of opposites , themselves characterized by complementarity. The dual pairs involved include : the masculine and the feminine, dark and light, order and disorder, hot and cold, life and death, being and non-being etc. The interdependence and higher union of the principles of life and death in Teotl, for example, was represented by Aztec artists of Tlatilco and Oaxaca in masks where one half is alive while the other half died, revealing the skull bones.

Reference: James Maffie, Aztec Philosophy, Internet Encyclopedia of Philosophy

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Viewpoint of a pole

Fig3Let us define the concept of point of view related to a given pole of an A/Ā duality: we get then, for example (at the level of the extension/restriction duality) the standpoint by extension, as well as the viewpoint by restriction. Similarly, the qualitative viewpoint or perspective results from it, as well as the quantitative point of view, etc.. (at the level of the qualitative/quantitative duality). Thus, when considering a given object o (either a concrete or an abstract object such as a proposition or a reasoning), we may consider it in relation to various dualities, and at the level of the latter, relative to each of its two dual poles.

The underlying idea inherent to the viewpoint relative to a given duality, or to a given pole of a duality, is that each of the two poles of the same duality, all things being equal, deserve an equal legitimacy. In this sense, if we consider an object o in terms of a duality A/Ā, one should not favour one of the poles with respect to the other. To obtain an objective point of view with respect to a given duality A/Ā, one should place oneself in turn from the perspective of the pole A, and then from that of the pole Ā. For an approach that would only address the viewpoint of one of the two poles would prove to be partial and truncated. The fact of considering in turn the perspective of the two poles, in the study of an object o and of its associated reference class allows to avoid a subjective approach and to meet as much as possible the needs of objectivity.

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Principle of dialectical indifference

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(Illustration from Wikimedia commons)

(PRINCIPLE OF DIALECTICAL INDIFFERENCE) When considering a given object o and the reference class E associated with it, from the angle of duality A/Ā, all things being equal, it should be given equal weight to the viewpoint of the A pole and the viewpoint of the Ā pole.

The principle of dialectical indifference can be enunciated as follows: if we consider an object o under the angle of a given A/Ā duality, there is no reason to favour the viewpoint from A with regard to the viewpoint from Ā, and unless otherwise resulting from the context, we must weigh equally the viewpoints A and Ā. A direct consequence of this principle is that if one considers the perspective of the A pole, one also needs to take into consideration the standpoint of the opposite pole Ā (and vice versa). The need to consider both points of view, the one resulting from the A pole and the other associated with the Ā pole, meets the need of analysing the object o and the reference class associated with it from an objective point of view. This goal is achieved, as far as possible, by taking into account the complementary points of view which are those of the poles A and Ā. Each of these viewpoints has indeed, with regard to a given duality A/Ā, an equal relevance. Under such circumstances, when only the A pole or (exclusively) the pole Ā is considered, it consists then of a one-sided perspective. Conversely, the viewpoint which results from the synthesis of the standpoints corresponding to both poles A and Ā is of a two-sided type. Basically, this approach proves to be dialectical in essence. In effect, the step consisting of successively analysing the complementary views relative to a given reference class, is intended to allow, in a subsequent step, a final synthesis, which results from the joint consideration of the viewpoints corresponding to both poles A and Ā. In the present construction, the process of confronting the different perspectives relevant to an A/Ā duality is intended to build cumulatively, a more objective and comprehensive standpoint than the one, necessarily partial, resulting from taking into account those data that stem from only one of the two poles.

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A Polar Concept Argument for the Existence of Abstracta

Preprint. In this paper, I present a polar concept argument for the existence of abstract objects. After recalling the fundamentals of the debate about the existence of abstracta, I present in a detailed way the argument for the existence of abstracta. I offer two different variations of the argument: one, deductive and the other, inductive. The argument rests primarily on the fact that our universe is well-balanced. This well-balanced property results from the fact that all instantiable polar dualities are instantiated. Hence, the abstract pole of the abstract/concrete duality must also be exemplified. Lastly, I review several objections that can be raised against the present argument.

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A Polar Concept Argument for the Existence of Abstracta

There are several famous problems about abstract entities. One of them consists of whether there exist any abstract objects. A second issue is concerned with the definition of which sorts of entities are genuinely abstract. A third issue relates to whether the abstract/concrete duality is exhaustive or not. The purpose of this paper is to address the first of these issues and to describe a polar concept argument that entails the existence of abstracta. Before stating the argument in detail and reviewing several objections that can be raised against it, it is worth recalling preliminarily the fundamentals of the debate about the existence of abstracta.

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