Paradoxes Of Infinity Research Articles

Bias in Numbers Part 3: Paradoxes of Infinity, 0 as Infinitesimal and the Logic of Superposition

Bias in Numbers Part 3: Paradoxes of Infinity, 0 as Infinitesimal and the Logic of Superposition

Fluids, Molecules and Paradoxes of Infinity

Several paradoxes of infinity have recently featured in this journal involving gases distributed in a denumerable infinite series of compartments. I shall demonstrate in this paper that:a) None of these new paradoxes applies where the gases comply with both Boyle’s law and Avogadro’s law. As several of these new paradoxes expressly require compliance with Boyle’s law, it is unclear, in principle, as to whether there is a plausible model of gas that is able to uphold them all.b) Notwithstanding a), any of the above paradoxes (and their variations) can be reinstated by acknowledging (contrary to what is widely assumed in the literature) that there are two distinct, non-equivalent concepts of ideal gas. Indeed, the various infinity puzzles actually enable a distinction to be made between the two concepts (which is a particularly elegant way of doing so).

A Note on some New Infinity Puzzles

In this short note I argue that, using the type of configurations put forward in a recent paper by Laraudogoitia in this same journal, new paradoxes of infinity of a completely different nature can be formulated.

Paradoxes Of Infinity And Foundations Of Transpersonal Psychology

Transpersonal psychology’s uniqueness comes from the point of infinity of the psyche, as the subject of the field. Jung being one of the predecessors of transpersonal psychology confirms the infinity of the psyche very clearly. But this has created another problem. What are the borders of the subject if it is infinite? And if psyche is infinite, how can we grasp it as whole? Can it be fully cognized? Or to give the opposite point of view, is it unknowable? In the search for the borders of the subject of transpersonal psychology, we are attempting to reflect on the paradoxes of infinity. As it turns out, the concept of “actual infinity” (opened by Georg Cantor in the late 19th century) allow us to create a new perspective in solving the infinity problems in psychology. The question arises that if the psyche is infinite, can the psyche be cognized? The idea of psyche being actually infinite allows us to resolve the issue of cognizability of the psyche in principle. This issue is whether a possibility exists for a person to complete the process of self-exploration. Such a solution may lay a new foundation for Transpersonal Psychology on a non-classical scientific basis. KEYWORDS Infinity, transpersonal psychology, self-exploration, enlightenment, perfection, unknowability, knowability,cognizability

Paradoxes of infinity and self-applications, I

Spinoza conceives infinity as all-inclusiveness with respect to a certain kind (genere). Thus, a limited extended region is finite by virtue of other ex? tended regions not included in it, but extension as such is infinite because there is nothing extended outside it. Moreover, according to him, infinity does not mean the containing of many items or being divisible ad infini tum. We should think of it as the organizing principle of an all-compre? hending system, where the principle is identified with the system itself. In modern terminology one could say that Spinoza characterizes infinity not in terms of cardinality (i.e., numerical quantity), but as a closure prop? erty the exhaustion of its kind (suo genere). Although today "infinite" brings to mind, iirst and foremost, a numerical concept, Spinoza's usage fits well certain fundamental intuitions. Certain philosophical puzzles that have come to play a central role result from attempts to conceive all ex? haustive closed systems, or to "close up" given systems in certain direc? tions. The "closing up" tendency appears to be a basic element of human thought and, in particular, it is manifested in mathematics, where thought is, in a sense, given free reign. I shall discuss paradoxes of two categories: Those that (for want of a better name) I shall ref?r to as logical paradoxes include the classical cases of set-theoretic and semantic paradoxes (Russell, Burali-Forti, Berry, the Liar etc). The others are what I shall call epistemic Gedankenexperiments; in these a rational judgement, or decision, is demanded of someone under certain hypothetical, but presumably concrete, conditions. An example of this kind is Newcomb's paradox, another is a puzzle suggested to me by Gideon Schwarz (both will be analyzed later, but for reasons of length the analysis of Newcomb's paradox is postponed to part II). The obvious differences between the two kinds notwithstanding, they share the same

Optimal Savings with Finite Planning Horizon

OPTIMAL SAVINGS programs for a nation have been discussed in the economic literature with an infinite time horizon in view. We may mention in particular the pioneering work of Ramsey on this question2. This approach is logical beeause without explicitly introducing uncertainty it is not possible, on the national plane, to choose a particular cut-off point and at the same time avoid being arbitrary. For individuals, there is only a span of life, but a nation's life may reasonably be assumed to extend indefinitely in time. The problem is that unless we introduce some crucial boundedness assumption (explicitly or implicitly) at some stage of the argument, infinite programs give rise to conceptual difficulties which may be briefly described as paradoxes of infinity.3 Examples of such boundedness assumptions are Ramsey's use of the concept of a finite bliss, defined as a maximum conceivable state of satisfaction attained for a level of consumption, or the common practice of using a pure rate of time preference in discounting future satisfaction. Neither of these assumptions is entirely unobjectionable.