In the Platonic conception of being and becoming, the being of a given entity corresponds to its unchanging existence in the world of forms. Meanwhile, the becoming of a given entity occurs in our material reality. The latter identification and conceptualization of becoming in the material world is intrinsic in the Heracletian scheme, which identifies the world as being in constant flux. Now, if we were to synthesize this idea of the universe being in constant change with the concept of infinitesimals that was later developed by Zeno of Elea and featured in his paradoxes, we could posit a framework wherein the universe is said to be made up of infinite frames of time (infinitesimals) that represent change, akin to that of a movie reel, wherein change occurs through the progression of frames in the reel, however in such an example, the number of frames are finite across a finite period of time, while in the framework I am positing, the number of frames are infinite, albeit still within a finite period of time - I am assuming that the universe will not exist for an eternal duration of time. This framework inherently assigns primacy to becoming, as opposed to being. However, I will soon inspect the concept of being as it applies to this framework.
Being could be understood as something that is at the core of a given entity and is merely subject to change over time - becoming - or not subject to change at all. This is fundamentally opposed to Plato’s conception of being as transcendent, and applicable only to the ultimate and true reality that is the world of forms. This conceptualization of being as something that is immanent in this postulated framework runs contrary to Plato’s framework. This also very evidently comes into conflict with Heraclitus’s idea that the fundamental nature of reality is that of change, which correlates to an implied rejection of being, or at least a heavy subordination of being to becoming. A discussion of change necessitates consideration of the concept of time, along with potential branching ideas therein.
The flow of time in the world can be quantified as occurring within an infinitesimal number of periods of time, for even within a second there are an infinite possible number of divisions in time that can be drawn. Time of course is a measure of change in this instance, which represents the “becoming” of an entity. If each of the infinitesimal frames of time that exist were to be considered individually in isolation, as opposed to being representative of change, then we could consider the existence of an infinite number of distinct realities, each consisting of all of the entities in the world, each with their own unique “being” in each distinct reality that exists within each infinitesimal frame. This is what I am proposing in the framework that I am now postulating and will soon deconstruct. I believe that the conclusions of my deconstruction will lead to profitable insights and questions into the fundamental nature of change itself.
For a given infinitesimal period of time in isolation there can be said to be a specific unchanging nature that exists in all things in that isolated infinitesimal period, for within this period alone, no change could occur; change would only be present across multiple infinitesimal frames. The nature in question, which I described as unchanging within the context of an infinitesimal period of time in isolation, could be said to be the being of an entity. Without any change within this infinitesimal frame, the being of the entity cannot undergo any change, and can thus be defined as unchanging in each frame independent from other frames.
If it is the case that there are infinite frames of time in which an entity occupies a certain static being, this raises the question: how can the entity change in being between frames if it is the change in frames themselves that consists of the change in the being of the entity? This question relates to an issue that is intrinsic in this framework, that being: the fact that an infinitesimal change between two values would only make sense as being zero, for if they were non-zero values, then they would sum to infinity, for it would be an infinite number of non-zero values that are part of the summation, and the summation of an infinite number of non-zero values would be infinity. However, mathematically, this may not inherently be the case, although my approach to this is not inherently mathematical, but is more so philosophical, and I am treating infinity more as a concept than mathematics, albeit mathematics very much treats it conceptually, for it is ultimately a concept, but my treatment is even more conceptual. Because of this, I will move forward with the concept that no change occurs between infinitesimals, which contradicts the established pillar that the period of time considered is finite. Thus, the change between each infinitesimal composing a finite space has to have a value of 0. It can then seemingly be concluded that no change at all is occurring between the infinitesimal values. Thus, to maintain this framework would essentially require the declaration of all change to be illusory, which makes reality pure being, and eliminates all becoming, for change, and thereby becoming, would be illusory. This, of course is a complete 180 from where we started, for therein we identified the universe as pure change, but now we identify the universe as pure being, and void of real change.
In this postulated framework I have evidently identified two paradoxes. The first of which is the fact that change must occur between these frames, yet change is composed of these frames. The second of which is the fact that change between two infinitesimals is reducible to an absence of change. The second paradox provides a paradoxical answer to the first paradox, that being: that the change between the two frames is reducible to an absence of change, and thus there is no change between these infinitesimal frames. This answer is paradoxical in that it poses the same dilemma that the second paradox is rooted in, that being: we cannot identify any non-zero value of change between two infinitesimal frames of time.
While these seemingly unanswerable paradoxes pose issues to this postulated framework, the issues do not exist here alone. The second paradox poses a problem to the very nature of change itself in the face of infinite division. If a given change in a given thing could be quantified and reduced into infinitesimals, then the concept of change as we know it would appear to be fundamentally paradoxical. The concept of infinitesimals is very troublesome and paradoxical.
Thank you for reading,
- Eli Gardenswartz
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