Exploring Infinity: Paradoxes, Philosophical Implications, and the Principle of Sufficient Reason

There are a number of problems and paradoxes one might a arrive at when contemplating the notion of infinity. Problems that have been amply agknowledged by the first philosophers and used to justify further conclusions. When engaging in thought about infinity one might arrive at some of these paradoxes, for example, thinking about the distance from point A to point B, what would happen if I were to each time walk exactly half the distance? Surely I would be walking infinitely and never reach point B because there would always be half the distance left. Does that mean motion is an illusion, that we dont actually move? Or, if I were to grab a piece of matter, and divide it by half each time, there would always be half of the whole that I cut, and in this sense one could go on indefinitely. Does this mean that everything only appears limited but is actually infinite? But if everything is infinite there can be no motion, for how can things with equal dimensions move in each other, one has to be smaller and the other greater. Further, something cannot come out of nothing for that would be contradictory. Now being comes out of non-being as, for example, when hot water cools, something which was not before, is. Therefore the world of the senses must be false and illusory.

Now, the solution to this is denying that the instance of cold is being, and affirming it as non-being. And that any being coming into existence is brought into it by being. Things which dissipate according to the principle of entropy characterize a loss of being, thus cold is but a loss of heat. In this sense, the things Parmenides would point to as examples of being coming from non-being, which is absurd, are actually being ceasing to be, which is amply observed in reality. The position of dualism in that it affirms the ontological subsistence of evil, ultimately leads to this absurd and contradictory point. Now one might ask, why is it that being coming out of non-being is absurd but not the converse, as non-being coming out of being? Well, that would certainly make sense to say of an absolute being, which is unlimited and wholly actual, but of a limited, partly potential, means that it is not its own source of being, and therefore is subject to dissipation and decay.

It is also an account that contradicts
empirical experience, this is a problem because it allows for one to arrive at different conclusions through different methodologies, namely through sense experience. Now what would happen when we try to give an account that is rationaly valid and does not contradict the sensory realm or takes it to be false? It would certainly be more inclusive, cohesive, coherent and have more explanatory power, as it allows for interdependent cross-confirmation. This is the hylomorphic account. And it begins by making a simple distinction in the starting problem. That is, between actual infinities and potential infinities. According to this account, there can be no instances of actual infinities in empirical, material reality. But only potential, which can be actualized by something already actual. In other words a distance or a piece of matter can only be divided up to the degree that we develop instruments that have the actual capacity for greater and greater precision in measurement. The numbers will rise, but will never reach infinity, because infinity by definition is unreachable. In effect, this illustrates a causal relation that accounts for infinity and sensory experience; and from this, one can exetend this scheme of act and potency, in due order, to all other things in the world tracing the notion of universal conditioning (that all happenings are causaly related according to a principle called the principle of sufficient reason[[Principle of Sufficient Reason]]). Thus, something that is flammable (has a potency to be on fire) can be set on fire by an actual fire or something that is actually hot. Like a candle and a lit match.

All of this gives us the ability to reason
through causal chains of acts and potencies. But not only that, it also leads to the conclusion that causes cannot regress infinitely since there can be no actual infinities in observable phenomena and that just as any effect terminates at its cause and causal chains cannot be unlimited lest it precludes the very conditions under which a thing can come into existence, so there must be an ultimate cause which, as per the principle of non-contradiction, must be purely actual, not potential and actual in the same respect. In other words the beginning to something gives its ontological grounding so that, without the first link there can be no final link and that thing cannot be, not because it doesn’t end, but because it never started in the first place. The ultimate first link to all chains would then be the first cause, uncaused, for it is purely actual.