Rationality and the World
While the rock may cause an immediate pain, reality seems to be ultimately infinite. Conceptually the universe can contain no end, although modern physical theory may say otherwise. For the monolith to exist, it is fundamental that there exists an expanse for which matter may repose. Infinity is a hard concept to grasp, perhaps even impossible for our minds, which is limited by its own structure. Also, it might be the case that infinity cannot exist because it cannot be easily conceived. If this is the case then it cannot be conceived therefore it must be thrown out because according to the dictum “if it can be conceived then it is possible”, since it cannot be conceived then it is not possible. Looking at it as a syllogism where implication is necessarily false when the antecedent is true, and the consequent is false. In this case if we claim that if it is conceivable then it is possible. If we find something conceivable but not possible then the implicature is false, does this apply in our example of finite space and matter?
What is the conception of the finite? Can it be said to exist conceptually as the dictum requires? While we can conceive of the finite as existing in itself, for example inside Aristotle’s Celestial Sphere, what lies beyond this sphere and how is it limited and therefore finite? If space is finite and space is bounded, then what must exist beyond the space that defines it? If it is bounded, we are thrown up again a never-ending wall of matter. Regarding space, can we try to think of something that goes on and on like an arrow thrown which travels outwards forever? Perhaps this can be understood but can it be conceived? Something that continues outward without end? Are there other options?
There seems to be four basic options underlying the nature of matter and space. Matter and Space can both be finite, matter and space can both be infinite, Matter can be infinite but spirit finite and lastly space can be infinite, but matter is finite. All formulations can be considered inconceivable and therefore not possible.
If we look at the supposition that both matter and space are finite this seems to contradict the dictum where if it is conceivable it is possible. In a finite universe it would be easy to conjecture that matter is finite, but how can it be accounted for that the universe is limited in some way? If the universe is not infinitely large, then what bounds the universe? It seems that the only thing that can bound the universe is infinite matter, or other mixes of matter and space.
Some physicists may claim that space is curved. While this may be someone understood with a new kind of thinking (can something like this be conceived?) it does seem to contradict the dictum as something that can be conceived. If one takes off on a journey through space one will (eventually) end up where they started. In this case space must be somehow limited in scope. When talking about infinity this does not seem possible. One might circle around space and end up where they started but it could not say all aspects of space are infinite because our traveler would invariably came back to the origin of their journey. What would it mean if our traveler continued to make this loop through space except as some sort of containment?
Such a thing that is inconceivable but possible could be the idea of curved space. While it is not conceivable modern mathematics shows that this is the case. Something can then can be inconceivable but still possible. If something is necessary then it exists in all possible worlds according to Leibniz. Something necessary is also possible.
Some things can be inconceivable not possible such as square circles or married bachelors. These analytics statement must be false when understanding language. Also water cannot be frozen at 70 degrees and lead is firm at 70 degrees.
If something is conceivable and therefore possible does not show that which is inconceivable is not possible. Our previous examples of curved space and married bachelors show that one is possible and the other is not. Therefore if it is conceivable only tells us what is possible, it does not tell anything about existence as being composed that which is inconceivable and what is possible. It is necessary to keep this narrow sense when examining the world. This idea is a sort of analytic analysis which veracity lies in the fact that something must be conceived in order to be possible. To conceive something implies that there is something that conceives. For example Descartes “I think therefore I am” is similar in the fact that to be something (to conceive) implies it is possible (may exist) although this approach.
Approaching knowledge in such a manner one needs to find if something is conceivable. If it is, then it is possible. An example can be arrived at by examining hypothetical statements with the goal is using this dictum to arrive at insight. In the following examples four possibilities are examined. First is the universe infinite but matter is finite. Also discussed is if the universe is finite but matter is infinite. Then the popular idea that the universe is infinite and matter is infinite.
This may not show much to the critical reader as it is almost common sense that the universe must be both infinite and matter is quite likely if no necessarily so to be infinite. The understanding of this idea is that foundationally nothing exists without space and nothing exists without matter. They are the minimum condition for existence. Our existence is predicated on these two constituents.
How about if matter is finite and the universe is infinite? First off there is the problem of understanding conceptually how the universe can be infinite. Also, as perplexing is how in an infinite universe can matter be finite? We see from the human perspective that matter and space are inexorably bound together. If matter is finite, then how are we and why do we have it hoarded in our parochial world? Also, this is inconceivable. If matter is indeed finite and the universe infinite, then ultimately at some point matter would dissolve into space and even cease to exist as dispersion approached infinity. There just would not be enough matter in space to go around. Even in an infinite degree is dispersement matter would seem to cease to exist at all. Matter that is necessarily a constituent part of space that then dissolves into space is inconceivable and therefore not possible.
Further what if matter is infinite and space is finite? Looking at matter in an infinite space, space would be filled and replaced by matter which ultimately too would be bounded by matter at its periphery and have matter expanding from the center infinitely. So it seems that matter cannot be finite.
Finally, what if matter is infinite and space is infinite. This perhaps looks the most promising of all the possibilities. In this formulation space makes adequate space for matter and matter find a uniform home. An Anthropocentric model can be avoided because there could be no center of the universe. But is infinite matter and infinite space conceivable? It might seem conceivable at first “glance” but is it? If the universe is uniform, then it is conceivable that infinite matter with infinite space is conceivable. Looking at matter and space in more detail and realizing that the variability in the possibilities of matter are infinite, then in infinity these material manifestations must manifest in infinity. Matter would not only vary in size, but in density, in magnitude, type (atomic variation), color, etc. When looked at microscopically the variation in size could be small, perhaps an inch, an atom or perhaps a quark. These variations in an infinite universe must occur infinitely large as well in all its particular characteristics. Since the possible variation in matter is infinite then it could not be replicated infinitely in an infinite universe. The case of infinite matter and infinite space then is beyond conception. Infinite space is not the problem, infinite matter is because the variation in matter seems infinite and cannot be replicated in infinite space. The variation would continue to be replicated both near and far, through possible other dimensions and other multiverses both of which too would exist infinitely. But perhaps like in mathematics, a series of numbers that approach infinity actually, do reach infinity. But is such a thing conceivable?
An argument might be made that universe is limited by physical laws and this would constrain the variety of variation that would occur; therefore, it could be said that the universe, with the constraining factors of the laws of nature could produce all of the variety that is possible. But if something is possible if it is conceivable, an unrestricted universe, in spite of natural laws would run up with problem of infinite variety compounding an infinite universe as was earlier said. The physical laws may be a constraint on variety, but such constraints are not limiting when one relies on the adage if it is conceivable it is possible which is not an empirical claim or something that is empirical in principle. Rather it is based on a rationalism.
Looking at the dictum, If it is conceivable it is possible” another objection might be that while if it is conceivable it is possible, can it be decided that if it is inconceivable is it impossible? Perhaps an infinite universe is such a place. While we cannot say that infinity is conceivable, although it may be claimed to be understandable, does that rule out a universe that is infinite? Are such things such as infinite universes, impossible to conceive, but can still exist? Previously the claim was to find what is possible, but the claim does not rule out all things that are beyond conception. Perhaps for example Einstein’s theory of relativity when light travel at the same rate from a source no matter what the movement of the source may be in relation to other objects. If it is true that something can be that is inconceivable and possible then our infinite universe might fit the bill. But this changes our requirements a bit for conceivability. While we can conceive of light as escaping from a point of reference at the same speed as from another point of reference, we cannot “understand” it, well at least I cannot. So, in this example such a thing is conceivable even though it may seem impossible.
While it is at least true that if it is conceivable it is possible, if it is impossible tells us little. Round cubes and square circles are impossible. Also, we can know if it is not possible it is inconceivable. But something that is inconceivable can be either possible or impossible. Round squares and circular blocks are inconceivable. Also unbounded space in the example of infinity is inconceivable too. Yet, the concept of infinity seems to demand such a thing so it cannot be ruled out!
Deciding on whether an infinite universe can exist depends on if it is conceivable. It seems not and most must take it on faith unless one finds reassurance in mathematical strategies which are privy to those with elite knowledge. Further can mathematical knowledge lead to a conception of the reality? Can something form a mental image based on mathematics? Even if one can is this available many or is it based on concepts that serve as illustrations of mathematic concepts (e.g. graphs of mathematics) or 3 dimensional construction (or four or five or more dimensions for that matter). Is such a thing conceptual. Does it serve as a picture, like a photograph, of the mathematical truth of is it simply a representation of it?
Can an infinite universe subsist with infinite variation? It does seem counterintuitive that infinity can exist in this matter but what other options are there? Perhaps infinity is being defined wrongly with our limited tools. Perhaps with our present tools we will have to find this formulation the most sustainable although it really does not stand up to scrutiny. Not only is an infinite universe not conceivable, even if it is possible, or possibly not, the crux of the matter is that it seems this formulation of the universe is reduced to a form of absurdity where infinity depends on only its nature of being infinite and nothing else, a sort of redundancy. Nothing about matter is important. It is reduced to a sort of flotsam and jetsam only existing to support infinite space. While perhaps an infinite universe and infinite matter is most promising, it fails to deliver. Yet still matter must exist.
