Views of the Essence of Numbers over the Course of History Essay

Views of the Essence of Numbers over the Course of History - Essay ExampleThe second is the idea that mathematics and numbers are just a look of interpreting and interacting with arbitrarily defined symbols, and that holds their only utileness (36). The final is the idea of the logicians led by Russel, who claim that mathematics are useful because the universe is structured in a logically coherent way, and mathematics are consequently simply an expression of that logic (36). The latter two theories construct enough holes in them that they have been considered disproven, so many mathematical philosophers rely on the first, Platonic possible action to describe the role of numbers in our universe. This, however, is on the whole un-provable, and sidesteps around the problem of describing what numbers are without actually explaining anything if numbers are simply things that be in another realm, that is not philosophically useful and thus not a very compelling theory. I believe t hat numbers and mathematics actually need to be explained by a new theory, and that piece we currently do not have a completely formulated theory to explain what numbers are and how mathematics work, each of the aforementioned theories has almostwhat of the components that a complete theory of mathematics must have. The single biggest problem with the Platonic theory is its lack of utility. Its main usefulness is in the fact that it describes mathematical principles as being profoundly true based on their existence in the Platonic realm, allowing mathematicians to pursue their goals unhindered by doubt. The theory, however, is impossible to prove, because if numbers exist in a non forcible realm that has no contact with our own then it obviously keisternot be observed (36). The theory that numbers exist in a non-physical realm is just as useful and un-proveable as the theory that numbers exist only in physical form inside of sorry holes it could be true, but if so, who cares? This theory does, however, hold one of the fundamental principles that must be in any theory of numbers, which is the idea that numbers, even though they may certainly not exist in any kind of physical way, are real. Their interaction with the physical world, such as the fact that one can use numbers to plot a path to the moon, execute that plot and then end up on the moon, shows that there is something fundamentally real. So objet dart the Platonic theory is fundamentally marred by its lack of usefulness and the impossibility of proving (or disproving) its accuracy, its assertion that numbers are real in some way must be part of any eventual theory of numbers. Without numbers being real things no theory of mathematics is complete. Like the platonic theory of numbers, formalism, which states that mathematics are simply a series of series of convention governing symbols (36), has both problematic and useful components for creating a useful theory of numbers. The fundamental proble m with formalism is that it fails to account for the fact that, as shown above, numbers do have some relationship to reality. It is useful, however, in admitting the failings of numbers when applied to the real world. Numbers, when interacting with physical bodies, rely fundamentally on human conceptions and sensibilities. For example when a person sees two coins, they can say that there are two coins and in some senses be correct. The problem, however, is that this relies on a human made category of what constitutes a coin. When someone shaves a small amount off of one of the coins,