Kozzmo

What is the relationship between Math, Science, and Philosophy?

Philosophy
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What is Philosophy?
Math, Science and Philosophy
John Maynard Keynes, Father of Modern Economics
Informationism
Sigmund Freud
Ancient Philosophy
Medieval Philosophy
Early Modern Philosophy
Early Industrial Era

Mathematics:  A series of deductive premises founded on the Axiom that X=X The value of X can be anything, such as 2=2, or 2=4/2(3+8)-(25-5). As long as the variable remains the same on both sides of the = sign, the statement is true.
  
    As such, mathematics is considered to be an apriori knowledge. It remains true in all cases, and as such is considered to be outside the realm of experience.
 
   Why is that? The square root of 4 is 2. Perfect. What then is the square root of 2.? There is no rational answer, hence it is considered an irrational equation.
 
  The universe that we experience is not mathematically perfect. Hence mathematics is flawed in the realm of experience in equal proportion to the imperfection of the universe as defined by mathematics. 
 
  For this reason, it must be concluded that mathematics, while a valuable tool, is not sufficient to define the perceivable universe.
 
Science: A methodology based on the scientific method, that seeks to understand the world of experience through the process of reason and observation in order to achieve pragmatic resolutions to definable complications.
 
 In general, science operates on theories, which, by Stephen Hawking's  definition, to be considered true, must meet two basic criteria.
  1. They must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements.

    2.  They must make definite predictions about the results of future observations.

   The scientific method generally could be considered to follow six steps

    1. Identification of the complication to be addressed

    2. Hypothesis is formed as to why this is

    3. The conceptualization of an experiment that will test if the hypothesis in fact resolves the identified complication

   4. The implementation of the experiment

   5. Analasys of the results of the experiment to see if it validates the hypothesis

   6. The stated problem is reviewed, if the hypothesis is valid, then the problem is resolved, and the theory proven, if the hypothesis is invalid, then a new hypothesis is needed, and the steps repeated until the issue resolved.

   For example, above we looked at the square root of 2. It was an irrational number. This lead to the theory that mathematics is not adequate in itself to describe the universe. How do we prove this?

 With a calculator, if we enter 2 and a square root sign, we get a very big number, 1.4142135623731 Now if we hit Y to the x power 2 = we should get a number, other than two. Lets try it, and find out. Calculator

 Wait a minute, it went back to 2. Is our hypothesis wrong? Maybe its correct, and we're encountering a new problem. I think the calculator has been programmed to recognize irrational numbers in the exp function. Lets try it again, however this time, after we punch in 2 and the square root key, lets multiply it manually by 1.4142135623731 What happens? 2.00000000000001 Our theory is correct. Mathematics alone is not sufficient to define the experienced world, for this reason we need science to further our understanding.

  Whats the point you say? Its only a .00000000000001 difference. What does it matter? Science doesn't answer that question however. (Other than to say its invalid data, therebye invalidating the evidence of an experiment gathered in a non-pragmatic sense. For now Statistical analysis is beyond our scope)

  Science, as we have seen, follows a methodology, and it is very stringent in its procedures to accomplish its goal. It in general seeks to resolve definable problems with pragmatic solutions. For this reason, science, while a valuable tool, is inadequate alone, or even paired with mathematics to define the experienced universe.

  Philosophy: A broad overview of knowledge as a thing in and of itself. It seeks to define the relevance of information and put the pieces together in a coherent and meaningful way so as to give meaning to the universe.

This leads to certain complications.

The philisophical crisis: In general the philosopher examines the universe in its entirity. If the universe follows certain principles, then does it not stand to reason that biological organisms, as part of the universe would follow the same principles? Unfortunately, any attempt to relate these similarities, leads to the observation of the drastic differences, and so skepticism  forces the philosopher to dismiss the theory.

  In general, most philosophers agree that there is a distinction between the world of Ideas, and the world of experience, as demonstrated above. The debate begins at this point as how to best reconcile these differences. In the earliest stages of these debates, Herclatius suggested that the nature of things is in change itself. In contrast Parmenides argued that the universe was an unchanging, ungenerated indestructable whole.

   Following the arguements of these presocratics, Plato argues that there is the world of perception, and the world of ideas. Truth can only be found in the world of ideas.

 Aristottle followed these arguements (which were important in that they introduced mathematic calculation into the application of knowledge) by the methodology of using observation to support the deductions of the platonistic philosophers. Added to this was the introduction of logic, which together helped to define the concept of science.

  Today philosophy has progressed, due to the compilation of centuries of debate, and a greater understanding of the dynamics upon which the universe appears to function, as scientific research has indicated. The cornerstone of debate is probably best expressed by the Unified field theory.

  At present it would appear that we can reconcile a general relationship between 3 of the 4 forces in the universe. (electro-magnetism, the weak nuclear force, and the strong nuclear force) While different they all act upon the general principles of Quantum Mechanics. (which is to say they interact on the sub-atomic level)

 Gravity, on the other hand is a constant, that is to say it interacts on the universe in its entirety. The problem is that in a singularity it breaks down, and so defies the theory of gravity as best we can define it. For this reason it cannot be reconciled with the principles of quantum mechanics, and so a unified fields theory cannot be demonstrated.

 Now to take this from the realm of science into the realm of philosophy, the question is how does this apply to the individual, and the interaction of society?

  The individual, as defined by Sigmund Freud is comprised of the three component systems of the Id, the Ego, and the Superego. These systems, while characteristic of all individuals, are unique to every individual. This development of personality could be compared to the concept of Freewill.

  Every individual must to some extent interact with society, and their environment. The rules for this interaction is however independent of the individual. Society is largely dictated by institutional ideologies, including economic policies, religiouse and scholastic traditions, and cultural identities. The environment is largely dictated by climate, population, and natural recources available to a region. These are beyond the control of the individual.

   Hence, like the unified fields theory, a complete theory of understanding human behavior is at this time beyond our reach.

  This leads to the question, to what extent is the individual capable of shaping the world around them, and to what extent is the individual shaped by the world around them?

 It seems reasonable to suggest that the individual is capable of shaping the world around them in equal proportion to how the world around them shapes the individual.

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