The main purpose of science is to trace, within the chaos and flux of phenomena, a consistent structure with order and meaning. This is called the philosophy of rationalism, rational as in conforming with reason. And the purpose of scientific understanding is to coordinate our experiences and bring them into a logical system.
Thoughout history, intellectual scientific efforts have been directed towards the discovery of pattern, system and structure, with a special emphasis on order. Why? Primarily, the control of the unpredictable driven by the fear of the unknown. Those who pursue answers are known as scientists. The main occupation of a scientist is problem solving with the goal of understanding the Universe.
Science is founded on the hope that the world is rational in all its observable aspects. Its possible that there may be some facets of reality which lie beyond the power of human reasoning, that there may be things with explanations that we could never grasp, or no explanation at all, but the fact that the world is rational is connected with the fact that it is ordered.
Science is also a dialogue between mankind and Nature. Science is far from a perfect instrument of knowledge, but it provides something that other philosophies fail to, concrete results. Science is a ``candle in the dark'' to illuminate irrational beliefs or superstitions. Science does not, by itself, advocate courses of human action, but it can certainly illuminate the possible consequences of alternative courses. In this regard, science is both imaginative and disciplined, which is central to its power of prediction.
Science is any system of knowledge that is concerned with the physical world and its phenomena and entails unbiased observations and/or systematic experimentation. In general, a science involves a pursuit of knowledge covering general truths or the operations of fundamental laws of nature.
Science is far from a perfect instrument of knowledge, but it provides something that other philosophies often fail to provide, concrete results. Science is a ``candle in the dark'' to illuminate irrational beliefs or superstitions.
Science does not, by itself, advocate courses of human action, but it can certainly illuminate the possible consequences of alternative courses. In this regard, science is both imaginative and disciplined, which is central to its power of prediction.
Science can be separated from pseudo-science by the principle of falsifiability, the concept that ideas must be capable of being proven false in order to be scientifically valid. For example, crop circles -> science is truth
The keystone to science is proof or evidence/data, which is not to be confused with certainty. Except in pure mathematics, nothing is known for certain (although much is certainly false). Central to the scientific method is a system of logic.
Scientific arguments of logic basically take on four possible forms; 1) the pure method of deduction, where some conclusion is drawn from a set of propositions (i.e. pure logic), 2) the method of induction, where one draws general conclusions from particular facts that appear to serve as evidence, 3) by probability, which passes from frequencies within a known domain to conclusions of stated likelihood, and 4) by statistical reasoning, which concludes that, on the average, a certain percentage of a set of entities will satisfy the stated conditions.
The fact that scientific reasoning is so often successful is a remarkable property of th e Universe, the dependability of Nature.
To support these methods, a scientist also uses a large amount of skepticism to search for any fallacies in hypothesis or scientific arguments. In order to draw conclusions, a scientist uses the scientific method, a rigorous standard of procedure and discussion that sets reason over irrational belief. Central to the scientific method is a system of logic.
The scientific method has four steps:
Note that there is an emphasis on falsification, not verification. If a theory passes any test then our confidence in the theory is reinforced, but it is never proven correct in a mathematically sense. Thus, a powerful hypothesis is one that is highly vulnerable to falsification and that can be tested in many ways.
The goal of the scientific method is the construction of models and theories, all with the final goal of understanding.
Reductionism is the belief that any complex set of phenomena can be defined or explained in terms of a relatively few simple or primitive ones.
To a reductionist, once a set of equations or mathematical relations has been found to describe a system, then the behavior of the system is considered to be explained.
Reductionism is very similar to, and has its roots from, Occam's Razor, which states that between competing ideas, the simplest theory that fits the facts of a problem is the one that should be selected.
Reductionism was widely accepted due to its power in prediction and formulation. It is, at least, a good approximation of the macroscopic world (although it is completely wrong for the microscope world, see quantum physics).
Too much success is a dangerous thing since the reductionist philosophy led to a wider paradigm, the methodology of scientism, the view that everything can and should be reduced to the properties of matter (materialism) such that emotion, aesthetics and religious experience can be reduced to biological instinct, chemical imbalances in the brain, etc. The 20th century reaction against reductionism is relativism. Modern science is somewhere in between.
Closely associated with reductionism is determinism, the philosophy that everything has a cause, and that a particular cause leads to a unique effect. Another way of stating this is that for everything that happens there are conditions such that, given them, nothing else could happen.
Determinism also implies that everything is predictable given enough information. Since Newtonian or classical physics is rigidly determinist, both in the predictions of its equations and its foundations, then there is no room for chance, surprise and creativity. Everything is as it has to be, which gave rise to the concept of a clockwork Universe.
Laws of Nature:
The rise of science during the Age of Reason produced the idea that there is a hidden order in Nature, which is mathematical in form and could be uncovered by investigation. This hidden order could be expressed in the form of mathematical principles, or laws of Nature.
The laws of Nature are eternal, absolute and have an independent existence outside the physical conditions of an experiment. Success in the scientific method rests on the reproducibility of the results. An experiment is repeated and the same laws of Nature apply, but the initial conditions of the experiment can be varied. There is a clear functional separation between laws and initial conditions, similar to the Platonic Forms.
Models and Theories:
Scientific theories are essentially models of the real world (or parts of it) and the vocabulary of science concerns the models rather than reality. Often when the term `discover' is used in a scientific model or theory (such as the discovery of Hawking radiation) this, in fact, refers to a mathematical relationship that is revealed. A true discovery would refer to the observation of the phenomenon in Nature (with respect to Hawking radiation, noone has yet directly observed a black hole).
Models or theories that are broad and encompass a significant fraction of a field of science are called paradigms. Reductionism was one of the founding paradigms of science, but was not a complete expression of the truth to Nature. However, the three hundred years of progress that accompanied reductionism was not rooted on a misconception, for this is not the role of paradigms. Rather a particular paradigm is neither right nor wrong, but merely reflects a perspective, an aspect of reality that may prove more or less fruitful depending on the circumstances. Science may not deliver the whole truth, but it certainly deals with truth and not dogma.
Mathematics and Science:
The belief that the underlying order of the Universe can be expressed in mathematical form lies at the heart of science and is rarely questioned. But is mathematics a human invention or does it have an independent existence?
There exists two schools of thought. One that mathematical concepts are mere idealizations of our physical world. The world of absolutes, what is called the Platonic world, has existence only through the physical world. In this case, the mathematical world would be though of as emerging from the world of physical objects.
Plato's Theory of Forms:
Plato believed that there exists an immaterial Universe of `forms', perfect aspects of everyday things such as a table, bird, and ideas/emotions, joy, action, etc. The objects and ideas in our material world are `shadows' of the forms (see Plato's Allegory of the Cave).
This solves the problem of how objects in the material world are all distinct (no two tables are exactly the same) yet they all have `tableness' in common. There are different objects reflecting the `tableness' from the Universe of Forms.
The laws of Nature are mathematical mostly because we define a relationship to be fundamental if it can be expressed mathematically.
Much of the philosophical foundation to our mathematical sciences is due to the Pythagorean school. Pythagoras lived in the 6th century B.C., most of the work we attribute to the individual is more than likely a composite of work done over many centuries by his school.
The Pythagorean school presented us with our first physical models, but the role of mathematics was much more dominate than it is today. For example, the Pythagoreans believe that matter was make of numbers. Not idealized numerous fragments, but actual numbers themselves. In some sense, this is an atomic theory, but with pure mathematics replacing matter objects.
The world being composed of numbers was reached by the Pythagoreans due to their interest in gnomones. This naturally led to the development of the Pythagorean Theorem.
The discovery of the Pythagorean Theorem led to a crushing blow to the Pythagorean school since it uses the idea of irrational numbers, which was repugnant to the philosophers of the time.
The Greeks constructed their whole theory of the Universe on the concepts of numbers and shape, arithmetic and geometry. An example of this was when Euclid discovered that there exist only 5 regular solids. Plato then proposed that these five solids correspond to the four atomic elements in the Universe (earth, water, air and fire) and hypothesized that there existed a five element, called quintessence, which made up the heavenly spheres.
Each of these five elements occupied a unique place in the heavens and, thus, Plato developed the first periodic table and, at the same time, proposed the first cosmological models looked something like the following diagram: