Rationalism:

The earliest beginnings of science was to note that there exist patterns of cause and effect that are manifestations of the Universe's rational order. We mostly develop this idea as small children (touch hot stove = burn/pain). But the extrapolation of a rational order to cosmology requires a leap of faith in the beginning years of science, later supported by observation and experimentation.

Thus, 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. The purpose of scientific understanding is to coordinate our experiences and bring them into a logical system.

Thoughout history, intellectual efforts are directed towards the discovery of pattern, system and structure, with a special emphasis on order. Why? control of the unpredictable, fear of the unknown, and a person who seeks to understand and discover is called a scientist.

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 humankind 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.

Scientific Method:

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 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.

Cause+Effect:

The foundation for rationalism rests squarely on the principle of locality, the idea that correlated events are related by a chain of causation.

There are three components to cause and effect:

The necessary connection in cause and effect events is the exchange of energy, which is the foundation of information theory => knowledge is power (energy).

Also key to cause and effect is the concept that an object's existence and properties are independent of the observation or experiment and rooted in reality.

Causal links build an existence of patterns that are a manifestation of the Universe's rational order. Does the chain of cause and effect ever end? Is there an `Initial Cause'?

Reductionism:

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.

For example, atomism is a form of reductionism in that it holds that everything in the Universe can be broken down into a few simple entities (elementary particles) and laws and interactions among them. Modern chemistry reduces chemical properties to ninety or so basic elements (kinds of atoms) and their rules of combination.

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.

Determinism:

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.

Implicit to determinism is the fact that every event happens of necessity. It has to happen; the Universe has no choice.

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.

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?

Idealization of physical phenomenon led Plato to hypothesize that there were two Universes, the physical world and an immaterial world 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.

Thus, there came into existence 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 is the same as the Platonic world and would be though of as emerging from the world of physical objects.

The other school is attributed to Plato, and finds that Nature is a structure that is precisely governed by timeless mathematical laws. According to Platonists we do not invent mathematical truths, we discover them. The Platonic world exists and physical world is a shadow of the truths in the Platonic world. This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math.

Mathematics transcends the physical reality that confronts our senses. The fact that mathematical theorems are discovered by several investigators indicates some objective element to mathematical systems. Since our brains have evolved to reflect the properties of the physical world, it is of no surprise that we discover mathematical relationships in Nature.

The laws of Nature are mathematical mostly because we define a relationship to be fundamental if it can be expressed mathematically.

Greek Cosmology

Both Plato and Pythagoras influenced the first logically consistent cosmological worldview, developed by the Greeks in the 4th century B.C. This early cosmology was an extrapolation of the Greek theory of matter proposed by Empedocles. This theory states that all matter in the Universe is composed of some combination of four elements: Earth, Water, Fire, Air. These four elements arise from the working of the two properties of hotness (and its contrary coldness) and dryness (and its contrary wetness) upon an original unqualified or primitive matter. The possible combinations of these two properties of primitive matter give rise to the four elements or elemental forms.

Perhaps only a culture whose leaders were involved with logic and geometry would put the concepts of chemistry in such a logical and geometric form. Fire and Water are obvious opposites, and so are Earth and Air. These opposites share no common properties. There are four properties, each shared by two non-opposite elements: fire and air share the property of hotness, water and air the property of wetness, and so on. Since the four elements are two pairs of opposite elements, so also are the four properties - hotness being the opposite of coldness and wetness the opposite of dryness. Each of the four elements was held to exist in an ideal pure form, which could not actually be found on earth. The real things around us were considered impure, or mixed, forms of these four ideal elements. Thus the different airs, or gases, were the form of air mixed with different proportions of the forms of fire or water; smoke was a mixture of the forms of air and earth with some of the form of fire added. But there was an ideal or pure form of earth, air, fire, and water, and the real ones which we see and use were not ideal but of lesser purity. In other words, the real or observed different kinds of the same element are due to different degrees of the same properties. The elements could be changed into one another by removal of one property and addition of another.

In a seemingly unrelated discovery, Euclid, a Greek mathematician, proved that there are only five solid shapes that can be made from simple polygons (the triangle, square and hexagon). Plato, strongly influenced by this pure mathematical discovery, revised the four element theory with the proposition that there were five elements to the Universe (earth, water, air, fire and quintessence) in correspondence with the five regular solids.

Elements had a natural tendency to separate in space; fire moved outwards, away from the earth, and earth moved inwards, with air and water being intermediate. Thus, each of these five elements occupied a unique place in the heavens (earth elements were heavy and, therefore, low; fire elements were light and located up high). Thus, Plato's system also became one of the first cosmological models and looked something like the following diagram:

Like any good scientific model, this one offers explanations and various predictions. For example, hot air rises to reach the sphere of Fire, so heated balloons go up. Note that this model also predicts some incorrect things, such as all the planets revolve around the Earth, called the geocentric theory.

Middle Ages

The distinction between what makes up matter (the primary elements) and its form became a medieval Christian preoccupation, with the sinfulness of the material world opposed to the holiness of the heavenly realm (which is interesting since modern cosmology is heavily consumed with the issue of dark matter). The medieval Christian cosmology placed the heavens in a realm of perfection, derived from Plato's Theory of Forms

Before the scientific method was fully developed, many cosmological models were drawn from religious or inspirational sources. One such was the following scheme taken from Dante's `The Divine Comedy'.

The political and intellectual authority of the medieval church declined with time, leading to the creative anarchy of the Renaissance. This produced a scientific and philosophical revolution including the birth of modern physics. Foremost to this new style of thinking was a strong connection between ideas and facts (the scientific method).

Since cosmology involves observations of objects very far away (therefore, very faint) advancement in our understanding of the cosmos has been very slow due to limits in our technology. This has changed dramatically in the last few years with the construction of large telescopes and the launch of space-based observatories.

Shape of the Earth:

The early Greeks knew the Earth was a sphere due to the shape of the Earth's shadow on the Moon during a lunar eclipse. They also knew the size of the Earth due to the efforts of Eratosthenes (220 B.C.). Eratosthenes succeeded in measuring circumference of Earth in the following manner; he knew that on a certain date that a stick placed in the ground at Syene cast no shadow. Whereas, a stick at Alexandria has a small shadow. Using simple ratios he showed the following: