Order and Science:

Some general remarks:

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.

Scientific Method:

Scientific arguments have two basic forms; 1) the pure method of deduction, where some conclusion is drawn from a set of propositions and 2) the method of induction, where one draws general conclusions from particular facts that appear to serve as evidence. The fact that inductive reasoning is so often successful is a remarkable property of the 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.

Continuing with the themes of order, reductionism and determinism and any other 'ism ya need:

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?

Isn't mathematics just a language and nothing more?

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 Empedocles discovered that there exist only 5 regular solids.

As you have just done in class, its not so hard to discover some of these regularities:

Reductionism at its best ...

Plato, so impressed by the elegance of this discovery, then proposed that four of these solids correspond to the four atomic elements in the Universe (earth, water, air and fire). Plate also hypothesized that there existed a fifth element, as yet undiscovered called ether, that corresponds to the fifth element which made up the heavenly speheres.

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:

Thus, according to Platonists, we do not invent mathematical truths, we discover them. Mathematics transcends the physical reality that confronts our senses. The fact that mathematical theorems have been discovered independently by several investigators indicates that there does exist some objective element to mathematical systems.

Or maybe that we are so unsophisticated that we can't think beyond our common language and merely rediscover the same thing in a different syntax

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.

Possibly we have de-evolved, substituting mathematical precision and elegance in place of a more visceral and sensory relationship with the Universe.

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

Mathematics went on to led the way in many scientific and technological developments over the next 2000 years. Architechture, navigation and mechanics are all examples of core elements to our civilzation that depend heavily on mathematics.

The Laws of Nature

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.

Direct connections between events are usually apparent to the senses. But the underlying causes assoicated with the laws of Nature are much more subtle. Observations of events are not generally intelligible. Often phenomenon requires an abstract theoretical framework to form a context for measurements in order to link them into a framework of understanding. This framework is called a scientific theory.

The laws of Nature are attempts to capture the regularities of the world systematically. The existence of regularties in Nature is an objective fact, thus we do not impose laws onto Nature. While the form of the laws are human inventions, they reflect, albeit imperfectly, real properties in Nature. It is this absolute invariance of the laws of Nature that underwrites the meaningfulness of the scientific enterprise and assured its success.

I dissent vehemently; absolute invariance creates the detector problem

Truly basic laws of Nature establish deep connections between different physical processes. When a new law is developed, it is tested under different contexts which often leads to the discovery of new, unexpected phenomena. This demonstrates that we are determining real regularities in Nature, not imposing them with our scientific structures.

Controversial Point #1: Is what is in the red italics above really correct or do we just want to believe it?

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.