What pattern connects the crab to the lobster, and the orchid to the primrose and all four of them to me? And me to you?
What are the organizing principles for the sciences? There are two major criteria for the differentiation of sciences:
The scientific method employed
The field of study, and the scope of the inquiry.
The scientific method is a method of inquiry which regards itself as fallible; it purposely tests and criticizes itself in order to correct and improve its findings. The goal is to let reality speak for itself, and to build a model of a certain aspect of reality. Systematic observation leads to a hypothesis as an explanation of phenomena: Why does it appear that way? The hypothesis has to be refutable, which means it has to be provable and testable. A hypothesis should allow the creation of predictions, which generates the design of tests. Experiments lead to the verification or rejection of the underlying hypothesis. Furthermore, this scientific procedure must be repeatable in order to exclude errors.
There is an ongoing philosophical discussion about the nature of scientific theories and their relationship to reality, or to truth. Even the falsification of a hypothesis that is derived from a particular theory may not lead to the rejection of the theory, but only to its modification. Scientific theories integrate related hypotheses into larger coherent structures. They also allow us to organize, document, and archive scientific knowledge, thereby making it possible to transmit and teach scientific insights to the next generation of researchers.
The scientific field itself can be subdivided in various ways. The boundaries between sciences are fluid, therefore there is much emphasis today on multidisciplinary approaches to certain phenomena. Generally, we distinguish between the following dimensions of science:
Formal sciences (math, logic, information theory, linguistics)
Physical sciences (physics, chemistry - they study non-living systems)
Life sciences (mainly biology - the study of everything that is alive: plants, animals, humans)
Social and behavioral sciences (everything that is concerned with human behavior and society: anthropology, archaeology, economics, education, linguistics, political science, sociology, geography, history, law, and psychology.)
Theoretical and practical sciences: studying phenomena is different from applying scientific insights: medicine, engineering sciences, technology.
Science is complex and multi-faceted, but the most important characteristics of science are straightforward:
Science focuses exclusively on the natural world, and does not deal with supernatural explanations.
Science is a way of learning about what is in the natural world, how the natural world works, and how the natural world got to be the way it is. It is not simply a collection of facts; rather it is a path to understanding.
Scientists work in many different ways, but all science relies on testing ideas by figuring out what expectations are generated by an idea and making observations to find out whether those expectations hold true.
Accepted scientific ideas are reliable because they have been subjected to rigorous testing, but as new evidence is acquired and new perspectives emerge these ideas can be revised.
Science is a community endeavor. It relies on a system of checks and balances, which helps ensure that science moves in the direction of greater accuracy and understanding. This system is facilitated by diversity within the scientific community, which offers a broad range of perspectives on scientific ideas.
Internet Encyclopedia: Links about Logic, Math,and Science.
arXiv is a free distribution service and an open-access archive for over 2.2 million scholarly articles in the fields of physics, mathematics, computer science, quantitative biology, quantitative finance, statistics, electrical engineering and systems science, and economics.
NewScientist: New Scientist reports, explores and interprets the results of human endeavour set in the context of society and culture.
An Overview of Logic: from Wesley Salmon. It's an older text, but well organized, clear and easy to understand.