"also called logistic system in logic and mathematics, abstract, theoretical organization of terms and implicit relationships that is used as a tool for the analysis of the concept of deduction. Models—structures that interpret the symbols of a formal system—are often used in conjunction with formal systems. "
"A formal system is like a game in which tokens are manipulated according to rules in order to see what configurations can be obtained. (Examples: chess, checkers, go, tic-tac-toe. Nonexamples: marbles, billiards, baseball). All formal games have three essential features: They are token manipulation games; they are digital; and they are finitely playable."
A first glance it might appear as though they are something different , but at the core they are formal logic or the use of formal logic.
To me a formal system is a body of organised(organised in what way is domain dependent) knowledge, procedures (for what?..domain dependent), domain specific terms and semantics, applicability (or limitations)..
The concern for formal logic seems to stem from the need to have a thorough scrutiny of systems or parts. e.g program-provers in computer science to ensure the program will function correctly in all set of conditions. These provers use second order predicate logic which is a formal logic system.
Every formal system is characterized by
- An organised body of knowledge
- Domain specific terms and semantics
- Procedures for working with/on knowledge
- A set of needs the system addresses
- A set of goals the system aims to meet
- Limitations of the system
What have we gained?
A formal system is needed whenever more than two people are involved . I can invent a new game and play it all by myself and there is no need to formalize it. But the moment I start to explain it to the next person, the two of us have to go through the motions of a formal system even if we don't write it down on paper.
A formal system is a mode of thinking or a pattern of thought and percolates just about every activity people are involved in. Just as maths enables counting in a variety of sittuations the notion of 'formal system' enables a better appreciation of what you are really upto.
Quite often people don't recognize a formal system when they see one and this is just as bad as people not being able to do simple math.
It is not as though it is general public ( or shall we say the laity) that is at fault. Well known scientists often fall prey to it. I read a newspaper report to the effect that the speed of light is different in some parts of the universe. An enlightened scientist would know that no theory can be better than the set of facts on which the laws,models and theory are based. Looking at science as a formal system immedietely enables you to ask 'what are the scope and limitations?' . Ofcourse these things are debated but we facilitate the process by weeding out the 'simple math'.
Lest you start feeling that the notions are only for high science let me add that the notion is useful to anyone embarking on a study of any subject political science, relegion, economics, sports...(name it and there you are with an avatar of formal system). Even if you are not studying recognizing a problem correctly is half the problem solved in real world sittuations.We will see some examples later on and I hope the notion sinks in.
