Thursday, December 27, 2007
Tuesday, November 6, 2007
What do I mean by Formal Systems
As I said before there is an implicit understanding of a formal system as something equivalent to formal logic. Here are a few of the results of search for "formal system".
"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
"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.
Thursday, October 25, 2007
Introducing the problem
A word at the outset about my interests.I am exposed to both formal systems as well as philosophy though I can hardly claim to have even scratched the surface let alone mastered these.
Motivation
I was discussing SUO-KIF ontology with a friend of mine and he said you are using words to complicate issues (words like ontology ,upper ontology domain ontology etc). I responded by saying that 'when you formalize a body of knowledge you do introduce special terms to simplify discussion of that domain'.
I was reading an article in TOI entitled 'Can India afford an ethical foreign policy?' (Oct 14) by SHASHI THAROOR. In my opinion he has used the words 'ethics' and 'morality' interchangeably. My answer was first you need a 'Formal Ethics' before can raise that question. I am aware that I am adding the implicit assumption that one way of distinguishing ethics from morality is to use it's normative sense. Should there be a distinction? . Is the distinction 'academic' and 'pedantic'?. I felt that in a multicultural ,multi religious society you do need an agreement - A Formal one against which we can say ethical or unethical. Besides it avoids the question 'whose morality?'.
I have also observed that any abstraction has a tendency to remove content from reality. e.g Newton's laws are an abstraction of the way real world bodies move.Of course it can be considered merely a modelling compromise (trade off of coverage vs simplicity&elegance).Let me remind you that you cannot use the laws to predict the motion of an insect.
So I said let me take a look at the search engine and see what shows up as Philosophy of formal systems. There were some 150 results and I was using a new search engine (AltKplus?) clubbing the google yahoo etc. All the entries implied Formal system = Formal Logic.
What are the problems? (my view)
Motivation
I was discussing SUO-KIF ontology with a friend of mine and he said you are using words to complicate issues (words like ontology ,upper ontology domain ontology etc). I responded by saying that 'when you formalize a body of knowledge you do introduce special terms to simplify discussion of that domain'.
I was reading an article in TOI entitled 'Can India afford an ethical foreign policy?' (Oct 14) by SHASHI THAROOR. In my opinion he has used the words 'ethics' and 'morality' interchangeably. My answer was first you need a 'Formal Ethics' before can raise that question. I am aware that I am adding the implicit assumption that one way of distinguishing ethics from morality is to use it's normative sense. Should there be a distinction? . Is the distinction 'academic' and 'pedantic'?. I felt that in a multicultural ,multi religious society you do need an agreement - A Formal one against which we can say ethical or unethical. Besides it avoids the question 'whose morality?'.
I have also observed that any abstraction has a tendency to remove content from reality. e.g Newton's laws are an abstraction of the way real world bodies move.Of course it can be considered merely a modelling compromise (trade off of coverage vs simplicity&elegance).Let me remind you that you cannot use the laws to predict the motion of an insect.
So I said let me take a look at the search engine and see what shows up as Philosophy of formal systems. There were some 150 results and I was using a new search engine (AltKplus?) clubbing the google yahoo etc. All the entries implied Formal system = Formal Logic.
What are the problems? (my view)
- While Formal Logic is a useful tool for modelling mathematics and computers is that all?
- One way to define a Formal system is as a model(abstraction) one which is capable of being manipulated by humans for various purposes including verifiability in appropriate domains.
- General characheristics of all formal systems-semantics,domain,purpose,limitations for example
- What are Modelling losses or trade offs?
- How many conceivable models? Recall that there are three geometries though they may not all model the real world
- Some sort of a Meta Formal system?
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