However, two meanings predominate in nonhistorical usage. The first is 'corollary,' a usage now mostly superseded by that term itself. The second (which may now be considered the 'modern' usage) is, "A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate, or capable of innumerable solutions" (Playfair 1792). Unfortunately, this definition is slightly inaccurate, because the proposition actually states the conditions, rather than affirming the possibility of finding them.
A proposition is a mathematical statement such as "3 is greater than 4," "an infinite set exists," or "7 is prime."
An axiom is a proposition that is assumed to be true. With sufficient information, mathematical logic can often categorize a proposition as true or false, although there are various exceptions (e.g., "This statement is false").
Principle is a loose term for a true statement which may be a postulate, theorem, etc.
A law is a mathematical statement which always holds true. Whereas "laws" in physics are generally experimental observations backed up by theoretical underpinning, laws in mathematics are generally theorems which can formally be proven true under the stated conditions. However, the term is also sometimes used in the sense of an empirical observation.
An ansatz is an assumed form for a mathematical statement that is not based on any underlying theory or principle.
From MathWorld
Posts
1 comentarios:
I believe that the definition of this terms is no so formal, may be is nessary a theory for that; i dont know if the proof theory has this kind of formalism, in fact, there is a formal theory for the theories? (this is a question for Lalinde) In the last couple of days i was trying to do a conceptual model using UML class diagrams to model all this concepts, I mean (law, proposition,..) and is no so easy....all the definitions are very informal and often contradictory.
Post a Comment