History of Symbolic logic

	Revision 15 . . November 4, 2001 11:24 am by AxelBoldt
	Revision 14 . . November 3, 2001 1:10 pm by (logged).21.196.xxx [substituted "acceptable" for "valid" to describe all wffs; added brief description of natural deduction]
	Revision 13 . . October 16, 2001 10:58 pm by AxelBoldt [Integrated Goedel's theorems into the text]
	Revision 12 . . October 16, 2001 1:35 pm by Anatoly Vorobey [/Talk]
	Revision 11 . . (edit) September 27, 2001 11:32 am by Justin Johnson [Added links, and changed "calculus" to "logic" in "propositional calculus"]

---

Difference (from prior major revision) (no other diffs)

Changed: 3c3

There are many different systems of symbolic logic. A system of symbolic logic has a number of components: the set of acceptable sentences, called well-formed formulas (or wffs); transformation rules for deriving new formulas from one or more initial formulas; the set of axioms, which is a subset of the set of wffs. The sets of wffs and axioms can be finite or infinite, so long as they are [recursively enumerable]?; i.e. so long as there exists a procedure for determining whether any given sentence is a wff or axiom, which could be carried out in a finite number of steps by a device such as a Turing machine.

There are many different systems of symbolic logic. A system of symbolic logic has a number of components: the set of acceptable sentences, called well-formed formulas (or wffs); transformation rules for deriving new formulas from one or more initial formulas; the set of axioms, which is a subset of the set of wffs. The sets of wffs and axioms can be finite or infinite, so long as they are recursive; i.e. so long as there exists a procedure for determining whether any given sentence is a wff or axiom, which could be carried out in a finite number of steps by a device such as a Turing machine (sometimes, it is enough to require that these sets be [recursively enumerable]?).