Example
Given a simple formal system (we shall call this one ) whose alphabet α consists only of three symbols {, } and whose formation rule for formulas is:
- 'Any string of symbols of which is at least 6 symbols long, and which is not infinitely long, is a formula of . Nothing else is a formula of .'
The single axiom schema of is:
- " * * " (where " * " is a metasyntactic variable standing for a finite string of " "s )
A formal proof can be constructed as follows:
- (1)
- (2)
- (3)
In this example the theorem produced " " can be interpreted as meaning "One plus three equals four." A different interpretation would be to read it backwards as "Four minus three equals one."
Read more about this topic: Intended Interpretation
Famous quotes containing the word example:
“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)