apoorv
Posts:
53
Registered:
4/11/13


Re: some amateurish opinions on CH
Posted:
Apr 15, 2013 12:02 PM


I have a few comments to make. It seems that the relation between sentential and predicate logic is not much discussed. Sentential logic can deal only with conjunction of a finite number of sentences. Predicate Logic,via the Universal Sentence allows us to make the leap from the finite to the infinite, ' to escape the prison of finitude' so to say . Yet, purely from the perspective of sentential Logic, the only wff or sentence that Implies an infinite number of independent sentences Is the Contradiction A&~A.In introducing the Universal Sentence ,we seem to be ignoring this. 'there is always a bigger number'representing ' potential infinity' actually represents infinite Information , and therefore carries with it the seeds of disconnect with reality. The point, as the actual limit of a sequence of segments of ever smaller lengths is The completed infinite, representing as it does, information to an infinite precision. But the fact remains that mathematics is amazingly successful in depicting and explaining Reality. That is its strength and the reason for its almost unquestioning acceptance by Everyone. Most other branches of knowledge have there share of diverse opinion and Theories, but peresent day Maths is almost unique in the sense of a monolithic edifice of knowledge. Yet , maybe it is worth to see if models of reality based on the assumption of the infinitely Divisible continuum and on the basis of a finite indivisible unit yield significantly different View of the world. Apoorv

