Natural languages may be thought in various ways to be ‘logically imperfect.’ Certain grammatical forms may mislead us about logical form; thus, ‘It is raining’ looks as if it refers to something (‘it’). More radically, certain concepts may even involve us in contradiction or incoherence. For example, Tarski argued that the ordinary concept ‘true’ did this, since it generated such paradoxes as the liar.
A logically perfect language would be one lacking these faults, as well, perhaps, as some other ‘defects’, such as ambiguity and redundancy. Frege attempted to create such a language (the Begriffsschrift [concept writing or concept notation]), in which to couch the truths of logic and mathematics. Rather later, the Logical Positivists were interested in the idea of a logically with which to express the whole of natural science.
Dr. Roger Teichmann in The Oxford Companion to Philosophy