logical system Quotes

Development of Western science is based on two great achievements: the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationships by systematic experiment (during the Renaissance). In my opinion, one has not to be astonished that the Chinese sages have not made these steps. The astonishing thing is that these discoveries were made at all.

As soon as science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms. We call such a system of thought a theory. The theory finds the justification for its existence in the fact that it correlates a large number of single observations, and it is just here that the 'truth' of the theory lies.

The present non-aristotelian system is based on fundamental negative premises; namely, the complete denial of 'identity.'

Science is the attempt to make the chaotic diversity of our sense-experience correspond to a logically uniform system of thought.

The paraphrase of Gödel's Theorem says that for any record player, there are records which it cannot play because they will cause its indirect self-destruction.

Axiomatization is what one does last, it's rubbish. It's the hygiene of mathematics, axiomatization.

All correct reasoning is a grand system of tautologies, but only God can make direct use of that fact.

Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos [mathematics], where pure thought can dwell in its natural home.

The system becomes logically closed when each of the logical implications which can be derived from any one proposition within the system finds its statement in another proposition in the same system.