You can only find truth with logic if you have already found truth without it.
A good puzzle should demand the exercise of our best wit and ingenuity, and although a knowledge of mathematics and of logic are often of great service in the solution of these things, yet it sometimes happens that a kind of natural cunning and sagacity is of considerable value.
Pure mathematics is, in its way, the poetry of logical ideas.
Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition.
Logic is the art of going wrong with confidence.
Mathematics is, as it were, a sensuous logic, and relates to philosophy as do the arts, music, and plastic art to poetry.
SOURCE: Philosophical Fragments