Philosophy
The philosophy that underlies the classical approach to education is that greatness of mind, both generally and in any specific field of study, proceeds from a broad study of the human experience expressed across the disciplines.  Classical educators concentrate on building a strong foundation for mental exercise through extensive study of the humanities before leading students into specialized study.  Classicists believe in guiding students in how  to think well, rather than in what to think.  This method presupposes that every human being has the innate desire for the intellectual life, which consists primarily in seeking wisdom through coming to know and love the Good, the True and the Beautiful.  As Christians, we further recognize that this end is only ultimately achieved through coming to know and love Christ.

An Analogy
In the world of classical education, one of the most common questions to arise is about the study of classical languages.  Why study Latin, for instance- isn't it a dead language?  Similarly, the relevance of the humanities is often questioned in relation to our science and technology-driven world.  The answers to these questions are analogous because the study of classical languages is to the study of modern languages as a classical formation is to advanced specialized study.
On the most basic level, the study of classical languages trains the memory and teaches many classical root words, thus laying the foundation for the study of vocabulary and spelling.  Studying a classical language also trains the mind to think analytically about language while teaching basic linguistic and grammatical components like verb conjugation, noun declension, the parts of speech, and principles of translation and expression.  This further builds the foundation for the study of modern languages, including English, and paves the way for attaining excellence in these disciplines.
Similarly, a classical education both trains the memory and supplies it with important foundational content.  Furthermore, the classical student is taught to think critically and analytically about his or her studies, the world, and the place of the Christian person within it.  Students are encouraged and given frequent opportunities to ask "the big questions" of life, and they are taught to express their answers with coherence, clarity, and consistency.