What is philosophy? The word is used often, and this suggests something about its meaning. To philosophize is to reflect on specific facts in order to reach general conclusions. Philosophy, in other words, is reflection and generalization. This is what we mean when we speak of the philosophy of art or the philosophy of history. The philosophical spirit – the kind of reflection that philosophy involves – can be defined as follows: The philosophical spirit is the need to justify all opinions, together with a strength of mind more or less sufficient to satisfy this need. The defining quality of the philosophical spirit is free reflection and examination. To reflect freely is to eliminate from our thinking every influence but logic, to reason according to the rules of logic alone. So the two main characteristics of the philosophical spirit are the tendency to reflect in order to generalize and freedom of reflection. From this second characteristic, it follows that philosophy is different from religion. Reason plays a role in religion, but religion also recognizes the authority of historical tradition. Philosophy is concerned only with matters of reason. So their domains are quite distinct.

If we look back on the history of philosophy, we see that philosophical reflection has proceeded in two different ways, taking two different forms. Sometimes philosophy proceeds by analysis, using the method of mathematics.