What we find is that rationalists find favour with the developments in mathematical and geometrical thinking in the seventeenth century and wish to employ them in regard to our general reasoning abilities. In regards to human thinking and a theory of epistemology rationalists assumed that the best ideas were based on reason, not observation. For example, the perfect triangle is an idea of reason, it can never be observed in the empirical world. Indeed, empirical triangles were thought of as imperfect copies of the perfect triangle.
The second assumption that rationalists made was that if reason could supply such perfect ideas then reason must be independent of experience, for experience was a copy of the empirical world which was it self full of imperfect copies of triangles, circles, squares. The third assumption that rationalists held was that if reason was more perfect than the senses in terms of the character of the knowledge it could generate, and if those ideas existed independently of the empirical world, then reason was close to the divine, to the way God would think.
On the basis of these assumptions and reasons rationalism became a major force in philosophy. It had support in the rationalism of Plato. It now became necessary to show others that rationalism was the best method to use in epistemology. The example used to show Descartes’ appeal is his ‘wax tablet argument’. Here Descartes demonstrates, solely by reason, how reason unlocks the door to reality. Descartes takes up a wax tablet. He notes its properties: it is solid, it has a certain shape, it makes a certain noise when tapped, it has an odour.
However, he places it near the fire and the wax changes its properties completely
His answer is that his senses change with the surface characteristics of the wax tablet. His senses follow the empirical and are confused when confronted by change. Descartes believes that the senses reach an impasse. They can go no further in explaining what the wax is. They cannot tell us what the reality of the wax is. But if we turn to reason we will find the reality of the wax. Now if we look at the way mathematics and geometry depict things, we find continuity and permanence rather than change. We find the perfect triangle which is what we work from, not impressions of triangles.
So, in the case of the wax, we find that the wax has certain necessary truths or a priori truths. If we use the same reasoning about our mind we come to a rather different conclusion than we did with matter. The mind intuits the permanence of matter or the continuity of things by reason alone. That an object can change over time does not spoil our knowledge of the object, it simply means that the object has certain necessary or a priori features and it also has certain accidental or a posteriori features. The former derive from reason, the latter from the senses.
The example of Plato’s ‘Meno’ where a slave boy ‘remembers’ truths that he had not learnt but discovered for himself is used to show that the mind has innate capacities for generating knowledge that must have been learnt in a non-empirical world. For rationalists the empirical world is a spur to reason and once passed beyond the empirical world is no longer necessary for certain knowledge. What we find here in rationalist thought is the justification of knowledge based on logical proof. Such logic is found in all human reasoning and we use it all the time when we use logical expressions such as ‘if’, ‘then’, ‘either’, ‘or’, ‘and’.