Rationalism is a core tenet of liberalism, regarding reason as the primary source of knowledge and relying on reason as a justification of arguments. According to Michael Oakeshott:
“The conduct of affairs, for the Rationalist, is a matter of solving
problems, and in this no man can hope to be successful whose reason
has become inflexible by surrender to habit or is clouded by the fumes
of tradition" -Michael Oakeshott, Rationalism in Politics.
Thus, at face value, Rationalism seems to be quite incongruous with Conservatism, which seeks to uphold traditional social and cultural institutions and practices. Rationalism would argue a pragmatic valuation of social and cultural institutions (i.e. this institution exists because it has value, and a new institution can and should replace it when the new institution is better able to provide societal value) whereas Conservatism holds that the existing institutions should be maintained. (It is unclear to me whether the Conservative viewpoint is that the institutions should be maintained because there is inherent value in durable or long-lasting ideas, or because they take the fact that the institution has long existed as implicit evidence of the institution's value).
However, Conservative legal schools of thought often appeal to Rationalism as the base justification, and Conservative legal practice (for instance Originalism or Textualism) in general treats the law almost as a set of rational principles from which coherent and logically consistent rulings can be derived. Some claim that a Rational interpretation of the law is inherently Conservative. In any case, at least within the practical confines of law Conservatism seems to have some claim to ties with Rationalism.
Given this apparent contradiction, I'm curious how Conservatism and Rationalism relate? Is Rationalism simply an argumentative tool used by reactionary Conservatives to fight for Conservative ideas and institutions, or is there some more internally consistent link between Conservatism and the idea of Rationalism?