Both Uses of

irrational
in
Middlemarch

He went to study in Paris with the determination that when he provincial home again he would settle in some provincial town as a general practitioner, and resist the irrational severance between medical and surgical knowledge in the interest of his own scientific pursuits, as well as of the general advance: he would keep away from the range of London intrigues, jealousies, and social truckling, and win celebrity, however slowly, as Jenner had done, by the independent value of his work.†
Chpt 2

irrational = unreasonable

But irrational reproaches were easier to bear than the sense of being instructed, or rather the sense that a younger man, like Lydgate, inwardly considered him in need of instruction, for "in point of fact," Mr. Wrench afterwards said, Lydgate paraded flighty, foreign notions, which would not wear.†
Chpt 3 *

Definitions:

(1) (irrational)
not reasonable
(2) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

More rarely, irrational numbers in mathematics are numbers that cannot be expressed as a fraction consisting of only an integer in the numerator and denominator. For example, pi is an irrational number while 1/3 is rational.