In the introduction to Chapter 2, the book introduces the reader to Thomas Gradgrind. This introduction uses verbal irony to explore Thomas’s worship of facts to the exclusion of all else.
Thomas Gradgrind, sir. A man of realities. [...] With a rule and a pair of scales, and the multiplication table always in his pocket, sir, ready to weigh and measure any parcel of human nature, and tell you exactly what it comes to. It is a mere question of figures, a case of simple arithmetic. You might hope to get some other nonsensical belief into the head of George Gradgrind, or Augustus Gradgrind, or John Gradgrind [...] but into the head of Thomas Gradgrind, no sir!
Thomas is a “man of realities,” who holds the (nonsensical) belief that human nature can be “weigh[ed] and measure[d]” to determine the sum total of its parts.
The irony lies in Dickens’s continual undercutting of the authority with which Thomas presents himself. Thomas sees himself as an excellent judge of others, someone who can “tell you exactly” what other people are worth, according to his very specific worldview. Dickens undermines Thomas’s image of himself by critiquing that worldview. Dickens makes utilitarianism sound petty, insubstantial, and pretentious, a philosophy unfit to deal with the complexities of human personality. Gradgrind is confident that a person is no harder to crack than “a case of simple arithmetic.” The statement is so ridiculous on its face that the reader knows implicitly not to take it seriously; Dickens’s contempt for Gradgrind bleeds through the page.
What’s more, Dickens mocks Thomas’s elitism and ego. In the last line (“You might hope…”), Dickens shows readers that Thomas thinks of himself as too clever to believe he could ever adopt a “nonsensical” idea. Other people may fall prey to them, but not Thomas. The irony is not only that he has already adopted a silly set of ideas, but that if he were honest enough with himself to examine them, he would be able to let them go (as he does by the end of the novel). If Thomas could be convinced that he might be wrong, he would realize that he is; but he won’t be, until his children correct him. The effect of this irony is that the reader cannot take Thomas Gradgrind or his ideas seriously from the very beginning of the novel. It is clear that he is in the wrong, and too weak to realize it on his own.