In december 1632 the Holy Office examined Galileo's Dialogue of the Two World Systems, and through his link with Niccolò Riccardi, Inchofer was chosen as one of a panel of three theologians appointed to assess the work, the others being Agostino Oreggi and Zaccaria Pasqualigo.

[5] There exists in the papers of the Congregation of the Index an unsigned statement, in Inchofer's hand, reviewing the anonymous denunciation of Galileo following the publication of The Assayer, which was undertaken by the panel in 1633.

Citing twenty-seven passages to support his judgment, he asked: 'What Catholic ever conducted such a bitter dispute against heretics... as Galileo does against those who maintain the earth's immobility?

[6] His dispute with Joachim Pasqualigo on the immorality of making castrati, and his appointment as member of the Congregation of the Index and of the Holy Office dissatisfied him with Rome, and at his own request he was transferred in 1645 to the college at Macerata where he intended to devote his leisure hours to the compilation of a history of martyrs.

[8] Following Galileo's trial, Inchofer published Tractus Syllepticus (Rome, 1633), which argues that belief in an immobile earth and a moving sun were matters of faith for Catholics.

In Historia sacrae Latinitatis (Messina, 1635), Inchofer elevated Latin to the rank of a heavenly court language and regarded it as the speech of the blessed.

He attained his main contemporary fame, however, by the anonymous Lucii Cornelii Europaei monarchia Solipsorum, ad virum clarissimum Leonum Allatium (Venice, 1645); the long-accepted view is that of François Oudin writing in 1736 for the Mémoires of Jean-Pierre Nicéron, namely that it was incorrectly attributed to him and was really by Giulio Clemente Scotti, but recently scholars have re-opened the question.