What is the definition of authority Pius IV uses in "The Syllabus Of Errors Condemned By Pius Ix"?
The Syllabus Of Errors Condemned By Pius Ix
"In fact, with respect to matters which concern the holy ministry, Our Lord did not put the mighty of this century in charge, but Saint Peter, whom he entrusted not only with feeding his sheep, but also the goats; therefore no power in the world, however great it may be, can deprive of the pastoral office those whom the Holy Ghost has made Bishops in order to feed the Church of God."
[Your question was vaguely worded; I'm supposing you want the definition of authority that is included within Pius IV's Syllabus text.]
The definition of authority is offered in the final sentence of the Syllabus of Pius IV (it is quoted above). In this definition Pius first excludes what the authority is not by saying that "the mighty" governments, princes and principalities of earth are not the repository of authority: "Our Lord did not put the mighty of this century in charge."
Pius then identifies by name whom the Lord did commission as the repository of authority; Saint Peter is the man in whom the Lord deposited authority. In a dual metaphor, Pius says that Peter was "entrusted" with "feeding the sheep" and the "goats." Goats are culturally seen as being of lesser value than sheep. Therefore the metaphor implies that Saint Peter has authority over and pastoral responsibility for those of greater value and those of lesser value: in the context of this document, that would be Catholic "sheep" and sect member critic "goats."
Pius's final comment is that none on earth can "deprive" the Catholic Church of the authority that was given by the Lord and handed down to them through the Holy Spirit. Thus the Catholic Church, built upon the foundation of Saint Peter's commission from Jesus Christ, is defined as the spiritual authority:
no power in the world, however great it may be, can deprive of the pastoral office those whom the Holy Ghost has made Bishops
Further, the Catholic Church is defined as the authority that can denounce fraudulent spiritual understanding and unjust laws permitting persecution of Catholics and the Catholic Church:
we intend to do Our duty by announcing openly to all those whom this matter concerns and to the whole Catholic world, that these laws are null and void because they are absolutely contrary to the divine constitution of the Church.