Despite placing the infamous Inquisitions in your washing machine set to "spin" to protect "the Church," the fact is that even your first misleading source admits:
"[Torture] was first authorized by Pope Innocent IV in 1252—not as a mode of punishment, but as a means of discovering truth."
For indeed, Pope
Innocent in
Ad extirpanda: required:
The head of state or ruler must force all the heretics whom he has in custody,{8} provided he does so without killing them or breaking their arms or legs,
as actual robbers and murderers of souls and thieves of the sacraments of God and Christian faith,
to confess their errors and accuse other heretics whom they know, and specify their motives, {9} and those whom they have seduced, and those who have lodged them and defended them, as thieves and robbers of material goods are made to accuse their accomplices and confess the crimes they have committed.
(31)
The head of state or ruler must send one of his aides, chosen by the Diocesan if there is one, with the aforesaid
inquisitors obtained from the Apostolic See, as
often as they shall wish, into the jurisdiction of the state and the district. This aide, as the aforesaid inquisitors shall have determined,
will compel three men or more, reliable witnesses, or, if it seem good to them, the whole neighborhood, to testify to the aforesaid inquisitors if they have detected any heretics, or want to expose their motives...
(32)The
head of state or ruler
must, within ten days after the
accusation, complete the following tasks: the
destruction of the houses, the imposition of the fines, the consigning and dividing-up of the valuables that have been found or seized, all of which have already been described in this decree.
(34)The head of state or ruler must divide up all the property of the heretics that is seized or discovered by the aforesaid officials, and the fines exacted from these heretics, in the form and manner following:
one-third shall go to the government of the state or district. The
second as a reward of the industry of the office
shall go to the officials who handled this particular case. The
third shall be deposited in some secure place to be
kept by the aforesaid Diocesan bishop and inquisitors,and spent as they shall think fit to promote the faith and extirpate{11} heretics, this policy prevailing in spite of any statute that has been or shall be enacted against this dividing-up of the heretics' property.
http://www.documentacatholicaomnia.eu/01p/1252-05-15,_SS_Innocentius_IV,_Bulla_'Ad_Extirpanda',_EN.pdf
It is such history as this that was partly instrumental in the prohibition of a state religion by the First Amendment, though it did not mean the state could not affirm religion in general.
The fact that the state did what the church required, exterminating the "heretics" and employed torture as sanctioned by the pope does not mean the state is only to be blamed for torture, or ever bears primary responsibility, any more than that the Romans are for the death of Christ.
For those who were tortured and killed by the state were in the hands of the latter because "The Church" commanded Catholic rulers to exterminate the heretics, as a prior
post substantiated, and to which can be added Pope
Innocent III, in Cum ex Officii Nostri of 1207:
In order altogether to remove the patrimony of St. Peter from heretics, we decree as a perpetual law, that whatsoever heretic, especially if he be a Patarene, shall be found therein, shall immediately be taken and delivered to the secular court to be punished according to the law. Cum ex Officii Nostri Pope Innocent III, 1207,
Inquisition, by Edward Peters, p. 49
review
Moreover, explaining torture simply as a means of "discovering truth" is merely a sophism for compelling, coercing confessions, even of suspected witnesses, as basically guilty based on mere suspicion.
Also,
The requirement that torture only be used once was effectively meaningless in practice as it was interpreted as authorizing torture with each new piece of evidence that was produced and by considering most practices to be a continuation (rather than repetition) of the torture session (
non ad modum iterationis sed continuationis).
[1]
Furthermore, the pope gave an economic incentive to the State to convict heretics by giving to the State a portion of the property and valuables confiscated from them, and also gave itself an economic incentive by granting a third of the same to the church to exterminate more heretics, etc.
In addition, the use of torture was affirmed by no less than St. Thomas
Aquinas (13th century):
...there are unbelievers who at some time have accepted the faith, and professed it, such as heretics and all apostates [that's many of us in Rome's heretical eyes]:
such should be submitted even to bodily compulsion, that they may fulfil what they have promised, and hold what they, at one time, received". — Living Tradition, Organ of the Roman Theological Forum;
LT119 - Torture and Corporal Punishment as a Problem in Catholic Theology: Part II. The Witness of Tradition and Magisterium
Moreover, the use of coercive physical punishment as a means of church discipline was still affirmed at least until more recent times:
The Church has the right, as a perfect and independent society
provided with all the means for attaining its end, to decide according to its laws disputes arising concerning its internal affairs, epecially as to the ecclesiastical rights of its members, also to carry out its decision, if necessary,
by suitable means of compulsion, contentious or civil jurisdiction. It has, therefore, the right to admonish or warn its members, ecclesiastical or lay, who have not conformed to its laws and also,
if needful to punish them by physical means, that is, coercive jurisdiction. — Catholic Encyclopedia
Jurisdiction CATHOLIC ENCYCLOPEDIA: Ecclesiastical Jurisdiction
And which means is not Scriptural, for church discipline was never that of physical compulsion, but disfellowship and punishment by spiritual means. (1Co. 5)
In addition, Pope Pius IX, in his The Syllabus (of Errors) asserted:
[It is
error to believe that] Hence it has been wisely decided by law, in some Catholic countries, that persons coming to reside therein
shall enjoy the public exercise of their own peculiar worship.”
(Section X, Errors Having Reference to Modern Liberalism, #78. Pius IX Syllabus)
But at least for the time being torture seems to be now condemned:
Pope Benedict XVI, in a speech of 6 September 2007.."In this regard, I reiterate that the prohibition against torture 'cannot be contravened under any circumstances'". — Torture and corporal punishment as a problem in catholic theology, September 2005:
However, if Rome was consistent with her past teaching then requirements such as this (which traditional RCs seem to long for) would apply:
Pope
Paul IV, Cum Ex Apostolatus Officio of 1559: Thus We will and decree [which language is that of perpetuity] that the aforementioned sentences, censures and penalties be incurred without exception by all members of the following categories:
(i) Anysoever who, before this date, shall have been detected to have deviated from the Catholic Faith, or fallen into any heresy, or incurred schism, or provoked or committed either or both of these, or who have confessed to have done any of these things, or who have been convicted of having done any of these things.
..moreover...
concerning those who shall have presumed in any way knowingly to receive, defend, favour, believe or teach the teaching of those so apprehended, confessed or convicted:
(i) they shall automatically incur sentence of excommunication;
(ii) they shall be rendered infamous;
(iii) they shall be excluded on pain of invalidity from any public or private office, deliberation, Synod, general or provincial Council and any conclave of Cardinals or other congregation of the faithful, and from any election or function of witness, so that they cannot take part in any of these by vote, in person, by writings, representative or by any agent;
(iv) they shall be incapable of making a will;
(v) they shall not accede to the succession of heredity;
(vi) no one shall be forced to respond to them concerning any business;
(vii) if perchance they shall have been Judges, their judgements shall have no force, nor shall any cases be brought to their hearing.;
(viii) if they shall have been Advocates, their pleading shall nowise be received;
(ix) if they shall have been Notaries, documents drafted by them shall be entirely without strength or weight;..
(xii) finally, all Kingdoms, Duchies, Dominions, Fiefs and goods of this kind shall be confiscated, made public and shall remain so, and shall be made the rightful property of those who shall first occupy them if these shall be sincere in faith, in the unity of the Holy Roman Church and under obedience to Us and to Our successors the Roman Pontiffs canonically entering office.
Note: This Constitution was reinforced in his Papal Bull Inter multiplices [December 21, 1566] by Pope St. Pius V; POPE PAUL IV's CUM EX APOSTOLATUS OFFICIO (cumexapo.htm)
And which decree many traditional RCS use against modern popes, such as forbid torture, and affirm that baptized "Bible Protestants" can be saved as being so.
Yet it should be added that using the sword of men to deal with theological dissent and false religion is something that early Prots also had to unlearn from Rome and the world
This issue relates to purgatory since not believing in this heresy makes one a heretic and obedience to the pope would require the Catholic ruler to exterminated us, lest he forfeit his rule.