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'Positive doubt' is a canonical term applied after a Rite or the administration of a sacrament has been found, by the correct authorities and in accordance to specific guidelines , to be lacking in some essential element to render it possibly invalid. 

Correct.  Many Trad clerics (including +Tissier from the sspx and Fr Scott) and many others who were non-sspx, have reached the same conclusion, since the 1970s.  This is not some new development.

Now you are correct when you state that very significant changes have been made to the episcopal rite of consecration, but has it been established as invalid? No.

These very significant changes = positive doubt.

Positive doubt = possibly valid.

Has a 'positive doubt' been established? Certainly there are serious reasons to cause one to have doubts - not knowing one way or another - but has a 'Positive doubt' been established?

Positive doubt = serious reasons to cause doubt.  Yes, these serious reasons establish doubt.

You make mention of the Anglican Rite that Pope Leo XIII declared to be "absolutely invalid, null, and void" but this has no bearing on the Catholic New Rite as it have not been declared upon.

The problems with the anglican rite are also present in the new rite.  This is part of the "serious reasons" why there are doubts.

In fact, as we have established, even his Lordship Williamson believed the New Rite to be valid. Why was that?

He's in the minority opinion.  But even he conditionally consecrated +Vigano, so he obviously had some doubts.

We have also established that His Grace Archbishop Lefebvre only re-ordained when each individual case was investigated on its own merits; not simply because they were ordained in the New Rite. Why was that?

In the time when the new rites came out, til Lefebvre's death (60s-early 90s), there were still TRUE RITE bishops who were ordaining.  These ordinations would've been valid.  But now...all the TRUE RITE bishops (pre-V2) are dead.  You can no longer compare +ABL's time to ours.  

Now along comes Mr. Ladislaus who declares that the SSPX are all modernists because they do not treat the New Rite of Ordinations as invalid as he wants them to.

  Positive doubt does not declare anything invalid.  You continue to misinterpret the argument.  Are you doing this on purpose?

If no 'positive doubt' has been established in the New Rite,

There are many, many reasons to establish positive doubt.  Go look up what Bishop Tissier said many times, and also go read the article posted from Fr Scott.  All these reasons still exist.

if it has not been declared as invalid,

Only the Church can declare it invalid.  This is stupid argument and has no place here.  All that is required is positive doubt, which is, AS CANON LAW SAYS, is to TREAT IT as invalid.  

The bar is pretty low for positive doubt, because The Church, through Canon Law, does NOT WANT THE FAITHFUL TO TAKE RISKS WITH SACRAMENTS.  Going to positively doubtful sacraments IS A RISK TO YOUR SALVATION.

then I as a Catholic must be content with this ruling trusting that the SSPX will make the right decision about each individual case as it has always done. 

1.  The new-sspx isn't infallible.
1b.  The new-sspx isn't the Church; they can't make "rulings".
2.  The new-sspx has changed their view on the new rites, in opposition to Bishop Tissier and Fr Scott (and others).
3.  The new-sspx has a similar view towards to the new rites as Indult communities and no longer agrees with the 'common opinion' of Traditional communities.

If you are content with placing your salvation in the hands of an organization which isn't infallible and which is no longer Traditional, then that's your decision.  But don't act like you weren't warned.  And don't act like your decision is based on canon law.  And don't act like your "contentment" to follow the new-sspx will absolve you from the moral consequences of going to doubtful sacraments. 

YOU have the job of saving YOUR soul.  The new-sspx can't save it for you.  I hope you will reconsider the above and pray about the huge, moral problems which positive doubtful sacraments cause.  Your duty to God outweighs your loyalty to the new-sspx.

'Positive doubt' is a canonical term applied after a Rite or the administration of a sacrament has been found, by the correct authorities and in accordance to specific guidelines , to be lacking in some essential element to render it possibly invalid. Now you are correct when you state that very significant changes have been made to the episcopal rite of consecration, but has it been established as invalid? No. Has a 'positive doubt' been established? Certainly there are serious reasons to cause one to have doubts - not knowing one way or another - but has a 'Positive doubt' been established?

You make mention of the Anglican Rite that Pope Leo XIII declared to be "absolutely invalid, null, and void" but this has no bearing on the Catholic New Rite as it have not been declared upon. In fact, as we have established, even his Lordship Williamson believed the New Rite to be valid. Why was that? We have also established that His Grace Archbishop Lefebvre only re-ordained when each individual case was investigated on its own merits; not simply because they were ordained in the New Rite. Why was that?

Now along comes Mr. Ladislaus who declares that the SSPX are all modernists because they do not treat the New Rite of Ordinations as invalid as he wants them to. And this is the crux of the matter isn't it? I am a traditional Catholic of the Roman Catholic Church. I am not a member of your personal church. If no 'positive doubt' has been established in the New Rite, if it has not been declared as invalid, then I as a Catholic must be content with this ruling trusting that the SSPX will make the right decision about each individual case as it has always done. It is the same of the New Rite Mass. You have declared it invalid. You have no right or authority to do that. You can think it if you want but you cannot impose that on other Catholics. Out of principle, I would never attend a New Rite Mass, but neither do I condemn a fellow Catholic for going to one. Bishop Williamson was of this mindset too. As I said, if it gives your personal peace of mind to formulate this list of transparency, then go for it, do your best - make sure you get those child abusers on there too. But don't use it as tool to bash the SSPX with. That's your own personal beef and has no place here.

Are they paying you to do this?

Monsignor Byrnes is in Georgia as of a few years ago.