Can you name a Modernist propositions from Pascendi?  

Why? How about Lamentabili?

Quote from Praestantia scripturae:
https://www.papalencyclicals.net/pius10/p10prasc.htm

Moreover, in order to check the daily increasing audacity of many modernists who are endeavoring by all kinds of sophistry and devices to detract from the force and efficacy not only of the decree “Lamentabili sane exitu” (the so-called Syllabus), issued by our order by the Holy Roman and Universal Inquisition on July 3 of the present year, but also of our encyclical letters “Pascendi dominici gregis” given on September 8 of this same year, we do by our apostolic authority repeat and confirm both that decree of the Supreme Sacred Congregation and those encyclical letters of ours, adding the penalty of excommunication against their contradictors, and this we declare and decree that should anybody, which may God forbid, be so rash as to defend any one of the propositions, opinions or teachings condemned in these docuмents he falls, ipso facto, under the censure contained under the chapter “Docentes” of the constitution “Apostolicae Sedis,” which is the first among the excommunications latae sententiae, simply reserved to the Roman Pontiff. This excommunication is to be understood as salvis poenis, which may be incurred by those who have violated in any way the said docuмents, as propagators and defenders of heresies, when their propositions, opinions and teachings are heretical, as has happened more than once in the case of the adversaries of both these docuмents, especially when they advocate the errors of the modernists that is, the synthesis of all heresies.

We need to remember the distinction here, though. If you hold to a condemned position with pertinacity, even after being properly corrected and given the knowledge that it is heresy, only then you would be subject to an ipso facto excommunication.

What Lad was addressing, paraphrasing +Williamson, is that many Catholics today hold to material heresies, such as Modernist ideas, out of ignorance. It is not that one is holding these ideas pertinaciously, but that many don't realize that they are in fact condemned propositions or errors. One could argue this is the case with someone like Fr. Robinson because he may be holding these Modernistic errors without realizing they are such in the first place, especially since his superiors in the neo-SSPX are affirming his positions.

Williamson didn't say that all trads are infected with modernism. He was talking about an infection with some liberal ideas.

St. Pius X condems all those who contradict his antimodernist writings.

What Lad was addressing, paraphrasing +Williamson, is that many Catholics today hold to material heresies, such as Modernist ideas, out of ignorance. It is not that one is holding these ideas pertinaciously, but that many don't realize that they are in fact condemned propositions or errors. One could argue this is the case with someone like Fr. Robinson because he may be holding these Modernistic errors without realizing they are such in the first place, especially since his superiors in the neo-SSPX are affirming his positions.

Bishop Williamson laid out the subjectivist philosophy that underlies "Modernism", the root thinking behind it.

While St. Pius X condemned some very specific, more egregious manifestations of this infection, it runs a lot deeper.

Wrong.  I was at the seminary where he stated very clearly that we've all been infected, himself included.

Modernism manifested itself in a set of propositions that were condemned, but the subjectivist principles behind it can also manifest themselves much more subtly.

I don't believe what you say about Williamson.

He publicly talked about liberal ideas, not modernism. St. Pius X explained what modernism is. It's a well described set of ideas.

It's right there at the very beginning of St. Pius X's description of Modernism in Pascendi

Modernists place the foundation of religious philosophy in that doctrine which is usually called Agnosticism. According to this teaching human reason is confined entirely within the field of phenomena, that is to say, to things that are perceptible to the senses, and in the manner in which they are perceptible; it has no right and no power to transgress these limits.

Bishop Williamson rightly traces this to the philosophy of Descartes and then to the PHENOMENology of Kant finding their way into the Church and applying that mentality to Catholic doctrine.  And it can be manifested in a limitless number of ways.  One of the most common activities of these early Modernists was opposing natural science against faith, the evolutionists like Chardin.  Father Robinson himself manifests that exact tendency in his approach to science, where we have to re-interpret and re-understand certain prior Catholic doctrine, such as always had been held by the Church Fathers, for instance regarding the Flood.  Because his "science" tells him that there could not have been a universal flood, instead of questioning the science on the authority of the Church Fathers, he rejects the Patristic consensus based on the science.  So he re-interprets Scripture to fit it with science.  That is in fact a clear manifestation of Modernism.

Quote from: Marion

Williamson didn't say that all trads are infected with modernism.

Wrong.  I was at the seminary where he stated very clearly that we've all been infected, himself included.

Any true Catholic, stating that he himself is infected with heresy, would get himself desinfected before lecturing others about errors of all trads.

How can you say such nonsense about Williamson, without any proof?

Any true Catholic, stating that he himself is infected with heresy, would get himself desinfected before lecturing others about errors of all trads.

Do you not understand the meaning of the word "infected"?  +W is saying we're all infected with Modernism, just like, after Adam's fall, the entire human race was infected with Original Sin and all it's spiritual consequences.