This pdf is a geometrical demonstration and explanation of several features of finite and infinite curvature.

I came up with this argument to help my section get past a particularly difficult part of Newton. After briefly presenting it in class, Dr. Wodzinski asked for a written copy for his own edification and to help the tutors understand the material. What you see here is the full-blown version (complete with to-scale diagrams). Reading this is now (part of) how several tutors prepare for class.

Hence, pro-life people always think that Roe V Wade was not based on the constitution, whereas pro-choicers can't imagine reading the constitution any other way. The LGBTQ(etc.) community thinks that the right of a man to marry a man is all but spelled out in the constitution, whereas anyone who opposes gay marriage can't imagine finding any legitimate grounds for the legalization of the practice in the same source. Similarly, LBTQ+ can't fathom the notion that anyone could read the constitution after desegregation and find any grounds for allowing a baker to refuse service to a gay man for his wedding. The list goes on. Pick any decision, and you'll find this born out: people always see what they want to see.

Hey, I totally see why conservatives don't want gay marriage, contraception and abortion legal anywhere. But regardless of what position you take, you must be willing to admit that the arguments of the SCOTUS for these cases are based entirely on the constitution. Roe V Wade was argued mainly from the Due Process Clause of the 14th Amendment. Obergefell V Hodges (the big gay marriage decision) was argued mainly from the Equal Protection, (which happens to be the adjacent clause in the 14th). Griswold V Connecticut? Well, that was argued again, through the 14th.

Now your average pro-life and pro-marriage American would stop me right there saying, "Show me where the 14th Amendment uses the word 'abortion' or 'marriage', and then we'll talk about how it doesn't follow from the constitution." This is the sort of person that, when faced with a SCOTUS decision that he doesn't like, will accuse the court of legislating from the bench, or he will accuse the court of adding words to the constitution, of offering dictionary definitions instead of legal applications, et cetera. (Sound familiar?) For example, as the sometimes-rather-annoying-and-grossly-overrated-blogger Matt Walsh so aptly put it, "There isn’t even a pretense of constitutional interpretation anymore." (See this post.) Now I highly doubt that Matt Walsh read the majority opinion, and if he already did, he has serious comprehension issues, because the argument for the decision was all about the constitution. (The syllabus in question is available here, by the way.) Fact is, the 14th amendment makes every liberty whatever into a qualified constitutional right; the 9th guards against thinking that all of the enforceable rights are spelled out in the constitution. It doesn't matter that abortion, contraception, gay marriage, etc. aren't explicitly contained in the constitution. They can be protected by the constitution anyways.

           Governments do not derive their authority from the consent of the governed. The US government isn't legitimate because we signed some invisible contract... It's legitimate because of human nature. My primary intent here is to show that consent is unnecessary for legitimacy.

          First in this order is to clarify what is meant by “necessity”. There are two sorts, hypothetical and absolute. Hypothetical necessity is what is meant when we say, “a heartbeat is necessary for an animal to be healthy,” whereas absolute necessity is what is meant when we say, “Triangles necessarily have internal angles equal to two rights.” In absolute necessity, the principle necessarily produces the effect; in hypothetical necessity, the principle is necessary for the effect but does not always produce it.

          That the consent of the governed is absolutely necessary for the legitimate authority of government can easily be dismissed, for then a government could legitimately promulgate an unjust law. Injustice is never legitimate.

          Nor can a legitimacy of a government require the consent of the individuals through hypothetical necessity. Were this true, any individual could waltz into a nation whose government he thought to be unjust and break laws at will without the government being able to legitimately stop him! One might retort that the majority has given consent and that this is sufficient, but this would be to posit that Democracy (which is a government type) has legitimate authority ipso facto.

          It follows then that if any government has legitimate authority, it is not through the consent of the governed.

          And yes, governments can have legitimate authority. Human nature proves this, for we are naturally social animals, but every society must be organized, and a government is a necessary principle of the organization of a society.

    After a bit of research, it seems clear to me that - except in exceedingly rare, if not totally nonexistent circumstances - the laity ought not take communion at an SSPX chapel, or otherwise formally participate in the illicit liturgy. That the priests themselves ought not administer or say the illicit Masses is given in that they are illicit, this fact being confirmed by multiple sources, one binding, one traditionalist.
 
    The argument itself is straightforward: The Church has spoken specifically to this matter in an interpretive fashion, and authoritative interpretation have the same force as the law itself, if not universally, at least in respect to particular cases. This is a particular case that has been spoken on, however, so the Church’s interpretation of the law is binding.
 
The interpretation:
From STATUS OF SOCIETY OF ST PIUS X MASSES, Commission Ecclesia Dei:

 
Why the interpretation is necessarily binding:

Nor is this solution repugnant to all notable traditionalist sources:
Fr. Z's take on it:

The referenced canon:

    Traditionalists will argue that a true spiritual advantage suggests it. Note, however, that it has been clarified with binding authority that "the fact of not being able to assist at the celebration of the so-called 'Tridentine' Mass is not considered a sufficient motive for attending such Masses."

    In more general terms, for any action to be moral, the object, circumstances and intent must all be acceptable. (Moral Theology 101) From this arises the generally accepted fact that anyone can attend even a protestant service so long as he does not formally participate in it (the object of the action), so long as he does not cause scandal (the circumstances of the action), and so long as he does so for a genuinely good reason (the intention of the action), and the same can be said of attending an SSPX Mass. Protestantism is further removed, so it makes sense that what we can do in regards to their services, we can also do in regards to SSPX's Masses. That the intention can be good need not be visited.

    For the object of the action to be morally acceptable, either he must be incapable of morally or physically participating in a licit Mass, or else he cannot formally participate in an SSPX Mass. In that taking communion does constitute formal participation (Lest there be any doubt, this is what the cited canon referred to specifically, for the sacrament itself is illicit), a person cannot licitly receive the sacrament unless it is morally or physically impossible to receive it licitly elsewhere.

    In regards to the circumstances, scandal must be avoided, schismatic attitudes and indifferentism must not be allowed to take root. The latter especially seems that it would be difficult to satisfy. When something is done often enough out of preference, the distaste for what it lacks (in this case licitness) is numbed, leading almost necessarily to an attitude of indifferentism in regards to whether a sacrament or liturgy is licit.

    Is it not fitting after all, that the Sacrament called "Communion" should be received in full union with Rome?

    Can brevity lead to ambiguity? Yes. But given a colorful vocabulary, articulately employed, it need not. When brevity is lost, however, interest is lost, and only a select few will actually retain anything, or even read until the end of the post.

Brevity is the Soul of Wit - William Shakespeare