Mathematics Platoism and Natural Law

One of the most interesting and vexing questions in (and about) mathematics is the so called discovery question. Is mathematics discovered or invented? The U.S. patent office, in the face of the common wisdom of antiquity, and I would say common sense, has declared that mathematics is invented, and therefore patentable. So is created the situation where one must pay a corporation thousands of dollars to use an algorithm which is the result of the flow of mathematical relationships.
Science News has an article which quotes a paper from last June's issue of the Newsletter of the European Mathematics Society which speaks against the discovery theory of mathematics, called the Plato theory of mathematics.
Platonist note that mathematical statements are either true or false independently of the personal beliefs of the mathematician. In base ten 1+1 will always equal 2. That makes mathematics independent of human belief and existence.
In his article in EMS Davies states:

Platonists believe that our understanding of mathematics involves a type of perception of the Platonic realm, and that our brains therefore have the capacity to reach beyond the confines of the physical world as currently understood, albeit after a long period of intense concentration. If one does not believe this then the existence of the Platonic realm has literally no significance. This type of claim has more in common with mystical religions than with modern science.

In that Davies makes the mistake of many secularist who ignore the theory of Natural Law and many physicists who while realizing that the universe is written in the language of mathematics fail to see the hand of the divine within that writing.
I remained unconvinced that calculus, which circumscribes the behavior of fluids in a piston or electron containment in an accelerator is a happy accident of human invention as opposed to a deep extension of divine will revealed to human knowledge by the grace of God.

On the Road Again

Now that very day two of them were going to a village seven miles from Jerusalem called Emmaus,and they were conversing about all the things that had occurred. And it happened that while they were conversing and debating, Jesus himself drew near and walked with them, but their eyes were prevented from recognizing him.
He asked them, "What are you discussing as you walk along?"
They stopped, looking downcast.
One of them, named Cleopas, said to him in reply, "Are you the only visitor to Jerusalem who does not know of the things that have taken place there in these days?"
And he replied to them, "What sort of things?"
They said to him, "The things that happened to Jesus the Nazarene, who was a prophet mighty in deed and word before God and all the people, how our chief priests and rulers both handed him over to a sentence of death and crucified him. But we were hoping that he would be the one to redeem Israel; and besides all this, it is now the third day since this took place. Some women from our group, however, have astounded us: they were at the tomb early in the morning and did not find his body; they came back and reported that they had indeed seen a vision of angels who announced that he was alive. Then some of those with us went to the tomb and found things just as the women had described, but him they did not see."
And he said to them, "Oh, how foolish you are! How slow of heart to believe all that the prophets spoke! Was it not necessary that the Messiah should suffer these things and enter into his glory?"
Then beginning with Moses and all the prophets, he interpreted to them what referred to him in all the scriptures.
As they approached the village to which they were going, he gave the impression that he was going on farther.
But they urged him, "Stay with us, for it is nearly evening and the day is almost over." So he went in to stay with them.
And it happened that, while he was with them at table, he took bread, said the blessing, broke it, and gave it to them. With that their eyes were opened and they recognized him, but he vanished from their sight.
Then they said to each other, "Were not our hearts burning while he spoke to us on the way and opened the scriptures to us?"
So they set out at once and returned to Jerusalem where they found gathered together the eleven and those with them who were saying, "The Lord has truly been raised and has appeared to Simon!"
Then the two recounted what had taken place on the way and how he was made known to them in the breaking of the bread.

If the Last Supper was the first Mass, and it surely was, then the second Mass took place in the village of Emmaus, on that first Easter Sunday. Amazingly the Apostles were not present, but instead two ordinary disciples and perhaps their families. As in Mass today, in all the forms of the many rites, first the scriptures were opened-- then Christ was made visible in the breaking of the bread, in the Eucharist. And for those present Christ who was with them all along, as He is with us was made truly present in the act of the Mass.
The location of Emmaus which is typically translated as seven miles from Jerusalem is described by Luke as sixty stades. A stade is a unit of distance equal to about 607 feet. Some manuscripts give other distances, up to eighteen miles outside Jerusalem. The location of Emmaus has been lost to history. The village was likely no more than a collection of huts and tents beside the road. But the most important event which ever happened in this little town has been preserved for two thousand years, by the Evangelist. The message of Emmaus is not apologetic, that is it is not aimed at defending Christian belief, rather it is catechetical.

Then beginning with Moses and all the prophets, he interpreted to them what referred to him in all the scriptures.

So how much of what is contained in the Gospels which explain the references to Jesus from the Psalms, the prophets, and even Genesis was first heard from the mouth of God himself on that road? We might never know, but the Gospel tells us that at least two heard it.
This passage should also touch catechists to their heart, because just has when we feed the poor, clothed the naked or visit the sick, when we catechize we are doing what Jesus did.

Pots & Kettles

I picked up or rather was given a copy of CATECHISTS, a magazine for, well, catechists. Generally it is fairly good, but.. (you knew that was coming) .. this issue contained an article which particularly irked me. Enough so that I sent a letter to the editor. It concerned a feature proporting to have advice from "Master Catechists."
My letter follows:

I am writing about an answer given by Kate Ristow's in answer to the question "Can a catechist disagree with Church teaching." While I certainly agree with Ms. Ristow's position that a catechist must teach in accordance with the Church's position on subjects, the example given by her in the article is an example of her doing exactly what she says a catechist must not do, impose her own beliefs in preference to the teaching of the Church.
Her example? To quote:

" Let's say, for example, that one of the topics your textbooks addresses is the Ten Commandments. As you teach the Fifth Commandment- You shall not kill -and the text rightfully emphasizes the sacredness of life, you simply can not tell the kids that you personally the death penalty is an acceptable option for punishing murderers. You must teach that it is our duty to protect life in all circumstances and that only God has the right to decide when someone's life should end."

A very nice sentiment, except it is not what the Church reaches. The Catechism of the Catholic Church (CCC 2266) says:

"2266 Preserving the common good of society requires rendering the aggressor unable to inflict harm. For this reason the traditional teaching of the Church has acknowledged as well-founded the right and duty of legitimate public authority to punish malefactors by means of penalties commensurate with the gravity of the crime, not excluding, in cases of extreme gravity, the death penalty. For analogous reasons those holding authority have the right to repel by armed force aggressors against the community in their charge."

While many individual Catholic leaders have, on their own authority, spoken out against the death penalty, the teaching of the Church itself is that use of the death penalty can be legitimate, depending on the circumstances, and Ms. Ristow's statement that it is not, is a case of her disagreeing with Church teaching, and presenting her view as the Churches. While elementary students are likely not capable of understanding the full scope of the Church's teaching on when it is legitimate to impose the death penalty, the use of force under the Just War doctrine and when it is permissible to kill in self defense and at other times these are subjects that high school students should be learning and the lesson needs to come out of the CCC and other Church documents and not from people's opinions.

And, of course the subject is even more complicated than that. A philosopher I know (really, she is a real Doctor of Philosophy, and teaches said subject,) can give a very precise and logical argument on why imposition of the death penalty is never morally defensible, based on the principle that execution for revenge is never moral, and that execution of a captive who no longer has the ability to harm society is also not morally right. These are very compelling arguments, perhaps enough to say that in the modern world, at least in the United States, capital punishment does not meet the requirements of CCC 2266, of execution being necessary to "rendering the aggressor unable to inflict harm." But this does not mean that execution is thus wrong in all cases in all places. Indeed this is the stand of the Church, that there are some circumstances where legitimate authority does have the right. and the duty, to impose the death penalty. And this is what a catechist should teach.