Wednesday, November 29, 2006

More on Limits

Finding the limit of f(x) as x approaches infinity is simple. Memorize the behaviors of the generic equation types:

higher degree/lower degree = No limit.
lower degree/higher degree = 0.
same degree/same degree = coefficient/coefficient.

If substitution produces a non-zero/zero, there is no limit and instead there is a vertical asymptote.
A hole occurs when the initial substitution produces zero/zero.

The following are the numbers to put outside of the box for given denominators in cases where synthetic division is possible:
(4-x) --> 4
(x-4) --> 4
(x+4) --> -4

Tuesday, November 28, 2006

If you are in Calculus, use the following method to find the exact value of the limit of f(x) as h approaches 0.

1. The form is as follows. The numerator is f(x+h) - f(x). Divide the numerator by h.
2. FOIL.
3. Combine terms.
4. Factor out h.
5. Simplify.

Here is an example which illustrates how to find the derivative.
Original Expression: x^3 - 4x + 1.
Derivative: 3x^2 - 4.

Reminder: f(x+h) = x^2 + 2xh + h^2.

Monday, November 27, 2006

Finding Limits of Complex Fractions

Are you in Calculus? Whether you're struggling or doing fine, I'd like to help you as an act of kindness. The following is the MASTER BLASTER method, which can be used to find the limit of f(x) as x approaches n and f(x) is a complex fraction:

1. Let every term have a denominator and change - (minus) to +- (plus a negative).
2. Find the LCD (Lowest Common Denominator).
3. Multiply all the numerators by the LCD.
4. Don't multiply out (FOIL: first, outer, inner, last) the numerator.
5. Distribute the x for the terms in the denominator.
6. FOIL the separate denominator terms.
7. Combine like terms.
8. Factor the denominator and cancel. Multiply the numerator by the quotient of the cancelation. For example (a-b)/(b-a) = -1.
9. Now substitute in n.
10. Finally, simplify.

Sunday, November 26, 2006

Upcoming posts:
  • Nestorianism, Theodoret, & Cyril
  • Antipopes
  • Limbo
  • File sharing
  • God and time
  • Bad popes
  • Christmas trees and other practices
  • "Happy Holidays" vs. "Merry Christmas" - a summary
  • Becoming Catholic, and my situation & story
  • Transubstantiation & Real Presence of Christ in the Eucharist
  • St. Hippolytus
  • Anti-Social Trinitarianism revisited
  • Dyotheletism vs. the heresy of Monothelitism, and Honorius I
  • Sola Scriptura elaborated
  • Judas
  • Petros vs. Petra
  • the Platinum Rule vs. the Golden Rule & the Silver Rule
  • much, much more

Wednesday, November 22, 2006

Catholic Congressman Tim Bishop & Church Teaching

Tim H. Bishop, it's time to align your political platform with Church teachings! Your recent voting record is out of sync with the values of Roman Catholicism, the faith you profess:

05/25/2005 Overseas Military Facilities Abortion Amendment Y
04/27/2005 Child Interstate Abortion Notification Act N
10/02/2003 Prohibit Partial-Birth Abortion bill N
06/04/2003 Prohibit Partial-Birth Abortion bill N
02/26/2004 Unborn Victims of Violence Act 2004 N
07/18/2006 Alternative Stem Cell Therapies Act N
07/18/2006 Same Sex Marriage Resolution N

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Pope Leo X and the "Fable" of Christ

Pope Leo X called the story of Christ a mere fable

The ill-informed Protestant objects:
1. Catholicism teaches papal infallibility, the doctrine that the Pope cannot err on matters of faith and morals.
2. Pope Leo X said, "All ages can testifie enough howe profitable that fable of Christe hath ben to us and our companie."
3. But Christ is not a fable, and so Pope Leo X was not infallible.
4. Therefore, Catholicism is false.

Pope Leo X (1475-1521) never said this. The quote comes from the satire The Pageant of the Popes by Protestant John Bale (1495-1563).

Wednesday, November 15, 2006


Purpose of Sacraments
The sacraments can be thought of as medicine for the spirit. God's providence provides, in accordance with human nature, signs that are corporeal and sensible to the spirit and intellect. There are seven sacraments. However, not all of these sacraments are essential for salvation.

Necessity of Baptism
Baptism is necessary for salvation. However, for those who cannot be baptized by immersion in water (this is how I will be baptized; however, sprinkling and pouring are sufficient as well, according to Ezek 36:25 and Heb 10:22), there are two other types of baptism that save: baptism of blood (martyrdom - Is 4:4) and baptism of desire. Baptism is to occur once (Eph 4:5). Baptism of blood is the most excellent kind of baptism (Jn 15:13).

Eucharist, The Chief Sacrament
The Eucharist is the chief sacrament because contains all the dimensions of Jesus Christ's body really, substantially, and immovably (Jn 6:50-59). However, it is not necessary for salvation.

Necessity of Penance
On the other hand, to be saved one must do Penance (Lk 13:3; James 1:15), for mortal sins cannot be forgiven without confessing them! Penance/holy water/bishop's blessing/Lord's Prayer is also necessary after venial sins. Unlike Baptism, it is a repeatable sacrament. Some sin still remains after the forgiveness of mortal sins (Mk 8:24).


Tuesday, November 14, 2006

Objections to the Resurrection Overview

Objection 1: Jesus didn't really die on the Cross.
Reply 1: Soldiers pierced Jesus' side with a spear. Blood and water flowed out of the wound, proving that physical death had occurred. [John 19:34]. Journal of the American Medical Association says that Jesus' death was ensured when the spear, thrust between His right rib, perforated His right lung and the pericardium of the heart. Jesus declared that He was dying. [Luke 23:46] Roman soldiers didn't bother breaking Jesus' legs, a common procedure used to hasten death. [John 19:33] Pilate double-checked to see if Jesus was dead before giving the corpse to Joseph for burial. [Mark 15:44-45] If Jesus was not dead from the crucifixion, he would have died while in the sealed tomb wrapped in about 100 lbs. of cloth and spices for three days [Matt. 27:60; John 19:39-40], due to lack of food, water, and medical treatment.
Objection 2: Jesus' post-resurrection appearances were unimpressive to the disciples who heard about them (and should have been expecting them) and even to those who witnessed them or they were cases of mistaken identity.
Reply 2: This is a gross misrepresentation of the accounts. Occasionally there was difficulty recognizing Jesus, but in every case it was only temporary. Perplexity, sorrow, the dimness of the light, visual distance, the suddenness of Jesus' appearance, the different clothes He was wearing, and spiritual dullness or disbelief were some factors causing this difficulty. Before the appearances were over, the witnesses had absolutely no doubt that Jesus Christ, whom they had known intimately for many years, had arisen in a literal, physical body.
Objection 3: Joseph of Arimathea stole Jesus' body from the tomb.
Reply 3: Since St. Joseph of Arimathea was a disciple [Luke 23:50-51] we can eliminate the motive of preventing the disciples from stealing it. Joseph could have produced the body and discredited the entire story if he was not a follower of Christ. Joseph, a pious Jew, would not have broken the Sabbath [Luke 23:50-56]. A Roman guard stationed in front of the tomb [Matt. 27:62-66] would have seen Joseph's torches at night. The women came at dawn the next morning [Luke 24:1]; there was no opportunity for Joseph to remove the body. Where would Joseph put the body? Christ's body was never found, despite the fact that almost two months passed before the disciples started preaching; this was an abundant time frame in which to expose a fraud. This theory, lacking a means, motive, and opportunity, is junk.
Objection 4: The Passover Plot is the best explanation of the so-called resurrection accounts.
Reply 4: The Passover Plot is false. It contradicts the Gospels' early dates, the known character of Jesus and His disciples, the permanently empty tomb, the explicitly physical nature of the resurrection appearances, the verification of Biblical narratives by history and archaeology, the multiplicity of the eyewitness accounts, and the incredible number of eyewitnesses of the resurrected Jesus Christ.
Objection 5: There are no good reasons to accept the Gospels' resurrection accounts over non-Christian resurrection claims.
Reply 5: Non-Christian resurrection claims must be rejected. In the cases of Apollonius of Tyana, Sabbatai Sevi, Rabbi Judah, and Kabir, there are no credible witnesses, no contemporary records, no physical evidence, only some claims to deification, and no corroborating miracles. However, in the case of Jesus Christ's resurrection, there are numerous credible witnesses, numerous contemporary records, abundant physical evidence, claims to deity, and numerous other confirming miracles.
Objection 6: David Hume proved that miracles are false. The resurrection is a miracle. Therefore, the resurrection story is false.
Reply 6: David Hume, in his "hard" argument against miracles, begs the question by saying that miracles are impossible by definition. In his "soft" argument, Hume begs the question, is inconsistent with his own epistemology, ignores contrary evidence, proves too much, and makes scientific progress impossible. Hume's test for the truthfulness of witnesses confirms that the New Testament witnesses, especially those to the resurrection, are trustworthy. Hume's self-canceling witness argument is false because not all miracles are created equal, either by the alleged miracles' nature, the physical evidence, and the number and reliability of witnesses. If wisdom is proportioning belief to the evidence, then Hume lacked wisdom.
Objection 7:
Reply 7:
Objection 8:
Reply 8:
Objection 9:
Reply 9:
Objection 10:
Reply 10:


Monday, November 13, 2006

Abortion Discussion Pt. 2: Rape

Rape is undeniably intrinsically wrong. It is violent and traumatic for the woman and she needs compassionate, prayerful counseling. Rape rarely results in pregnancy, but what about the times when a child is conceived? Abortion (murder of the baby) does not follow; two wrongs do not make a right, and to abort the baby would be to match violence with violence against an innocent person. The child conceived is not at fault; it is unjust to murder an innocent unborn baby for the grave sin of his father. The baby is a victim; it is only the rapist who is the aggressor. It is better for the woman to give birth to her child; she will not have the guilt of murdering the baby.

One fact of life is having to care for persons when it is not convenient for us; we are still obligated to care for those people. Bearing a child would be laborious, but it just unjust to murder someone of whom it is inconvenient to take care. The intelligent, dedicated, and hardworking Roman Catholic apologist Dave Armstrong made a perfectly analogous scenario. A young, helpless child turns up at the door of an isolated, warm home in the arctic. Leaving the child to die would be wrong; instead, it is necessary to give the child food and shelter. If the pregnant woman does not have the resources to care for a child, she may arrange for care by loving foster parents for the time being.

Right now the weather is utopic, just like the weather on May 20, 2006. The conditions combine to form extraordinarily pleasant weather:
Mostly Cloudy
Feels Like:
29.87 in and rising
10 mi
E 17 mph
6:36 am
4:35 pm

Sunday, November 12, 2006

Demonic Possession

Demonic possession is just mental illness and not supernatural

Do the following sound like ordinary mental illness?

Mark 1:23-27
23 Now there was a man in their synagogue with an unclean spirit. And he cried out, 24 saying, "Let us alone! What have we to do with You, Jesus of Nazareth? Did You come to destroy us? I know who You are--the Holy One of God!" 25 But Jesus rebuked him, saying, "Be quiet, and come out of him!" 26 And when the unclean spirit had convulsed him and cried out with a loud voice, he came out of him. 27 Then they were all amazed, so that they questioned among themselves, saying, "What is this? What new doctrine is this? For with authority[a] He commands even the unclean spirits, and they obey Him."

Mark 5:1-20
1 Then they came to the other side of the sea, to the country of the Gadarenes.[a] 2 And when He had come out of the boat, immediately there met Him out of the tombs a man with an unclean spirit, 3 who had his dwelling among the tombs; and no one could bind him,[b] not even with chains, 4 because he had often been bound with shackles and chains. And the chains had been pulled apart by him, and the shackles broken in pieces; neither could anyone tame him. 5 And always, night and day, he was in the mountains and in the tombs, crying out and cutting himself with stones.6 When he saw Jesus from afar, he ran and worshiped Him. 7 And he cried out with a loud voice and said, "What have I to do with You, Jesus, Son of the Most High God? I implore You by God that You do not torment me." 8 For He said to him, "Come out of the man, unclean spirit!" 9 Then He asked him, "What is your name?" And he answered, saying, "My name is Legion; for we are many." 10 Also he begged Him earnestly that He would not send them out of the country. 11 Now a large herd of swine was feeding there near the mountains. 12 So all the demons begged Him, saying, "Send us to the swine, that we may enter them." 13 And at once Jesus[c] gave them permission. Then the unclean spirits went out and entered the swine (there were about two thousand); and the herd ran violently down the steep place into the sea, and drowned in the sea. 14 So those who fed the swine fled, and they told it in the city and in the country. And they went out to see what it was that had happened. 15 Then they came to Jesus, and saw the one who had been demon-possessed and had the legion, sitting and clothed and in his right mind. And they were afraid. 16 And those who saw it told them how it happened to him who had been demon-possessed, and about the swine. 17 Then they began to plead with Him to depart from their region. 18 And when He got into the boat, he who had been demon-possessed begged Him that he might be with Him. 19 However, Jesus did not permit him, but said to him, "Go home to your friends, and tell them what great things the Lord has done for you, and how He has had compassion on you." 20 And he departed and began to proclaim in Decapolis all that Jesus had done for him; and all marveled.

Mark 9:14-29
14 And when He came to the disciples, He saw a great multitude around them, and scribes disputing with them. 15 Immediately, when they saw Him, all the people were greatly amazed, and running to Him, greeted Him. 16 And He asked the scribes, "What are you discussing with them?" 17 Then one of the crowd answered and said, "Teacher, I brought You my son, who has a mute spirit. 18 And wherever it seizes him, it throws him down; he foams at the mouth, gnashes his teeth, and becomes rigid. So I spoke to Your disciples, that they should cast it out, but they could not." 19 He answered him and said, "O faithless generation, how long shall I be with you? How long shall I bear with you? Bring him to Me." 20 Then they brought him to Him. And when he saw Him, immediately the spirit convulsed him, and he fell on the ground and wallowed, foaming at the mouth. 21 So He asked his father, "How long has this been happening to him?" And he said, "From childhood. 22 And often he has thrown him both into the fire and into the water to destroy him. But if You can do anything, have compassion on us and help us." 23 Jesus said to him, "If you can believe,[a] all things are possible to him who believes." 24 Immediately the father of the child cried out and said with tears, "Lord, I believe; help my unbelief!" 25 When Jesus saw that the people came running together, He rebuked the unclean spirit, saying to it, "Deaf and dumb spirit, I command you, come out of him and enter him no more!" 26 Then the spirit cried out, convulsed him greatly, and came out of him. And he became as one dead, so that many said, "He is dead." 27 But Jesus took him by the hand and lifted him up, and he arose. 28 And when He had come into the house, His disciples asked Him privately, "Why could we not cast it out?" 29 So He said to them, "This kind can come out by nothing but prayer and fasting."[b]


Saturday, November 11, 2006

Happy Veteran's Day 2006

Happy Veteran's Day. God bless the Veterans, and those soldiers serving a just cause everywhere, particularly our troops in Iraq and Afghanistan. Read my January 10 post for why it is necessary to support our VFW at Today I had the good fortune to see the Veteran's Day Parade in New York City.

Friday, November 10, 2006

Abortion = Murder, Double Effect, Catholic Teachings, and Research on Aborted Fetuses

This will be a longer paper on abortion that combines and fleshes out my previous posts on it...

Humanity is not a measure of development. A one-week old embryo is as human as an eight-month old fetus, for they both have human DNA and an immaterial soul, made in the image of God, and a spirit. In other words, human nature is present from conception.

1. Murder is prohibited in the Fifth Commandment.
2. The Fifth Commandment is from God.
3. Abortion is murder.
4. Therefore, abortion is prohibited by God.

Premise 3 is demonstrably true. Abortion truly is murder because it is the direct and intentional slaughter of an innocent person. Doctors need to do everything in their power to save the lives of the mother and the unborn child if, for example, surgery is clearly and immintently necessary to save the mother's life. The superbly just principle of Double Effect demands that the action is intrinsically good or morally neutral, that the evil effect of must not cause the good effect and the evil effect must be merely permitted and not desired in itself, and permission of the evil must only be granted for sufficiently grave reasons. If and only if all these conditions are met is the death of the baby morally acceptable, since it would be an unintended side effect of a legitimate medical procedure and not murder.

Research on aborted fetuses is also wrong. Not only is aborted tissue not very useful, but the results of abortions are linked to the objectively evil means by which they were obtained, and thus the use of aborted tissue makes one complicit in the murder of unborn children.

The Didache, from the first century A.D., records apostolic teachings which include an explicit ban on abortion and infanticide.

The baby must not be treated simply as disposable property, which is how slaves were treated in the New World. Because the unborn child is a person, it has that same right of every innocent being: the inalienable right to life.

The fact that abortion is legal does not make it moral. Humans in the age of exploration were treated as cattle; slavery was legal, but not moral.
Coming in Part 2: Discussion of abortion in the cases of incest and rape.

Requirements for Trinitarian Orthodoxy

An orthodox model of the Trinity must not diminish the divinity of the persons. It must state that the Father is fully God, the Son is Fully God, and the Holy Spirit is fully God. At the same time, it must deny that each of the persons is a "part" of God or 1/3 of God. It must not say that the persons are divine because of their participation in the Trinity; rather, the persons participate in the Trinity but they are intrinsically fully divine. In other words, the persons, having the same essence, are necessarily infinitely divine in themselves.


Thursday, November 09, 2006

Models of the Trinity

What is the best model of the Trinity? Surely there exists a Trinity of persons in God, for that is what God Himself revealed to us, and God must have a plurality of persons in Him in order to be a perfectly loving being. But which is the superior illustration of the nature of the Trinity? Social trinitarianism or anti-social trinitarianism? Which model is independently plausible and does not suffer from the defects of the other models? At this point Social Trinitarianism seems doubtful to me.

Wednesday, November 08, 2006

Anti-Social Trinitarianism

In their wonderful and must-buy book Philosophical Foundations for a Christian Worldview, William Lane Craig and J.P. Moreland critique Thomistic anti-social Trinitarianism. Their criticisms do not seem to defeat St. Aquinas' model of the Trinity, however, and I will try to show this by presenting their arguments in a fair and accurate way and providing links to the relevant sections of Aquinas' must-read theological masterpiece Summa Theologica where their objections are answered.

Is ATS truly orthodox (truly Trinitarian), or does it collapse into the heresy of modalism?
Their logical argument against ATS is composed of the following basic ideas.
1. Persons cannot be equated with relations.
St. Aquinas: Relation is the same as person in God.
2. If God is absolutely simple, there are no real relations in God.
St. Aquinas: God is altogether simple and yet there are real relations in God; they are intrinsic to the Divine essence and are four in number.
3. Furthermore, given divine simplicity, the relations cannot really be distinguished from another.
St. Aquinas: The relations are truly distinct from each other.
4. It is not correct to say that there is procession or generation in God.
St. Aquinas: There is procession in God, and one of the processions is generation. The Father is the Principle and it is proper to Him to be unbegotten; the holy doctors correctly assigned attributes to each person. The three persons are co-eternal, and the Father begetting and the Son being begotten are consistent with the omnipotence of all the persons. The persons are co-equal and this fact is harmonious with there being an order of nature in the Trinity. The Father and Son are but one principle of the Holy Ghost, Who proceeds from the Father through the Son.
5. The persons aren't distinguished by the relations and so there cannot really be a plurality of persons.
St. Aquinas: The relations distinguish and constitute the persons, and this is consistent with divine simplicity.

But, let's assume the relations in God really do constitute distinct persons, Craig and Moreland say. Their ideas, enumerated below, lead to the false conclusion that AST's proposed subsisting relations do not fit the bill of true personhood.
1. Then there would be an infinite regress of persons who understand and love themselves.
St. Aquinas: There are only two processions in God, and only three persons in the AST model.
2. The Son cannot be said to be in the Father.
St. Aquinas: The Son is in the Father, and the Father is in the Son.

Tuesday, November 07, 2006

Overview of Objections To Eucharist

Objection 1: Drinking blood is prohibited in Gen 9:4; Dt 12:16; Acts 15:20.
Reply 1: The prohibition refers to animal blood, not the Lord's blood as Jesus commanded us to drink in Jn 6:53-57.
Objection 2: A literal Eucharist is cannibalism.
Reply 2: It's not cannibalism, because we eat the accident of bread and drink the accident of wine, but the substances supernaturally present are Jesus' real Body and Jesus' real Blood.
Objection 3: The Eucharist is not to be found in the Apostles' Creed.
Reply 3: This is because a creed is simply a brief summary and doesn't contain nearly ALL the doctrines of a given belief system.
Objection 4: There are no good linguistic or historical reasons to accept the Real Presence.

Reply 4: In 700 A.D., an Italian priest who was starting to doubt the Real Presence saw the Host become real flesh and the wine become real blood, which were fresh through 1970 and confirmed by scientific testing. There are many other confirmed Eucharistic miracles. Secondly, many of Jesus' disciples were so disturbed by Jesus' teaching as to walk away, but Jesus did not say, "Wait, I meant that this is a symbol or representation of My Body and Blood." He emphatically affirmed several times that it IS His real Blood and real Body.


Monday, November 06, 2006

God & Numbers

There is one God.

One of the three persons in God has two natures, a divine nature as well as a human nature.

There are four relations in God: paternity, filiation, spiration, and procession.

There are five notions in God: innascibility, paternity, sonship, common spiration, and procession.

Friday, November 03, 2006

Today was not a good day for school sports teams. During football, huge snowflakes started to come down, which was fun and was the first snow of the year out here; it'll probably be a white Christmas, considering how cold the weather's been over the past several weeks. In cross country, my pace should have been up to 30 seconds faster, and the other faster guys on the team did not do well compared to what they could have done either, had the weather not been so cold and constricting on the lungs, and perhaps had the race been at a different time of day. Just before Cardiac Hill at the Meadow, my legs died and so I was extremely slow going up Cardiac, adding about a minute to my time. The last race is on Monday and I hope the conditions favor my time being reflective of my true muscular strength and cardiological fitness.

Wednesday, November 01, 2006

Happy November. The days continue to pass very quickly, as they have since 2005.