Papist Orthodoxy

November 30, 2009

Why Most High School Students Hate Math

Filed under: Education — Tags: , , — Antiochian-Thomist @ 6:45 pm

Also entitled: THE GROWING DIVIDE BETWEEN THE LINGUISTIC & MATHEMATICAL ARTS

The denial of axioms, those first principles that are either self evident or derived from a higher science, has led to an utter separation of the mathematical arts from the linguistic arts in the general liberal arts to the detriment of both general fields of study. This process began with force with the reformulation of the ancient order of the mathematical arts beginning with the reconsideration of the classical geometry of Euclid. Once the primacy of Euclid was destroyed and geometry seen in a new light of symbolic signs from which new and further abstractions could be gleaned, the mathematical arts further developed which gave rise to the new primacies of the algebras and calculus. Though the new primacies are not necessarily to be lamented in themselves, the preoccupation with the manipulation of numbers, variables, and other symbols abstracted from nearly all intelligible realities has led the mathematical arts into an isolated world with minimal contact and sharing with the world of the linguistic arts.

I. GEOMETRY OVERTHROWN

The classical geometry of Euclid had a multitude of benefits which contributed to its long reign as the basic mathematical art. Firstly, it proceeded from indemonstrable first principles which were (and are) self-evident, and, thus, common to many arts and sciences. Common notions such as “the whole is greater than the part” or “things which are equal to the same thing are also equal to each other”1 were the bedrock principles upon which Euclid’s geometry was based. Secondly, the fundamental geometric realities that were the considerations of classical geometry were and are immediately abstracted from the natural, material world. Thus the concepts of magnitude, square, circle, and triangle, once the varying qualities of matter were left behind, could be considered in their perfections. Thus this conceptual art was eminently intelligible to the intellect as its conceptual realties were immediately abstracted from nature and its proofs were based on arguments that proceeded from self-evident first principles.

While its intelligibility was without question, certain aspects of the classical geometry underwent further development especially in the realm of abstraction. The proofs, although well argued, possessed an inefficiency of expression that could be “streamlined” if further abstractions were performed. Further, with these additional abstractions, alternate considerations could be applied to the signified magnitudes that were not able to be performed previously, viz. arithmetic operations. Many, including the likes of Dr. Otto Bird, assert that René Descartes pioneered this consideration. In Descartes’ work, The Geometry, he asserts:

“Any problem in geometry can be reduced to such terms that a knowledge of the lengths of certain straight lines is sufficient for its construction. Just as arithmetic consists of only four or five operations, namely, addition, subtraction, multiplication, division, and the extraction of roots…so in geometry, to find required lines it is merely necessary to add or subtract other lines.”2

In short, Descartes takes a magnitude and reduces it to a unity which serves to be the measure of other magnitudes. Geometric magnitudes, then, are reduced to numbers. This is done by way of assigning letters to the magnitudes themselves and then performing an arithmetic operation. With this assertion, many claim, came the dawn of analytic geometry and the birth of the Cartesian coordinate system3 and the subordination of geometry to algebra as all geometric realities become a relation of numbers, with numbers themselves as expressed as variables, and not magnitudes, becoming the principle object of consideration. It is for this reason Dr. Bird says:

“Since all the variable letters in our equation represent numbers the geometric line is no longer anything that need be done geometrically; it can be done with numbers. So lines, curves, figures, solids and their relations can all be determined by equations which ultimately are but variable expressions for numbers. Thus Euclid’s Pythagorean Theorem4 proven as a relation between the sides of a triangle, and squares erected on them can now be stated, as we saw, much more simply as A2 + B2 = C2, where at issue is a matter of numbers even though they may also be taken as the lengths of the sides of the triangle. The arithmetical algebraic expression is admittedly more abstract than the corresponding geometric expressions, but it is simpler and easier to work with. Geometry has been arithmetized.”5

In addition to the additional abstraction applied to geometry further removing the signs from the original signification, mathematicians like Descartes established a new precedent by beginning their works not from axioms or any principle from a higher science but from postulates. Granted, Euclid worked from postulates as well, but not exclusively. Rather, he proceeded from postulates stemming from axioms and definitions thus rooting his art and argument in principles that require not blind ascent but common, rational experience. Further, Galileo and Newton also proceeded from axiomatic principles, but their era saw the dawn of arts that posited their own principles that defied scrutiny from other arts and sciences. Other developments in the mathematical arts certainly contributed to the replacement of geometry as the basic mathematical art, but non so much as the first introduction to numeric abstractions and the abandonment of axiomatic principles.

II. MATHEMATICAL STUDIES AFFECTED

With new primacies came new considerations. With old boundaries removed, so went many of the old obstacles. With the advent of variable numeric representation came the reconciliation, or rather the “ever approaching reconciliation”, of that which was formerly believed to be utterly irreconcilable: the curve with the straight and the discreet with the continuous. The efforts of Copernicus, Kepler, Brahe, Galileo, Descartes, Newton, Bonola, etc. allowed for curved realities to be given representation with discreet alphanumeric signification. Naturally, this called the necessity of the traditional mathematical arts as the principle mathematical arts of consideration into question, or, at least, called them into question insofar as how they were considered. Music and astronomy as the principle arts of ratios and mobile magnitudes respectively were replaced by more universal and abstract algebraic understanding of ratios and more universal applications of calculus to mobile beings in general. As stated before, these developments are not necessarily to be lamented insofar as they are productive of more profound knowledge of realities, whether they be concrete or conceptual. But the arts, or, rather, their proponents did not stop there.

Coupled with the abandonment of the scholastic understanding of the universe and its causes, including the disavowal of traditional metaphysics and theology, mathematics took on a new import which it previously did not enjoy and consequently affected its study insofar as its import was concerned. Theology and philosophy were no longer the highest sciences. With the sloughing of the scholastic world-view, the essence of things, natures as such, were no longer the most sought after knowledge for the means to know natures were abandoned. Instead, that which was most knowable to man became the most sublime to him: quantity. As a result, mathematics ascended to primacy among the sciences, a status it enjoys to this day. Let us return again to Descartes and his peers:

“Since the only known natural sciences with some degree of systematic coherence were astronomy and mechanics, and the key to the understanding of mechanics and astronomy was mathematics, mathematics became the most important means to understanding the universe. Moreover, mathematics with its convincing statements was itself the brilliant example that truth could be found in science. The mechanistic philosophy of this period thus came to a conclusion that was similar to that of the Platonists, but for a different reason. Platonists, believing in the harmony of the universe, and Cartesians, believing in a general method based on reason, both found in mathematics the queen of the sciences.”6

This new pedestal upon which mathematics was placed perpetuated infatuations that exacerbated its abstract nature and considerations. Abstractions and their manipulations themselves became the primary concern in many circles resulting in a “science of symbols” where often the symbols themselves were abstracted from any meaning whatsoever. Weber, Frege, and Peano were pioneers in this filed. As bizarre as this may sound its effects were far reaching, the evidence of which can be seen in most high school math textbooks to this day, much to the chagrin and consternation of many a high school student. Struik notes it well:

“…Algebra changed its ancient character. Instead of merely encompassing the theory of algebraic equations and the associated theory of invariants and covariants, it became the abstract doctrine of today with its rings, fields, ideals, and related concepts. One of the origins of the newer algebra was the development of group theory from Galois theory of algebraic equations into an abstract theory in its own right, especially in the theory of finite groups, thus setting a model for the transformation of algebra as a whole.”7

As history has shown, those arts which enjoyed primacy, if not in reality then by popular acclamation, subordinated others arts and often attempted to subsume them to themselves. Advocates of mathematics were no different. The venerable art of logic was the target for this attempted annexation with the most poignant attempts by the likes of Russel, Whitehead, Cantor, and Frege. Logic itself became the target of abstract symbols for its signification with the imposition of symbolic logic with its two subcategories, propositional and predicate. The attempt as noted by both Struik8 and Bird9 ultimately failed but the efforts persisted. The effects are still seen today in texts and graduate institutions that insist upon teaching symbolic logic in their philosophical programs.

III. THE GULF BETWEEN THE TRIVIUM & QUADRIVIUM WIDENED

Mathematics has abandoned the axiomatic system. This was the first and most fundamental break which has led to other divisions between the mathematical and linguistic arts. Without self-evident first principles, how can real knowledge be had? What relation then exists between the linguistic arts which are eminently grounded in reality and an art which seeks not sound and indemonstrable principles? Can mathematics now claim what it once could as expressed in the mouth of Dr. Bird?

“In fact it’s no exaggeration to claim that mathematics has provided the clearest and most explicit instance of reason, of reason itself at work, of reason reasoning, in its development of the axiomatic method. The earliest and most extensive use of this method is to be found in the thirteen books of Euclid’s Elements.

[…]

In denying that there aren’t any self-evident axioms these people are denying that there are any axioms in the old sense as principles distinct from postulates, with the result that the two words have come to be used interchangeably. In any case, an axiomatic system is one that begins from certain indemonstrable principles from which certain other propositions can be deduced as conclusions. “10

Ironically, the attempt to bridge the gap between the linguistic and mathematical arts by attempting a pure mathematics that could be propositionally inferred from earlier principles only served to broaden the chasm between the two general arts. The attempt at reducing logic to a branch of mathematics was intrinsically an attempt at reducing all sciences to the jurisdiction of mathematics –sciences that had concerns over and above that which was quantifiable. As a result, symbolic logic has been relatively ineffectual in the other arts (including philosophy in spite of its persistence) and has only enjoyed any real and lasting effects in mathematical logic. Instead of subsuming logic, mathematics, or rather mathematicians, developed its own language of logic apart from the linguistic arts. But this was not always the case with mathematics and logic. As Dr. Bird points out so well:

“…It is better to retain the old understanding of logic as the study of the principles that assure the validity of inference, and that its laws are those of the laws of the other sciences. Logic is thus the science of sciences, as Aristotle called it, or the art of arts, as Saint Thomas called it.

[…]

Mathematics since the time of its development by the ancient Greeks has always been prized for the power and beauty of its reasoning, and indeed for its ability to form and train the faculty of reasoning itself. As long as Euclid was studied as the basic introductory work to mathematics, Euclid’s geometry provided the basic training for the logic of argument. It provided the basic understanding of what a proof is and the means of constructing and establishing a proof. “11

The former complementarity enjoyed by the trivium and quadrivium through the cooperation of geometry and logic has died. If logic is found to be taught at all in schools, it is done so independent from geometry when this would never have been the case in ancient or medieval education. Hence we have one clear rift between the mathematical and linguistic arts.

Finally, a rift exists between mathematics and reality. Due to the aforementioned obsession with the manipulation of abstractions without any reference to that which is meant to be quantified, mathematics, at least in the general sense of the liberal arts as found in high school and undergraduate institutions, is practically divorced from all reality, concrete or conceptual, since it has become a “science of symbols” meant to arbitrarily signify anything in general or nothing in particular. The ancient considerations of mathematics, whether it was geometry, algebra, or calculus, though abstracted, abstracted from that which was real and considered that which was real. This was true for Euclid’s Elements, Apollonius’s Conic Sections, Ptolemy’s Almagest, Galileo’s Two New Sciences, Descartes’ Geometry, or Newton’s Principia. Now, reference to the real which was once found in the ancient quadrivium can often be more readily found in the more advanced and specialized mathematics proper to certain vocations –not to education in general. The linguistic arts have not suffered this problem; thus the widening between the linguistic and mathematical arts.

BIBLIOGRAPHY

1. Bird, Otto, Ph. D. “The Mathematical Arts of the Quadrivium II”, a lecture given for the International Catholic University and Holy Apostles College & Seminary for the course, “Liberal Arts: Their History & Philosophy”, 2005.

2. Euclid. The Elements of Geometry, Thomas Health (translator), Dover Publications, New York. 1956.

3. Descartes, Rene. The Geometry, David Smith & Marcia Latham (translators), Dover Publications, New York. 1954.

4. Struik, Dirk J. A Concise History of Mathematics, fourth edition, Dover Publications, New York. 1987.

1Euclid. Elements of Geometry, Book I, Common Notions 1 and 5.

2Descartes, René. The Geometry, Book I

3Struik, D. A Concise History of Mathematics, pp. 96-99. Struik points out that many others that preceded Descartes used what could be considered a numeric coordinate system, including the likes of Apollonius of Perga, Ptolemy, and Oresme. Nonetheless, he does not deny that Descartes work was of the greatest influence on coordinate systems and analytic geometry.

4Euclid. Elements of Geometry, Book I, Proposition 47

5Bird, Otto, Ph. D. “The Mathematical Arts of the Quadrivium II”, a lecture given for the International Catholic University and Holy Apostles College & Seminary, 2005.

6Struik, D. A Concise History of Mathematics, Chapter VI, Section 3

7ibid. Chapter IX, Section 6

8ibid. Chapter IX, Section 7

9Bird, Otto, Ph. D. “The Mathematical Arts of the Quadrivium II”

10 ibid.

11 ibid.

Advertisements

Analogy in St. Thomas’ Philosophy

Filed under: Philosophy, Uncategorized — Tags: , , — Antiochian-Thomist @ 1:55 am

Philosophy, the love of wisdom, is a general title covering many particular disciplines which should lead its practitioners to the knowledge of the highest things from a human perspective. From the proper Christian perspective, it should culminate in and serve as a handmaid to theology for true knowledge and wisdom culminates in its highest, first, and final cause which is God. One difficulty man encounters is that he cannot know God as He knows Himself. Man must proceed from God’s effects, viz. the created material order. Even with divine revelation, that same revelation is put in the words of human language, the tongues of men. Thus it was also for the Incarnation of the Word and His redemption of mankind. Christ spoke by similitude, using analogy and parables to instruct man about God. But the infinite God is beyond the powers of the finite intellects of men. Therefore we can only get to God by a likening of Him to His effects. As all men are meant to know God in some way, to philosophize in a meaningful manner requires man to use analogy, likening the highest object of our inquiries, God, to His effects, the sensible order. Thus it was for the Common Doctor, St. Thomas Aquinas. Thomas rooted his philosophy in the common, sensible, and named experiences of men rendering it accessible to everyone, and by use of analogy, unified his philosophy into an integrated whole which brought man from the his common, sensible experiences to the highest considerations of things divine.

Aristotle distinguishes between things named equivocally and univocally.1 Equivocal terms are terms which have more than one meaning, these meanings themselves having no apparent relation to each other. Univocal terms carry its meaning throughout its various uses. St. Thomas, in view of the end for which he wrote, refined Aristotle’s distinctions by employing analogous terms, terms which have more than one meaning, those meanings having some sort of relation to each other by way of comparison. D.Q. McInerny sums it up well when he says:

An analogous term might be described as a hybrid between a univocal term and an equivocal term. Analogous terminology, and behind that analogous thinking, is based upon the act of comparison, which is one of the most elemental movements in human reasoning.2

So it was that the Common Doctor, in seeking to keep an accessible consistency in his philosophy, employed analogous terms drawing comparisons between the sensible order, that order which is first known to man, and its cause – God. In order to illustrate this claim more clearly, let us look at St. Thomas’ considerations of “act” and “potency”.

In the De Potentia of the Disputed Questions, St. Thomas first asserts that one cannot consider act apart from potency for the terms are correlated. By way of a similitude, it would be difficult to consider “up” apart from “down”. Then, Thomas considers act as twofold: 1) as form, and 2) as operation. The first is first absolutely, but the second is first by our sensible experience:

I answer that to make the point at issue clear we must observe that we speak of power in relation to act. Now act is twofold; the first act which is a form, and the second act which is operation. Seemingly the word ‘act’ was first universally employed in the sense of operation, and then, secondly, transferred to indicate the form, inasmuch as the form is the principle and end of operation.3

So he begins with the sense experience wherein man sees ‘act’ as an operation – something doing something. The formal aspect of ‘act’ received its nomenclature from the operation even though the form as the principle of the operation is the cause of that operation. St. Thomas asserts that the term was literally “carried over” or “transferred” (translatum). Thus the first meaning or understanding of the term ‘act’, viz. its operation, was stretched, as it were, to encompass the cause of the operation, viz. the form, for the cause is related to the effect, the form is related to the operation. Now we have a term that has multiple but related meanings as we proceed “up”.

But before Thomas proceeds up, he proceeds “across”, for his next consideration is potency or power. He draw a similitude (similiter) with act and asserts that potentia is twofold as well drawing a direct relation with the respective twofold consideration of actus. Immediately following upon the above quotation, St. Thomas goes on to say:

Wherefore in like manner power is twofold: active power corresponding to that act which is operation—and seemingly it was in this sense that the word ‘power’ was first employed:— and passive power, corresponding to the first act or the form,—to which seemingly the name of power was subsequently given.4

Thus what was first attributed to actus by experience was similarly first attributed to potentia. If a thing acts, it follows that it has the power to act. This potency, to distinguish it, was give the appellation, “active potency” (potentia activa). Likewise, as the term, actus, was ‘transfered’ to encompass the cause which is the form, so the term, potentia, was transferred to encompass that sufferable or perfectible aspect of the form and was entitled, “passive potency” (potentia passiva). Whence it is that, by way of example, Orville the pianist can become the better pianist.5 Therefore, that which is prior absolutely received its name from its effect or operation.

This series of ‘stretching’ or ‘transferring’ from the action to the principle of action by way of analogy must find a termination; and so it does in the first act. However, as St. Thomas ascends he must begin a series of negations by which those things which cannot be attributed to God’s nature must be sloughed. As we see in Thomas’ arguments for the existence of God, that which is “able to be” must be brought into being by that which is (in act) already.6 And as God cannot suffer change and as He must be perfect, He cannot admit of a passive potency. We see how he argues this in the second part of his corpus of the same question we have been treating thus far:

Now, just as nothing suffers save by reason of a passive power, so nothing acts except by reason of the first act, namely the form. For it has been stated that this first act is so called from action. Now God is act both pure and primary, wherefore it is most befitting to him to act and communicate his likeness to other things: and consequently active power is most becoming to him: since power is called active forasmuch as it is a principle of action.7

An operation can only occur because of the form, i.e. an act can only be performed by something in act. But as we ascend up the material order to God, we must negate that passive power, for God cannot suffer or be perfected because He is perfect in Himself. Therefore, God has not passive potency but active potency, for though He cannot suffer, He is able to perform or not perform operations as He is the first principle of action.

Thomas explores this consideration of negation further to solidify and unify his argument, and he also takes the time to note the human need for analogous terminology:

We must also observe that our mind strives to describe God as a most perfect being. And seeing that it is unable to get at him save by likening him to his effects, while it fails to find any creature so supremely perfect as to be wholly devoid of imperfection, consequently it endeavours to describe him as possessing the various perfections it discovers in creatures, although each of those perfections is in some way at fault, yet so as to remove, from God whatever imperfection is connected with them.8

In short, we can only know God through his effects and name him analogously. As we believe and endeavor to describe Him as perfect, our attributions are imperfect, for no human term can adequately describe God; even our positive assertions ultimately fail. To illustrate this, the Common Doctor goes on the give the example of “being”, “substance”, and “subsistence”. “Being” describes something as complete but without the notion of “subsistence”. The term, “substance”, denotes subsistence but as also the subject of something else. Yet we still ascribe “being” and “substance” to God. We do this because our first experience with beings and substance are in the sensible order of creation. As we proceed up and as we carry over or transfer terms, we negate aspects that would be erroneous to attribute to God. Thus, though we see being as simple but inhering in something, when we speak of God, we keep the notion of simplicity as we slough the notion of inherence. Likewise, when we speak of substance as attributed to God, we keep the notion of that continuing or persisting existence while sloughing the notion of “standing under” as individual of a species or as species of a genus.9 With this illustration, St. Thomas goes on to conclude his arguments regarding act and potency in respects to God thusly:

In like manner we ascribe to God operation by reason of its being the ultimate perfection, not by reason of that into which operation passes. And we attribute power to God by reason of that which is permanent and is the principle of power, and not by reason of that which is made complete by operation.

To restate, after we have seen His effects in the created order, we ascribe operation and power, act and (active) potency, to God but not as they are exhibited in His effects, but by abstracting from the material order and negating any imperfections associated with the terms. Thus, by way of analogous naming, St. Thomas has taken us from our sensible experiences and our common usage of terms and, while preserving and expanding those terms, brought us to a better understanding of God, however indirect.

This is just one illustration of many of how the Common Doctor proceeds from effect to cause using fundamental knowledge of the material order to considerations of divine things. St. Thomas uses analogy throughout his whole philosophical system, and in so doing, unites it together into an integrated whole that proceeds from common experience and nomenclature. Truly, he could not do otherwise. Equivocal terminology would not advance knowledge as various definitions of one term are unrelated. Univocal terminology would be just as unsuccessful, for the one-to-one relation of definition to term could not apply in every circumstance, especially when treating of God. God and nature are not a computer programs which can be discerned by way of language bricks, those univocal terms which seem only to work as technical terminology in the mechanical arts. The relation cannot be one-to-one, lest we say that God is being without subsistence, or that He is a substance that is the subject of something else. Nonetheless, if philosophy is properly undertaken, it should lead us to God as from effect to cause. St. Thomas’ use of analogous terminology in his philosophy allows us to do this. The Common Doctor gives an example of the veracity of St. Paul’s declaration:

For what can be known about God is plain to them, because God has shown it to them. Ever since the creation of the world his invisible nature, namely, his eternal power and deity, has been clearly perceived in the things that have been made.10

ADDENDUM

The text in Latin of the De Potentia used for this essay.

From Question 1, article 1, corpus.

Respondeo. Ad huius quaestionis evidentiam sciendum, quod potentia dicitur ab actu: actus autem est duplex: scilicet primus, qui est forma; et secundus, qui est operatio: et sicut videtur ex communi hominum intellectu, nomen actus primo fuit attributum operationi: sic enim quasi omnes intelligunt actum; secundo autem exinde fuit translatum ad formam, in quantum forma est principium operationis et finis. Unde et similiter duplex est potentia: una activa cui respondet actus, qui est operatio; et huic primo nomen potentiae videtur fuisse attributum: alia est potentia passiva, cui respondet actus primus, qui est forma, ad quam similiter videtur secundario nomen potentiae devolutum. Sicut autem nihil patitur nisi ratione potentiae passivae, ita nihil agit nisi ratione actus primi, qui est forma. Dictum est enim, quod ad ipsum primo nomen actus ex actione devenit. Deo autem convenit esse actum purum et primum; unde ipsi convenit maxime agere, et suam similitudinem in alias diffundere, et ideo ei maxime convenit potentia activa; nam potentia activa dicitur secundum quod est principium actionis. Sed et sciendum, quod intellectus noster Deum exprimere nititur sicut aliquid perfectissimum. Et quia in ipsum devenire non potest nisi ex effectuum similitudine; neque in creaturis invenit aliquid summe perfectum quod omnino imperfectione careat: ideo ex diversis perfectionibus in creaturis repertis, ipsum nititur designare, quamvis cuilibet illarum perfectionum aliquid desit; ita tamen quod quidquid alicui istarum perfectionum imperfectionis adiungitur, totum a Deo amoveatur. Verbi gratia esse significat aliquid completum et simplex sed non subsistens; substantia autem aliquid subsistens significat sed alii subiectum. Ponimus ergo in Deo substantiam et esse, sed substantiam ratione subsistentiae non ratione substandi; esse vero ratione simplicitatis et complementi, non ratione inhaerentiae, qua alteri inhaeret. Et similiter attribuimus Deo operationem ratione ultimi complementi, non ratione eius in quod operatio transit. Potentiam vero attribuimus ratione eius quod permanet et quod est principium eius, non ratione eius quod per operationem completur.

BIBLIOGRAPHY

Aquinas, St. Thomas. Quaestiones disputatae de potentia dei. Corpus Thomisticum, Universidad de Navarra, Fundación Tomás de Aquino. 2006

http://www.corpusthomisticum.org/qdp1.html

_______. Quaestiones disputatae de potentia dei. translated by the English Dominican Fathers, Westminster, Maryland: The Newman Press, 1952, reprint of 1932, Html edition by Joseph Kenny, O.P.

http://www.op-stjoseph.org/Students/study/thomas/QDdePotentia.htm#1:1

Aristotle. Categories. H.P. Cooke (translator), Loeb Classical Library, Campbridge, Massachusetts; London, England: Harvard University Press, 1949 & 1996.

McInerny, D.Q. The Philosophy of Nature. Lincoln, Nebraska: Alquin Press, 2001.

McInerny, Ralph. “Analogy”. The third lecture for the course, “Introduction to Thomas Aquinas”, given by Dr. McInerny for the International Catholic University (Notre Dame, Indiana) working in conjunction with Holy Apostles College & Seminary (Cromwell, Connecticut), 2002.

1Aristotle. Categories, 1a, 1-10

2D.Q. McInerny. The Philosophy of Nature, chapter 3, p. 80.

3St. Thomas Aquinas. De Potentia, q.1, a.1, co.

4ibid.

5Dr. Ralph McInerny. “Analogy”. The third lecture for the course, “Introduction to Thomas Aquinas”, given by Dr. McInerny for the International Catholic University working in conjunction with Holy Apostles College & Seminary (2002).

6St. Thomas Aquinas. Summa Theologiae, I, q.2, a.3, co.

7St. Thomas Aquinas. De Potentia, q.1, a.1, co.

8ibid.

9ibid.

10Romans. 1:19-20

November 5, 2009

The American Way of Abandonment

Filed under: Politics — Tags: , , — Antiochian-Thomist @ 1:06 am

by Patrick Buchanan

from Chronicles Magazine

When America is about to throw an ally to the wolves, we follow an established ritual. We discover that the man we supported was never really morally fit to be a friend or partner of the United States.

When Chiang Kai-shek, who fought the Japanese for four years before Pearl Harbor, began losing to Mao’s Communists, we did not blame ourselves for being a faithless ally, we blamed him. He was incompetent; he was corrupt.

We did not lose China. He did.

When Buddhist monks began immolating themselves in South Vietnam, the cry went up: President Diem, once hailed as the “George Washington of his country,” was a dictator, a Catholic autocrat in a Buddhist nation, who had lost touch with his people.

And so, word went out from the White House to the generals. Get rid of Diem, and you get his power and U.S. support. Three weeks before JFK was assassinated, Diem and his brother met the same fate.

When the establishment wished to be rid of a war into which it had plunged this country, suddenly it was “the corrupt and dictatorial Thieu-Ky regime” in Saigon that was simply not worth defending.

Lon Nol, our man in Phnom Penh, got the same treatment.

“In this world it is often dangerous to be an enemy of the United States, but to be a friend is fatal,” said Henry Kissinger.

READ THE REST OF THE ARTICLE HERE.

Newt, Sarah, and a New GOP

Filed under: Politics — Tags: , , — Antiochian-Thomist @ 12:58 am

by Pat Buchanan

from Chronicles Magazine

“Sometimes party loyalty asks too much,” said JFK.

For Sarah Palin, party loyalty in New York’s 23rd congressional district asks too much. Going rogue, Palin endorsed Conservative Party candidate Doug Hoffman over Republican Dede Scozzafava.

On Oct. 1, Scozzafava was leading. Today, she trails Democrat Bill Owens and is only a few points ahead of Hoffman, as Empire State conservatives defect to vote their principles, not their party.

Newt Gingrich stayed on the reservation, endorsing Scozzafava, who is pro-choice and pro-gay rights, and hauls water for the unions.

Scourged by the right, Newt accused conservatives of going over the hill in the battle to save the republic, just to get a buzz on. “If we are in the business about feeling good about ourselves while our country gets crushed, then I probably made the wrong decision.” How Scozzafava would prevent America’s being “crushed” was unexplained.

The 23rd recalls a famous Senate race 40 years ago. Rep. Charles Goodell was picked by Gov. Nelson Rockefeller to fill the seat of Robert Kennedy in 1968. To hold onto it, Goodell swerved sharp left, emerging as an upstate Xerox copy of Jacob Javits, the most liberal Republican in the Senate.

In 1970, Goodell got both the GOP and Liberal Party nominations, and faced liberal Democrat Richard Ottinger. This left a huge vacuum into which Conservative Party candidate James Buckley, brother of William F., smartly moved.

Assessing the field, the Nixon White House concluded that, with liberals split, Goodell could not win. But Buckley might. Signals were flashed north that loyalty to the president was not inconsistent with voting for Buckley. To send the signal in the clear, Vice President Agnew described Charlie Goodell to a New Orleans newspaper as “the Christine Jorgensen of the Republican Party.”

The former George Jorgensen, Christine had undergone the most radical sex-change operation in recorded history.

Liberals went berserk, calling on New Yorkers to rally to Goodell, who began surging, at Ottinger’s expense. Buckley scooted between them both to win. Hoffman may also. But even if he does not, Palin, a conservative of the heart, did the right thing.

And the GOP has been sent a necessary message.

READ THE REST OF THE ARTICLE HERE.

November 4, 2009

The Great Adventure

Filed under: Education, Sacred Scripture and Theology — Tags: — Antiochian-Thomist @ 9:14 pm

This post does not necessarily constitute an endorsement of the featured product. I am just calling it to the attention of those who wish to potentially profit more from the study of Sacred Scripture. I invite those who read this blog to review the product and offer their opinions in the comment box for this blog-post. Thank you and I look forward to reading your opinions. There is potential for interesting discussion.

–Antiochian-Thomist


From the website for “The Great Adventure”

The Great Adventure is a Catholic Bible learning system that makes the complex simple by teaching the story (the narrative) of the Bible. Every day, more and more people are encountering God’s Word through the methods taught in The Great Adventure.
Jeff Cavins developed The Great Adventure in 1984 when he realized that most people, despite their strong faith, did not grasp the big picture of the Bible. Though they knew selected stories, they were not able to connect them into a full narrative. His answer was to identify the books of the Bible that tell the story from beginning to end. By reading just these 14 narrative books, a chronological story emerges.
From this idea grew the immensely popular Bible Timeline program, which teaches the story in a way that is easy to remember and helps people to continue reading Scripture on their own. Hundreds of thousands of Catholics have learned to read the Bible through this system, which provides a solid foundation for all other reading and study.
Since the creation of The Bible Timeline, The Great Adventure has grown into a remarkable system designed to give the average Catholic a solid foundation for a lifetime of Bible reading. Parishes around the world are finding renewed faith and increased involvement among parishioners whose lives have been changed by this exciting study series.

Testimonials:

“I am impressed with the methodology and growth of The Great Adventure: A Journey Through the Bible. The canonical approach that The Great Adventure employs is a marvelous way to introduce the faithful to salvation history. When Sacred Scripture, Sacred Tradition, and the Magisterium are all brought together in study the result is a clearer picture of God’s will, resulting in a road map for living. The Great Adventure, being faithful to Dei Verbum (the Second Vatican Council’s Constitution on Divine Revelation), is bearing much fruit in the Church today and contributing to a stronger, more informed laity.”

–Francis Cardinal George, O.M.I., Archbishop of Chicago

“I have seen real change in many of my parishioners. They have not only learned about the ‘big picture’ that contextualizes salvation history, but they’ve gained practical insights into walking with the Lord and learning to trust Him. If every parish did this program, we’d see a true revolution in the Church.”

–Rev. Tomi Thomas, St. Matthew Catholic Church, Norwalk, CT

“Wondering whether a twenty-four week course would work, I started The Bible Timeline in the parish. A solid group of about twenty-five stayed with it for the whole time. I myself got a great deal from it; for the first time I have a grasp of the chronological aspect of the story of salvation. The same group followed through with Matthew. This was a more in-depth, probing study that touched everyone’s heart. We are looking forward to the study of Acts and Revelation next year. I consider The Great Adventure to be one of the most important contributions I have made to the parish, a legacy I leave my successor after my retirement soon.”

–Msgr. Charles Quinn, St. Stanislaus, Pleasant Valley, NY

November 3, 2009

THE DOMESTIC CHURCH (PART 2): THE UNIVERSAL CALL TO RELIGIOUS LIFE

Filed under: domestic church, Liturgy, Sacred Scripture and Theology — Tags: , , , — Antiochian-Thomist @ 12:56 am

According to Christians of the East, both Catholic and Orthodox, the Domestic Church is the Christian family comprising the smallest unit of the Christian community based upon the dictates of Our Lord as found in St. Matthew’s Gospel (18:20): “For where two or three are gathered in my name, there am I in the midst of them.” Based on this, logic clearly shows that essentially the Christian home is the gathering of two or more people because of and in the name of Christ. As the smallest extant example of the Church, it has in its microcosm the same general duties of, let’s say, a parish church: worship, Christian fellowship, charity, education in the faith, growth in virtue, evangelism, hospitality and works of mercy.

It is here that the notion of the “universal call to religious life” is to be understood. Too often Christians misinterpret this “universal call” as a universal call to some version of monasticism or priestly (ministerial) life, as if this is all that comprises what is “religious” or what is Christian. The laity, by this mindset, are relegated to something that has to be tolerated — as a group that should show up and shut up — “pay, pray, and obey” — for the laity are “weak” since they did not follow the “universal call” but instead accepted the barely tolerable state of the lay, family life. This attitude is regularly conveyed if not outright spoken. This attitude, my friends, is nothing short of CLERICALISM and is condemned by the Church. In spite of the efforts of various Popes going back to Bl. Pius IX to curtail this error, it seems that many Catholics embrace this attitude and dub it as “traditional”. “Traditional” because of what –it’s antiquity? Heresy is ancient too.

Further, some of my friends and I have been told that we must have a vocation to the ministerial priesthood because we pray, read the Bible, and go the Divine Liturgy/Mass regularly. The normal has become mistaken for the extraordinary (and folks, I’ll be the first to admit that I could afford to spend more time praying — so in this I do not feel I even meet what should be the “norm”), and the universal call of the Christian is mistaken for the special call to the ordained life. Fulfilling the basic norms of the Christian, whatever his state, is not a sign of a special calling to the priesthood or monastic life.

The universal call to the religious life is nothing more than what is fulfilled in a loving and devout Christian home, the Domestic Church: worship, Christian fellowship, charity, education in the faith, growth in virtue, evangelism, hospitality and works of mercy. St. Benedict, the Father of Western Monasticism, even says that the Christian home, too, is to be “a school for the Lord’s service”. We are ALL called to the religious life; however, NOT ALL  are called to be monks and nuns. Yes, shocking as it may be to some…marriage is a VOCATION and a SACRAMENT.

The universal call to the religious life is best exemplified in prayer; and in the Domestic Church, it is the prayer of the family. What prayer? Which prayers? Well, any really; but if you want to “bring the Church home”, as it were, then bring the prayer of the Church home as best epitomized in the liturgies. The most ancient practice of this, both East and West, was the praying of the psalter as a family around the house shrine, the icon corner, the home altar.  St. Hippolytus as far back as the second century makes reference to its common practice among the laity. The psalter, the Divine Office or the Liturgy of the Hours as it is more commonly referred to today, is the official liturgical prayer of the Church, second ONLY to the Divine Liturgy/Mass due to its sacred origins. The Psalms are divine poetry composed by God through human instrumentality and directed back to God. Who better to praise God than God? Who better to instruct in Wisdom and show us the prophecies than God? So, instead of the smorgasborg of personal, private devotions for one’s morning and night prayers, why not pray Prime or Lauds for morning prayer and Vespers or Compline for night prayer? Why not pray it as a family? This is the Devotio Antiqua. If you do this, then those artificial distinctions between “lay spiritualities” and “monastic spiritualities” and “clerical spiritualities” disappear, for the spirituality simply becomes a scriptural and liturgical spirtuality — the spirituality of the Apostolic Fathers, the Desert Fathers, and the Fathers of the Church.

Yes, be a religious, for we are all called to pray and perform works of mercy. Some of us are even called to be monks, nuns, and priests.

A Transfigured Faith?

Filed under: Uncategorized — Tags: , , , — Antiochian-Thomist @ 12:22 am

In the late summer of this year, I made a retreat at the Melkite monastic foundation of Our Lady of Solitude Cloister & Retreat in Warren Center, PA. At the end of the retreat, Rev. Hieromonk Angelus, superior of the foundation, asked me to compose an article for the Melkite Eparchy of Newton’s journal, Sophia, touching upon my retreat and the feast with which it coincided: the Transfiguration of the Lord. I did as he requested and the results are here: the article was published this month and a copy of it can be read on-line. If you are so interested, you  can find the article HERE. The piece is entitled, “A Transfigured Faith?” and can be found on page 18. If you like it or are edified by it, then praise be to God. If not, all I can do is apologize.

IMG_1435

Festal Icon for the Transfiguration of the Lord

IMG_1473

Chapel and Festal Icon

The Retreatant's Chapel (Left) and the Festal Icon (Right)

IMG_1424

The Retreatant's Cabin