VII. Credo.

Five years had passed away, and their close found Mary Lee welcoming back

to her home her long‐absent brother, now a priest. Augustine Percival

returned, the same, and yet changed. There was the same tender, earnest

nature; but upon that nature grace had built up a superstructure of such

strength and virtue that, in most respects, he was a different

man—purified by suffering, sanctified by penance, and now consecrated by

the sacrament of Holy Orders.

It was a happy circle that gathered around the blazing wood‐fire on that

cool October evening—so happy that they were almost subdued, and thought

more than they talked. It was towards the end of the evening that Father

Percival said quite incidentally:

“Mr. Carlisle returned in the steamer with me. I suppose he will soon pay

his respects to the ladies.”

Assunta did not start. Why should she? Had the name of one long since dead

been mentioned, it might have caused an emotion of tenderness; but that

would have been all. Mr. Carlisle was dead to her, and every memory of him

had long been buried. So, though her face became a shade paler, she went

on with her work, and her hand did not tremble.

“Is he well?” asked Mary, continuing the conversation, “and is he as fine‐

looking as he used to be?”

“He is just recovering from a very severe illness,” replied her brother.

“It has told upon him fearfully, so that you will find him much changed.

Still, I hope his native air will restore him to health; and no doubt,

Mary, his good looks will follow. He was already much better when I parted

from him yesterday.” And then Father Percival questioned Mary about her

absent husband and her children, and listened with interest to the young

mother’s enthusiastic description of Harry’s brilliancy and the little

Assunta’s sweetness.

The next evening, as Father Percival was giving the two ladies an account

of his last days in Rome, Mr. Carlisle’s name was announced, and

immediately he himself entered the pleasant drawing‐room. He was indeed

much altered, for the traces of sickness and suffering were only too

visible. There was another change, perceptible to one who had known him

well. In his bearing there seemed to be less pride than of old, and more

dignity; in his face the expression of bitterness had given place to one

more contented, more peaceful. Suffering had evidently done a work in that

proud spirit. But as Mr. Carlisle extended his hand to Assunta, who

greeted him with the frank simplicity so peculiar to her, the same old

smile lighted up his thin, pale face, and he truly seemed her guardian

once more. Assunta was for the moment surprised to see the cordiality with

which Mr. Carlisle took the hand of the young priest, and held it in both

his, as if a brother’s affection were in the pressure, and which was

returned as warmly. A comfortable arm‐chair was placed near the fire for

the guest; and while he seated himself, as if fatigued, he said:

“Augustine, have you kept my secret?”

“Most faithfully. I did not even betray that I had one, as a woman might

have done.” And Father Percival glanced at his sister, who pretended

indignation, but said nothing.

“Then,” said Mr. Carlisle, “I must tell my own story. Assunta, come and

sit by me.” And he pointed to the vacant chair beside him, while Assunta

obeyed at once, the words and manner were so like those of the old days.

“Forgive me,” Mr. Carlisle went on, “if I call you to‐night by the

familiar name. I could not say Miss Howard, and tell you what I have to

tell. And, Mrs. Lee, if I seem to address myself too exclusively to your

friend, I beg you will pardon me, and believe that, if my story interests

you, I am more than glad that you should know all. Assunta, put your hand

here.” And taking her hand in his, he laid it upon his brow. “In that

Roman sickness it has often rested there, and has soothed and healed. Tell

me, child, do you feel no difference now?”

Assunta looked at him wonderingly—still more so when she caught sight of a

meaning smile on Father Percival’s face.

“Mr. Carlisle, you puzzle me,” she said.

Again that peculiar and beautiful smile, as he continued:

“The sign of the cross has been there; do you understand now, my child?

No? Then, in one word, I will explain all. _Credo_—I believe! Not yet?

Assunta, you have, I know, prayed for me. Your prayer has been answered. I

am a Catholic, and, under God, I owe all to Augustine Percival.”

Assunta could not speak. For a moment she looked in his face with those

earnest blue eyes, as if to read there the confirmation of his words, and

then she bowed her head upon her hands in silence. Mr. Carlisle was the

first to break it.

“And so you are not sorry, _petite_, to welcome so old a sinner into the

fold?”

“Sorry!” exclaimed Assunta at last. “Life will not be long enough to thank

God for this happiness.”

“You are so little changed, child, after all these years, that I must look

at myself to realize how the time has gone. But shall I tell you how all

this has come about? Three months ago I was as miserable an unbeliever as

ever lived.”

“Please tell us all,” murmured Assunta.

“All the story of these five years would be long and wearisome. Life to me

has been simply an endurance of existence, because I dared not end it. I

have travelled a great deal. I have _stood_, not _kneeled_, in the Chapel

of the Holy Sepulchre, and have wandered as a sight‐seer through the holy

places in Jerusalem. I have been in almost every part of Europe. Need I

tell you that I have found satisfaction nowhere? And all this time I was

drawn, by a sort of fascination, to read much on Catholic subjects; so I

sneered and cavilled and argued, and read on.

“At last, about four months since, the same uneasy spirit which has made a

very Wandering Jew of me for the last five years possessed me with the

idea of returning home, and I started for Paris. I engaged my passage in

the next steamer for New York; and, though feeling far from well, left for

Havre. I reached the hotel, registered my name, and went to my room for

the night. The steamer was to sail the next morning. I knew nothing more

for three weeks. Fortunately, I had fallen into good hands, or I should

never have been here. They said it was brain‐fever, and my life was

despaired of. Assunta, child, you need not look so pale. You see it is I

myself who have lived to tell it.”

Father Percival here rose, and, excusing himself on the ground of having

his Office to say, left the room. As soon as he was gone Mr. Carlisle

exclaimed:

“There is the noblest man that ever lived. No words can tell what he has

been to me. It seems that, when I was beginning to give some hope of

recovery, Father Percival arrived at the same hotel on his way to America.

The landlord happened to mention the fact of the illness of a fellow‐

countryman, and showed the name upon his books. Father Percival at once

gave up his passage, and remained to perform an act of charity which can

only be rewarded in heaven.”

“You remember, Assunta,” said Mrs. Lee, “Augustine wrote that he was

detained a few weeks by the illness of a friend.”

“Yes,” said Assunta; “but how little we dreamed who the friend was!”

“And a most ungrateful friend he was, too, at first,” said Mr. Carlisle.

“When he came to see me, and I learned his name, and that he had become a

priest, it was nothing but weakness that prevented my driving him from the

room. As it was, I swore a little, I believe. However, with the tenderness

of a woman he nursed me day and night; and even when I was better, there

was still no word about religion, until one day I introduced the subject

myself. Even then he said but little. I was too weak to have much pride,

or that little would not perhaps have made the impression that it did. My

pride has always been the obstacle, and it is not all gone yet, _petite_,”

he added, looking at Assunta, who smiled in answer.

“One night, from what cause I do not know, I had a relapse, and death

seemed very near. Then Father Percival came to me as priest. I can hear

now the solemn tones in which he said: ‘Mr. Carlisle, I will not deceive

you. I hope that you will recover, but you may not. Are you willing to die

as you are now, unbaptized?’ I answered, ‘No.’ ‘Do you, then,’ he said,

‘believe the Catholic Church to be the infallible teacher of truth, and

will you submit to her teaching?’ Here I paused. The question was a

difficult one; the word _submit_ was a hard word. But death was very near,

and at last, with desperate energy, I said: ‘Yes; baptize me!’ He then

knelt beside me, and made for me an act of contrition—for I seemed to be

sinking fast—and in a moment more I was baptized, a Catholic. He then left

me instantly, and went for the parish priest, who came and administered

Extreme Unction to—as they supposed—a dying man. But the sacrament did its

work for life, and not for death. From the moment of receiving it the

scale turned. Of course much that I have told you I have learned since

from Augustine. I was conscious only of the one act—the _submission_.

“And how mean a specimen of a man I have since felt myself to have

been—resisting God year after year with all the strength of human pride

and that most powerful auxiliary of the devil—pride of intellect; and

then, when life was at its last gasp, and everything had slipped from

under me but that one foothold—then to say, ‘Life is going; the world has

already gone. I have lost everything else; now I, a sinner, will

condescend to receive the portion of the saints—God and heaven!’ Do you

think, Assunta, that the angels would have had much cause for rejoicing

over such an addition to their bright company?”

“That is a genuine drop of your old bitterness, Mr. Carlisle,” replied

Assunta, laughing, nevertheless, at his frankness.

“Oh! there is plenty of it left, _petite_. But to go on: when I found that

I was to live, I was determined, before leaving for home, to make my

profession of faith in the church, as a Christian should who is not

ashamed of his colors. Augustine would do nothing official for me after

the baptism, but he was ever the kindest friend, and I love him with a

real David and Jonathan affection. Oh! child, how often have I thought of

you and of how much you would have been amused to see me, Severn Carlisle,

meekly receiving instruction in Catholic doctrine and practice from that

simple French priest. Truly, I needed some one to identify me to myself.

Well, to bring this long story to an end, the day before sailing I made my

profession of faith and received Holy Communion in the quiet little parish

church. And now I am here, the same proud, self‐sufficient man as of old,

I fear, but with a peace of soul that I have never known before.”

“How good God is!” exclaimed Assunta.

“What does your sister say?” asked Mrs. Lee.

“My sister? I do not think she took in the idea. Her thoughts would have

to travel miles before they would approach a religious sentiment. Poor

Clara! I find her much changed. I spent two or three hours with her this

afternoon. She was very gay, even brilliant—too much so, I thought, for

real happiness. She did not imagine how transparent her mask was, and I

would not destroy her illusion. I did not see Sinclair at all. But,”

exclaimed he, looking at his watch, and rising hastily, “it is eleven

o’clock. I ordered the carriage for ten, and no doubt it has been waiting

a long time. I owe you ladies many apologies for my thoughtlessness and

egotism.”

“Mr. Carlisle,” began Assunta, placing her hand in his, as she bade him

good‐night; but the words would not come as readily as the tears.

Mrs. Lee had gone to summon her brother, so the two, so long parted, were

left alone.

“My child,” said Mr. Carlisle in a low voice, “I know all that you would

say, all the sweet sympathy of that tender, unchanged heart. I have much

to say to you, Assunta, but not to‐night—not in the presence of others.”

Then turning to Father Percival, who entered the room, “Augustine,” he

said, “I am going for a few days to my place in the country for rest, and

also that I may see how much it has suffered from my long neglect. Come

and see me there. It will do me good, heart and soul.”

“I will try to arrange my plans so as to give myself that pleasure,”

replied the priest, as he assisted Mr. Carlisle into the carriage.

What strange contradictions there are in human nature! How little can we

account for our varying moods and the motives which influence our actions!

And how often we seem to get at cross‐purposes with life, and only see how

far we have been wrong when a merciful Providence, overruling all, unknots

the tangled thread and straightens the crooked purpose!

Excepting the visit of a few hours paid by Father Percival to his friend,

two months passed by, and nothing was heard of Mr. Carlisle. Those two

months were to Assunta longer, more wearisome, than the five years that

had preceded them. We may talk of hopes that are dead, and may honestly

believe them buried deep down in the grave which duty has prepared and

time has covered. But hope is the hardest thing in this world to kill; and

thank God that it is so! Let but a gleam of sunshine, a breath of the warm

upper air, into that sepulchre, and the hopes that have lain buried there

for years will revive and come forth with renewed vigor. It is much more

difficult to lay them to rest a second time.

Assunta had borne her trial nobly; but, as she sat alone on Christmas Eve,

and her thoughts naturally dwelt upon that happy return, and then the

unaccountable disappearance of Mr. Carlisle, her courage almost failed

her, and her brave heart sank within her, as she thought how dreary the

future looked. She had excused herself from joining the others at a little

family party, and for an hour she had sat idle before the fire—a most

unwonted self‐indulgence for one so conscientious as Assunta Howard.

A ring at the door and a voice in the hall made her start and tremble a

little, as she had not done on that first evening of Father Percival’s

return. She had scarcely recovered herself when Mr. Carlisle entered the

room.

“I have come to account for myself,” were his first words. “I hoped that I

should find you alone to‐night.”

“Mrs. Lee has gone to her mother’s,” was the reply.

“Yes, I knew it. Assunta, what have you thought of me? Still more, what

will you think of me now? I have suffered much in these two months;

perhaps it is ungenerous in me to say this to you. Assunta, never for one

moment have I been unfaithful to the love I told you of so many years ago;

but I had given up the hope of ever possessing yours. Even when the

obstacle you know of had been removed, I thought that I could bear to see

you happy, as I believed you were, in a life in which I had no share. I

felt that it would not be right even to ask you to marry one so much older

than yourself, with broken health and darkened spirits. And your fresh

beauty, still so girlish, so all‐unchanged, confirmed my purpose. Ah!

child, time, that has silvered my hair, has not dimmed the golden aureola

which crowns your dear head. But in the many lonely hours that I have

passed since my return, my courage has grown faint. I have longed for your

sweet presence in my home, until an answering voice has urged me to come

to you. Assunta, once, beneath the shadow of the cross, in the moonlit

Colosseum, I offered you my love, and you put God between us. Again I

urged my suit, and again you erected the same impassable barrier. To‐night

I am so selfish that, even as I have described myself to be, I come to you

a third time with a love which years have but strengthened. My darling,

God no longer comes between us; can I ever hope to win that true, brave

heart?”

With a child‐like simplicity and a true womanliness Assunta put her hand

in his, and said:

“Mr. Carlisle, it has long been yours. ‘Unless he can love you _in God_,’

my mother said. I believe that the condition is now fulfilled.”

“And may God bless the love he sanctions!” said Mr. Carlisle solemnly.

After a silence—for where hearts understand each other there is no need of

many words—Assunta said in her own sweet tones:

“Do you regret now the decision of that night in Rome? Was I a true

prophetess?”

“But we have lost so many years,” said Mr. Carlisle.

“Yes, lost for time, but gained for eternity.”

When Mrs. Lee returned, she greeted the guest with surprise, as well as

pleasure; but both those emotions were lost in a still greater joy when

Mr. Carlisle, drawing Assunta towards him, said:

“Mrs. Lee, this is my Christmas gift—a precious treasure, is it not, to be

entrusted to one so undeserving?”

“Indeed it is a precious treasure,” echoed Mary enthusiastically; “but,

Mr. Carlisle, there is not a man in the world in whose possession I would

like to see it so well as in yours.”

“Bless you, Mrs. Lee, for your kind words! _Petite_, perhaps your taste is

not so much in fault after all.”

“And, Mary,” said Assunta archly, “he may yet recover his good looks, you

know.”

“Yes,” said Mr. Carlisle, “love and happiness are said to be great

beautifiers. I have no objection to trying the experiment.”

One bright morning, soon after Easter, there was a nuptial Mass at the

cathedral, celebrated by Father Percival, and after the ceremony and a

quiet breakfast, Mr. and Mrs. Carlisle drove in their private carriage to

the beautiful country residence which was to be their future home.

Just at sunset, as they entered the long avenue which with many windings

led towards the house, Mr. Carlisle said:

“My darling, we are at home. I have waited, like Jacob, almost seven years

for my Rachel. I cannot say, as he did, that the days have seemed _few_,

though I believe my love has been no less.”

“And suppose,” replied Assunta, with the happy confidence of a loving

wife—“suppose your Rachel should turn out a Lia after all?”

“In that case,” said her husband coolly, “I should insist that the

description of that much‐injured lady had done her great injustice. And I

should consider myself a lucky fellow to have been cheated into the

mistake, and be ready to wager my Lia against all the Rachels in the

world. And now, my precious wife, welcome home!”

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Ten years later. It is not always a pleasure to look in upon loved friends

after a lapse of ten years. Sickness, sorrow, death, or disgrace may each

do a mighty work in even fewer years, and, at the best, time itself brings

about marked changes. But a glance at Carlisle Hall, on this tenth

anniversary of that happy wedding‐day, will only show that same happiness

ripened into maturity. In a marriage like that of Severn and Assunta

Carlisle, whatever life might bring of joy or sorrow would come to both

alike, and nothing could divide them. Even death itself would but _seem_

to part them, for their union was _in God_. In Assunta the added dignity

of wife‐hood and motherhood had taken nothing from the charm of earlier

years; and, if the beauty of the young girl had faded somewhat, the ever‐

growing grace and purity of soul more than supplied its want, even in her

husband’s eyes. And Mr. Carlisle? Noble by nature, and possessing the

finest qualities of mind and heart, his soul was now developed to the full

stature of its manhood. He was a proud man still, but with a pride which

S. Paul might have commended. He was so proud that he was never ashamed to

kneel beside the poorest villager in the little church. In his pride he

gloried in Jesus Christ, and him crucified. The beautiful church itself

had been erected as a thank‐offering, by Mr. Carlisle and his wife, in the

factory village two miles from their home; and for some years Father

Percival had been parish priest of the Church of the Assumption. And

Carlisle Hall resounded with the merry voices of three children at the end

of those ten years: Severn, the pride of his mother’s heart; Augustine,

Father Percival’s godchild and special favorite, already destined for the

priesthood by the wishes of the senior trio; and the baby, her father’s

darling, to whom he would give the name of Mary, and no other, “to show,”

he said, “how he had progressed in Mariolatry since his first lesson in

Sienna.”

Father Percival had been the only guest at this anniversary‐dinner,

except, indeed, the children, who must appear on this occasion, at no

matter how great a risk of noise and accident. They had now returned to

the nursery, but the others still lingered at the table.

“Father Augustine,” said Assunta—for she had learned to follow the little

ones in their name for the priest they loved so well—“I received a letter

yesterday from dear old Father Joseph. He is just as happy in our marriage

to‐day as he was when he first heard of it, and he blesses it, and us, and

the children so sweetly and kindly. How much I should like to see him

again!”

“I suppose,” said Father Percival, “he looks upon the marriage as a

striking illustration of the wonderful ways and goodness of God, as it

surely is. S. Ignatius ought to send Father Dupont here, to see for

himself the result of his direction, and, I must add, of your generosity

and faithfulness, Mrs. Carlisle.”

“I am so sorry, Severn,” said Assunta after a pause in the conversation,

“that Clara would not come to us to‐day. I think a glimpse of quiet

country life might be a pleasant change for her.”

“I fear,” replied her husband sadly, “that poor Clara has much to suffer

yet. It is my opinion that Sinclair has no intention of returning from

Europe at all. But who could have made her believe, in those sunshiny

days, that she would ever live to be a deserted wife? _Petite_, the

subject is a very painful one. I am going to change it for one of which I

am never weary. Augustine, it is not the custom, I believe, for a man to

toast his wife on such an occasion, but I am going to be an exception to

the rule to‐day. Lord Lytton has in that grand work of his, _My Novel_,

two types of women—the one who exalts, and the one who consoles. He

probably had never seen the combination of the two types in one person. I

now propose—and, my darling, you must drink and not blush—‘Assunta

Carlisle: blessed be the woman who both exalts and consoles!’ And let me

add that a happy man was I—unworthy—when, ten years ago, that woman became

my wife.”

Matter. V.

Although continuous matter cannot be proved to exist, yet its existence,

as every one knows, is still very commonly believed, even by philosophers,

on the ground that it was believed for centuries by all great men, and has

never been conclusively refuted. From some hints which we have given in

our previous article about the difficulties of this ancient doctrine, the

intelligent reader may have already satisfied himself that material

continuity is not merely “a philosophical mystery,” as Goudin confesses,

but a metaphysical absurdity. As, however, this last conclusion, owing to

its paramount importance in metaphysics and in natural philosophy,

deserves a more explicit and complete demonstration than we have yet

given, we propose to develop in the present article a series of arguments,

drawn from different sources, to show _the absolute and intrinsic

impossibility of continuous matter_. The prejudices of our infancy may at

first resist the demonstration, but it is to be hoped that they will

finally yield to reason.

_First argument._—We know, and it is conceded by the advocates of

continuous matter, that a _finite_ being cannot involve in its composition

an _infinite_ multitude of distinct terms; for evidently the infinite

cannot be the constituent of the finite. Now, we have shown in our

preceding article that, if there were a piece of continuous matter, it

should involve in its continuous constitution an infinite multitude of

distinct terms, every one of which should have its own distinct existence

independently of the others. Therefore continuous matter cannot exist.

_Second argument._—A primitive substance cannot absolutely be made up of

other substances. But if there were any continuous matter, a primitive

substance would be made up of other substances. Therefore no continuous

matter can exist. The major of this syllogism is quite evident; for a

primitive substance, if made up of other substances, would be primitive

and non‐primitive at the same time. The minor can be easily proved. For it

is plain that continuous matter, if any such existed, would necessarily

consist of continuous parts, substantially distinct from one another, and

therefore having their own distinct matter and their own distinct

substantial act, and ranking as distinct, complete, and separable

substances, as we have shown in our last article. Now, assuming that

either of these parts is a primitive substance, it is evident that the

primitive substance would be made up of other substances; for such a part,

being continuous, is itself made up of other parts, which are likewise

distinct and complete substances, as we have just remarked. And since a

continuum cannot be resolved into any but continuous parts, the conclusion

cannot be avoided that the primitive material substance would always be

made up of other substances. To elude this argument, the advocates of

continuous matter are compelled to deny that there is any _primitive_

material substance mathematically continuous. But, even so, their position

is not improved. For if there is no primitive material substance

mathematically continuous, the combination of such primitive substances

will never give rise to continuous matter, it being obvious that all the

elementary constituents of continuum must be continuous, as all

philosophers agree. Whence we again conclude that no continuous matter is

possible.

_Third argument._—No continuum can be made up of unextended constituents,

as we have just observed, and as our opponents not only concede, but also

demonstrate most irrefragably in their own treatises. Now, continuous

matter, if any such existed, would be made up of unextended

constituents—that is, of mere mathematical points. Therefore continuous

matter would be a formal contradiction. The minor of our syllogism is

proved thus. All the points which can be designated within the dimensions

of the continuum are _immediately_ united with one another, and therefore

no room is to be found between any two consecutive points; which shows

that in the constitution of the continuum we would have nothing but mere

points. For let there be a continuous plane and a continuous sphere. The

sphere, if perfect, cannot touch the plane, except in a single indivisible

point, as is proved in geometry; nevertheless, the sphere may move along

the plane, and, always touching the plane in a single point, may measure a

linear extension of matter, which, accordingly, would contain nothing but

mathematical points immediately following one another. In other terms, the

extended matter would be made up of indivisible points; and since all

admit that this is impossible, it follows that continuous matter is

impossible. Against this argument the objection is made that it proves too

much; as it would prove the impossibility of measuring space by continuous

movement. But this objection has no good foundation, as we shall show

after concluding the series of our arguments.

_Fourth argument._—All the points that can be designated in a material

continuum would necessarily touch one another in such a manner as to form

a continuous extension; hence their contact would necessarily be

_extensive_. But an _extensive_ contact of indivisible points is

intrinsically impossible. Therefore material continuity is intrinsically

impossible. The major of this syllogism is a mere corollary from the

definition of continuum; for, if there be no contact, the continuum will

be broken, and if the contact be not extensive—that is, such as to allow

each point to extend beyond its neighbor—no continuous extension will

result. The minor of our syllogism can be proved as follows:

The contact of a point with a point is the contact of an indivisible with

another indivisible; and, since the indivisible has no parts, such a

contact cannot be partial, but must needs be total. Accordingly, the

second point, by its contact with the first, will be _totally_ in the

first; the third, by its contact with the second, will be _totally_ in the

second, and consequently in the first; the fourth, by its contact with the

third, will be _totally_ in the third, and consequently in the second and

in the first, and so on. Therefore all the points which are in

mathematical contact will necessarily correspond to the same point in

space. Now, to be all in the same point, and to form a continuous

extension, are contradictories. And thus it is manifest that material

continuity is a mere contradiction.

Some will say that the contact is indeed made in the points, but that the

parts, which touch one another in a common point, are quite distinct. But

this appeal to the parts of the continuum, though much insisted upon by

many ancient philosophers, is of no avail against our argument. For the

existence of these parts cannot be assumed, without presupposing the

continuity of matter. Such parts are, in fact, assumed to be continuous;

and therefore, before we admit their existence, we must inquire whether

and how they can have intrinsic extension and continuity. And dividing

these parts into other parts, and these again into others without end, of

all these parts of parts the same question must be asked—that is, whether

and how they can have intrinsic extension and continuity. Hence one of two

things will follow: either we shall never find the intrinsic reason of

material continuity, or we shall find it only after having exhausted an

infinite division—that is, after having reached, if possible, a term

incapable of further division, viz., a mathematical point. But in the

mathematical point it is impossible to find the intrinsic reason of

material continuity, as we have just shown. And therefore the material

continuity of the parts has no formal reason of its constitution, or, in

other terms, the parts themselves are intrinsically impossible.

Moreover, the very distinction made by our opponents between the points of

contact and the parts which touch one another in those points, is

altogether irrational. For _a parte rei_—that is, considering the

continuum as it is in itself—there is no foundation for the said

distinction, it being evident that in a homogeneous continuum no place is

to be found where we cannot mark out a point. Hence it is irrational to

limit the designability of the points in order to make room for the parts.

In other words, the parts themselves cannot be conceived as continuous

without supposing that all the neighboring points which can be designated

in them form by their contact a continuous extension, which we have proved

to be inadmissible. The aforesaid distinction is therefore one of the

subterfuges resorted to by the advocates of material continuity, to evade

the unanswerable difficulties arising from their sentence; for it is true

indeed, as Goudin remarks, that material continuity is “a philosophic

mystery, against which reason objects more than it can answer,” though not

because in this question “reason proves more than it can understand,” but

because continuous matter is shown to be an absolute impossibility.

_Fifth argument._—It is a known metaphysical principle that “nothing can

possibly become actual, except by the intervention of an act”—_Impossibile

est aliquid fieri in actu nisi per aliquem actum_ (S. Thomas _passim_).

But no act can be imagined by which matter would become actually

continuous. Therefore no actually continuous matter can possibly exist.

The minor of our syllogism is proved thus. Acts are either substantial or

accidental; hence if any act could be conceived as giving actual

continuity to matter, such an act would be either substantial or

accidental—that is, it would give to its matter either its first being or

a mere mode of being. Now, neither the substantial nor the accidental act

can make matter actually continuous. For, first, no substantial act can

give to its matter a being for which the matter has no disposition. But

actuable matter has no disposition for actual continuity, for where there

are no distinct terms requiring continuation, there is no disposition to

actual continuity, as is evident; and it is not less evident that the

matter which is to be actuated by a substantial act involves no distinct

terms, and does not even connote them, but merely implies the privation of

the act giving it its first being, which act is one, not many, and gives

one being, not many, and consequently is incapable of constituting a

number of actual terms actually distinct, as would be required for actual

continuity. To say the contrary would be to deny one of the most

fundamental and universal principles of metaphysics, viz., _Actus est qui

distinguit_, which means that there cannot be distinct terms where there

are no distinct acts.

Moreover, continuity presupposes quantity; hence, if the substantial act

gives actual continuity to its matter, it must be conceded that a certain

quantity exists potentially in the actuable matter, and is reduced to act

by the first actuation of matter. This quantity would therefore rank among

the essentials of the substance, and could not possibly be considered as

an accident; for the immediate result of the first actuation of a term by

its substantial act is not a mere accident, but the very actuality of the

essence of which that act and that term are the principles. Whence it

follows that so long as quantity remains an accident, it is impossible to

make it arise from the substantial act; and, accordingly, no substantial

act can make matter actually continuous.

That actual continuity cannot arise from any accidental act is no less

evident. For the only accidental act which could be supposed to play a

part in the constitution of a material continuum would be some actual

composition. But as composition without components is impossible, and the

components of continuous matter, before such a composition, are not

continuous (since we must now consider continuity as a result of the

composition), our continuous matter would be made up of components

destitute of continuous extension—that is, of mere mathematical points.

But, as this is avowedly impossible, it follows that it is as impossible

to admit that matter becomes actually continuous by the reception of an

accidental act.

_Sixth argument._—In a philosophico‐mathematical work published in England

a few years ago,(108) from which we have already borrowed some plain

arguments concerning other questions on matter, the impossibility of

continuous matter is proved by the following argument: “A compound which

has no first components is a sheer impossibility. Continuous matter, if

admitted, would be a compound which has no first components. Therefore

continuous matter is a sheer impossibility. In this argument the first

proposition is self‐evident; for the components are the material

constituents of the compound; and therefore a compound which has no first

components is a thing which is constituted without its first constituents,

or a pure contradiction. The second proposition also is undeniable. And,

first, there can be no doubt that continuous matter would be a _compound_;

for continuous matter would be extended, and would have, accordingly,

parts distinct from parts; which is the exclusive property of compounds.

Now, that this compound would be _without first components_, can be proved

as follows: If continuous matter has any first components, these

components will either be extended or unextended. If they are supposed to

be _extended_, then they are by no means the _first_ components; since it

is clear that in this case they have distinct parts, and therefore are

themselves made up of other components. If they are supposed to be

_unextended_, then they are by no means the _components_ of continuum;

since all know and admit that no continuum can be made up of unextended

points. And, indeed, unextended points have no parts, and therefore cannot

touch one another partially; whence it follows that either they touch each

other totally, or they do not touch at all. If they do not touch at all,

they do not make a continuum, as is evident. If they touch totally, the

one will occupy exactly the same place which is occupied by the other, and

no material extension will arise. And for this reason geometrical writers

consider that a mathematical line cannot be conceived as made up of

points, but only as the track of a single point in motion. We see, then,

that a material continuum is a compound, of which the first components

cannot be extended, and cannot be unextended. And since it is impossible

to think of a third sort of first components which would be neither

extended nor unextended, we must needs conclude that continuous matter is

a compound which has no first components. And therefore continuous matter

is a mere absurdity” (p. 30).

This argument is, in our opinion, altogether unanswerable. Those

philosophers, in fact, who still venture to fight in favor of continuous

matter, have never been able to solve it. When we urge them to declare

whether they hold the first components of continuous matter to be extended

or unextended, they constantly ignore and elude the question. They simply

answer that the components of material substance are “the matter” and “the

form.” But if the matter which lies under the form has no distinct parts,

it is evident that the substance cannot be continuous. The composition of

matter and form does not, therefore, entail continuity, unless the matter

which is under the form has its own material composition of parts; and it

is with reference to the composition of these parts of matter, not to the

composition of matter and form, that we inquire whether the first

components of continuous matter be extended or unextended. To ignore the

gist of the argument is, on the part of our opponents, an implicit

confession of their inability to cope with it.

_Seventh argument._—Material substance, as consisting of act and potency,

like everything else in creation, is both active and passive, its activity

and passivity being essentially confined, as we have already

explained,(109) to the production and the reception of local movement.

Hence, so long as material substance preserves its essential constitution,

it is impossible to admit that matter is incapable of receiving movement

from natural causes. But continuous matter would be incapable of receiving

movement from natural causes. Therefore it is impossible to admit

continuous matter. To prove the minor of this syllogism, let there be two

little globes of continuous matter, and let them act on one another. Since

no finite velocity can be communicated by an immediate contact of matter

with matter, as shown in a preceding article, it follows that the velocity

must be communicated by virtual contact in accordance with the law of the

inverse squared distances. Hence, since some points of the two globes are

nearer to one another, and others are farther, different points must

acquire different velocities. Now, one and the same piece of matter cannot

move onward with different velocities, as is evident; it will therefore be

unable to move so long as such different velocities are not reduced to a

mean one, which shall be common to the whole mass. Such a reduction of

unequal velocities to a mean one would meet with no difficulty, if the

globes in question were made up of _free_ and _independent_ points of

matter; for in such a case the globes would be compressed, and each point

of matter would act and react according to known mechanical laws, and thus

soon equalize their respective velocities. But in the case of material

continuity the reduction of different velocities to a mean one is by no

means possible. For “in a piece of continuous matter,” to quote again from

the above‐mentioned work of molecular mechanics, “any point which can be

designated is so _invariably_ united with the other points that no impact

and no mutual reaction are conceivable; the obvious consequence of which

is that no work can be done within the continuous particle in order to

equalize the unequal velocities impressed from without. Moreover, in our

case the reduction ought to be rigorously instantaneous; which is another

impossibility. In fact, if distinct points of a continuous piece of matter

were for any short duration of time animated by different velocities, the

continuum would evidently undergo immediate and unavoidable resolution;

which is against the hypothesis. Since, then, the said reduction cannot be

made instantaneously, as we have proved above, nor, indeed, in any other

way, and, on the other hand, our continuous particle cannot move onward

before the different velocities are reduced to one of mean intensity, it

is quite evident that the same continuous particle will never be capable

of moving, whatever be the conditions of the impact. And since what is

true of one particle on account of its supposed continuity is true also of

each of the other particles equally continuous, we must conclude that

bodies made up of particles materially continuous are totally incapable of

receiving any communication of motion.”(110)

This argument, though seemingly proving only the non‐existence of

continuous matter in nature, proves in fact, also, the impossibility of

its existence. For, if a substance could be created possessing intrinsic

extension and continuity, that substance would essentially differ from the

existing matter, and would therefore be anything but matter. Hence not

even in this supposition would continuous matter exist.

_Eighth argument._—The inertia of matter, and its property of acting in a

sphere, might furnish us with a new argument against material continuity.

But we prefer to conclude with a mathematical demonstration drawn from the

weight of matter. The weight of a mass of matter depends on the number of

material terms to which the action of gravity is applied, and it increases

exactly in the same ratio as the number of the elementary terms contained

in the mass. This being the case, let us assume that there is somewhere an

atom of continuous matter. The action of gravity will find in it an

infinite multitude of points of application; for it is of the nature of

continuum to supply matter for an endless division. Hence if we call _g_

the action of gravity on the unit of mass in the unit of time, the action

of the same gravity on any of those infinite points of application will be

_g_ ρ _dx dy dz_,

ρ being the density of the mass, and _dx_, _dy_, _dz_ the three dimensions

of an infinitesimal portion of it.

Now, since we know that gravity in the unit of time imparts a finite

velocity to every point of matter in the atom, we must admit that the

action exerted on the infinitesimal mass ρ _dx dy dz_ has a finite value;

and therefore, since the volume _dx dy dz_ is an infinitesimal of the

third degree, the density ρ must be an infinite of the third order. But a

continuous mass whose elements have an infinite density has itself an

infinite density; hence, if its volume has finite dimensions, the mass

itself (which is the product of the volume into the density) is

necessarily infinite, and will have _an infinite weight_. Hence the

assumption of continuous matter leads to an absurdity. The assumption is

therefore to be rejected as evidently false.

We will put an end to the series of our proofs by pointing out the

intrinsic and radical reason why matter cannot be continuous. The matter

which is under the form is _a potency_ in the same order of reality in

which its form is _an act_. Now, the only property of a potency is to be

liable to receive some determinations of a certain kind; and the property

of a potency whose form is an active principle of local _motion_ must

consist in its being liable to receive a determination to local

_movement_. Hence, as the matter receives its first being by a form of a

spherical character, and becomes the real central point from which the

actions of the substance proceed, so also the same matter, when already

actuated by its essential form, receives any accidental determination to

local movement; and, inasmuch as it is liable to local movement, it is in

potency to extend through space—that is, to describe in space a continuous

line; and when it actually moves, it actually traces a continuous

line—that is, it extends from place to place, continuously indeed, but

successively; whence it is manifest that its extension is nothing but

_Actus existentis in potentia ut in potentia_ Aristotle would say, viz.,

an actual passage from one potential state to another. Such is the only

extension of which matter is capable. Such an extension is always _in

fieri_, never _in facto esse_; always dynamical, never statical; always

potential and successive, never formal or simultaneous. We can, therefore,

ascribe to matter _potential_ continuity, just as we ascribe to its active

principle a _virtual_ continuity; for the passivity of the matter and the

activity of the form correspond to one another as properties of one and

the same essence; and whatever can be predicated actively or virtually of

a substance on account of its form can be predicated passively or

potentially of the same substance on account of its matter.

These remarks form a complement to our fifth argument, where we proved

that no substantial and no accidental act could make matter _actually_

continuous. For, since matter cannot receive any accidental act, except

the determination to local movement, and since this movement, although

continuous, is essentially successive, it follows that by such a

determination no actual and permanent continuity can arise, but a mere

continuation of local changes. Thus matter, according to its potential

nature, has only a potential extension; or, in other terms, it is not in

itself actually continuous, but is simply ready to extend through space by

continuous movement.

The preceding proofs seem quite sufficient, and more than sufficient, to

uproot the prejudice in favor of material continuity; we must, however,

defend them from the attacks of our opponents, that no reasonable doubt

may remain as to the cogency of our demonstration.

_First objection._—The globe and the plane, of which we have spoken in our

third argument, though destitute of proportional parts suitable for a

statical contact, become proportionate to one another, says Goudin, by the

very movement of the one upon the other; and thus our third argument would

fall to the ground. For a successive contact partakes of the nature of

successive beings. Hence, as time, although having no present, except an

indivisible instant, becomes, through its flowing, extended into

continuous parts, so also the contact of the globe with the plane,

although limited to an indivisible point, can nevertheless, by its

flowing, become extended so as to correspond to the extended parts of the

plane. For, according to mathematicians, a point, though indivisible when

at rest, can by moving describe a divisible line.

To this we answer that a globe and a plane cannot by the movement of the

one on the other acquire proportionate parts. For, although it is true

that a successive contact partakes of the nature of the successive being

which we call movement, it is plain that it does not partake of the nature

of matter. In fact, the material plane is not supposed to become

continuous through the movement of the globe, but is hypothetically

assumed to be continuous before the movement, and even before the

existence, of the said globe. The continuous movement is, of course,

proportionate to a continuous plane; but it is evident that it cannot

originate any proportion between the plane and the globe; because this

would be against the essence of both. No part of the plane can be

spherical, and no part of the globe can be plane; hence, whatever may be

the movement of the one upon the other, they will never touch one another,

except in a single point.

That time, although having no present, except an indivisible point,

becomes extended by flowing on, is perfectly true; but this proves

nothing. For, in the same manner as the act of flowing, by which time

flows, has nothing actual but a single indivisible instant, so also the

act of flowing, by which the contact of the globe with the plane flows,

has no actuality but in an indivisible point of space; and as an

indivisible instant by its flowing draws a line of time without ever

becoming extended in itself, so also an indivisible point by its flowing

draws a line in space without ever becoming extended in itself; and as the

instant of time never becomes proportionate to any finite length of time,

so also the point of contact never becomes proportionate to any finite

line in space.

That a line, therefore, arises from the flowing of a point in the same

manner as time from the flowing of an instant, is a plain truth, and there

was no need of Goudin’s argumentation to make it acceptable. To defeat our

argument, he should have proved that the _actual_ flowing of an instant

takes up a length of time. If this could have been proved, it would have

been easy to conclude that the flowing contact also extends through a

length of space. But the author did not attempt to show that an instant of

time flows through finite lengths of time. It is evident, on the contrary,

that an instant flows through mere instants immediately following one

another. And thus the objection has no weight.

_Second objection._—If a material continuum is impossible, all continuum

is impossible, and thus we are constrained to deny the continuity of both

space and time. For space and time—as, for instance, a cubic‐foot and an

hour—include within their respective limits an infinite multitude of

indivisible points, or indivisible instants, just as would continuous

matter include within its limits an infinite multitude of material points;

for it is clear that space and time cannot be made up of anything but

points and instants. Hence, if, in spite of this, we admit continuous

space and continuous time, we implicitly avow that our first argument

against continuous matter is far from conclusive.

We reply that there is no parity between the continuity of space and time

and the continuity of matter; and that the impossibility of the latter

does not show the impossibility of the former. The continuity of space and

of time is intimately connected with the continuity of local movement.

Movement, though _formally_ continuous, or rather owing to its formal

continuity, is necessarily successive, so that we can never find one part

of the movement coexisting with another part of the same movement; and

consequently there is no danger of finding in such a movement any _actual_

multitude, whilst we should necessarily find it in continuous matter. Time

also, as being nothing else than the actuality or duration of movement, is

entirely successive; and consequently no two parts of time can ever be

found together; which again prevents the danger of an _actual_ multitude

of coexisting instants. As to space, we observe that its continuity is by

no means formal, but only virtual, and that space as such has no parts

into which it can be divided, whatever our imagination may suggest to the

contrary. We indeed consider space as a continuous extension, but such an

extension and continuity is the property of the movement extending through

space, not of space itself. Space is a region _through which movement can

extend in a continuous manner_; hence the space measured, or mensurable,

is styled _continuous_ from the continuity of the movement made, or

possible. We likewise consider the parts of the extension of the movement

made or possible as so many _parts of the space measured or mensurable_.

And thus space is called _continuous_, _extended_, and _divisible into

parts_, merely because the movement by which space is, or can be, measured

is continuous, extended, and divisible into successive parts; but space,

as such, has of itself no _formal_ continuity, no _formal_ extension, and

no _formal_ divisibility, since space, as such, is nothing else than the

virtuality, or extrinsic terminability, of divine immensity, as we may

have occasion hereafter to show.

Hence neither space, nor time, nor movement is made up by composition of

points or of instants; but time and movement owe their continuous

extension to the flowing of a single instant and of a single point, whilst

space, which is only virtually continuous, owes its denomination of

continuous to the possibility of continuous movement through it. But if

there were any continuous matter, its formal extension would arise from

_actual_, _simultaneous_, and _indivisible_ points constituting a _formal

infinite multitude_ within the limits of its extension. Hence there is no

parity between continuous matter and continuous space or time; and the

impossibility of the former does not prove the impossibility of the

latter.

_Third objection._—Accelerated movement is a movement the velocity of

which increases by continuous infinitesimal degrees—that is, by

indivisible momenta of motion. It is therefore possible for a quantity of

movement to arise from the accumulation of indivisibles. Why, then, should

not the quantity of matter arise in a like manner from the accumulation of

indivisible points? That which causes the acceleration of movement is, in

fact, continuous action—that is, a series of real, distinct, and

innumerable instantaneous actions, by which the movement is made to

increase by distinct infinitesimal degrees; which would show that it is

not impossible to make a continuum by means of indivisibles.

We reply, first, that there is no degree of velocity which can be styled

indivisible; for however small may be the acceleration of the movement, it

may become smaller and smaller without end, as we shall presently explain.

But, waiving this, we reply, secondly, that intensive and extensive

quantity are of a very different nature, and, even if it were true that

intensive quantity can arise from an accumulation of indivisibles, the

same would not be the case with extension. The degrees of intensity never

unite by way of composition; for all intensity belongs to some _form_ or

act, whilst all composition of parts regards the _material_ constituents

of things. Hence movement, though increasing or decreasing, by continuous

degrees, is not _composed_ of them; whereas the continuum of matter, if

any such existed, should be _composed_ of its indivisible elements. In

movement the increased velocity is not a multitude of distinct acts, but a

single act, equivalent to all the acts which we may distinguish under the

name of degrees of velocity. Hence such degrees are only virtually

distinct, and do not constitute a formal multitude; whence it follows that

there is no absurdity in the notion of accelerated or retarded movement.

But with a material continuum the case is entirely different; for such a

continuum would be an extensive, not an intensive, quantity, and would

have parts not only mentally or virtually, but entitatively and formally,

distinct, and making an actual infinite multitude within the limits of a

finite bulk.

As to the continuous action which causes the acceleration of movement, it

is not true that it consists of a sum of distinct instantaneous actions.

The action may be considered either _in fieri_ or _in facto esse_. The

action _in fieri_ is the exertion of the agent, and the action _in facto

esse_ is the determination received by the patient. Now, the exertion of

the agent is successive; for its continuity is the continuity of time, and

is therefore _continuation_ rather than _continuity_. Hence nothing exists

of the action _in fieri_, except an instantaneous exertion corresponding

to the moment of time which unites the past with the future. All the past

exertions have ceased to be _in fieri_, and all the future exertions have

still to be made. Accordingly, continuous action is not made up of other

actual actions, and, though passing through different degrees of

intensity, is not an actual multitude.

On the other hand, if we consider the action _in facto esse_—that is, the

determination as received in the patient—we shall find that, although such

a determination is the result of a continued exertion, and exhibits its

totality under the form of velocity, nevertheless this result consists of

intensity, not of continuity, and therefore contains no formal multitude,

but is, as we have said, a simple act equivalent to many. Hence

accelerated movement is one movement, and not many, and a great velocity

is one velocity, and not a formal multitude of lesser velocities. In a

word, there is not the least resemblance between continuous acceleration

and continuous matter.

Although the preceding answer sufficiently shows the flimsiness of the

objection, we may yet observe that actions having an infinitesimal

duration are indeed infinitesimal, but are not _true indivisibles_. For

the expression of an accelerating action, in dynamics, contains three

variable functions—that is, first, the _intensity_ of the action at the

unit of distance in the unit of time; secondly, its _duration_; thirdly,

the _distance_ from the agent to the patient. Hence, in the case of an

action of infinitesimal duration, there still remain two variables, viz.,

the _intensity_ of the power, and the _distance_ from the patient; and

their variation causes a variation of the action in its infinitesimal

duration. Thus it is manifest that actions of infinitesimal duration can

have a greater or a less intensity, and therefore are not _true

indivisibles_ of intensity. If, for instance, two agents by their constant

and continuous action produce in the same length of time different

effects, it is evident that their actions have different intensities in

every infinitesimal instant of time; hence such infinitesimal actions,

though bearing no comparison with finite quantities, bear comparison with

one another, and form definite geometric ratios.

_Fourth objection._—If the contact of one indivisible with another cannot

engender a continuum, we must deny the existence of time and of local

motion. For time is engendered by the flowing of an instant towards the

instant immediately following, and movement is engendered by the flowing

of a point in space towards the point immediately following. If, then,

indivisibles cannot, by their contact, give rise to continuous extension,

neither time nor local motion will acquire continuous extension.

Our answer to this objection is that time and movement are not engendered

by a formal contact of a real instant with the instant following, or of a

real point with the point following. Duration is not a sum of indivisible

instants formally touching one another, nor is the length of space a sum

of indivisible points touching one another. We may have points _in space_,

but not points _of space_; and in like manner we have instants _in

succession_, not instants _of succession_, though in common language we

usually confound the latter with the former. Yet, when we talk of a point

of space, our meaning is not that space is made up of points, but simply

that a point of matter existing in space marks out its own ubication, thus

lending to the space occupied the name of _point_. Hence no movement in

space can be conceived to extend by successive contacts of points, or by

the flowing of a point towards other points immediately following; for

these _points immediately following_ exist only in our imagination. Nor

does a flowing point engender a line of space, but only a line of

movement; and even this latter is not properly _engendered_, but merely

_marked out_ in space; for all possible lines are already virtually

contained in space, and therefore they need no engendering, but simply

marking out by continuous motion.

The same is to be said of the origin of time. Time is not a formal sum of

instants touching one another. The instant just past is no more, hence it

cannot touch the instant which is now; and the instant which is to follow

is not yet, hence it cannot be touched by the instant which is now.

Accordingly, as the movement of a single point marks out a continuous line

in absolute space, so also the flowing of a single instant extends a line

in absolute duration. For, as S. Thomas teaches, in the whole length of

time there is but a single instant _in re_, though this same instant

becomes virtually manifold _in ratione prioris et posterioris_ by shifting

from “before” to “after.” And in the same manner, in the whole length of a

line measured in space by continuous movement, there is but a single point

_in re_ actually shifting its ubication from “here” to “there,” and thus

becoming virtually manifold in its successive positions. And for this

reason both movement and time are always and essentially developing (_in

fieri_), and never exist as developed (_in facto esse_); since of the

former nothing is actual but a point, and of the latter nothing is actual

but an instant.

It is scarcely necessary to repeat that, if there were any continuous

matter, its parts would all be actual and simultaneous. Its continuous

extension would therefore be properly engendered by the contact of

indivisible points, not by the shifting of a point from one end of its

dimensions to another. This sufficiently shows that from the continuity of

movement and of time nothing can be concluded in favor of continuous

matter.

_Fifth objection._—Between two given points in space infinite other points

can be placed. Now, what is possible can be conceived to be done; and thus

we can conceive an infinite multitude between the two points. Accordingly,

an infinite multitude can be contained within limits; and if so,

continuous matter is not impossible, and our first argument has no weight.

We answer that, although an infinite multitude of points can be placed

between any two given points, yet nothing can be inferred therefrom in

favor of continuous matter. For those innumerable points either will touch

one another or not. If they do not touch, they will not make a continuum;

and if they touch, they will, as we have shown, entirely coincide, instead

of forming a continuous extension. It is plain, therefore, that the

distance between the two given points cannot be filled _continuously_,

even by an infinite multitude of other points. And therefore the objection

has no force.

Nor is it true that by the creation of an infinite multitude of points

between two given points such a multitude would be an infinity _within

limits_. For the two given points are limits, or rather terms, of a local

relation, but they are no limits of the multitude, or discrete quantity,

which can be placed between them; for, without altering the position of

those two points, we can increase without end the number of the

intervening points. As volume is not a limit of density, so the distance

of two points is not the limit of the multitude that can be condensed

between them.

_Sixth objection._—All the arguments above given against the continuity of

matter are grounded on a false supposition; for they all take for granted

that _a continuum must be made up of parts_—an assumption which can be

shown to be false. For, first, in the geometric continuum there are no

actual parts; for such a continuum is not made up by composition, but is

created, such as it is, all in one piece. Whence it must be inferred that

the primitive elements of matter, though exempt, as primitive, from

composition of parts, and really simple, may yet possess extension.

Secondly, who can deny that God has the power to create a solid body as

perfectly continuous as a geometric volume? Such a body, though divisible

into any number of parts, would not be a compound; for its parts would be

merely possible, not actual; and therefore it would be simple, and yet

continuous. Thirdly, those who deny the possibility of continuous matter

admit a vacuum existing between simple points of matter. Such a vacuum is

a continuous extension intercepted between real terms, and is nothing else

than the possibility of real extension. But the real extension, which is

possible between real terms, is not, of course, a series of points

touching one another, for such a series, as all admit, is impossible. It

is, therefore, an extension really continuous, not made up of parts, but

only divisible into parts. Hence matter may be continuous and simple at

the same time.(111)

This objection tends to establish the possibility of _simple‐extended_

matter. Yet that simplicity and material extension exclude one another is

an evident truth; in other terms, material continuity, without composition

of parts, is utterly inconceivable. If, therefore, we persist in taking

for granted that a material continuum must be made up of actual parts, we

do not make a gratuitous supposition.

The three reasons adduced in the objection are far from satisfactory. The

first makes an unlawful transition from the geometric extension of volumes

to the physical extension of masses. Such a transition, we say, is

unlawful; for the geometrical extension is only _virtually_ continuous,

and therefore involves no actual multitude of parts; whereas the physical

extension of the mass of matter would be _formally_ and _materially_

continuous, thus involving a formal multitude of actual parts perfectly

distinct from one another, though united to form one continuous piece. The

geometric extension is measured by three linear dimensions, and has no

density. Now, a geometric line is nothing else than the trace of the

movement of a point; and accordingly its continuity arises from the

continuity of the movement itself, which alone is _formally_ continuous;

for the space measured by such a movement has no formal continuity of its

own, as we have already explained, but is styled “continuous” only

inasmuch as it is the region of continuous movement. There is no doubt,

therefore, that geometric extension is merely virtual in its continuity;

and for this reason it is not made up of parts of its own, but simply

corresponds to the parts of the movement by which it can be measured.

Material extension, on the contrary, would be densely filled with actual

matter, and therefore would be made up of actual parts perfectly distinct,

though not separated. To apply, as the objection does, to material

extension, what geometry teaches of the extension of volumes, is therefore

a mere paralogism. It amounts to saying: _Vacuum is free from composition;

therefore the matter also which would fill it is free from composition._

We may add that even geometric extension, if real, involves composition.

For, evidently, we cannot conceive a geometric cube without its eight

vertices, nor can we pretend that a figure requiring eight distinct points

as the terms of its dimensions is free from composition. Now, if an empty

geometric volume cannot be simple, what shall we say of a volume full of

matter? Wherever there is real extension, there are real dimensions, of

which the beginning, and the end, and all the intermediate terms are

really distinct from one another. Hence in a material extension there

should be as many distinct material terms as there are geometric points

within its limits. And if this is _simplicity_, we may well ask what is

_composition_?

The second reason adduced in the objection is a mere _petitio principii_.

For he who says that God can create “a solid body as perfectly continuous

as a geometric volume” assumes that such a continuous body involves no

contradiction; he therefore begs the question. On the other hand, to

affirm that God can create a solid body as perfectly continuous as a

geometric volume, is to affirm that God can create a body of infinite

density—that is, an infinite mass within finite dimensions. For the mass

of a body of matter is the product of its volume into its density; hence,

if its volume be finite, and its density infinite, the mass will be

infinite. Now, a body materially continuous implies infinite density; for

it excludes porosity, and it supplies matter for an endless division.

Hence a continuous mass of matter filling a finite volume would be _an

infinite mass contained within limits_. We think we are not presuming too

much when we say that God cannot create such a metaphysical monstrosity.

“Such a body,” says the objection, “though divisible into any number of

parts, would not be a compound.” This is evidently false; for all that is

divisible into parts has parts, and therefore composition. Nor is it true

that the parts of a continuous body “would be merely possible, not

actual”; for if such parts are not actual, how can the body be actual? No

actual continuum can exist without actual parts. The divisibility of

continuum is not the possibility of actual parts, but the possibility of

their actual separation.

The third reason is based on our admission of a vacuum between material

points. Such a vacuum, it is objected, is a continuous (virtual)

extension, founding the possibility of some other (formal) extension. This

we concede; but when it is argued that this other extension which is

possible between the material terms is the extension of continuous matter,

we deny the consequence. It is only continuous local movement, not

continuous matter, that can formally extend from term to term, as we have

proved. When two real points of matter have a distinct ubication in space,

the interval between them cannot be estimated otherwise than by the extent

of the movement which can be made from one point to the other. We cannot

perceive the distance between two terms, except by drawing, at least

mentally, a line from the one to the other; and for this reason, as we

have remarked elsewhere, the relation of distance is conceived by us as a

quantity measured by movement, not by matter, and representing the

extension of continuous movement, not of continuous matter. Hence a vacuum

intercepted between real points is a _real_, though only _virtual_,

extension; and that other _real_ and _formal_ extension, which is possible

between the same real points, is the extension of local movement. Our

opponent concedes that “the real extension possible between real terms is

not a series of points touching one another; for such a series, as all

admit, is impossible.” Now, this suffices to show that the real extension

possible between such real terms is not the extension of continuous

matter; for such an extension, as we have abundantly proved, would be made

up of nothing but of a series of points touching one another.

Nothing, perhaps, more evidently shows the unquestionable solidity of the

thesis we have undertaken to defend than the necessity felt by our

opponents of admitting in matter _an extended simplicity_ and a

_simplicity divisible into parts_, as witnessed by this last objection,

which we have transcribed from a grave and learned professor of

philosophy. _Extended and simple matter_ is such an absurdity as few would

admit to be a corollary of their own theories; yet it cannot be escaped by

those who consider the _first_ elements of matter as endowed with bulk.

For physical simplicity is an essential attribute of all primitive beings;

and, if primitive elements are nevertheless supposed to be intrinsically

extended, it is plain that their simplicity will be an extended

simplicity.

The main reason why some philosophers still cling to material continuity

is their fear of _actio in distans_. We have already shown that such a

fear, though very common, cannot be justified. We grant that, owing to

popular prejudice and an incorrect notion of things, many are apt to dread

action at a distance as a dangerous shoal; but when they resort to an

“extended and divisible simplicity,” they steer their ship directly

against the reefs.

To Be Continued.

Christmas In The Thirteenth Century.

Few are the hearts that do not feel the benign and joyful influence of

Christmas. It is the one feast that neither the all‐destroying zeal of the

Reformation nor the cold indifferentism of the present age has dared to

abolish or desecrate. To how many is it the sole remaining word that

reminds them of the sacred name of Christ! There _was_ a time when

Christmas was but one of the many holydays that with each succeeding month

recalled to Christian hearts some great event in the life of their divine

Master; but heresy has swept away one by one those sacked days of repose

and prayer. Even in Catholic countries the church has found it necessary

to reduce the number of Days of Obligation, so cold have grown both faith

and devotion.

Wealth and material prosperity—these are the sole ends for which a

heartless world would have us exert all our energies, and it would fain

clog with the sordid love of gain all the higher aspirations of the soul.

But we are forgetting that this is Christmas time—a time for innocent

pleasure, and not for moralizing; so, leaving the present age, with all

its faults, we will ask our readers to transport themselves with us, in

imagination, some six centuries back, and witness how was celebrated in

those Ages of Faith the holy night of the Nativity of our Lord.

The period selected is about the middle of the XIIIth century. Religion

was then in the fullest splendor of its power. It was the light of

civilization, the custodian of all learning. Every art had combined to

render its outward expression worthy of the great and holy mysteries it

taught. Gothic architecture had at this date attained its highest

perfection; painting and sculpture were almost exclusively devoted to the

decoration of God’s temples; poetry and music were united to render

attractive the sublime and rarely‐interrupted Offices of the church. The

liturgical works of the period are mines of poetic and musical riches that

for the most part lie hidden and uncared for in their musty tomes.

Some will doubtless smile when we speak of the Latin poetry of the middle

ages, and certainly those who seek in it the polished and classical verses

of a Horace or a Virgil will be disappointed. They will, however, find

that, despite their somewhat strange Latinity, these productions of a so‐

called barbarous age contain a depth of feeling, a strength and freshness

of expression, quite unknown to the pagan poets, and were as appropriate

to those grand old cathedrals under whose roofs they were to resound as

were the classic odes and songs to the luxurious banquet‐halls of Rome or

the effeminate villas of Naples. In fact, to adequately judge of the

poetry contained in the Offices of the mediæval period, we must place

ourselves amid the surroundings in which they were performed; we must

_not_ view it from the stand‐point of the present age, with its entirely

different ideas of both religious life and religious art.

It will be, then, in an old French cathedral that we shall ask our readers

to spend this Christmas night; for the office, or rather religious drama,

at which we intend to make them assist, is taken from a Roman‐French

missal of the XIIIth century.

The night has closed in. Within the city walls the tortuous and narrow

streets are nearly deserted; but lights gleam from many a diamond pane,

for inside joyous circles are gathered around the glowing logs that

brightly sparkle in the ample chimneys. Old stories are repeated by

venerable grandfathers to merry grandchildren, who in return sing with

silvery voices quaint old carols. Suddenly a well‐known sound fills the

air; from the high cathedral towers burst forth the joyous chimes that

herald the approach of Christ’s natal hour. The notes that ring out so

clearly in the cold December air are those of the familiar Christmas hymn,

_Christe Redemptor omnium_.(112) Soon a hurrying throng begin to fill the

streets, all wending their way towards the same point, through narrow and

winding streets. By gabled house and arched doorway, by mullioned window

and jutting tower, they press forward until they reach the central square,

where rises, in all its splendor, the old cathedral church.

Beautiful and imposing at all times is a Gothic cathedral, but never more

so than when the trembling light of a winter moon throws around it a soft

halo, just enough to make its grand proportions visible amid the

surrounding gloom, while leaving all the finer details wrapt in sombre

mystery. Doubly lofty appear tower and spire, and strangely weird each

fantastic gargoyle, as a stray moonbeam falls athwart its uncouth

countenance.

Let us follow the crowd, and enter beneath the richly‐sculptured doorway.

Dim is the light within, only just sufficient to find your way among the

throng that now begins to fill every part of the vast edifice. The

numerous assemblage of priests and choristers are singing the Office of

Matins, the grand old melodies of S. Gregory resounding beneath the

vaulted roof with that wonderful effect that makes them, when sung by

choir and congregation, the most truly religious music that exists. As the

last solemn notes of the _Te Deum_ die out, a white‐robed chorister‐boy

representing an angel advances into the centre of the choir, and in sweet,

clear accents chants the words of the angelic message, “Nolite timere:

ecce enim evangelizo vobis gaudium magnum, quod erit omni populo, quia

natus est vobis hodie Salvator mundi, in civitate David. Et hoc vobis

signum: Invenietis infantem pannis involutum, et positum in

præsepio”—“Fear not: for behold, I bring you good tidings of great joy,

that shall be to all the people: for this day is born to you a Saviour,

who is Christ the Lord, in the city of David. And this shall be a sign

unto you: You shall find the infant wrapped in swaddling‐clothes, and laid

in a manger.”

Then from the high triforium‐gallery seven pure young voices ring out, as

if from heaven, the words sung by the angel‐host on the first Christmas

night: “Gloria in excelsis Deo, et in terra pax hominibus bonæ

voluntatis.” These familiar words that herald the pious representation of

the holy scenes whose reality centuries ago hallowed this night in the

mountains of Judæa, are listened to by the vast congregation with rapt and

devout attention. In their simple and earnest faith the assistants feel

themselves transported back to the days of Herod and to the village of

Bethlehem, as they behold emerging from the western porch, and slowly

advancing up the nave, a train of shepherds with staves in their hands,

singing, as they proceed in search of their newborn King, the following

hymn. Both words and music are full of beauty, and the cadence is well

suited to a Christmas carol:

Pax in terris nunciatur,

In excelsis gloria.

Terra cœlo fœderatur,

Mediante gratia.

Mediatur homo Deus

Descendit in propria,

Ut ascendat homo reus

Ad amissa gaudia.

Eia! Eia!

Transeamus, videamus

Verbum hoc quod factum est

Transeamus, ut sciamus

Quod annunciatum est.

In Judea puer vagit,

Puer salus populi,

Quo bellandum se præsagit

Vetus hostis sæculi.

Accedamus, accedamus

Ad præsepe Domini,

Et dicamus:

Laus fecundæ Virgini.

(Peace on earth is announced, and in heaven glory,

Earth is reconciled through divine grace. The Mediator God‐Man

descends amongst his own, that guilty man may ascend to lost joys.

Let us go over, let us see this word that is come to pass.

Let us go over, that we may learn what has been announced.