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have been ordered on a perfectly sound method. The desire for an equality which may seem natural, but is really altogether artificial, is no doubt a very strong one; but it must yield to the overpowering force of circumstances when there is no deus ex machinâ in the shape of a benevolent proprietor to give it an apparent satisfaction.

Social arrangements will present no difficulty. It is an essential characteristic of communities of this kind, that they claim to regulate the whole life of their members. They thus unloose, or, at least, cut many knots, which perplex society as it is ordinarily constituted. They might, and doubtless would, make and enforce, for instance, any restrictions on population that might seem advisable.

These, however, are subjects on which I cannot enter. Generally I may express my belief that the experiment of Ralahine may be repeated with success—not, indeed, with the ease and uninterrupted prosperity of which Mr. Pare tells us, for such undertakings are not more exempt than other human things from the necessity of the labor improbus, but still with ultimate success; that its mistakes were not of its essence, and might be remedied without radically changing its character; that, therefore, it is full of good auguries for the future, shows us a gleam of light in a region where the prospect has hitherto been very dull indeed.

I must not conclude without quoting a very valuable suggestion which Mr. Pare makes in his preface :

“ It would be well if intending emigrants would unite their means and exertions in co-operative farming, under skilled direction. They would thus escape the difficulties, discomforts, and utter dreariness—sometimes almost despair-which attend the isolated settler, especially when an emigrant from some populous locality. In travelling through Canada and some of the Northern States of America, a few years since, as also in Algeria (though the observation applies less to this latter country), I was pained to witness the usually hard lot of the settler under the individual system. Buried in the primeval forest, or, if in Algeria, a squatter on some dreary plain, often miles away from his nearest neighbour, I found the emigrant performing an amount of irksome toil, and subjected to a loss of resources, which would be quite unnecessary under co-operative arrangement, and which was the more wearisome from his sad loneliness. In cases of sickness or accident, the evils of this melancholy isolation are intensified, and the sufferer feels positively severed from human sympathies; whilst anything in the shape of instruction and amusement is just out of the question."

It is here, perhaps, in the fields of emigration, free from the complications of an old and crowded country, that the “Ralahines” of the future will most readily be founded. But I should be sorry to abandon the hope that they may rise up here also for the benefit of a class which suffers privations almost beyond belief with a patience which must surprise all those who know how sorely it is tried.

ALFRED CHURCH.

ON INFINITY.

THERE
THERE are few words that have done more harm, in the way

of confusing thought, of mixing up matters entirely distinct, and turning speculation into mere puzzle, than the word Infinite. Let me endeavour to show something of this.

Two most noteworthy examples in our day are furnished by Sir W. Hamilton, both in his wonderful paper on the Philosophy of the Unconditioned and his lectures on Metaphysics, and by Dean Mansel in his Bampton Lectures. Manifold as was the criticism which the latter called forth, I am not aware that the question which I now wish to raise received much attention. It is as follows: Are not our puzzles in this matter the result of a phantom conjured up by ourselves ? The term infinite may, indeed, serve a legitimate purpose in scientific reasoning ; but has it a corresponding reality ? Is there an infinite in actu ?

“Infinitum in potentiâ ab infinito actuali toto cælo diversum."

“Infinitum enim illud in potentiâ non concipitur tanquam aliquid fixum et constans, sed velut aliquid semper crescens, quod quidem semper finitum est eâ sui parte quæ actu existit, sed quod semper limites suos prætergreditur et prætergredietur.” (Abraham Trembley. “Theses Mathematicæ de Infinito et Calculo Infinitesimali.” Geneva, 1730.)*

*.“Theses Variæ Philosophicæ,” vol. iii. Public Library, Geneva.

There is more to the same purpose.

What manner of man Abraham Trembley was I have not the faintest notion ; but I approve highly of what follows; though some may think that I have exceeded the sanction, and put myself outside the justification, for which it may be cited :

“Et eo magis in hac nostrâ sententiâ fuimus confirmati, quod nostrum systema gloriæ Dei apprimè congruum nobis videretur: illius enim ope, spatium infinitum, materia æterna, indigna illa numinis æmula penitus extirpantur.”

This, then, is our question. Not whether Thought cannot launch itself into the Indefinite; not whether all numeration and quantity cannot be potentially increased in imagination ad infinitum ; but whether there is an infinite in actu.

It is often said that matter is infinitely divisible, and those who hesitate to pronounce this, affirm space to be so.

When we ask ourselves what we really mean by either proposition, we shall be led, I think, to doubt our warrant for either.

1st. When I say that matter is infinitely divisible, I can only mean that I never saw matter, however small, that did not admit of division, and that I am quite unable to imagine such. This is true; but then I have never seen matter which I knew to be in the last possible stage of compression—what matter would be in such a condition I have no means of judging—I cannot tell whether it would then exhibit what are commonly called its primary qualities, or whether, if it presented some, it would present all; whether, if it retained the attributes of resistance and impenetrability, it would also retain that of extension. So far, then, as I know, it is not the divisibility of matter which is infinite, but my faculty of tracing its possibilities of division which is finite.

2ndly. Now let us turn to space. No doubt it is impossible to conceive space otherwise than as divisible, because extension and space are identical, and extension implies divisibility. therefore, and imagine space not divisible, would be to try and imagine a contradiction, to endeavour to think of space that should

But there is no infinitude here. As in the case of matter, the limitation is in our faculties. We cannot divide space up to the point of annihilation, and this is all that we mean when we talk of its infinite divisibility. And when we consider that it is and can be nothing in itself, that it is but a relation in which alone material objects can be manifested to our minds, we shall see that to apply the term infinite to it, in either of its directions, either in respect of its divisibility or its extension, is to commit an absurdity.

I do not mean to question the value of the infinitesimal calculus, which, so far as my very imperfect insight into it enables me to

To try,

not be space.

judge, in no way involves the notion of a divisibility that is really infinite in actu.

And so of number. There is no such thing as an infinite sum. The very notion of a sum implies limit, and just therefore because every sum is finite, can we always suppose it carried further. The same applies, of course, to magnitude and to weight. Each amount of either must be finite, and therefore could be enlarged. But this continual possibility of enlargement in thought is something quite different from infinity in actu, and never even contemplates that.

As to actual Infinity, too, there is a good deal of loose and confused thought amongst those who use the term. The divine perfection is nowhere expressed in Scripture by means of it, and seldom by the Fathers. The immensus of the Athanasian Creed is not an equivalent for it. And, on the whole, the terms Absolute and Eternal seem better to denote God's perfection than this of Infinite, which runs so easily into a Pantheistic sense, if we mean anything by it, or else into profitless puzzles and endless antinomies of reason.

But is not God infinite? In all reverence, I would ask the inquirer what he means by suggesting the proposition. We cannot predicate Infinity in the category of substance—the term has no meaning there. Substance, as such, is neither finite nor infinite; we can only affirm or deny either of an attribute or attributes. The extension of all substance may be spoken of as finite or infinite, though an infinitely extended substance is altogether inconceivable, and there would be no piety, but the reverse, in speaking of God as such. But we may speak of His Attributes—His power, wisdom, goodness, and love—as infinite, because these have no limits, except such as He Himself may assign to their exercise.

If, therefore, there be no such thing as actual Infinity, it seems desirable to steer clear in our language of whatever might make the impression of such. There is something, however, tempting in both name and thought, and so we find philosophers continually calling infinite that which is merely indefinite. Thus Malebranche, and, in the present day, Gratry, who quotes the former with approbation, speak of every universal, and therefore of all, law as infinite ; and Gratry constantly styles that part of the inductive process which he calls transcendence a passing from the finite to the infinite. Let us briefly consider this.

The specimens which we encounter of any class are, of course, finite in number; but when we have found the universal, the type to which they are to be referred, or, which is the same thing, the law to which they are conformed, we are told that we have passed from the finite to the infinite, because such an universal type, or

law, is of unlimited application. Have we a right to be sure of this ?

We may admit, indeed, that its possibilities of application are altogether illimitable by us. When I have found specific character, I have found that which fashions not only all the specimens before me, but all which exist, and all which ever can exist; and I possess no faculty enabling me to say how many should or can exist. I go to Africa, and find a large animal of the feline genus, which has the specific marks of panther. Those specific marks constitute an universal, which is quite irrespective, in our conception, of the number of actual panthers. It would be the same if we supposed that number indefinitely enlarged. After any imaginary enlargement, we can always suppose one further still, and the universal, or type, will remain unchanged.

Now I am well persuaded that the Nominalist utterly fails in explaining universals, and that the Conceptualist gives but a very partial and inadequate account of them. They are in our minds, because they have been from everlasting in God's, and in His creative wisdom and by His perfect method, the individual specimens are all conformed to them, and fashioned by them. This is true; but the Realist seems often to have overlooked, what must be equally true, that the universal, the type, is not more eternally in the mind of God than the individuals, than each individual, predestined to be moulded by it. And who shall say that the individual is more predestined to be conformed to the type, than the type is designed to the situation, the circumstances, the wants, and the end of the individual ? Natural History is beginning to trace this, even in such matters as the colour of the animal, and the marks on his skin.

Now if this be so, we dare not affirm that the type and the destined number of the individuals which are to present it are not exactly adjusted to each other. The mind of God, from which both has doubtless arranged both for reasons often far beyond our ken and above our comprehension. Observation, however, may sometimes give us a little insight into these. We do see that the wild beast performs certain functions in the arrangement of the scene around him. When man's time and turn arrive for entering on that scene, and for playing his part on it, the other has to give way, and finally disappear. To recur, then, to our example, while beyond all doubt each individual panther is predestined to be conformed to the specific type of panther, it seems equally necessary to believe of that type that it is designed and prepared for the peculiar situation and wants of the individual panther. And if there may be unknown to us why the number of such individuals should be precisely fixed, these are reasons why the type is of application pro

proceed,

reasons

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