who will give me a clear idea of infinity? i have never had an idea of it which was not excessively confused — possibly because i am a finite being.
what is that which is eternally going on without advancing — always reckoning without a sum total — dividing eternally without arriving at an indivisible particle?
it might seem as if the notion of infinity formed the bottom of the bucket of the dana?des. nevertheless, it is impossible that infinity should not exist. an infinite duration is demonstrable.
the commencement of existence is absurd; for nothing cannot originate something. when an atom exists we must necessarily conclude that it has existed from all eternity; and hence an infinite duration rigorously demonstrated. but what is an infinite past? — an infinitude which i arrest in imagination whenever i please. behold! i exclaim, an infinity passed away; let us proceed to another. i distinguish between two eternities, the one before, the other behind me.
when, however, i reflect upon my words, i perceive that i have absurdly pronounced the words: “one eternity has passed away, and i am entering into another.” for at the moment that i thus talk, eternity endures, and the tide of time flows. duration is not separable; and as something has ever been, something must ever be.
the infinite in duration, then, is linked to an uninterrupted chain. this infinite perpetuates itself, even at the instant that i say it has passed. time begins and ends with me, but duration is infinite. the infinite is here quickly formed without, however, our possession of the ability to form a clear notion of it.
we are told of infinite space — what is space? is it a being, or nothing at all? if it is a being, what is its nature? you cannot tell me. if it is nothing, nothing can have no quality; yet you tell me that it is penetrable and immense. i am so embarrassed, i cannot correctly call it either something or nothing.
in the meantime, i know not of anything which possesses more properties than a void. for if passing the confines of this globe, we are able to walk amidst this void, and thatch and build there when we possess materials for the purpose, this void or nothing is not opposed to whatever we might choose to do; for having no property it cannot hinder any; moreover, since it cannot hinder, neither can it serve us.
it is pretended that god created the world amidst nothing, and from nothing. that is abstruse; it is preferable to think that there is an infinite space; but we are curious — and if there be infinite space, our faculties cannot fathom the nature of it. we call it immense, because we cannot measure it; but what then? we have only pronounced words.
of the infinite in number.
we have adroitly defined the infinite in arithmetic by a love-knot, in this manner ∞; but we possess not therefore a clearer notion of it. this infinity is not like the others, a powerlessness of reaching a termination. we call the infinite in quantity any number soever, which surpasses the utmost number we are able to imagine.
when we seek the infinitely small, we divide, and call that infinitely small which is less than the least assignable quantity. it is only another name for incapacity.
is matter infinitely divisible?
this question brings us back again precisely to our inability of finding the remotest number. in thought we are able to divide a grain of sand, but in imagination only; and the incapacity of eternally dividing this grain is called infinity.
it is true, that matter is not always practically divisible, and if the last atom could be divided into two, it would no longer be the least; or if the least, it would not be divisible; or if divisible, what is the germ or origin of things? these are all abstruse queries.
of the universe.
is the universe bounded — is its extent immense — are the suns and planets without number? what advantage has the space which contains suns and planets, over the space which is void of them? whether space be an existence or not, what is the space which we occupy, preferable to other space?
if our material heaven be not infinite, it is but a point in general extent. if it is infinite, it is an infinity to which something can always be added by the imagination.
of the infinite in geometry.
we admit, in geometry, not only infinite magnitudes, that is to say, magnitudes greater than any assignable magnitude, but infinite magnitudes infinitely greater, the one than the other. this astonishes our dimension of brains, which is only about six inches long, five broad, and six in depth, in the largest heads. it means, however, nothing more than that a square larger than any assignable square, surpasses a line larger than any assignable line, and bears no proportion to it.
it is a mode of operating, a mode of working geometrically, and the word infinite is a mere symbol.
of infinite power, wisdom, goodness.
in the same manner, as we cannot form any positive idea of the infinite in duration, number, and extension, are we unable to form one in respect to physical and moral power.
we can easily conceive, that a powerful being has modified matter, caused worlds to circulate in space, and formed animals, vegetables, and metals. we are led to this idea by the perception of the want of power on the part of these beings to form themselves. we are also forced to allow, that the great being exists eternally by his own power, since he cannot have sprung from nothing; but we discover not so easily his infinity in magnitude, power, and moral attributes.
how are we to conceive infinite extent in a being called simple? and if he be uncompounded, what notions can we form of a simple being? we know god by his works, but we cannot understand him by his nature. if it is evident that we cannot understand his nature, is it not equally so, that we must remain ignorant of his attributes?
when we say that his power is infinite, do we mean anything more than that it is very great? aware of the existence of pyramids of the height of six hundred feet, we can conceive them of the altitude of 600,000 feet.
nothing can limit the power of the eternal being existing necessarily of himself. agreed: no antagonists circumscribe him; but how convince me that he is not circumscribed by his own nature? has all that has been said on this great subject been demonstrated?
we speak of his moral attributes, but we only judge of them by our own; and it is impossible to do otherwise. we attribute to him justice, goodness, etc., only from the ideas we collect from the small degree of justice and goodness existing among ourselves. but, in fact, what connection is there between our qualities so uncertain and variable, and those of the supreme being?
our idea of justice is only that of not allowing our own interest to usurp over the interest of another. the bread which a wife has kneaded out of the flour produced from the wheat which her husband has sown, belongs to her. a hungry savage snatches away her bread, and the woman exclaims against such enormous injustice. the savage quietly answers that nothing is more just, and that it was not for him and his family to expire of famine for the sake of an old woman.
at all events, the infinite justice we attribute to god can but little resemble the contradictory notions of justice of this woman and this savage; and yet, when we say that god is just, we only pronounce these words agreeably to our own ideas of justice.
we know of nothing belonging to virtue more agreeable than frankness and cordiality, but to attribute infinite frankness and cordiality to god would amount to an absurdity.
we have such confused notions of the attributes of the supreme being, that some schools endow him with prescience, an infinite foresight which excludes all contingent event, while other schools contend for prescience without contingency.
lastly, since the sorbonne has declared that god can make a stick divested of two ends, and that the same thing can at once be and not be, we know not what to say, being in eternal fear of advancing a heresy. one thing may, however, be asserted without danger — that god is infinite, and man exceedingly bounded.
the mind of man is so extremely narrow, that pascal has said: “do you believe it impossible for god to be infinite and without parts? i wish to convince you of an existence infinite and indivisible — it is a mathematical point — moving everywhere with infinite swiftness, for it is in all places, and entire in every place.”
nothing more absurd was ever asserted, and yet it has been said by the author of the “provincial letters.” it is sufficient to give men of sense the ague.
