Charles Bradlaugh - Ancient and Modern Celebrated Freethinkers

VIII. By eternity I understand existence itself, in as far as it is conceived necessarily to follow from the sole definition of an eternal thing.

AXIOMS.

I. Everything which is, is in itself, or in some other thing.

II. That which cannot be conceived through another, per aliud must be conceived, per se .

III. From a given determinate cause the effect necessarily follows, and vice versa . If no determinate cause be given, no effect can follow.

IV. The knowledge of an effect depends on the knowledge of the cause, and includes it.

V. Things that have nothing in common with each other cannot be understood by means of each other – that is, the conception of one, does not involve the conception of the other.

VI. A true idea must agree with its original in nature.

VII. Whatever can be clearly conceived as non-existent does not, in its essence, involve existence.

PROPOSITIONS.

I. Substance is prior in nature to its accidents. Demonstration. Per definitions three and five.

II. Two substances, having different attributes, have nothing in common with each other. Dem. This follows from def. three; for each substance must be conceived in itself and through itself; in other words, the conception of one does not involve the conception of the other.

III. Of things which have nothing in common, one cannot be the cause of the other. Dem. If they have nothing in common, then (per axiom five) they cannot be conceived by means of each other; ergo (per axiom four,) one cannot be the cause of the other. – Q. E. D.

IV. Two or more distinct things are distinguished among themselves, either through the diversity of their attributes, or through that of their modes. Dem. Everything which is, in itself, or in some other thing (per ax. one) – that is (per def. three and five,) there is nothing out of ourselves ( extra intellectum , outside the intellect) but substance and its modes. There is nothing out of ourselves whereby things can be distinguished amongst one another, except substances, or (which is the same thing, per def. lour) their attributes and modes.

V. It is impossible that there should be two or more substances of the same nature, or of the same attributes. Dem. If there are many different substances they must be distinguished by the diversity of their attributes or of their modes (per prop. 4.) If only by the diversity of their attributes, it is thereby conceded that there is, nevertheless, only one substance of the same attribute; but if their diversity of modes, then, substance being prior in order of time to its modes, it must be considered independent of them – that is (per def. three and six,) cannot be conceived as distinguished from another – that is (per prop, four,) there cannot be many substances, but only one substance. – Q. E. D.

VI. One substance cannot be created by another substance. Dem. There cannot be two substances with the same attributes (per prop, five) – that is (per prop. two,) that hare anything in common with each other; and, therefore (per prop, three,) one cannot be the cause of the other.

Corollary 1. Hence it follows that substance cannot be created by anything else. For there is nothing in nature except substance and its modes (per axiom one, and def. three and five.) Now, this substance, not being produced by another, is self-caused.

Corollary 2. This proposition is more easily to be demonstrated by the absurdity of its contradiction; for if substance can be produced by anything else, the conception of it would depend on the conception of the cause (per axiom four,) and hence (per def. three,) it would not be substance.

VII. It pertains to the nature of substance to exist. Dem. Substance cannot be produced by anything else (per coroli. prop, six,) and is therefore the cause of itself – that is (per def. one,) its essence necessarily involves existence; or it pertains to the nature of substance to exist. – Q. E. D.

VIII. All substance is necessarily infinite. Dem. There exists but one substance of the same attribute; and it must either exist as infinite or finite. But not finite, for (per def. two) as finite it must be limited by another substance of the same nature, and in that case there would be two substances of the same attributes, which (per prop, five) is absurd. Substance therefore is infinite. – Q. E. D.

"Scholium I. – I do not doubt but that to all who judge confusedly of things, and are not wont to inquire into first causes, it will be difficult to admit the demonstration of prop. 7, because they do not sufficiently distinguish between the modifications of substances, and substances themselves, and are ignorant of the manner in which things are produced. Hence it follows, that the commencement which they see natural things have, they attribute to substances; for he who knows not the true cause of things, confounds all things, and feigns that trees talk like men; that men are formed from stones as well as from seeds, and that all forms can be changed into all other forms. So, also, those who confound the divine nature with the human, naturally attribute human affections to God, especially as they are ignorant of how these affections are produced in the mind. If men attended to the nature of substance, they would not, in the least, doubt proposition seven; nay, this proposition would be an axiom to all, and would be numbered among common notions. For by substance they would understand that which exists in itself, and is concerned through itself — i. e. , the knowledge of which does not require the knowledge of anything as antecedent to it. But by modification they would understand that which is in another thing, the conception of which is formed by the conception of the thing in which it is, or to which it belongs. We can have, therefore, correct ideas of non-existent modifications, because, although out of the understanding they have no reality, yet their essence is so comprehended in that of another, that they can be conceived through this other. The truth of substance (out of the understanding) lies nowhere but in itself, because it is conceived per se . If therefore any one says he has a clear idea of substance, and yet doubt whether such substance exist, this would be as much as to say that he has a true idea, and nevertheless doubts whether it be not false (as a little attention sufficiently manifests;) or if any man affirms substance to be created, he at the same time affirms that a true idea has become false, than which nothing can be more absurd. Hence it is necessarily confessed that the existence of substance, as well as its essence, is an eternal truth. And hence we must conclude that there is only one substance possessing the same attribute, which requires here a fuller development. I note therefore – 1. That the correct definition of a thing includes and expresses nothing but the nature of the thing defined. From which follows – 2. That no definition includes or expresses a distinct number of individuals, because it expresses nothing but the nature of the thing defined; ergo , the definition of a triangle expresses no more than the nature of a triangle, and not any fixed number of triangles. 3. There must necessarily be a distinct cause for the existence of every existing thing. 4. This cause, by reason of which anything exists, must either be contained in the nature and definition of the existing thing (viz., that it pertains to its nature to exist,) or else must be beyond it – must be something different from it.

"As therefore it pertains to the nature of substance to exist, so must its definition include a necessary existence, and consequently from its sole definition we must conclude its existence. But as from its definition, as already shown in notes two and three, it is not possible to conclude the existence of many substances — ergo , it necessarily follows that only one substance of the same nature can exist."