DEFINITIONS.
I. By that which is self-caused,
I mean that of which the essence involves existence, or that of
which the nature is only conceivable as existent.
II. A thing is called finite
after its kind, when it can be limited by another thing of the same
nature; for instance, a body is called finite because we always
conceive another greater body. So, also, a thought is limited by
another thought, but a body is not limited by thought, nor a
thought by body.
III. By substance, I mean that
which is in itself, and is conceived through itself: in other
words, that of which a conception can be formed independently of
any other conception.
IV. By attribute, I mean that
which the intellect perceives as constituting the essence of
substance.
V. By mode, I mean the
modifications of substance, or that which exists in, and is
conceived through, something other than itself.
VI. By God, I mean a being
absolutely infinite-that is, a substance consisting in infinite
attributes, of which each expresses eternal and infinite
essentiality.
Explanation—I say absolutely
infinite, not infinite after its kind: for, of a thing infinite
only after its kind, infinite attributes may be denied; but that
which is absolutely infinite, contains in its essence whatever
expresses reality, and involves no negation.
VII. That thing is called free,
which exists solely by the necessity of its own nature, and of
which the action is determined by itself alone. On the other hand,
that thing is necessary, or rather constrained, which is determined
by something external to itself to a fixed and definite method of
existence or action.
VIII. By eternity, I mean
existence itself, in so far as it is conceived necessarily to
follow solely from the definition of that which is eternal.
Explanation—Existence of this
kind is conceived as an eternal truth, like the essence of a thing,
and, therefore, cannot be explained by means of continuance or
time, though continuance may be conceived without a beginning or
end.
AXIOMS.
I. Everything which exists,
exists either in itself or in something else.
II. That which cannot be
conceived through anything else must be conceived through
itself.
III. From a given definite cause
an effect necessarily follows; and, on the other hand, if no
definite cause be granted, it is impossible that an effect can
follow.
IV. The knowledge of an effect
depends on and involves the knowledge of a cause.
V. Things which have nothing in
common cannot be understood, the one by means of the other; the
conception of one does not involve the conception of the
other.
VI. A true idea must correspond
with its ideate or object.
VII. If a thing can be conceived
as non-existing, its essence does not involve existence.
PROPOSITIONS.
PROP. I. Substance is by nature
prior to its modifications.
Proof.—This is clear from Deff.
iii. and v.
PROP. II. Two substances, whose
attributes are different, have nothing in common.
Proof.—Also evident from Def.
iii. For each must exist in itself, and be conceived through
itself; in other words, the conception of one does not imply the
conception of the other.