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senses； since I have sometimes seen bodies triangular in
shape； because I can form in my mind an infinitude of other
figures regarding which we cannot have the least conception of
their ever having been objects of sense； and I can
nevertheless demonstrate various properties pertaining to
their nature as well as to that of the triangle； and these
must certainly all be true since I conceive them clearly。
Hence they are something； and not pure negation； for it is
perfectly clear that all that is true is something； and I have
already fully demonstrated that all that I know clearly is
true。 And even although I had not demonstrated this； the
nature of my mind is such that I could not prevent myself from
holding them to be true so long as I conceive them clearly；
and I recollect that even when I was still strongly attached
to the objects of sense； I counted as the most certain those
truths which I conceived clearly as regards figures； numbers；
and the other matters which pertain to arithmetic and
geometry； and； in general； to pure and abstract mathematics。
But now； if just because I can draw the idea of something
from my thought； it follows that all which I know clearly and
distinctly as pertaining to this object does really belong to
it； may I not derive from this an argument demonstrating the
existence of God？ It is certain that I no less find the idea
of God； that is to say； the idea of a supremely perfect Being；
in me； than that of any figure or number whatever it is； and I
do not know any less clearly and distinctly that an ＇actual
and＇ eternal existence pertains to this nature than I know
that all that which I am able to demonstrate of some figure or
number truly pertains to the nature of this figure or number；
and therefore； although all that I concluded in the preceding
Meditations were found to be false； the existence of God would
pass with me as at least as certain as I have ever held the
truths of mathematics （which concern only numbers and figures）
to be。
This indeed is not at first manifest； since it would seem
to present some appearance of being a sophism。 For being
accustomed in all other things to make a distinction between
existence and essence； I easily persuade myself that the
existence can be separated from the essence of God； and that
we can thus conceive God as not actually existing。 But；
nevertheless； when I think of it with more attention； I
clearly see that existence can no more be separated from the
essence of God than can its having its three angles equal to
two right angles be separated from the essence of a
＇rectilinear＇ triangle； or the idea of a mountain from the
idea of a valley； and so there is not any less repugnance to
our conceiving a God （that is； a Being supremely perfect） to
whom existence is lacking （that is to say； to whom a certain
perfection is lacking）； than to conceive of a mountain which
has no valley。
But although I cannot really conceive of a God without
existence any more than a mountain without a valley； still
from the fact that I conceive of a mountain with a valley； it
does not follow that there is such a mountain in the world；
similarly although I conceive of God as possessing existence；
it would seem that it does not follow that there is a God
which exists； for my thought does not impose any necessity
upon things； and just as I may imagine a winged horse；
although no horse with wings exists； so I could perhaps
attribute existence to God； although no God existed。
But a sophism is concealed in this objection； for from
the fact that I cannot conceive a mountain without a valley；
it does not follow that there is any mountain or any valley in
existence； but only that the mountain and the valley； whether
they exist or do not exist； cannot in any way be separated one
from the other。 While from the fact that I cannot conceive
God without existence； it follows that existence is
inseparable from Him； and hence that He really exists； not
that my thought can bring this to pass； or impose any
necessity on things； but； on the contrary； because the
necessity which lies in the thing itself； i。e。 the necessity
of the existence of God determines me to think in this way。
For it is not within my power to think of God without
existence （that is of a supremely perfect Being devoid of a
supreme perfection） though it is in my power to imagine a
horse either with wings or without wings。
And we must not here object that it is in truth necessary
for me to assert that God exists after having presupposed that
He possesses every sort of perfection； since existence is one
of these； but that as a matter of fact my original supposition
was not necessary； just as it is not necessary to consider
that all quadrilateral figures can be inscribed in the circle；
for supposing I thought this； I should be constrained to admit
that the rhombus might be inscribed in the circle since it is
a quadrilateral figure； which； however； is manifestly false。
＇We must not； I say； make any such allegations because＇
although it is not necessary that I should at any time
entertain the notion of God； nevertheless whenever it happens
that I think of a first and a sovereign Being； and； so to
speak； derive the idea of Him from the storehouse of my mind；
it is necessary that I should attribute to Him every sort of
perfection； although I do not get so far as to enumerate them
all； or to apply my mind to each one in particular。 And this
necessity suffices to make me conclude （after having
recognised that existence is a perfection） that this first and
sovereign Being really exists； just as though it is not
necessary for me ever to imagine any triangle； yet； whenever I
wish to consider a rectilinear figure posed only of three
angles； it is absolutely essential that I should attribute to
it all those properties which serve to bring about the
conclusion that its three angles are not greater than two
right angles； even although I may not then be considering this
point in particular。 But when I consider which figures are
capable of being inscribed in the circle； it is in no wise
necessary that I should think that all quadrilateral figures
are of this number； on the contrary； I cannot even pretend
that this is the case； so long as I do not desire to accept
anything which I cannot conceive clearly and distinctly。 And
in consequence there is a great difference between the false
suppositions such as this； and the true ideas born within me；
the first and principal of which is that of God。 For really I
discern in many ways that this idea is not something
factitious； and depending solely on my thought； but that it is
the image of a true and immutable nature； first of all；
because I cannot conceive anything but God himself to whose
essence existence ＇necessarily＇ pertains； in the second place
because it is not possible for me to conceive two or more Gods
in this same position； and； granted that there is one such God
who now exists； I see clearly that it is necessary that He
should have existed from all eternity； and that He must exist
eternally； and finally； because I know an infinitude of other
properties in God； none of which I can either diminish or
change。
For the rest； whatever proof or argument I avail myself
of； we must always return to the point that it is only those
things which we conceive clearly and distinctly that have the
power of persuading me entirely。 And although amongst the
matters which I conceive of in this way； some indeed are
manifestly obvious to all； while others only manifest
themselves to those who consider them closely and examine them
attentively； still； after they have once been discovered； the
latter are not esteemed as any less certain than the former。
For example； in the case of every right…angled triangle；
although it does not so manifestly appear that the square of
the base is equal to the squares of the two other sides as
that this base is opposite to the greatest angle； still； when
this has once been apprehended； we are just as certain of its
truth as of the truth of the other。 And as regards God； if my
mind were not pre…occupied with prejudices； and if