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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 my thought
did not find itself on all hands diverted by the continual
pressure of sensible things； there would be nothing which I
could know more immediately and more easily than Him。 For is
there anything more manifest than that there is a God； that is
to say； a Supreme Being； to whose essence alone existence
pertains？21
And although for a firm grasp of this truth I have need
of a strenuous application of mind； at present I not only feel
myself to be as assured of it as of all that I hold as most
certain； but I also remark that the certainty of all other
things depends on it so absolutely； that without this
knowledge it is impossible ever to know anything perfectly。
For although I am of such a nature that as long as22 I
understand anything very clearly and distinctly； I am
naturally impelled to believe it to be true； yet because I am
also of such a nature that I cannot have my mind constantly
fixed on the same object in order to perceive it clearly； and
as I often recollect having formed a past judgment without at
the same time properly recollecting the reasons that led me to
make it； it may happen meanwhile that other reasons present
themselves to me； which would easily cause me to change my
opinion； if I were ignorant of the facts of the existence of
God； and thus I should have no true and certain knowledge； but
only vague and vacillating opinions。 Thus； for example； when
I consider the nature of a ＇rectilinear＇ triangle； I who have
some little knowledge of the principles of geometry recognise
quite clearly that the three angles are equal to two right
angles； and it is not possible for me not to believe this so
long as I apply my mind to its demonstration； but so soon as I
abstain from attending to the proof； although I still
recollect having clearly prehended it； it may easily occur
that I e to doubt its truth； if I am ignorant of there
being a God。 For I can persuade myself of having been so
constituted by nature that I can easily deceive myself even in
those matters which I believe myself to apprehend with the
greatest evidence and certainty； especially when I recollect
that I have frequently judged matters to be true and certain
which other reasons have afterwards impelled me to judge to be
altogether false。
But after I have recognised that there is a God￥because
at the same time I have also recognised that all things depend
upon Him； and that He is not a deceiver； and from that have
inferred that what I perceive clearly and distinctly cannot
fail to be true￥although I no longer pay attention to the
reasons for which I have judged this to be true； provided that
I recollect having clearly and distinctly perceived it no
contrary reason can be brought forward which could ever cause
me to doubt of its truth； and thus I have a true and certain
knowledge of it。 And this same knowledge extends likewise to
all other things which I recollect having formerly
demonstrated； such as the truths of geometry and the like； for
what can be alleged against them to cause me to place them in
doubt？ Will it be said that my nature is such as to cause me
to be frequently deceived？ But I already know that I cannot
be deceived in the judgment whose grounds I know clearly。
Will it be said that I formerly held many things to be true
and certain which I have afterwards recognised to be false？
But I had not had any clear and distinct knowledge of these
things； and not as yet knowing the rule whereby I assure
myself of the truth； I had been impelled to give my assent
from reasons which I have since recognised to be less strong
than I had at the time imagined them to be。 What further
objection can then be raised？ That possibly I am dreaming （an
objection I myself made a little while ago）； or that all the
thoughts which I now have are no more true than the phantasies
of my dreams？ But even though I slept the case would be the
same； for all that is clearly present to my mind is absolutely
true。
And so I very clearly recognise that the certainty and