Key Arguments

• He compares degrees of obviousness among clear and distinct truths using the right‑angled triangle: some properties, like the base being opposite the greatest angle, are ‘more manifest at first’ than the Pythagorean relation, but once the latter is understood, we are ‘as firmly persuaded of the truth of the former as of the latter.’
• He then says that, freed from prejudice and the imagination’s images, he ‘should know nothing sooner or more easily then the fact of his being’ and asks rhetorically: ‘For is there any truth more clear than the existence of a Supreme Being, or of God, seeing it is to his essence alone that [necessary and eternal] existence pertains?’
• He now feels not only as assured of this truth as of any other, but ‘remark[s] further that the certitude of all other truths is so absolutely dependent on it that without this knowledge it is impossible ever to know anything perfectly.’
• Because he cannot keep his mind fixed on proofs and often remembers judgments without their grounds, he may later meet reasons that might cause him to change his opinion ‘if I did not know that God existed,’ so without God he would have only ‘vague and vacillating opinions.’
• He illustrates with the triangle: while attending to the geometrical demonstration that its three angles equal two right angles, he ‘find[s] it impossible to believe otherwise’; but when he stops attending, he could come to doubt the demonstrated truth ‘if I do not know that there is a God,’ by imagining that his nature might sometimes deceive him even in what seems most evident.
• After discovering that God exists, that all things depend on him, and that he is no deceiver, he infers that ‘all which I clearly and distinctly perceive is of necessity true’; thus, ‘although I no longer attend to the grounds of a judgment, no opposite reason can be alleged sufficient to lead me to doubt of its truth, provided only I remember that I once possessed a clear and distinct comprehension of it.’
• He concludes that this same security extends ‘to whatever I remember to have formerly demonstrated, as the truths of geometry and the like,’ since objections about his deceptive nature are answered by the known existence and veracity of God: ‘I already know that I cannot be deceived in judgments of the grounds of which I possess a clear knowledge.’

Source Quotes

And although, of the objects I conceive in this manner, some, indeed, are obvious to every one, while others are only discovered after close and careful investigation; nevertheless after they are once discovered, the latter are not esteemed less certain than the former. Thus, for example, to take the case of a right-angled triangle, although it is not so manifest at first that the square of the base is equal to the squares of the other two sides, as that the base is opposite to the greatest angle; nevertheless, after it is once apprehended, we are as firmly persuaded of the truth of the former as of the latter. And, with respect to God if I were not pre-occupied by prejudices, and my thought beset on all sides by the continual presence of the images of sensible objects, I should know nothing sooner or more easily then the fact of his being.

Thus, for example, to take the case of a right-angled triangle, although it is not so manifest at first that the square of the base is equal to the squares of the other two sides, as that the base is opposite to the greatest angle; nevertheless, after it is once apprehended, we are as firmly persuaded of the truth of the former as of the latter. And, with respect to God if I were not pre-occupied by prejudices, and my thought beset on all sides by the continual presence of the images of sensible objects, I should know nothing sooner or more easily then the fact of his being. For is there any truth more clear than the existence of a Supreme Being, or of God, seeing it is to his essence alone that [necessary and eternal] existence pertains?

And, with respect to God if I were not pre-occupied by prejudices, and my thought beset on all sides by the continual presence of the images of sensible objects, I should know nothing sooner or more easily then the fact of his being. For is there any truth more clear than the existence of a Supreme Being, or of God, seeing it is to his essence alone that [necessary and eternal] existence pertains? And although the right conception of this truth has cost me much close thinking, nevertheless at present I feel not only as assured of it as of what I deem most certain, but I remark further that the certitude of all other truths is so absolutely dependent on it that without this knowledge it is impossible ever to know anything perfectly.

For is there any truth more clear than the existence of a Supreme Being, or of God, seeing it is to his essence alone that [necessary and eternal] existence pertains? And although the right conception of this truth has cost me much close thinking, nevertheless at present I feel not only as assured of it as of what I deem most certain, but I remark further that the certitude of all other truths is so absolutely dependent on it that without this knowledge it is impossible ever to know anything perfectly. For although I am of such a nature as to be unable, while I possess a very clear and distinct apprehension of a matter, to resist the conviction of its truth, yet because my constitution is also such as to incapacitate me from keeping my mind continually fixed on the same object, and as I frequently recollect a past judgment without at the same time being able to recall the grounds of it, it may happen meanwhile that other reasons are presented to me which would readily cause me to change my opinion, if I did not know that God existed; and thus I should possess no true and certain knowledge, but merely vague and vacillating opinions.

Thus, for example, when I consider the nature of the [rectilinear] triangle, it most clearly appears to me, who have been instructed in the principles of geometry, that its three angles are equal to two right angles, and I find it impossible to believe otherwise, while I apply my mind to the demonstration; but as soon as I cease from attending to the process of proof, although I still remember that I had a clear comprehension of it, yet I may readily come to doubt of the truth demonstrated, if I do not know that there is a God: for I may persuade myself that I have been so constituted by nature as to be sometimes deceived, even in matters which I think I apprehend with the greatest evidence and certitude, especially when I recollect that I frequently considered many things to be true and certain which other reasons afterward constrained me to reckon as wholly false. But after I have discovered that God exists, seeing I also at the same time observed that all things depend on him, and that he is no deceiver, and thence inferred that all which I clearly and distinctly perceive is of necessity true: although I no longer attend to the grounds of a judgment, no opposite reason can be alleged sufficient to lead me to doubt of its truth, provided only I remember that I once possessed a clear and distinct comprehension of it. My knowledge of it thus becomes true and certain.

But after I have discovered that God exists, seeing I also at the same time observed that all things depend on him, and that he is no deceiver, and thence inferred that all which I clearly and distinctly perceive is of necessity true: although I no longer attend to the grounds of a judgment, no opposite reason can be alleged sufficient to lead me to doubt of its truth, provided only I remember that I once possessed a clear and distinct comprehension of it. My knowledge of it thus becomes true and certain. And this same knowledge extends likewise to whatever I remember to have formerly demonstrated, as the truths of geometry and the like: for what can be alleged against them to lead me to doubt of them? Will it be that my nature is such that I may be frequently deceived?

Key Concepts

• thus, for example, to take the case of a right-angled triangle, although it is not so manifest at first that the square of the base is equal to the squares of the other two sides, as that the base is opposite to the greatest angle; nevertheless, after it is once apprehended, we are as firmly persuaded of the truth of the former as of the latter.
• And, with respect to God if I were not pre-occupied by prejudices, and my thought beset on all sides by the continual presence of the images of sensible objects, I should know nothing sooner or more easily then the fact of his being.
• For is there any truth more clear than the existence of a Supreme Being, or of God, seeing it is to his essence alone that [necessary and eternal] existence pertains?
• I remark further that the certitude of all other truths is so absolutely dependent on it that without this knowledge it is impossible ever to know anything perfectly.
• although I no longer attend to the grounds of a judgment, no opposite reason can be alleged sufficient to lead me to doubt of its truth, provided only I remember that I once possessed a clear and distinct comprehension of it.
• My knowledge of it thus becomes true and certain. And this same knowledge extends likewise to whatever I remember to have formerly demonstrated, as the truths of geometry and the like

Context

Closing section of Meditation V, where Descartes connects the ontological proof back to his general epistemology, arguing that the non‑deceptive, necessarily existent God provides the ultimate foundation for the certainty of mathematics and all other clear and distinct knowledge, especially across time via memory.