1. ¶1 – Intro
“I have seen what to do and what to avoid in order to reach the truth”
Namely, separate what’s clear from what’s obscure, trust my clear and distinct perceptions, and withhold judgment on everything else.
“[T]he most pressing task... try to escape from the doubts [of] a few days ago”
“[S]ee whether any certainty can be achieved regarding material objects”

2. ¶2, 3, 4 – Distinct ideas of material objects
Start with my ideas of material objects.
Separate the distinct ideas from the confused ideas.
Distinct ideas: quantity (i.e., the extension of quantity, or just extension), parts, sizes, shapes, positions, local motions, durations.
[We’ll see that, for Descartes, the essence of matter is extension. Here extension is the principal attribute, and all the others are just modes]
These things are clear when regarded generally, and I clearly perceive particular features when I pay attention.
Seems not so much like learning, but like memory, or noticing what was always there.
[He is probably suggesting that these ideas are innate]

3. ¶5 – Ideas of essences I have lots of ideas of things that:
are real in some sense, even if they don’t exist in the world (they “cannot be called nothing”)
are not invented by me
“have their own true and immutable natures”
Example: idea of a triangle
perhaps there aren’t any triangles in the world
still, “there is... a determinate nature, or essence, or form of the triangle which is immutable and eternal”
after all, “various properties can be demonstrated of the triangle”
these properties are not invented by me
I “clearly recognize” them, “whether I want to or not”

4. ¶6 – Ideas of essences These ideas aren’t adventitious.
Perhaps I’ve encountered some triangular things in the world
But “I can think up countless other shapes... [which I’ve never] encountered through the senses”
[This is against Aristotle, who thinks that ideas of essences comes from experience of things, and abstracting features off of them]
The properties are ‘true’.
“I am clearly aware of them” so they’re something (i.e., not nothing).
And “everything of which I’m clearly aware of is true”
In any case, the way my mind is set up, I can’t help but assent to them.
[remember the 4th Meditation]
Even back when I trusted the senses, I thought that the “most certain truths of all” were those relating to “pure and abstract mathematics”

5. Note on essences
If they’re not invented, and they’re not adventitious, then they must be innate.
The internal structure of these essences is necessary and fixed—you can’t change it, add to it, subtract from it, or think of them any other way.
Even if nothing exists in the real world that ‘fits’ or instantiates these essences, the essences still set requirements on what they would be like if they did exist.

6. ¶7 – Descartes’ ontological argument
If I have an idea of x, then anything I clearly and distinctly perceive as belonging to x really does belong to x.
[Example: I have an idea of a triangle. And so, since I clearly and distinctly perceive the property HAVING ANGLES THAT ADD UP TO 180 DEGREES as belonging to it, it follows that this property really does belong to it.]
I have an idea of God. So anything I clearly and distinctly perceive as belonging to God really does belong to God.
I clearly and distinctly perceive the property ALWAYS EXISTING as belonging to God.
Therefore, the property ALWAYS EXISTING really does belong to God. [That is, God really does exist]
(So the truth of God’s existence is at least as certain as mathematical truths.)

7. ¶8 – Does existence belong to God?
For most things, existence and essence are separate.
I don’t clearly and distinctly perceive existence as belonging to triangles, or other shapes or numbers.
That is, existence can be separated from the essence of a triangle.
But, if I carefully focus on my idea of God, I see that existence is connected with God’s essence.
The property of having angles that add up to 180 degrees cannot be separated from the essence of a triangle.
The idea of a mountain [upward slope] cannot be separated from the idea of a valley [downward slope]
Likewise, the property of existing cannot be separated from the essence of God.
It is a contradiction to think of God lacking existence.
Just as it is a contradiction to think of a mountain without a valley [or a triangle that doesn’t have angles adding up to 180 degrees]

8. Why exactly does Descartes think existence belongs to God?
Here’s a clue: “it is... a contradiction to think of God (that is, a supremely perfect being) lacking existence (that is, lacking a perfection)”
Check out those parenthetical remarks!
Descartes must think that existence is a perfection, and that it is a contradiction to think of God, a supremely perfect being, lacking a perfection.
Then the argument is something like this:
(I c/d perceive that) existence is a perfection.
(I c/d perceive that) all perfections belong to God.
So (I c/d perceive that) existence belongs to God.
If I c/d perceive that something belongs to x, then it really does belong to x.
So existence belongs to God.

9. ¶9 – Objection: can thought impose necessity?
I can’t think of a mountain without a valley; but just because I think of a mountain with a valley, that doesn’t mean there really is a mountain in the world.
Likewise, the objection goes, I can’t think of God except as existing; but just because I think of God as existing, that doesn’t mean God really exists.
“[M]y thought does not impose any necessity on things”
“[J]ust as I can imagine a winged horse even though no horse has wings, so I may be able to attach existence to God even though no God exists.”

10. ¶10 – Reply: necessity not imposed by thought
Since I cannot think of a mountain without a valley, it follows that a mountain and a valley are “mutually inseparable”
Though it doesn’t follow that mountains or valleys actually exist anywhere.
Likewise, since I cannot think of God except as existing, it follows that “existence is inseparable from God, and hence that he really exists”
This necessary connection between existence and God is not imposed by my thought.
The necessity is contained within the very essence of God.
I’m not imposing necessity, I’m the one with my hands tied: I can’t think of God any other way (unlike with horses, where I can imaginatively attach or detach wings).

11. ¶11 – Objection: unnecessary supposition
Objection: Sure, if you think of God as having all perfections, then it would follow that God exists. But the conclusion comes only because you made that supposition (i.e., that ‘if’). And there’s no need to make that supposition.
Analogy: If you [falsely] think that all quadrilaterals can be inscribed in a circle, then it would follow that a rhombus can be inscribed in a circle (which is obviously false). But there’s no need to make that [false] supposition.
Reply: This is the only way one can think of God—there’s no way to think of God except as having all perfections. This isn’t some false supposition, it’s a “true ide[a] innate in me”.

12. ¶11 – Fictitious/invented ideas vs
¶11 – Fictitious/invented ideas vs. ideas of a true and immutable nature
The idea of God is not dependent on my thought [my will]; it’s not an invented idea.
It is the only idea I have where existence belongs to something’s essence.
This gets me to uniqueness and everlastingness.
It also gets me to “many other attributes of God, none of which I can remove or alter”
[Which just goes to show that this idea is not an invented idea]

13. ¶12 – Clear and distinct ideas
Some things clearly and distinctly perceived are “obvious to everyone”
But others require more work—they “are discovered only by those who look more closely and investigate more carefully”
But both are equally certain.
Example: Regarding right triangles, the fact that the hypotenuse is opposite the largest angle is much more obvious than the fact that the hypotenuse squared equals the sum of the other two sides squared. But both are equally certain.
If I weren’t “overwhelmed by preconceived opinions” and “the images of things perceived by the senses”, I’d see why God exists “sooner and more easily than anything else”

14. ¶13, 14 – Certainty depends on knowledge of God’s existence
“The certainty of all other things depends on this [God’s existence], so that without it nothing can ever be perfectly known”
While perceiving something clearly and distinctly, I cannot help but believe it to be true.
But I can’t always focus on it, and later I can think of it ‘distantly’, without focusing on the reasons why it is true.
So reasons for doubt can occur to me, and it won’t be certain anymore—I’ll be stuck with “shifting and changeable opinions”.
Awareness of God keeps this from happening.

15. ¶14 - Example
When I focus on the nature of a triangle, I clearly and distinctly perceive that its angles add up to 180 degrees, and so I can’t help but believe it to be true.
But when I stop focusing on it, even though I remember having clearly and distinctly perceived it, still reasons for doubt can occur to me.
I can think “I have a natural disposition to go wrong” even when I think I have clear and distinct perception.
I can remember all the other times I’ve gone wrong even though I thought I had clear and distinct perception.
Without God, certainty is unattainable.

16. ¶15 – How God rescues us
Now I clearly and distinctly perceive that God exists, that everything depends on him, and that whatever I clearly and distinctly perceive must be true.
So now memory is enough:
Now I don’t have to clearly and distinctly perceive all this to be certain of it.
I can just remember that I did clearly and distinctly perceive it, and conclude that it must be true.
So with geometry, what reasons for doubt are there?
I might be ‘made for error’? But I know when I can trust myself.
That I’ve screwed up before? But I never clearly and distinctly perceived those things; I didn’t even know the general rule.
That I might be dreaming? But still anything “evident to the intellect” is “wholly true”

17. ¶16 - Conclusion
So “certainty and truth of all knowledge depends uniquely on my awareness of the true God”
Before that, I was incapable of perfect knowledge.
So now I can move on to gain further “full and certain” knowledge.