Incomplete.

Pierre Gassendi objects to Descartes's cogito:
you conclude that the proposition I am or I exist is true whenever it comes before you, i.e. is conceived by your mind. But I can't see that you needed all this apparatus, when you were already rightly certain, on other grounds, that you existed. You could have made the same inference from any one of your other actions, since it is known by the natural light that whatever acts exists.
Descartes responds:
You say that I could have made the same inference from any one of my other actions, but that is far from the truth, because my thought is the only one of my actions of which I am completely certain-- I'm talking here about metaphysical certainty, because that's what this is all about. For example, I can't say 'I am walking, therefore I exist', except by adding to my walking my awareness of walking, which is a thought. The inference is certain-- meaning that it makes the conclusion certain-- only if its premise concerns this awareness, and not the movement of my body; because it can happen, e.g. in dreams, that I seem to myself to be walking but am really not doing so. And so from the fact that I think I am walking I can very well infer the existence of a mind that thinks but not the existence of a body that walks. And the same holds for all the other cases.
Discuss this disagreement, identify the central issue, and give your own reasons for resolving it in favor of Gassendi or Descartes.
I am walking. I look around me and see a tree, a streetlamp, and a dog. I hear the dog barking. I feel the wind on my skin. I must exist. One would be foolish to argue my lack of existence. In particular, Pierre Gassendi would argue that I exist.

I wake up. What had appeared to be a concrete world was only a manifestation of my mind. The seemingly obvious conclusion that I existed because I was walking, that I was seeing, that I was hearing and feeling was founded on a betrayal of my perception. In this way, Descartes defends his cogito against Gassendi’s attack that “I think, therefore I am” is too narrow. Gassendi asserts that any action, not just thinking, implies existence. Essentially he iterates that one could say that “I walk, therefore I exist” or perhaps “I see, therefore I exist” or even “I feel therefore I exist.” The discrepancy between their statements is an issue of what exactly implies existence. Can an action alone prove existence?

As seen in the aforementioned example, it cannot. The actions themselves are not substantial, because they have proved unreliable indicators of existence previously (e.g. dreams). If I am fooled to think that I exist in a dream because I was walking or hearing or feeling, then I am a fool to not doubt that whenever I walk or whenever I hear, then perhaps I am not existing. Instead I could possibly think that I am walking or think that I am hearing, but never be absolutely certain. The inability to assign these actions universally to confirm existence makes Gassendi’s statement only a contingent truth. “I walk, therefore I exist” only works under normal conditions. The flaw in Gassendi’s argument is that walking and hearing and any action for that matter are merely what the mind perceives. What can I be certain of then? I can only be completely certain that I think I walk and that I think I hear. Clearly the basis of both of these statements is that “I think”. All other actions can be systematically broken down, but eventually all things lead back to thought.

Another approach to establishing “thinking” as the only plausible method for proving existence is by breaking down the world around oneself. This justification would be externalist while the previously discussed argument relies on internalist justification. Instead of breaking down the thoughts themselves, an externalist must break down the existence of the world itself. Descartes suggests an exercise of convincing himself that there is “absolutely nothing in the world, no sky, no earth, no minds, no bodies,” that there is “a deceiver of supreme power and cunning who is deliberately and constantly deceiving me.” The existence of the world around him could be thought away, but inevitably he could not think his own thoughts away. Again all actions and perceptions lead back to thought.

This is not close to being finished, but I'm all out of juice.

What choo tink? (Oh. No.)