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My attempts so far:

  • Descartes, being a rationalist, used "cogito, ergo sum" to lead to the concept of innate ideas.

  • Hume, being a radical empiricist, believed in experience based epistemology.

  • Kant reconciled both by the Copernican Revolution by propounding a theory of levels of formation of knowledge.

But I think that I'm connecting the implication of "cogito, ergo sum" very remotely and mainly explaining rationalism vs empiricism and their reconciliation.

Any direct implications?

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    At that level of "slogan" you are right: Descartes was a rationalist and Hume was an empiricist. Kant’s work: The Critique of Pure Reason addresses the question “What can we know?” "Kant responded to his predecessors by arguing against the Empiricists that the mind is not a blank slate that is written upon by the empirical world, and by rejecting the Rationalists’ notion that pure, a priori knowledge of a mind-independent world was possible." So, at a very simplified level, we can say that Kant's project is aimed at "reconcile both"...
    – Mauro ALLEGRANZA
    Commented Jul 13, 2018 at 12:56
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    ... or maybe at solving the open issues with both doctrines.
    – Mauro ALLEGRANZA
    Commented Jul 13, 2018 at 12:57
  • Hume assumed the existence of non-empirical knowledge, I'm not sure that's radical empiricism.
    – rus9384
    Commented Jul 13, 2018 at 12:58
  • @rus9384, I thought of avoiding "radical" word, considering the arguments against "Hume's skepticism", now your comment made the decision easy.
    – Deepak Chaudhary
    Commented Jul 13, 2018 at 13:03
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    This question strikes me as over-loaded. Descartes, Hume & Kant can't be adequately dealt with in an answer of reasonable length.
    – Geoffrey Thomas ♦
    Commented Nov 2, 2018 at 9:01

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Hume was very clear in claiming that the existence of any real being could be asserted only through cause-and-effect reasoning, what we would call induction.

He was equally clear in claiming that cause-and-effect reasoning is in no way a priori: it must proceed from propositions grounded in experience.

So, the Cogito: "Je pense, donc je sui." (Cogito, ergo sum), which asserts that the real existence of "I" is implied by the truth of the proposition "I think" or "I am thinking," cannot be known to be true a priori. It cannot, therefore be the basic proposition of a series of deductions reaching to every corner of human knowledge, as Descartes hoped.

So, how does the Cogito effect Hume? He dismisses it as sophistry and illusion.

The effects on Kant will be another day's work.

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