Proving God from the idea alone
On the axis: Existence of God · God
Can one conclude, from the mere idea of a perfect being, that it necessarily exists, or is existence never deduced from a concept?
Justification
The cogito at first secures only my own existence: so long as an evil genius could deceive me even in my self-evident truths, doubt is not defeated. Proving God therefore becomes the keystone of the system. Descartes offers two proofs: the idea of infinity within me, which cannot arise from a finite being, demands an infinite cause (Meditation III); and existence belongs to the essence of the perfect being as the equality of its angles belongs to the triangle, the ontological proof (Meditation V). Now a perfect God cannot be a deceiver, deception betraying a defect: his veracity therefore guarantees that what I conceive clearly and distinctly is true. Far from inherited theism, the position is the keystone that lifts doubt and grounds the whole of science.
Meditations on First Philosophy, III and V · Discourse on Method, IV
Justification
Since all knowledge is bounded to phenomena, God, who is not one, escapes proof: Kant dismantles the proofs of God's existence one by one (ontological, cosmological, physico-theological), the first failing in its leap from concept to existence. Yet what is barred to knowledge is required by morality: without God and immortality, the accord of virtue and happiness (the highest good) would stay unthinkable. God thus returns as a postulate of practical reason, an object of rational faith and not of knowledge, which warrants a moderate rather than an assertive theism.
Critique of Pure Reason, "Transcendental Ideal" · Critique of Practical Reason, Dialectic