Many of the arguments for the existence of the classical concept of God conclude, not with God per se, but with "pure actuality", or "pure existence." You can find these arguments all over this blog. Then it is argued that pure actuality must have the typical divine attributes. In this article I will lay out the most contentious attribute that pure actuality is argued to have, and arguably the biggest dividing line between theists and atheists: intelligence. Many atheists will cautiously accept the existence of pure actuality, but then deny that it is intelligent. So this seems to be the key feature that separates theism from atheism.
I. Immateriality of the Intellect
First we need to distinguish between internalism of the mind, and externalism of the mind. Philosophy of mind is a HUGE topic that cannot be done justice in an article of this size, so I invite the reader to check out this Oxford course, which shows why dualism and materialism fail, and ends with a suggestion of externalism as the solution. If you are impatient, just read this PDF on externalism vs internalism. This argument presupposes externalism as the correct account of the mind.
Now, when we think about something abstractly (such as elephants), we are thinking about their form. But when matter is conjoined with form, it literally becomes that object. So matter plus the form of elephant equals an actual elephant. But when we think about the form of elephants, our minds do not literally become the object we are thinking of, which is what would happen if our minds were material. Intellect, in other words, depends upon being free from matter (and for a different argument, see this article). The more immaterial an object is, the more intellectual activity it can have. Pure actuality is completely immaterial, and therefore is complete in knowledge.
II. First Movers are Intelligent
Pure actuality actualizes things the way a hand moves a stick that moves a rock. That is to say, in a concurrent chain. The intermediate members are sort of "instruments" of the first mover, as the stick is an instrument of the hand. We see intelligent beings using sticks to move rocks, but never rocks using sticks to move intelligent beings. So intelligence is a property of things that act as first movers, and as the very first mover of everything, pure actuality must be intelligent.
III. "Ignorance" is a Lack of Something
Ignorance is a lack of knowledge. Ignorance is not a positive reality of its own."Pure actuality" does not lack anything, and does not have any potentials. So if pure actuality is ignorant, that would translate to: the thing with no potentials has a potential. This is a logical contradiction. So it is logically impossible for pure actuality to be ignorant.
IV. Effect Must be in Cause
A cause can only give to an effect what it has to give. As pure actuality is the cause of intelligent beings such as ourselves, then pure actuality must have intelligence.
V. Intelligence as a Perfection
"Intelligence" is a perfection, as it means being able to take on the form of many different things rather than just one thing. E.g., a rock can only have the form of rock, but a human can in a sense take on the form of elephant by thinking about elephants, then the form of quarks by thinking about quarks, and so on. As pure actuality does not lack anything, it is perfect, and as perfection includes intelligence, pure actuality must be intelligent.
VI. The Setting of Goals and Ends Implies Intelligence
Consider matter bopping around, clumping into other matter, moving this way and that, at the whims of the laws of physics. Something cannot move towards an end unless it is either A) intelligent, as when a human moves his body with purpose to build a building, or B) directed by intelligence, as when (unintelligent) concrete and steel is directed with the goal of becoming a building. But unintelligent matter does have goals in the form of dispositions. See here for a full explanation of dispositions.
Being the cause of the existence of everything else, the first mover sets goals and ends for everything that exists, and is therefore intelligent.
VII. Plato's Cosmological Argument
We can look to Plato's original argument for an unmoved mover as to why self-movers must be intelligent. Matter is a passive recipient of motion, so if it is to move, something else must bump it, push it, or attract it. Matter is not a self-mover. Only intelligent beings, such as humans, are capable of self motion.
VIII. Location of Abstract Objects
Since pure actuality is the source or foundation of all reality, it is also the source or foundation for abstract objects, such as mathematical truths, sets, categories, and universals. But abstract objects are not "made" of anything; they can only exist in a mind. Therefore, pure actuality must be intelligent.