Beliefs from the senses or induction:
Thus, both of these — all the beliefs we derive from our senses — can be doubted.
Beliefs from reason:
i.e. math, philosophy, etc.
The distinction is that the former is inductive logic while the latter is deductive logic.
These can, however, also be doubted: what if a malicious entity is deceiving us, and changing our perceiption of logic?
Alone the act of thinking proves the existence of the meditators thinking mind.
Thus, the doubts and thoughts of Meditation 1 prove, in Meditation 2, that something must be having these doubts and thinking these thoughts; ergo, the meditator must exist and their mind is that something.
A thing that thinks, that which:
Descartes argues that these things, these thoughts, must be contained by the mind.
The mind understands: through that understanding (reason, logic, etc.), we can now more things for certain.
The senses can only capture aspects of the world that keep changing; only reason can make senses of what stays the same.
Everything that our senses tell us is pure, uninterpreted information—we need the mind to tell us what something is: the wax stays wax while it is unchanging, melting, and simply a puddle on the floor.
Reason is what allows us to comprehend what something is, what unit or property. That physical things are extended (occupies space, three dimensions-ish, etc.)
aaaand the thinking thing can know itself better than it knows the body.
The essence of matter and the second proof of God’s existence.
Defining God as infinitely perfect: if it were created/born, there would be a time before God, meaning it would not be perfect: therefore, God must have existed always and always exist.
In today’s terms:
Possesing the dimensions of length, breadth, depth, and time.
This is to say that matter is perfectly understandable through mathematics.
Originally he refered to time not as a dimension but rather as being able to assign duration to all components of matter.
Therefore
First: Descartes uses circular logic to argue that a perfect being exists, as a perfect being must exist to be perfect, and as he can conceive the being in its perfection it must also exist.
Second: Descartes does, however, assume that perfection, which he cannot fathom, includes God being good; this is obviously a fallacy.