Descartes's Basic Epistemological Argument:

1. Knowledge is justified true belief (JTB; the "classical" or "traditional" view)

2. To be "justified" a belief must be shown to be necessarily true, or "certain." [The Enlightenment's buzzword for "necessarily true"]

3. "Certainty" means "beyond any logically possible doubt." [Descartes starts with a reaction of doubt regarding past teachings, not an Aristotelian reaction of wonder: What is this being before me? ]

4. So a method to find knowledge would be to try to doubt a belief; if it is logically possible to doubt, it is not certain. [Cartesian "methodological doubting"]

5. It is impossible to doubt each and every belief, so as a method, we will doubt the foundations on which such beliefs rest; if the foundation is dubitable, all the beliefs it supports are equally dubitable. [Basic presupposition of foundationalism: justification is no better than justification of the foundations on which belief rests.}

6. All attempts at justification of beliefs appeal either to the senses or to reason. [Presupposition already present in Plato and Aristotle, the old contrast of the sensory vs. that apprehended by nous]

7. In the state of dreaming I hold beliefs on the basis of what I see, hear, feel, or otherwise perceive while dreaming, but which on waking I recognize were not true beliefs, and the objects of which did not exist apart from my dream. [Presumably uncontroversial experience]

8. There is no certain way to distinguish the state of dreaming from being awake. [The Dream Hypothesis]

9. Therefore, on the hypothesis that I could be dreaming, it is logically possible to doubt any belief based on the foundation of sensory perception. [deduction from 7 and 8}

10. Beliefs based on reasoning would not be affected by the skepticism induced by this dream hypothesis, because they do not rest on a sensory foundation. [see 6]

11. If my reasoning faculty to deduce valid conclusions were given to me by an evil being (or were under the control of such), then beliefs based on this rational foundation would not necessarily be true. [This is really the definition of 'evil' from an epistemological view: that which causes one to believe what is false. Note that scu an "evil deceiver" is by hypothesis capable of deceiving me in a way so "cunning" as to never be detectable; in short, it cannot be my fault that I did not 'catch' the deception.]

12. Therefore, on the hypothesis that I could have been created by (or am under the control of) such an "evil spirit" (malin genie) or "Evil Deceiver," beliefs based on both the reasoning faculty and the sensory faculties could be doubted. [The "Evil Demon" hypothesis]

13. Even if all beliefs based on senses or reasoning are doubtful, i.e. they are false, it is at least true that be they T or F, I, a thing which thinks, am now thinking them. [The premise of the Cogito Argument]

14. Therefore, it is logically impossible for the thinker to doubt his/her own existence as a thing which thinks (aka a "mind" or a "consciousness"). [the conclusion of the Cogito Argument]

15. Therefore, for each thinker, that of which that thinker is certain is his or her own existence as a thinking thing. [Note the important move here: each potential knower, starts from a basic foundation alleged to be known only to him or her. This is the "subjective" turn of the "modern" period in contrast to objective or "metaphysical" starting point of the Ancient philosophers.]

16. Everything this thinking thing (mind) thinks is generically called an "idea." The faculty of the thinking thing which presents ideas to consciousness is called the "faculty of understanding." [Definitions]

17. Insofar as the existence of the thinking thing is indubitable, so equally indubitable is the existence of the ideas -solely as ideas- which the thinking thing is thinking. [Unfortunately the conception of the "existence" of a thing as an idea in some mind or another came to be called by the misleading label "objective reality" because it was a way of saying the thing exists as an object of thought; this leads to the strange way of speaking that if I think of something, that which I think of has 'objective reality.']

18. Therefore, my ideas, as ideas, really do exist. [This is expressed by the label 'formal reality,' which means exist in the more or less 'normal' sense of exist on their own, or simply, "are real." Thus, for example the statement: "People really do have ideas of Santa Claus, but in reality there is no Santa Claus." Would be expressed by saying: "Santa Claus has objective reality (people can think about Santa Claus), but no formal reality (there is no real Santa Claus)." However, if this is true, you could also say "Ideas of Santa Claus have formal reality. " Where the point is that though there is no real Santa, the ideas of him are as real as any idea ever is.]

19. I have an idea of an Infinitely Perfect Being (henceforth IPB). [So by the above terminology: My idea of an IPB has formal reality (i.e., the idea is a real idea) while the IPB has at least objective reality (i.e., is an object of thought)]

20. Everything that is real has a cause for its being real. [universal principle of causality; known directly by the 'light of nature']

21. The more perfect a thing is, the more 'real' it is; therefore the more perfection in an object of an idea, the more perfection must be contained in that idea. [This is also presumably obvious by the 'light of nature.']

22. My idea of God (aka, an IPB) is an idea of something that is infinitely perfect, so that idea contains in it an infinite degree of perfection. [In Descartes's language: "My idea of God really exists because I can think of it, so it must have a cause, that cause must have formally at least as much perfection as is contained formally and objectively in its effect, the idea of God (which is 'objectively' (thought of) infinite perfection)]

23. The only possible cause of my idea of God is either a) another idea of God or b) God him/herself. [The only possible cause of that which contains objectively infinite perfection is that which also contains either a) objectively infinite perfection (another idea of God), or b) formally infinite perfection (i.e. really is infinitely perfect = God)] Deduction from 19, 20, 21, and 22

24. The option of 24a) would lead to an infinite regress of causes, which is impossible, b/c then the effect would never exist, but the effect (my idea of God) really does exist. [So the ultimate (or first) cause of my idea of IPB cannot be another idea of IPB.]

25. Therefore, the only possible ultimate cause of my idea of God is nothing ess than that which has formally infinite perfection, i.e. really is infinitely perfect, i.e. is God. [Deduction from 23 and 24]

26. Not only that, but the same argument applied to the existence of me, as a mind (a thinking thing) with this idea of an IPB leads by the same reasoning to the conclusion that the cause for my being can be nothing less than the IPB her/himself. [The point is that not only does Descartes's idea of God need a cause which ultimately has infinite perfection, so does Descartes as a thinking thing thinking this idea of God.]

27. I am therefore the 'product' of an infinitely perfect creator. [Deduced from all of above.]

28. Therefore, if I use my faculties correctly, they will not deceive me [Elsewise it would be (oops!) the fault of the IPB. This conclusion also shows that the hypothesis of the "Evil Deceiver" cannot possibly be true; so henceforward we may trust the dictates of reason.]

29. I discover that as a thinking thing, in addition to entertaining ideas (the faculty of understanding), I have a faculty of judgment, which leads me to make assertions on the ideas before my consciousness. [Note that ideas, considered as ideas either exist (we have them) or don't (we don't have them). Only at the level of judgment does the question of truth/falsity arise. We ask of a judgment we make on the basis of the ideas in our mind, is that judgment T or F? Equally, we can only ask if a judgment is justified or not; on Descartes's vocabulary it makes no sense to ask if an "idea" is "justified."]

30. I also discover as a thinking thing I possess a faculty of will which is free from the constraints of what is physically or technologically possible, i.e. I can will anything that is not logically impossible. [Free will, not only to be used here for D's epistemological purposes, but also for ethical purposes elsewhere. Note Descartes's defense: it is directly obvious to the willing subject that when he/she chooses to make a decision freely the he/she could also have made the other choice; there was no impossibility in another alternative becoming true]

31. Therefore I can freely choose to assert or deny or withhold judgment on any judgment I can make.

32. Of my ideas some are like "representations" of that of which they are the ideas. [This is a crucial move: this view is called the representational theory of perception: sense perceptions are like little mental pictures of that of which they are perceptions. ]

33. Such "representations" or "images" take as their object the appearance of the object to my senses.

34. Since sensory perception represents only the appearance of things to my senses (not the reality), judgments based on sense perception are based on ideas which are 'obscure' and 'confused.' [Note that 'obscure' and 'confused' (and their opposites: 'clear' and 'distinct.' are now technical terms in our epistemological vocabulary. Note also that this implies that the only role of 'observation' is to 'demonstrate' (in the sense of 'show an example of') truths which are justified not by observation but by reason.]

35. Judgments based not on ideas originating in sensory perceptions, but rather those ideas which are drawn from the mind itself (unfortunately rendered as "innate") are based on "clear" and "distinct" ideas. [This is obvious by the 'light of nature']

36. If judgments based on such clear and distinct innate ideas -also known as "concepts"- were to be false, then if would be the fault of the Creator which gave me these innate ideas, but inasmuch as that Creator is infinitely perfect that cannot be the case. [The IPB is the guarantor of the certainty of judgments based on clear and distinct innate concepts.]

37. Therefore, judgments based on clear and distinct innate ideas (concepts) are indubitable, therefore justified, therefore knowledge. [This is core rationalistic foundationalism, the base position against which the entire Enlightenment epistemological development is a series of attacks.]

38. The concepts of mathematics are just such clear and distinct innate concepts; the mechanistic world view (MWV) describes the world in a purely mathematical language. [In short, God is a mathematician. This was, of course, the goal all along.]

39. Therefore the mathematical description of nature provided by the MWV gives justified necessarily true beliefs about the physical universe (take that, Aristotle!). [Note that the certainty claimed here concerns only that which can be described by the mathematical methods of the MWV; Descartes wants also to keep alive the option for a different class of certainties expressed in different clear and distinct concepts concerning not the physical universe, but the thinking thing, the "mind" or in more religious language, the "soul." This leaves an epistemological opening to accept the new mathematical physics and also keep religious claims about the 'spirit.']