• Descartes' Mathematical Model
• Modeled his approach on Geometry {1}
• Begin with axioms and definitions which are grasped with certainty by intellectual intuition. {2} {3} {4}
• Proceed to deduce consequences (theorems) by infallible methods of inference. {5}
• Contrast Hobbes
• Descartes: mathematical knowledge gives insight into an objective and rational reality by deducing consequences from truths about that reality that intellectual intuition "perceives": (Platonic realism)
• Hobbes: mathematical knowledge gives no insight into an objective reality because it just deduces consequences definitions we assign to arbitrarily chosen names: nominalism.

1. Method . . . contains everything which gives certainty to the rules of Arithmetic. (160)
2. We shall here take note of all those mental operations by which we are able, wholly without fear of illusion, to arrive at the knowledge of things.  Now I admit only two, viz. intuition and deduction. (159)
3. By intuition I understand . . . the conception which an unclouded and attentive mind gives us so readily and distinctly that we are wholly freed from doubt about that which we understand. (159)
4. Intuition . . . springs from the light of reason alone. (159)
5. By a method I mean certain and simple rules such that, if a man observe them accurately, he shall never assume what is false is true. (159)

Of the 
Human 
Mind 
and
That it 
is more 
easily
known 
than the
body.

• Methodological Doubt
• Objective: to arrive at certain truths to supply a foundation for the sciences {1}
• doubt all that is in the least dubitable {2} beginning with certain very basic beliefs on which many others are based {3}
• the evidence of the senses: basis of our belief in the external world
• Argument from hallucinations & illusions
• senses sometimes deceive
• therefore, their deliverances are generally suspect
• Dream argument: no experiential evidence possible that all is not a dream {4}
• conclusion: it's not certain that there is an external world like what the senses seem to us to reveal
• intuition basis of our knowledge of a priori -- non-observation-based -- e.g., truths of mathematics
• Evil Demon Argument {5}: a mighty evil genius is using all his powers to deceive me. 
• So, perhaps even mathematical beliefs & beliefs concerning conceptual "truths"  are mistaken. 
• Cogito Argument & Thought Experiment
• assume nonexistence of body: what the senses reveal is false
• does not follow that I don't exist
• Conclusion: "I am, I exist" {7} is the Archimedian Point {6}
• If I could think falsely "I exist": then I'd exist
• if a demon is deceiving me
• then I am deceived (hence existing)
• Further conclusion concerning self's nature & knowability
• bodily characteristics not essential to me: assumed nonexistence of my body doesn't entail my nonexistence 
• self "identifiable with the power (or exercise) of reason: "to speak accurately I am not more than a thing which thinks." {8} {9}
• Expansion of Archimedian Point: "I am" too slim a foundation
• Existence of thoughts as well as thinkers indubitable {10}
• Self portrayed as a field of "inward" subjective conscious experiences. {11}
• denatured "sensations" also indubitable mental contents {12}
• Concerning the nature of bodies & our knowledge of them
• all the sensible qualities are inessential (e.g., the wax)
• reason alone reveals the true nature of matter as extended substance. {13}
• Knowledge of bodies less certain than of my own mind {14}

1. I must once, for all, seriously undertake to rid myself of all the opinions which I had previously accepted and commence to build anew from the foundation, if I wanted to establish anything firm and lasting in the sciences. (Med. 1)
2. [Since] reason already persuades me that I ought no less carefully withhold my assent from matters which are not entirely certain and indubitable than from those which appear to me manifestly to be false, if I am able to find in each one some reason to doubt, this will suffice to justify my rejecting the whole. (Med. 1)
3. [O]wing to the fact that the destruction of the foundations of necessity brings with it the downfall of the rest of the edifice, I shall only in the first place attack those principles upon which all my former opinions rested. (Meditation I)
4. I see so manifestly that there are no certain indications by which we may clearly distinguish wakefulness from sleep. (163)
5. I shall then suppose . . . some evil genius not less powerful than deceitful, has employed his whole energies in deceiving me; I shall consider that . . . all . . . external things are but illusions and dreams of which this genius has availed himself to lay traps for my credulity. (163)
6. Archimedes, in order that he might draw the terrestrial globe out of its place . . . demanded only that one point should be fixed and immovable, in the same way I shall have . . . high hopes if I . . . discover one thing only which is certain and indubitable. (Med. 2)
7. "I am, I exist" is necessarily true each time that I pronounce it, or that I mentally conceive it. (164)
8. [Thought] alone cannot be separated from me. (Med. 1)
9. To speak accurately I am not more than a thing which thinks, that is to say a mind or a soul, or an understanding, or a reason. (Med. 1)
10. What is a thing which thinks? It is a thing which doubts, understands, [conceives], affirms, denies, wills, refuses, which also imagines and feels. (Med. 2)
11. It is so evident that it is I who doubt, who understand, and who desire, that there is no reason here to add anything to explain it. (Med. 2) 
12. [I]t is at least quite certain that it seems to me that I see light, that I hear noise and that I feel heat. That cannot be false; properly speaking it is what is in me called feeling; and use in this precise sense that is no other than thinking. (Med. 2)
13. We must then grant that I could not even understand through the imagination what this piece of wax is, and that it is my mind alone that perceives it. (Med. 2)
14. I see clearly that there is nothing that is easier for me to know than my own mind. (Med. 2)

• Preliminaries
• All he knows so far: a thinker -- this "I" -- and its thoughts: exist
• How he knows: clarity and distinction of his "'perception" of it: by intellectual intuition or "the natural light" {1}
• things whose denials would be self-contradictory are true {2} 
• Residual doubt if God is a deceiver?
• Classification of Thoughts
• motives (volitions) & emotions (affections)
• ideas: innate, adventitious, invented {3}
• judgments: true or false combinations of ideas
• considered as representative ideas vary in objective reality content : modes or accidents < substances < God {4}
• Maker's Mark Argument
• There must be as much reality in the cause as the effect {5}
• An idea with X amount of objective reality must have a cause that has at least X amount of formal reality. {6}
• I find in myself an idea of God that is possessed of infinite objective reality {7}
• Only God could cause such an idea.
• So, God exists. {8}
• Honest God Argument
• Deception necessarily proceeds from some defect {9}
• God has no defects.
• So, God is no deceiver 
• Ontological Proof Preliminary: Platonic Realism
• Two varieties of mind independent things 
• particulars: objects: modes of matter occupying space (minds?)
• universals: properties, or "natures, forms, or essences" {10} 
• Ontological Proof 
• The idea I have of God is "the idea of a supremely perfect Being" {11} 
• Existence is a good thing or "perfection"
• Therefore: God exists. {12}{13}
• Criticisms of the Proof(s)
• Hobbes: we have no such idea (can form no image) of an infinite being
• Others: idea of an infinite being is invented (not innate)
• Jones: draws on dubious assumptions

1. I can establish as a general rule that all things which I perceive very clearly and distinctly are true. (Med. 3)
2. Let who will deceive me, He can never cause . . . any . . . thing in which I see a manifest contradiction. (Med. 3)
3. Among . . . ideas, some appear . . . to be innate, some adventitious, and others to be formed [or invented] by myself. (Med. 3)
4. When we consider [ideas] as images, one representing one thing and the other another, it is clear that [some] . . . contain so to speak more objective reality within them [that is to say, by representation participate in a higher degree of perfection] than [others].  (Med. 3)
5. Now it is manifest by the natural light that there must be as much reality in the efficient and total cause as in the effect. (Med. 3)
6. But in order that an idea should contain some one certain objective reality . . . it must without doubt derive it from some cause in which there is at least as much formal reality as this idea contains of objective reality. (Med. 3)
7. By the name God I understand a substance that is infinite, independent, all-knowing, all-powerful, .and by which I myself and everything else, if anything else does exist, has been created. (Med. 3)
8. God, in creating me, placed this idea within me to be like the mark of the workman imprinted on his work. (Med. 3)
9. [T]he light of nature teaches us that fraud and deception necessarily proceed from some defect. (Med. 3)
10. When I imagine a triangle, although there may nowhere in the world be such a figure outside my thought, or ever have been, there is nevertheless in this figure, a certain determinate nature, form, or essence, which is immutable and eternal, which I have not invented, and which in no wise depends on my mind. (Med. 5)
11. I not less find the idea of God, that is . . . the idea of a supremely perfect Being, in me, than that of any figure or number. (Med. 5)
12. I clearly see that existence can no more be separated from the essence of God than can its having its three angles equal to two right angles can be separated from the essence of a triangle, or the idea of a mountain from the idea of a valley. (Med. 5)
13. [N]ot that my thought can bring this to pass, or impose any necessity on things, but, on the contrary . . . the necessity which lies in the thing itself . . . determines me to think this way. (Med. 5) 

• Imagination <> Intellect: Chiliagon v. Myriagon thought experiment {1}
• can distinguish conceptually
• what we can't distinguish imaginatively
• Power of Imagination is inessential to self/thinker {2}
• Hypothesis
• imaginative power depends on something besides thought
• probably it depends on the presence of "corporeal images" {3}
• Proof of the Existence of the External World
• Must be an agent power of producing the perceptual images
• can't be in me (qua thinker) without be my knowing it
• so it must be in another: either spirit or body
• not a spirit -- whether God or another
• since I'd be irremediably deceived 
• God would be a deceiver -- or abetting my deceit 
• But God is no deceiver (as proved in Med. 3)
• Therefore, the cause is physical: i.e., an external world exists {4}
• Nature of the external world
• sensuous (secondary) qualities are not in the things (just in their images) {5} {15}
• rationally apprehended (primary) qualities intrinsic to things: just length, breadth, and depth. {16}
• Mind & Body: their natures: two distinct substances {6} {7} {8}
• minds: thinking, unextended, indivisible agents
• body: unthinking, extended, divisible stuff
• The interaction problem: re the "intermingling" {9}
• hard to understand how minds can physically affect or be affected by anything
• how bodies can mentally affect or being affected by any thought 
• and yet it seems they do 
• physical changes cause thoughts: sense perception
• thought causes bodily motion: willed acts {10}
• Descartes "solution": the minimization strategy {11}
• don't see how they can intermingle
• but they don't have to intermingle much
• just in the pineal gland
• The Other Minds Problem: How do I know there are other thinkers? {12}
• creativity: only thought (being immaterial) could account for it
• two tests for creativity & thought {13}
• language test
• behavior test
• conclusions 
• other humans beings think: the creative character of speech and behavior evidence
• no other animals think since they lack creativity
• mechanical principles suffice to explain all they do {14}
• Basic Metaphysical Framework
• Substances: depending on nothing else for their existence
• Uncreated
• Created
• Minds
• Matter
• Attributes: features constituting the essence of a substance, i.e., such that the substance never occurs without this attribute: the one feature such that if this be taken away, the substance would not be.
• minds: thought or consciousness
• matter: extension
• Modes: other features of minds & bodies: these being are but modifications of their essential attributes
• minds: beliefs, decisions, doubts, etc.
• bodies: shape, motion, etc.

1. [I]t may happen that in imagining a chiliagon, I confusedly represent to myself some figure, yet it is very evident that this figure is not a chiliagon since it in no way differs from that which I represent to myself when I think of a myriagon or any other many-sided figure. (Med. 6) 
2. This power of imagination . . . inasmuch as it differs from the power of understanding, is in no wise a necessary element in my nature . . . from which we might conclude that it depends on something which differs from me. (Med. 6)
3. [Imagination] differs from pure intellection . . . inasmuch as the mind in its intellectual activity in some manner turns on itself and considers . . . ideas which it possesses in itself; while in imagining it turns toward the body . . . . (Med. 6)
4. But, since God is no deceiver, it is very manifest that He does not communicate to me these ideas immediately and by Himself.  . . .  For since He has given me no faculty to recognize that this is the case, but on the other hand a very great inclination to believe that they are conveyed to me by corporeal objects, I do not see how he could be defended against the accusation of deceit if these ideas were produced by causes other than corporeal objects.  Hence we must allow that corporeal things exist. (173)
5. [I]n approaching fire I feel heat, and in approaching it a little too near I even feel pain [and] there is . . . no reason in this which could persuade me that there is in the fire something resembling this heat any more than there is something resembling the pain; all that I have any reason to believe from this is that there is something in it, whatever it may be, which excites in me these sensations of heat or pain. (Med. 6)
6. [Although] I possess a body with which I am very intimately conjoined. . . . it is certain that this [that is to say, my soul by which I am what I am[ is entirely and absolutely distinct from my body, and can exist without it. (Med. 6) 
7. [E]ach substance has a principal attribute, and . . . the attribute of the mind is thought, while that of body is extension. (175)
8. [Body] is by nature always divisible, and the mind is entirely indivisible. (Med. 6)
9. Nature also teaches me by the sensations of pain, hunger, thirst, etc. that I am not only lodged in my body as a pilot in a vessel, but that I am very closely united to it, and so to speak so intermingled with it that I seem to compose with it one whole. (Med. 6)
10. I consider the body of a man as being a sort of machine so built up and composed of nerves, muscles, veins, blood and skin, that though there were no mind at all, it would not cease to have the same motions as at present, exception being made of those movements which are due to the direction of the will and in consequence depend on the mind [as opposed to those which operate by the disposition of the organs. (Med. 6)
11. [T]he mind does not receive the impressions from all parts of the body immediately, but only from one of its smallest parts, to wit, from that in which the common sense is said to reside. (Med. 6)
12. [S]ince the mind when engaged in private meditation, can establish its own thinking but cannot have any experience to establish whether the brutes think . . . it must tackle that question later on, by an a posteriori investigation of their behavior. (Reply to Gassendi)
13. [I]f there were machines bearing the image of our bodies, and capable of imitating our actions as far as it is [practically] possible, there would still remain two most certain tests whereby to know that they were not therefore, really men. Of these the first is that they could never use words or other signs arranged in such a manner as is competent in us in order to declare our thoughts to others . . . so as appositely to reply to what is said in its presence. The second test is . . . to act in all the contingencies of life in the way in which our reason makes us act. (Discourse on Method, Part 5)
14. [Animals] are destitute of reason . . . and . . . it is nature that acts in them [mechanically]. (Discourse on Method, Part 5)
15. [T]he principal error and the commonest which we may meet with in them, consists in my judging that the ideas which are in me are similar or conformable to the things which are outside me . . . . (181)
16. [T]he nature of body in its universal aspect, does not consist of its being hard or heavy, or coloured, or one that affects our senses in some other way, but solely in the fact that it is a substance extended in length, breadth, and depth.  (177)
17. By substance, we can understand nothing else than a thing which so exists that it needs no other thing in order to exist.  (174-175)
18. Created substances, however, whether corporeal or thinking, may be conceived under this common concept; for they are things which need only the concurrence of God order to exist. (175)
19. Thus extension in length, breadth and depth, constitutes the nature of corporeal substance; and thought constitutes the nature of thinking substance.  For all else that may be attributed to body presupposes extension, and is but a mode of this extended thing; as everything that we find in mind is but so many diverse forms of thinking.  (175)