Course Notes for Early Modern Philosophy Phil 301

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Summary of arguments in Descartes' Meditations on First Philosophy, I.

Cartesian Doubt: Des. wants to find out what propositions (claims, statements, etc.) we know with complete certainty (100%), therefore, he rejects everything that can be doubted. (Even if the doubts seem unreasonable, they are still possible, and thus we can't hold that we have certain knowledge of the claim's truth.)

A priori: knowledge gained entirely through reason (the truth or falsity of the claim can be known without appealing to experience of the world).

A posteriori: knowledge gained entirely through experience of the world (the truth or falsity of the claim can be known only by appealing to experience of the world).

All knowledge gained a posteriori can be doubted due to the possibility that (1) we may be dreaming all our experiences, and (2) our experience may be illusory or distorted somehow. Most knowledge gained a priori can be doubted due to the possibility that an "evil genius" (all-powerful being) may be deceiving us: We may think "2 + 2 = 4", but it really doesn't because the "evil genius (EG)" causes errors in our a priori reasoning. That is, each time we try to add "2 + 2", the evil genius causes us to make a mistake, so we really can't be sure that "2 + 2" really does equal "4" (and not some other number, instead).

Summary of arguments in Meditations..., II.

There is one thing we can know with complete certainty, however (and from this, Des. will use this one piece of certain knowledge as the cornerstone of his theory of knowledge). There are different versions of the argument (confusingly) presented in the Meditations (or at least these three different interpretations can be given):

1st interpretation: The EG is deceiving me, thus, at the least, I know that I exist as the subject of the EG's deception (a deceiver must have a deceivee, so I exist as the deceivee).

2nd interpretation: By doubting, I am thinking, and thoughts must belong to a mind. Thus, I know that I exist as the source or basis of my doubts (doubts necessitate a doubter, so I exist as the doubter).

3rd interpretation: "I exist" is simply an intuitive fact that is so obvious or fundamental that it doesn't require any further justification.

Problem: Des. seems to assume the truth of the laws of logic in his argumentation: Should he doubt the laws of logic, too (such as, "for any statement, it is either true or false, but not both at the same time and in the same way.")? Possible reply: The idea of "certain" knowledge may be inseparable from the laws of logic (?). Thus, searching for certain knowledge presupposes the truth of the laws of logic. More problematic, however, is that Des. is assuming a substance-property distinction is operative in this case, such that all properties (like a thought) must be in a substance (a mind). The substance-property distinction holds that all "things" in existence can be divided into these two categories (a substance or a property); and that no substance can exist without its "essential" property; and that no property can exist outside a substance. Should Des. be allowed to make these assumptions?

After establishing the existence of the self as a "thinking thing", Des. concludes (assumes?) that the thinking self is a mental "thing", and not a bodily "thing" (or "substance", which is usually defined as a distinct type of being that can exist independently of any other being, except God). Des. reaches this conclusion based on the following sort of (simplified) reasoning: The claim "I doubt I have a body" seems possible given his skeptical method (all a posteriori knowledge is suspectˇand the source of my presupposed knowledge of my body comes from experience), yet the claim "I doubt I have a mind" is not possible (in fact, it is a contradictory statement) since doubting requires or necessitates a mind. This argument is thereby used to support Cartesian dualism: there are two substances in Des. ontology; namely, corporeal (matter) and mental (mind). But, God may be a third substance (?)

The Principle of the Indiscernibility of the Identicals (PII) is in effect, here, such that "if two things are identical, then they must have all of their properties in common". If one has a property that the other does not have, then they are not identical. So, since my body has a property that my mind doesn't have˝namely, my body has the property that "I can doubt it" but my mind lacks this propertyˇit follows that my mind and body are not identical. Yet, this same form of reasoning can be used to prove that water is not identical to H20 (which is false, because they are identical), thus PII is not a valid (i.e., truth-preserving) principle of reasoning. To be specific: I may be ignorant of chemistry (which I largely am!) so that I declare that H20 does not exist, but I do claim to know that water exists. So, H20 has a property "I doubt that it exists" whereas water does not have this property (that is, regardless of the fact of whatever I may take water to be, I certainly don't doubt its existence). Consequently, the PII must also conclude that water is not identical to H20, which is clearly false, and thus shows how faulty the PII really is.

Des. argues that we understand the nature (essence, defining property, etc.) of body by the same innate reasoning that we came to know the nature of the self as mind. He uses the "wax example" to demonstrate this: After the wax has melted, all the empirical properties of the wax (gained by the senses, a posteriori) that it had before the melting have all changed. (That is, no sense property that the wax possessed before the melting, such as a particular color, shape, feel, etc., is the identical to the properties that the wax now possesses after it has melted.) Yet, we know the wax remains the same throughout the process even though none of the sensory properties remains the same. Only the understanding (innate reasoning capacity) can explain this knowledge of an unchanging basis for the wax. In short, the essence of material substance is extension in space and time. Moreover, the "imagination" capacity of humans can't explain the sameness of the wax, since imagination can't grasp the infinitude of possible changes in shape and volume that an extended substance, like wax, can undergo and yet still remain the same extended thing (a curious argument). The imagination, of course, is the mental (?) capacity to take (a posteriori) experiences and imagine them in various alternative ways: Des. seems to think that if imagination were to comprehend the "sameness" of the wax, it would need to have the entire infinity of possible shapes present to the mind (which is impossible because one can't "imagine" that may shapes at one time). But, why should we accept this interpretation of the faculty of the imagination?

Summary of Meditations..., III.

Des. needs to prove the existence of a non-deceiving God in order to eliminate the possibility of the evil genius, and thus gain certain knowledge of the physical world (required for his science, or anybody's science, for that matter).

Des. reasons that the idea that I have of an infinite God could not have originated in my self, since a finite being (myself) cannot be the cause on an infinite idea. Des. uses the objective/formal reality distinction, here: the reality represented by an idea ("objective" reality) must be caused by a "really" existing thing ("formal" reality) at least as great as the reality represented in that idea. For example, the idea of stone in my mind (objective reality) must be caused by a being (formal reality) at least as great as the reality represented in that idea of a stoneˇthis means that the idea of the stone must either be caused by a stone or a greater being (such as an angel or God). Accordingly, a "really" existing infinite God must be the cause of my idea of an infinite God. This causal principle is based, in turn, on his more general causal principle: there must be at least as much reality in the cause (of an effect) as there is reality in the effect. (In short, "you can't get something from nothing.") He likewise argues (in a rather Platonic fashion), that I could not have generated/constructed the knowledge of an infinite being from my experience of finite beings (as Aristotle believed), since I only know that I am a finite being in the first place due to the fact that innate knowledge of perfection (and infinity) has been built-into my mind (and that knowledge allows me to know that I am not perfect and not infinite). Consequently, an infinite, perfect, all-powerful, etc., God exists; and this God must likewise not be a deceiver (since this would constitute a defect in violation of God's perfection). (This whole argument is a variation on St. Anselm's "Ontological" argument for God's existence.) Moreover, it can't be the case that I've existed forever (i.e., so that I am actually infinite, and thus do not require an outside source for my idea of infinity), since there is only a "distinction of reason" between creating the world and keeping the world in existence: that is, from the fact that I existed a moment ago, I know that I do not have the ability to guarantee that I will continue to exist in the next moment; so, there must be some infinite being who does guarantee the existence of the world at each moment of time, and that is God.

Summary of Meditations..., IV-VI.

In Med. IV, Des. treats the problem of human error. This is a problem since it threatens God's all-goodness (as a non-deceiver). He reasons that we make mistakes when we allow our faculty of "willing" (which is the faculty of choosing, desiring, etc.), and which has unlimited scope or range, to go beyond the quite limited (in scope) faculty of "understanding" (which is, by now, the familiar innate reasoning ability). As long as we do not allow our will to go beyond the bounds of our understanding (i.e., make judgments without the aid of the understanding), we will not fall into error.

In Med. V, Des. offers another proof for God's existence; which is, essentially, the "Ontological" argument (once again): "existence" is part of the essence (defining properties) of God, thus God must exist (since I have a clear and distinct idea of God via our understanding... .......and, of course, God ensures that our clear and distinct perceptions/ideas are true... .....or something......uh, huh, huh.........uh, what?)

In Med VI, Des. tries to provide the foundation for our common-sense notions of the external, physical world. He begins by demonstrating that the faculty of imagination is different from the faculty of understanding: I can understand a thousand-sided figure, but I can't imagine it. That is, according to Descartes, the faculty of "imagination" involves bringing/constructing a "picture" or image in the mind, much like a photographˇbut, since one can't clearly and distinctly construct a thousand-sided figure in one's mind (how could you count up all those sides in one's mind?), it must be the case that our knowledge of such figures comes from another faculty of the mind that does not rely on forming images; namely, the "understanding". By the same faculty of understanding, I come to know the "real" properties of material substance (i.e., essential properties), as opposed to the properties that are not essential to matter. He argues that we have perceptions of corporeal bodies, ("adventitious" perceptionsˇwhich are not formed by our "passive" faculty of perception, but come from "outside" us; e.g., particular sounds, colors, smells, etc.), and since God is not a deceiver, there must exist some cause of these ideas that comes from something outside me. (He also reasons that the "active" faculty of producing sensations of extended things cannot be within me because I'm a limited, mental, non-extended thing, or mind; although God can do it, of course.) The cause of these perceptions must then come from real corporeal bodies. But, once again, our understanding informs us which properties of corporeal substance are essential, and thus are really "in" bodies (i.e., those that can't be separated from extension, such as figure, motion, etc., and are usually known as "primary" properties), and which properties of corporeal substance are not essential to bodies (i.e., those properties more closely linked to the five senses in an "a posteriori" manner; such as color, tastes, smells, tactile sensations, etc., and usually referred to as "secondary" properties). He seems to reason that the secondary properties are not really in the bodies, or at least may not be (which explains why we often confuse themˇbut, we can't confuse the primary properties, since we clearly and distinctly perceive them). He also provides his final argument for the real distinction between the mind and the body (that is, the two are separate substances): Des. reasons that the body is divisible and the mind is not divisible, thus they cannot be the same substance (once again, he is presuming PIIˇsee previous notes for this principle and its problems).

Finally, with our certain knowledge of the external, material world, he has reached his final goal: the "new" science (which for him, are geometric shapes in motion, much like the atomists) is based epistemologically/ontologically on the all-good God's existence. Yeeaahh! (Are you convinced?!)


Summary of arguments in Spinoza's Ethics.

Spinoza was a strange dude, with even stranger philosophical views, but there is a weird beauty to his thought, nonetheless.

Much of Spinoza is based upon his view that substance is something that is so self-dependent that it can be totally conceived "through itself" (def. 3): that is, its concept and existence are entirely without need of any outside concepts, causes, or existing things. From this seed, as it were, the whole of Spinoza's philosophy blossoms. Prop. 5 is also very important for he argues that there cannot be two substances with the same attribute (i.e., essence, or defining property). His reasoning seems to be that substances can only be distinguished by their attributes, so if two things possess the same attribute, then they must be identicalˇso there is only one substance, after all, and not two. Also, by Prop. 6, a substance cannot be caused to exist by another substance since it (the first substance) would then be dependent on that outside (second) substance for its existence (which violates def. 3 that a substance is independent and does not rely upon anything external for its conception or existence). Since a substance cannot be caused by anything else, then it must be self-caused (prop. 7), and thus its essence (attribute) must include existence. Given this, it soon follows (prop. 8) that substance must be infinite, since a substance can only be finite if it is limited by the existence of another substance with the same attribute (e.g., a material body is finite because its extension is limited by other material bodies which surround and define its surface and volume)ˇbut there can only be one substance with the same attribute (prop. 5), so nothing can limit a substance.

At this point, Spinoza argues that God exists, wherein he defines God as a substance of infinite attributes (that is, this substance has an infinity of different attributes, each attribute being non-limited, as in prop. 8). Spinoza's arguments for God are rather dubious, to say the least. For one, he seems to think that God's existence follows from Props. 7 and 8ˇbut they don't, since these props. merely say that if there is a substance it must be self-caused and infinite, not that there really does exist such substances. Also, props. 7 and 8 concern substances with only one attribute, not an infinity of attributes, which is how he defines God. Spinoza also offers the argument that for God not to exist there must be a valid argument proving this claim: if no such argument can be made, then God must exist. Wow, this is probably the most blatant form of "argument from ignorance" ever conceived (i.e., an "argument from ignorance" claims, fallaciously, that "if something can't be disproved, then you have a good reason to believe in it"ˇso, since I can't disprove the existence of the "Santa Claus", he must exist). Overall, Spinoza's arguments for God are versions of Anselm's "Ontological argument" (God is defined as perfect, so non-existence is contradictory because it would be a limitation).

In prop. 14, Spinoza reaches the final conclusion that God is the only substance. This follows from the fact that if there existed another substance, then it must have some attribute; but since God contains all attributes, both God and this other substance would have the same attribute, and thus there would be two substances with the same attribute (which is impossible from prop. 5). So, in essence, Spinoza's view of substance eventually leads to the view that there is only one substance in the entire world. (He could have reached the conclusion, however, as did Leibniz, that there are many substances that are entirely separate and independent of one another). So, Spinoza's view is that there is only one substance, and that individual objects are just properties or modes (affections) of this one substance; much like a single wave is just a small part of the larger ocean. Later, he concludes that motion is thus necessary for the individuation of bodies (part 2, prop. 13). This is "new-age holism" seventeenth-century style, to say the least! On this issue, remember that Spinoza rejects the view that twenty men could be a substance because there is no, so to speak, internal reason why just twenty men should exist (the number "twenty" isn't part of their attribute). Or, put differently, individual humans are a product of there experience and outside external influencesˇbut this means that a human can't be a substance since its existence, and concept, is dependent on outside causes (which violates the definition of substance, def. 3).

Spinoza has a very interesting view of the attributes of this one, infinite substance (God). He argues in prop. 10 that one substance can be conceived or viewed from the perspective of its individual attributes. He says that each attribute can be "conceived through itself", so that, for example, I can think of God purely in terms of its mental attribute (thought), or I can conceive God purely in terms of its physical properties (extension). But, just because I can conceive of God (one, infinite substance) from these two different perspective that doesn't mean that they are two substances (they are merely different attributes of the same substance). For modern thinkers worried about the mind-body interaction problem, this interesting view offers a way of resolving the problem (possibly): i.e., mind and brain are not different substances, as Descartes would have us believe, but merely two "ways" of conceiving, or "perspectives", of the same thing; such that we can explain human cognitive abilities purely in terms of thoughts (feeling, pains, etc.) or purely in terms of material, electro-chemical processesˇbut they are just two different views of the same thing. More importantly, you can't explain mind through bodily attributes, or vice versa, since attributes can only be conceived through themselves, as he constantly reminds us. This is an attempt to solve the mind-body problem because it says that, properly speaking, there is no causation between the mind and body because there is only one thing (substance), and mind and body are just two separate ways of conceiving of this same substance.

Finally, it should be remembered that Spinoza accepts a very rationalist theory of knowledge, much like Descartesˇthat is, that there are many things we know by pure reason without the aid of experience. The majority of Spinoza's views show this rationalism. For example, based on reason, and his earlier propositions and definitions, he also concludes that there can be no contingency in the world (accidental facts or truths) but that everything must be necessary (all facts and truths must have occurred exactly as they did: see props. 28-33). If the one substance (God) had contingent aspects, then God would be dependent on something else for those contingent properties, but then God would no longer be a substance (a familiar argument, from def. 3). Thus, the one substance and all its attributes are necessary˝much like the necessary truths contained in a geometryˇso that everything, including God (since God is the one substance) must occur exactly in one way. Therefore, there is no free will, either for humans or God, such that we could have chosen, or can in future chose, to act differently. No wonder he was kicked out of every religious group he tried to join!!


Summary of arguments in Leibniz's Discourse on Metaphysics.

Leibniz was greatly influenced by Spinoza and Descartes, needless to say, and this becomes quite evident when you look at the conclusions he reaches, if not in the details of his arguments.

Leibniz accepts a theory of truth which holds that all true statements are statements where the concept of the predicate is contained in the concept of the subject. That is, in the claim, "all triangles have three sides", the predicate "three sides" is conceptually contained in the subject "triangles"ˇthis is the case because "triangle" is defined as a three-sided figure. Thus, the concept of the predicate is contained in the concept of the subject. (These types of statements are also known as analytic statementsˇwhere "analytic" means, "true by definition". Statements such as, "today is cloudy", are not analytic, but synthetic, since the predicate "cloudy" is not part of the definition of "today". In other words, whether today is cloudy or not is merely a contingent, and not necessary fact about "today". Analytic statements, in addition, can be viewed as a form of "identity" statement, "A=A", since the predicate is contained in the subject, and thus "three sided" is identical with "triangle".) Now, Leibniz wants all the truths of the world to partake of this "analytic" form, since it would remove the problem of contingency and uncertainty from the world. Hence, like Spinoza, he wants to develop a concept of "substance" which is self-dependent and does not depend on anything that exists outside of itself. In fact, Leibniz apparently accepts, just like Spinoza, that if a substance were to depend on anything else for its existence, then it would not be a substance. A Substance must, therefore, contain within itself everything that will ever happen to itˇin this way, it partakes of the form of an analytic statement since all of its predicates (properties) are contained in its subject (substance)ˇso, "today is cloudy" becomes an analytic statement for Leibniz. In fact, all of a substance's properties constitute its essence, or defining trait. Leibniz worries, though, about the possibility of two substances that contain all the same properties: Are they now the same substance/subject, since they have the same properties/predicates? (If two geometric figures had the same definition, for example, they would be the same figure.) Leibniz rejects the possibility that the two substances could differ only numerically (haecceity, or "thisness"), probably because there is no such concept of "pure numerical difference" in the study of logic or geometry; so, he concludes that if there are two substances in existence, then they must differ from one another in some qualitative way, and not just numerically: i.e., two different substances must have at least one different property between them, or they wouldn't be different! This principle is the famous "Identity of the Indiscernibles" (PII)

With each substance possessing all of its properties "internally", as its collection of defining properties, Leibniz embraces a view of the world where there is no causation among, or between, substances: all that exists are substances and their internal properties, which are merely "phenomena"ˇthat is, the properties that are internal to each substance are its mental thoughts (sense-data, desires, beliefs, etc.). Leibniz states that "the whole world is built into each substance" which demonstrates that each substance does not interact with any other substance or thing (except God, of course, who can do anything). Now, to overcome the PII problem of several substances with the same properties (since each substance mirrors the world, and there is only one world to mirror), Leibniz reasons that each substance views, or mirrors, the world from a different perspective or position (e.g., I see the world from my point of view, and you see the world from a different point of view, and so on for each individual substance), thus the mental phenomena that make up each substance are qualitatively different, which avoids violating the PII. God, according to Leibniz, harmonizes the perceptions or thoughts of all these substances so that all of our experiences are synchronized, and thus give the "illusion" of causal interaction between substances. For example, my perception of giving you back your paper with an "F" on it is exactly correlated with your perception of getting the paper from meˇbut, of course, there is no real interaction between our substances since everything merely happened internally within each one of us. This thesis became known as "preestablished harmony". As mentioned in class, a large part of the justification for this view of substance was derived from his work in physics, particularly mechanics (which studies the forces and interactions of physical bodies). Leibniz believed that Descartes' theory of the essence of material bodiesˇi.e., that bodies were only comprised of extension (in breadth, length, and width)ˇhad been proven false. Bodies were not comprised of extension alone; rather, they also housed some form of internal "force" (since they would not resist one another under collision if they were mere extensionˇand they do resist one another during impact). This internal "force" (which Leibniz equated in some manner with his conservation principle for "size times the square of velocity", in contrast to Descartes' conservation principle for "size times speed") apparently suggested to Leibniz that bodies could contain internal "properties" other than just extension.

Of course, with Leibniz' notion of substance, everything that happens to a substance is necessary (since it part of its definition), and thus there would appear to be no free will. Also, it would appear to be the case that God is constrained to make this world "the best of all possible worlds" (since anything less than that would violate God's "all-goodness", and thus every event or feature of the world must ultimately help to constitute this "best of all possible worlds"). Consequently, God is likewise bound by necessity, and thus has no free will: God must make this world the best possible (which means that our world really is the best of all possible worldsˇa problem in itself, needless to say, given all the faults we see in the world). Leibniz, in at least some passages, apparently tries to respond to this problem by stating that God only "chooses" to make the best of all possible worlds (and thus is not bound by necessity to make the best possible). Yet, does this mean that God, correspondingly, only chooses to be all-good (and thus God could choose to be all-evil)?ˇand, of course, many theologians/philosophers would not like a theory of God that allows for such philosophical possibilities! There are many other problems related to the Free-will/determinism issue, as it is called. In response to the question, for example, "Does this mean that I am destined by the necessity of my internal properties to lead a life of moral perversity and TV addiction (just a random exampleˇno personal revelations!?), and that I cannot change (even if I wanted to)?", Leibniz has the great response that: since my internal properties define who I am, if I change these properties, then I would not be the same person any longer! In a sense, any attempt to change one of my properties or characteristics is an attempt to stop being me, and an attempt to be somebody else (which is absurd, of course). It's comforting, in a way (and/or scary), to know that my deviant thoughts are so integral to my very definition!!! Another attempt proposed by Leibniz to resolve the free-will/determinism problem was to claim that, whereas the definitions of geometric/mathematic concepts are necessary (since their denial involves a contradiction), there is no necessity to the internal properties that define each substance. Each substance could have been different, it would seem, if God had given us a different set of internal properties. Unfortunately, God's all-goodness and the "best of all possible worlds" thesis would seem to sink this suggested solution, as well: if this is truly the best of all possible worlds, then my internal properties could not have been any different, since any other possible collection of properties must not contribute to that best possible state-of-affairs. 


Summary of arguments in Locke's Essay Concerning Human Understanding

In Book I, Chap. II, Locke is intent on undermining the belief that we have innate knowledge (such as the law of noncontradiction; "it is impossible for something to be and not to be"). He offers many arguments against this view. His main claim, or definition, is that an "idea" is such that one must be aware of it: viz., it is impossible to have an idea that one is not aware of. Thus, since children and idiots are not aware of the noncontradiction law, it must not be innate, contra the Cartesians. Locke does not believe that one can come to know or discover these truths through the use of reason, since (for him) reason is simple deduction from known premises, and thus you need to know the premises (i.e., the innate ideas) to deduce the innate ideas (which shows the absurdity of this position). Locke also states that while reason is necessary to come to know these truths (of the noncontradiction law and other such math/logic truths), it is not sufficient to know these truths: viz., you need reason to acquire this knowledge, but just having reason does not guarantee it. Locke also argues that if a claim is innate by simply being such that one "assents to it" on first hearing, then our mind has a potentially infinite stock of innate ideas: e.g., "white is not black", "white is not red", etc. This potential infinity of innate ideas Locke takes as demonstrating the implausibility of the view (that an idea is innate if we assent to it immediately). Finally, if certain statements are known innately, like the noncontradiction law, then it must be the case that the words that make up this law must also be known innately. That is, Locke seems to be arguing that it impossible to know the meaning of a statement without first knowing the meaning of the words that make up that claim. But, then it would seem that the ideas that make up certain instances of the noncontradiction law, such as 'red' and 'blue' in the claim "nothing can be both red and blue at the same time in the same way", must be known innately˝but this is absurd because we come to know colors by experience, and not by reason. This is an interesting argument that will make a reappearance (but formulated more effectively) in Kant.

Rather, Locke argues that we only gain knowledge of such truths (as the noncontradiction law) by an elaborate process of reflection on our simple sense impressions. Sensory perceptions (sense ideas, sense-data) come into our minds, such as "white (at time 1, location 1)", and by reflection on these sense-data (both presently occurring sense-data and those sense-data stored in memory) we acquire ideas of general concepts, such as "whiteness", and then statements (such as "it is impossible for something to be white and not to be white"), and then laws ("it is impossible for something to be and not to be").

In Book II, Chap. I, Locke begins to lay out in more detail his theory of knowledge vis-ř-vis the origin of our ideas. All knowledge is ultimately founded on experience. Our ideas (from experience) come in two forms: sense perception and reflection. Reflection, as the second source of simple ideas, is when the mind observes (so to speak) its own operations and "receives into its understanding" a new set of distinct ideas: these are the simple ideas of individual thoughts, doubts, desires, etc. Next, Locke goes on to consider a series of objections to his views based on the following argument (probably based on Cartesian views): Just as body and extension are inseparable (which is the essential property of body), so are "souls" and thoughts/ideas inseparable (which is its essential property); therefore souls must always think. This argument is problematic for Locke because he holds that ideas/thoughts only come about as a result of the acquisition of sense-data and the reflections upon them˝thus, our minds enter the world without thought (it would seem), which the Cartesian claim refutes. Locke offers many arguments (some convoluted) on why the "soul" (mind?) and thought do not have to always be conjoined (i.e., the mind is sometimes without thought/ideas). First, he appeals to our experience of sleep to argue that many times during the night we do not dream, thus our minds are without thought. In response to the possible Cartesian view that there is an area of our minds that is always thinking but we are not aware/conscious of it, he claims that this is an absurdity. Unconscious thoughts are (apparently) akin to innate ideas for Locke: thoughts are, by definition, consciously perceived. Also, if we are not conscious of these thoughts, then it is like having a separate individual housed in my body (an obvious absurdity)˝e.g., Socrates asleep, and Socrates awake; Castor and Pollux. Likewise, if we are not conscious of these thoughts, how do we know that they really do occur?

In Book II, Chap. II, Locke argues that simple ideas are the material of all of our knowledge. All we can do with simple ideas is unite, compare, and repeat them (and thus form complex ideas), but we cannot destroy, create, or (apparently) change them in any way. Thus, they are "atomistic" in the sense that they are indestructible, and the smallest unit. Also, Locke states that our minds are passive as to the reception of simple ideas (chap. XII), which also seems to confirm the view that simple ideas cannot be altered by the mind at any stage in their reception˝thus, simple ideas are the "given" of experience (which means that they are what the world gives to us without our effort or influence). We could be constructed (by god) so as to have more senses than the five we do have, and thus have more simple ideas than we can conceive now; but, it is also the case that if you do not have a sense capability, and never did, then you could not have the simple ideas associated with that sense (so a person blind from birth cannot have the simple ideas of color).

In Book II, Chap. V-VIII, he goes into more detail on the origin of our simple ideas. A "quality" of a material body (outside my mind) is the "power" of that body to produce simple (sense) ideas in us. Thus, a snow ball has the power to produce in us the simple ideas of "cold", "round", and "white", to name a few. Remember, here, that these simple ideas are not complex or conceptual at this stage: only after the mind has stored many simple ideas of the same kind (through memory, the whole process being, presumably, automatic) can the mind use the "understanding" to compare and contrast these simple ideas to form the complex idea of "whiteness", or "roundness" (as a concept over and above the simple sense idea of "round (time 1, location 1)", etc.). Locke states that the qualities in bodies are inseparable from the bodies, but be careful here. The "primary qualities", as for Descartes, are the qualities that are in bodies and of which our simple ideas (which come from those bodies) give a fairly accurate representation. Therefore, "solidity, extension, figure, motion, rest, and number" are simple ideas produced by the primary qualities of solidity, extension, etc.. Secondary qualities are not qualities that are in bodies in this way, since they are only the power of the primary qualities to produce a (different) set of simple ideas in us (viz., simple ideas of color, taste, sound, etc.). Thus, colors, sounds, etc., are not really in bodies (but the primary qualities of extension, motion, etc., are in bodies). Presumably, the motion of the extended bulks of matter produce in us, through our bodies and sense organs (which are also extended bulks of matter), simple ideas of colors, sounds, etc.; so, primary qualities are the complete cause of these simple (sense) ideas. (Locke mentions a third quality, as well, which is merely the power of primary qualities to affect other primary qualities, as when fire melts the wax.)

In Book II, chap. XII, he describes the types of complex ideas we have. Of interest later is the complex idea of "substance", which is the idea of a "distinct particular thing which can subsist by itself", such as "man", or "chair", etc.. These complex ideas can be of a single substance, such as a "man", or of a plural sort, such as "men" (which is just a combination of many complex ideas of "man", individually speaking). "Modes" are "dependencies on, or an affection of, substances". What this means is that modes are properties of substances, such as "triangle", "gratitude", "murder", etc. (which can only exist in a substance): in short, modes are complex ideas which do not contain in them the possibility of existing by themselves (as substances can, of course). Modes can come in simple or a mixed form (but you can look this up yourself).

In Book II, Chap. XXIII, Locke makes his famous remark that we can not really know just what "substance" underlies the qualities that exist in the material world (those qualities being the primary ones separate from my mind). The primary qualities of bodies produce the simple ideas in us, but these qualities must exist in a substance (thus primary qualities appear to be modes, which cannot exist outside a substance). yet, if the only access we have of the material world is through our simple sense ideas, and these ideas originate from primary qualities, how do we know that a substance underlies these primary qualities? This is Locke's dilemma: we seem to have this complex idea of a substance that unites the primary qualities of bodies (and thus all the simple ideas that are produced in us), but we don't have any experience of this underlying substance (since all we have is the experience of the primary qualities, and nothing more). Consequently, Locke concludes that "he knows not what" substances are, or where his complex idea of them comes from. Obviously, Locke has accepted the substance/property distinction: i.e., the world is made up of two things, substances and properties˝and properties cannot exist outside of a particular substance. The question is, given Locke's empiricism (that all knowledge is ultimately based on sense experience of simple ideas) is he justified in accepting this thesis? Locke goes on to make other dubious inferences, by the way. He thinks he can prove God's existence by "demonstration" using a variant of the principle of sufficient reason (namely, the old "you can't get something from nothing" hypothesis, which supposedly proves an infinite being must be the cause of the world, etc.) Here, 'demonstration' is a form of knowledge which reaches certainty by using many steps in a proof˝each of these steps qualifying as certain knowledge by means of 'intuition' (where we immediately know the truth of the fact or proposition in question, such as "red is not yellow"). Thus most mathematical proofs reach certain knowledge by demonstration because the truth of the conclusion is not immediately obvious to us (and hence we need to construct a proof). The third category of knowledge is sensation, which Locke thinks we are certain of because our simple ideas must come from the real objects in the outside world˝but can really claim that has certain knowledge of this (if he, in fact, does claim certain knowledge of this)? Doesn't Descartes' "dreams and illusions" argument raise doubt, and thus eliminate certainty, of the source of our simple ideas?


Summary of arguments in Berkeley's Three Dialogues between Hylas and Philonous

Berkeley's resolution of the mind-body problem (of the alleged causation between nonmaterial mind and material body) is to simply deny the existence of body! Without the need to explain how a body can cause a thought in something non-material, Ber. thinks he has eliminated skepticismˇsince all we know are the ideas in our minds, and we have an immediate and certain knowledge of these ideas, we can never be fooled!

Most of the first dialogue concerns his attempt to deny the existence of a material world, especially the belief (of Locke) that primary properties of bodies really come from the external world, whereas the secondary properties are only in the mind. Ber. tries to show that the primary properties of bodies are as equally subjective as the secondary. For example, the shape of a body changes as you look at it from different angles or distances. But, then, the same object has two contradictory properties at the same time (it is both round and elliptic, large and small, etc.) which is the problem we noted earlier with respect to the secondary properties (the water is both cold and hot, etc.); thus the primary properties of bodies are as equally subjective as the secondaryˇto believe that such properties exist in bodies in the outside world leads to the absurdity that contrary properties could be in the same body at the same time. (If Ber. had known projective geometry, he would have discerned the error in his reasoning: primary properties, like shape, are "objective" in the sense that I have a mathematical formula which tells me what the shape will look like when I move from my perspective to yours; but there is no such formula which informs me how my experience of the color "blue" will look as viewed through your cognitive faculties. In this sense, there is a definite distinction between the two types of properties). It should be further noted that Ber. relies quite heavily on the principle that "any change in the properties of a body must be caused by a real change in the body". By this principle, Ber. concludes that primary properties can't be in the real world, because of the instances (noted above) of changes in our perceptions of primary bodies without any corresponding changes in the actual bodies (i.e., the shape of the body changes as I view it from different angles, but that is a change in its properties caused by me, and not the bodyˇthis demonstrates, for Ber., that such properties are totally subjective, like the secondary).

Another favorite argument of Ber. is his repeated claim that it is contradictory to talk about the existence of bodies outside of the mind, especially "matter" and "substance", which contain primary properties and cause sensations in us, since this would be tantamount to claiming that there is a non-mental container which contains mental items; or, put differently, that a non-mental thing can cause mental thoughts in us˝an apparent violation of those much cherished causal principles often grouped under the general designation, "the principle of sufficient reason"; such as "the effect must be like the cause", or "the effect must not be greater that the cause", etc. Finally, Ber. offers the (bad) argument that since any concept of a body is a mental item, this proves that all bodies are really mental things. But, as Thomson, points out, just because I can't conceive of bodies without the use of my mind, this doesn't demonstrate that they are only mental things. To be more specific, Berkeley appears to offer the following argument: since I cannot have the thought "a tree existing outside of all minds and thought" without falling into a contradiction (why? well, because it is a thought, and thus this thought can't exist outside of all thought!), there are no trees that exist outside of our minds (or, put differently, trees are just thoughts in our minds). Needless to say, Berkeley's argument is more a source of amusement than a serious philosophical position.

Abstract concepts are equally problematic for Ber., since he believes that we can only perceive particular ideas (sensations). For Ber., the general concept of a triangle is a triangle without any particular length of its sides, angles, etc., but this would be a triangle which is not a triangle (i.e., a triangle without an angle, length of sides, etc.ˇa contradiction), just as a general motion would be a motion without a particular speed (another contradiction). Ber. seems to think that we form general concepts by examining a particular idea in our mind, and then trying to generalize away the particular features of that idea (i.e., we examine an idea of a particular triangle in our mind, and then try to generalize away its particular features so as to arrive at the features that are general to all triangles). As Thomson hints, this may be what Locke meant by a complex idea of abstraction (i.e., an idea which represents what is common to all triangles, horses, etc.). More interestingly, Ber. claims that the meaning of the word "triangle" doesn't come from representing a general idea, as it does for Locke; rather, the term is meaningful without having to be tied to an idea, so that it only has to be used in a particular way to convey meaning (which comes close to the theory that the meaning of language comes from its use, not from what it represents). As regards general ideas, Ber. may actually be resurrecting an argument from Descartes, here. As you will recall, Des. argued that you couldn't imagine a 1,000 sided figure, but you could understand its concept. Ber. may be saying the same thing: if sensory ideas are like pictures (which is what he does assume), then the meaning of general ideas can't come from perceiving these idea in your mind (since the pictorial representation of such an idea is impossibleˇjust like counting up all the sides of Descartes' 1,000 sided figure is impossible), thus we can only come to know these ideas by some other mental faculty (such as, understanding?)

Problems arise for Ber. when he tries to argue for the existence of other minds and God. Ber. doesn't want his philosophy to amount to solipsism (i.e., that the only thing that exists is myself and my thoughts/ideas), so he reasons that we can be sure that the tree exists in the woods even when I'm not looking at it because there are other minds, or simply God, who perceive the tree in my absence (i.e., since "to exist is to be perceived", there must always be someone perceiving the tree to ensure its continuous existenceˇa very strange conclusion, indeed). In fact, Ber. seems to think that there are many things we know besides ideas/perceptions: (1) we know we exist (which he agrees with Descartes is known immediately by intuition); (2) we know that we are a mind/mental substance (since, it would appear, he believes that ideas/perceptions cannot just float around in mid-air without some substance to contain themˇhere, we may add, he appears to be assuming the substance/property distinction; but how can he claim to know that such a principle is true if all knowledge is based on experience? Do we experience the truth of this principle through experience?!); (3) we can know other minds exist (actually, I'm not sure how he argues for this, but it is certainly problematic because we don't experience other minds, but only sense perceptions that we infer come from other minds); (4) we can know that God exists. Ber. offers the most elaborate arguments for (4). First, he claims that since we know that our perceptions/ideas are not consciously caused by our own mind, but seem to be imposed on us from, as it were, "the outside", it must be case that some being (far greater than us) is the cause of those ideas in us; namely, God. Ber. seems to think that this argument has the certainty of a demonstrative proof (as in mathematics), and that the orderliness and harmony of our ideas of perception can only come from a being that is infinitely powerful and all-goodˇbut can he really claim that this argument actually constitutes a proof, or for that matter, that it is even remotely plausible? In another, even worse, argument, he appears to argue that the very fact that objects continue to exist when we don't perceive them is proof that a God must exist in order to always perceive these objects (and thus guarantee that they continue to exist)ˇbut, how can he claim to know that objects continue to exist when we don't look at them (for he needs to prove this premise in order to get his argument to work)? Rather, he merely assumes that this premise is true. Finally, he tries to avoid the problem, "How do we determine if our ideas/perception are 'real' (i.e., caused by God) or merely dreams?", by holding that whereas the ideas that comprise our dreams are very vague and fuzzy, the ideas/perceptions of our awake states are quite vivid and robust, so that this difference provides a means of determining whether or not we are awake or asleep. Whether or not these arguments are successful I leave as a proof for the reader.


Summary of arguments in Hume's An Inquiry Concerning Human Understanding

For Hume, the two main ways of justifying any of your beliefs are:

1) Showing that its contrary leads to a contradiction

2) Showing that its contrary does not lead to a contradiction, which is ultimately the same as showing that the claim is based on your past experience.

If a belief could be justified in the first way, Hume called it a "relation of ideas". If it could be justified in the second way, Hume called it a "matter of fact".


1) The belief that "1+3 = 2+2". The contrary of this belief says that "1+3 = 2+2". But, by definition, "2" is just "1+1" and "3" is just "1+1+1", so this would become "1+1+1+1 = 1+1+1+1". Hence the contrary of "1+3 = 2+2" contradicts the fact that "1+1+1+1 = 1+1+1+1". So "1+3 = 2+2" is a "relation of ideas", and you are justified in believing it. (Hume says that all the truths of arithmetic, geometry, and algebra are justified in this way, and are relations of ideas.) A more obvious example is "triangle is a three sided figure": To deny this is an outright contradiction since the definition of "triangle" is "three-sided" figure!

2) The belief that "the sun came up this morning". This is something you can justify by pointing to your past experienceˇperhaps you saw the sun coming up this morning as you were driving in to school. So "The sun came up this morning" is a "matter of fact", and you are justified in believing it. (A great many of your everyday beliefs about the world are of this sort.) Of course, this claim is a "matter of fact" because to deny that "the sun will come up tomorrow" does not lead to a contradictionˇi.e., this is a logically possible state-of-affairs (although it may be physically impossible).

Hume was mainly interested in undermining the claims of the rationalists, who believed that we knew many things "a priori" (based only on reason, not experience), such as God's existence or the types of allowable/unallowable causal relationships in the world (i.e., body-body, body-mind, mind-mind; that is, all those causal beliefs that come under the general title "principle of sufficient reason"). Hume held that all of our knowledge was ultimately based on simple sense experiences, which he called "impressions", and the ideas that are based on these impressions. This view, of course, is nearly identical to Locke's views. Hume thought that the difference between our impressions and our ideas is that ideas are only a dim or rough copy of the more vivid impressions. Once again, one of our Early Modern philosophers has espoused a "representationalist" theory of mental contentˇi.e., sense-experiences (impressions) and ideas are like pictures in the mind, since they bear information on the external, material world by resembling that world (much like a picture of your friend bears information about your friend by resembling your friend). Of course, the ultimate question is, as before: "How do we know our ideas and impressions really function like pictures, rather than some other process?" In fact, this presumption by Hume (of a representationalist theory of mental content) is probably the weakest link in his, otherwise excellent, philosophy.

Now, since Hume held that there are only two ways to justify your beliefs (if something cannot be justified in either of the two ways above, then you have no rational or deductive justification for believing it), he used this conclusion as a basis for undermining the rationalist's (or anybody's, for that matter) concept of causation. Belief in causation, he states, ultimately resides in a belief in the Principle of Inductionˇand to argue inductively is really to argue that the future will resemble the past. Thus the sun will continue to come up each morning, food will continue to nourish us, walking out of high windows will continue to be dangerous, etc., because it has always done so in the past! Since such claims involve "matters of fact" (whose denial does not lead to a logical contradiction), we can only appeal to the truth of such claims if we assume that the past occurrences of these "constantly conjoined" eventsˇi.e., "eating the bread", and "being nourished by the bread"ˇwill continue to be conjoined in the future. This is how Hume understands causation, for it is merely the constant conjunction of two events (which are "matters of fact") in space and time: e.g., the event, "striking of the match", has always been followed (constantly conjoined) in space and time by the event, "lighting of the match", etc. In short, Hume believes that people who argue that a "causal" relationship holds between the event "striking of the match" and the event "lighting of the match" must ultimately be making the following argument: from the premise "every time I struck a match in the past it has lighted", they conclude that, "every time in the future I strike a match it will light". But, this argument is missing a premise, namely, "the future will be like the past"ˇand, unfortunately, the truth of this premise can never be known (which is the main reason for the skeptical worries that people associate with Hume's analysis of causation.)

More specifically, Hume says that your belief that the future will resemble the past is without justification, since this belief cannot be justified either as a "relation of ideas" or as a "matter of fact". Let us consider these points separately:

1) "The future will resemble the past" is not a "relation of ideas". Its contrary is "The future will not resemble the past," but there is nothing contradictory about this statement. We can easily imagine that, in the future, things will go completely haywire, behaving in new and unexpected ways: Your car will float rather than riding on the ground, eating bread will not nourish you while eating rocks will, the moon will begin to turn and do zig-zags in the sky, etc. (These are admittedly strange thoughts to entertain, but the point is that it we can entertain themˇthey do not lead us into a logical contradiction.)

2) "The future will resemble the past" is also not a "matter of fact". It cannot be justified on the basis of your past experience. To try to justify it in this way, you might say: "My experience has been that, in the past, each new day has resembled the ones that have gone before, i.e. the future has always resembled the past. So I expect that, in the future, the future will continue to resemble the past." But, in applying your past experience to the future in this way, you are assuming that your past experience is an appropriate guide to what the future will hold, i.e. you are assuming that the future will resemble the past. And this is the very belief that you are trying to justify. You can't assume it in your attempt to justify it. In short, Hume argues that all causal reasoning involving "matters of fact" relies on the claim, "the future will resemble the past", so you can't state that you know this claim is a "matter of fact" without getting into circularity problems (as above).

So the belief that the future will resemble the past, i.e. the Principle of Induction (or Uniformity Principle, in Thomson), is not justified, either as a "relation of ideas" or as a "matter of fact". However, Hume seems to think that we do have an idea of causation, and that we base this notion on the fact that we have become conditioned by experience, or "habit", to always anticipate or expect the effect ("the lighting of the match") given the cause ("the striking of the match"). Hume explains at length that this form of conditioning is crucial to our survival, and that only a fool, therefore, would not "believe" in causationˇbut, of course, we have no philosophical understanding of causation as the rationalists, or even Locke, believed: that is, causation is not a logically necessary relationship between events which we can know either a priori or a posteriori. And, of course, the positive side of Hume's philosophy is that his undermining of any a priori certainty about causal knowledge opens the door for the existence of many types of causal relationships which the rationalists (and some empiricists) ruled out as a priori impossibleˇe.g., mind-body causation. Since certain mental events are constantly conjoined with certain bodily events, these types of relationships have just as good a reason to be labeled "causal" as any other event relationship.

Finally, and very briefly, Hume is skeptical of any certain knowledge of the "self". Everyone we have studied thus far seems to take it for granted we have an a priori intuition, or at least a direct experience, of the self, especially if we take the self to be a distinct "mental substance" (which is separate from our perceptions). That is, previous philosophers believed that one cannot be mistaken about the existence of our individual "self" as a distinct kind of entity that remains constant (does not change) over the course of our life (since the "self" is commonly believed to be an unchanging part of our experience of the world). Hume states, however, that when he examines the contents of his thoughts, he doesn't find any perception of a "self", nor does he find any sense impressions which remain constant over time: all I find when I examine my perceptions are various, particular perceptions which exist for only a short time ("hot", "round", "wet", etc., and others of a more perverse sort I can't mention in the notes)ˇthese perceptions (impressions or ideas) don't have "Ed" stamped on them, since they are just anonymous (but deviantly interesting) perceptions. In addition, these sense impressions do not remain constant over time; rather, they are in constant flux. Hume states that "he never catches himself" in his perceptions (as an unchanging impression), which demonstrates that we can't claim to have knowledge of the existence of the self from experience (where all knowledge based on experience comes from sense impressions, once again). Of course, if Hume is only claiming that he have no knowledge of the self as a mental "substance" (which is distinct from bodily substance), then his argument is very convincing. However, if he is claiming that we have no knowledge of the self at all, so that we are merely bundles of changing perceptions (as he does seem to suggest in his account of personal identity over time), then this view becomes very odd (e.g., How does a bundle of perception think, desire, will, etc.?) Finally, it should be noted that Hume also rejects any knowledge, through experience, of "substance" (either of physical or mental substance). So, the Rationalists can't claim to have knowledge of the world, and its causal relationships, based on some sort of empirical knowledge of substance (and Hume rejects any a priori knowledge of substance, which is based on reason alone, of course).


Summary of arguments in Kant's Prolegomena to Any Future Metaphysics.

Kant is very difficult, to say the least, but his thought rewards the effort.

First of all, Kant argued that previous philosophers had not gone far enough in categorizing the different types of statements with respect to their epistemological content (i.e., how we know that they are true, etc.). Kant accepts LeibnizÝ distinction between what we he (Kant) calls "analytic", and "synthetic": analytic statements are such that they are true by definition, i.e., (as in "all bachelors are unmarried males", and "x=x"; here, the concept "unmarried males" is contained in the definition of the concept "bachelors", etc.). Synthetic statements, however, are not true by definition, since the concept of their predicate is not contained in their subject (such as, "this cup is hot", which is not analytic since the predicate "hot" is not contained in the definition of the concept "cup"). Kant, furthermore, accepts the distinction between "a priori", which he defines as a necessarily true statement (i.e., true of all possible experiences) known by reason, and "a posteriori" statements, which are not true of all possible experience and are thus known only through individual experiences. Kant then considers the four conjunctions of these four types of statements.

1) Analytic A Priori: These types of statements are true by definition and true of all possible experience. Hence, these are just the statements usually dubbed "a priori" by most of Kant's predecessors (although Hume called them "relations of ideas"). Examples: "all bachelors are unmarried males", "x=x" , "triangles have three sides".

2) Analytic A Posteriori: These types of statements are impossible because they would be true by definition but known only through experience (i.e., not true of all possible experience)˝but how could something known to be true only through the meanings of its own words also be known to be true only through experience!

3) Synthetic A Posteriori: These statements are not true by definition and are only known to be true by experience; thus, most of the contingent facts of the world would fit this category (such as "today is cold", "my coffee rules", etc.)

4) Synthetic A Priori: These statements are not true by definition, but are necessarily true of all possible experiences. This is Kant's contribution to the problem, since no one before him had ever made this distinction (as far as I can tell). Kant places most mathematical and geometrical knowledge in this category: While "1=1" is analytic a priori, because the definition of the two concepts are identical, he wants to claim that statements such as "7+5=12" are synthetic a posteriori because the concept "7+5" is a different concept than "12" (i.e., the concept of the one is not contained in the concept of the other). Kant reasons that the denial of "7+5=12" does not lead to a contradiction in the way that the denial of "1=1" does lead to contradiction (remembering, of course, that Kant also defines an "analytic" statement as one whose denial leads to a contradiction). If all math statements were analytic, he argues, then many very difficult mathematical theorems and equations (which were eventually proven to be true) should have been easily recognized as true (by definition) by just thinking about the meaning of the concepts involved.

Kant worries, of course, how we can know that synthetic a priori statements are true. This provides the reason for his introduction of the "forms of intuition". (Kant uses the term 'intuition' to designate sense experience.) Kant claims that all of our possible sense experiences (intuitions) are filtered through a "conceptual framework" which our minds impose upon those sense experiences˝these "forms of intuition" are the categories of space and time: all sense data is represented, or manifested, to us as possessing spatiotemporal properties (i.e., all of our sense experiences, say, of a coffee cup, "represent" the coffee cup as taking up space and enduring through time). Here, it is important to remember that the "content" of a sense experience is "what the experience is about" whereas the "form" of a sense experience is "how the experience is presented/represented". For example, if I see a table, a desk next to it, and some papers on top of it, then the desk, table, and papers are the content of this experience; while the spatial relationships ("next to", "on top off") are the form of this experience since they concern the way in which the table, desk, and papers are represented.

The really interesting (and controversial) claim that Kant makes is that the form of the mindÝs experiences are contributed by the mind itself. The mind imposes the "forms of intuition" on all sense experience˝so it is just a brute fact that all possible sense experience will have spatiotemporal properties. But, Kant often says that these forms of intuition are preconditions for having experiences; that is, in order to have any sensory experience at all, such as "seeing the coffee cup", you must be equipped with the space and time mental framework necessary for the very perception of the cup. (Since the cup is a spatiotemporal object˝remove space and time from your experience of the cup and you have nothing left!!) Yet, Kant also claims that these forms of intuition are means by which our minds acquire knowledge of synthetic a priori statements. Our minds are able to arrive at synthetic a priori truths by applying our space and time categories of understanding (the forms of intuition) to analytic a priori concepts, such as "point", "line", "5", etc: e.g., "a line is the shortest distance between two points" cannot be known by just examining the meaning of the analytic a priori concept "line", since this concept does not incorporate any information about distance (or how distances are determined, etc.)˝but, if the line is embedded (placed) in a (Euclidean) space, then it becomes quite obvious that a line is the shortest distance between two points. Hence, our synthetic a priori claim, "a line is the shortest distance between two points", is revealed to us as true by means of the spatial "form of intuition". (Kant says that arithmetical statements, which are also synthetic a priori, are known through the application of time's "form of intuition", since our experience of the succession of temporal moments provides us with our understanding of arithmetical progression˝i.e., addition.). Moreover, since the "forms of intuition" are applied to all possible experiences, we thus know that synthetic statements such as, "a line is the shortest distance between two points" will be true a priori (i.e., true of all possible experience). By this clever means, we acquire knowledge of synthetic a priori statements.

Problems for Kant, or, more accurately, for the neo-Kantians, began to surface with the development of non-Euclidean geometries in the later 19th century. In many of these theories, such claims as, "a line is the shortest distance between two points", no longer hold true (since the shortest distance could be a curve, etc.)˝and, in addition, it is possible that a posteriori experience of the world might be able to determine if space is either Euclidean or non-Euclidean. Thus, Kant's claim that geometrical (and mathematical) statements are a priori synthetic is apparently undermined, since now it appears that our experience of the world (as regards content, and not form) can reveal the truth or falsity of many of these claims (such as "a line is the shortest distance between two points"), and so they would appear to be synthetic a posteriori, after all. In other words, they were not necessarily true of all possible experiences, which is what Kant would need if they were to qualify as a priori. (The Neo-Kantian attempt to resolve this difficulty are discussed in my philosophy of space and time seminar.)

Kant's synthetic a priori also demonstrates how he attempted to synthesize the Empiricists with the Rationalists. Kant was a big fan of Hume, and wanted to preserve Hume's doctrine that we can only know what is revealed through experience. However, Kant wanted also to argue, along with the Rationalists, that we have a priori, or necessary, knowledge about the world. The synthetic a priori accomplishes this daunting task in the following manner: Kant claims that we can never know the world separate, or apart, from our experience, since how can you claim to know anything that transcends all possible experience? Thus, the world as it exists apart from intuition (experience), which he calls "noumena", is forever unknowable. So, this conclusion would appear to agree with Hume's philosophy. However, since we know that all possible experience will partake of the forms of intuition (space and time), then any knowledge that we acquire from investigating the properties/features of these forms of intuition (such as synthetic a priori mathematical and geometrical propositions, as above) must be true a priori! Conclusion: we can have certain, a priori knowledge of many facets of the world of experience, which he dubs "phenomena"; and this a priori knowledge is in keeping with the spirit of Rationalism, of course.

But, if our synthetic a priori knowledge is only limited to phenomena, and we can never know noumena (things-in-themselves, as he calls them), does that mean he is an idealist like Berkeley (where "idealism" means that the only existing things are minds and God)? Kant vehemently rejects idealism, and wants to claim that we have a direct access, or experience, of the outside, external world. In fact, he wants to reject the whole "representationalist" theory of perception (which holds that we gain knowledge of the outside world by means of ideas or sense perceptions in our minds, and that these sense perceptions are like "little pictures" in our minds which "represent" the world by resembling it˝this is, by the way, how photographs "represent" their content). Overall, Kant says we directly experience the world (or so some passages seem to suggest) since it is not the case that our sense experiences function as some sort of go-between, or middle-man, betwixt the external world and our minds (which is how they would need to function, moreover, if sense experiences really were like little pictures in our minds). However, if we can never know the world as it exists outside all possible experiences, doesn't that entail idealism all the same? Its not quite clear how to resolve this problem entirely, but Kant also claims that noumena (things-in-themselves) are not really things, but only the limitations of our perceptual faculties˝i.e., it is the limit of all our possible experiences. Thus, Kant's noumena could just be another way of saying that we can only talk about those features/properties of the world that we can ultimately experience, and thus it is fruitless to try to describe the properties of the world which will forever be outside any possible experience. On this interpretation of Kant, his concept of noumena seems compatible with his rejection of idealism. (But is it what he meant?)

Besides the forms of intuition, our minds also are equipped with innate principles of understanding that likewise hold true˝or, more correctly are applied to˝all possible experience, and thus they are synthetic a priori, too. Causation, and the Laws of Nature, are among these a priori categories of "understanding", hence causal relationships hold true of all possible experiences. In short, Kant held that the way in which "the future resembles the past", as Hume would put it, is a part of our experience that is contributed by our minds. That is, causation is something we can believe with justification because our minds automatically work in such a way that future experiences resemble past ones. Kant claims, by the way, that the existence of the synthetic a priori categories of understanding are not derived from experience, but are presupposed by experience˝in other words, you need to have the a priori forms of intuition and categories of understanding operating/functioning in your mind before you can even have an experience (and so, Kant claims he has turned Hume's arguments on their head). In addition, Kant likewise argues that any argument for the existence of the "self" ultimately presupposes the existence of the self, thus you can't prove the existence of the self without circularity. Overall, Kant thinks that the "self" is a "given" in experience, and is presupposed in all of our possible experiences (so that it, too, is a category of the understanding). Finally, Kant agrees with Berkeley that a general idea (i.e., concept) in your mind is not an image, as many empiricists believe, since a concept cannot be an image of a general, or universal, object. (In short, the "idea of a triangle in general" is an impossible image or picture˝it cannot picture all triangles at once.) Rather, Kant argues that conceptual knowledge is like having a rule or formula in your mind which allows you to form an image of any particular idea in your imagination (i.e., having the concept "triangle" is to possess a sort of rule in one's mind for creating the image of any particular triangle). This is an important breakthrough, since everyone we have examined (including Berkeley) seems to think that conceptual knowledge is representational (i.e., it is like, say, a picture of a triangle in your mind which somehow represents all triangles).

Updated to this point, 11/28/01


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