October 15, 2003

Providence in George Eliot’s Middlemarch

What does George Eliot’s Middlemarch tell us about Providence? In order to answer this question, we need to discover what the novel’s characters believe about it.

Casaubon views Providence as an agent primarily concerned with his best interests. Although he believes Providence has blessed him by making Dorothea his wife (28, Norton Critical Edition), he never bothers to consider whether “Providence had taken equal care of Miss Brooke in presenting her with Mr. Casaubon” (176). He is “the centre of his own world,” being “liable to think that others were providentially made for him” and only considering them “in the light of their fitness for” himself (54). Similarly, Fred, in the beginning of the novel at least, only views Providence in terms of how he believes it intends to benefit him: he thinks he will inherit Featherstone’s farm “without study or other inconvenience,” but “purely by the favor of providence in the shape of an old gentleman’s caprice” (213).

Like Casaubon and Fred, Bulstrode views Providence as an agent that is consumed with blessing him. He believes Providence sanctioned his decision to rob his first wife’s daughter out of her inheritance (382). When he thinks that Raffles only told Caleb Garth about his past sins, he claims that “Providence intended his rescue from worse consequence” (431). Moreover, he believes that Providence might save him by bringing death to Raffles (380), and when Raffles falls sick, he claims that he will be “in gratitude to Providdence” if the man dies (438).

Unlike the aforementioned characters, Dorothea does not believe in Providence. Although she begins the novel as an orthodox Christian, she goes on to reject this faith. As she tells Ladislaw towards the middle of the book, whereas she used to “pray so much,” now she “hardly ever” prays. Rejecting Christianity, Dorothea adopts her own religious views. Her new religion is based, not on passively sitting back and praying that God accomplishes good in the world, but on being an active agent in the world, on serving others, on becoming “part of the divine power against evil” (244).

Whether or not Providence really exists is not a subject that the novel takes up. We know what various characters think about the matter, but the narrator never gives us the “definitive” answer. However, if we put all our findings together, we can discover one important claim that the novel makes about Providence: the novel contends that Providence need not exist in order for morality to exist. The relationship of God and morality was important for many Victorian thinkers, as many worried that a diminishing belief in God would result in diminishing moral standards. Middlemarch confronts this concern and claims that, to the contrary, people can be moral even if they do not believe in Providence. As we saw, those who have the strongest belief in Providence tend to be the most selfish and immoral characters; instead of allowing their belief in Providence to spur them on to good deeds, such characters as Casaubon and Bulstrode (and, to a lesser extent, Fred) use their belief in Providence to justify ego-centrism. On the other hand, the character who does not believe in Providence, Dorothea, ends up being the novel’s most selfless and virtuous character.

Kant Mid-Term

1. Explain the difference between transcendental realism (using Leibniz and Hume as examples) and Kant’s transcendental idealism. Why does Kant call his turn to transcendental idealism a “Copernican Revolution”? (DO NOT use the terms “analytic” or “synthetic,” or the phrases “a priori” or “a posteriori” in this answer.)

Transcendental realism claims that the world exists independently of human subjectivity. (The world is here defined as that which is distinct from human thought or perception.) In other words, transcendental realism claims that human thought or perception does not effect the constitution of the world. To put it yet another way, it claims that the world is not determined by the way humans interpret it. For example, according to transcendental realism, an object that possesses certain qualities would possess those qualities even if a person interpreted it as having less than or more than those qualities. For instance, we may say that a particular steak knife possesses the qualities of being rectangular, of being silver, and of being sharp. According to transcendental realism, if someone should happen to see the knife and interpret it as being rectangular and silver but not sharp, it would not follow that the object was only rectangular and silver; it would also remain sharp. And if someone should happen to see the knife and interpret it as being rectangular, silver, sharp, and frightening, it would not follow that the object was frightening; it would only remain rectangular, silver, and sharp.

If we assume that transcendental realism is true, then we can only have necessary knowledge of the world if we resort to dogmatism. If we assume transcendental realism but reject dogmatism, then we must embrace skepticism. To see why this is the case, we should briefly look at the philosophies of Gottfried Wilhelm Leibniz and David Hume, who both embraced transcendental realism.

Leibniz embraced transcendental realism, believing that God made the world as it is and that it would exist as it is regardless of the way humans might think about it or perceive it. Although the world’s constitution is in no way dependent upon human subjectivity, Leibniz believed that humans can have necessary knowledge of the world. He believed this is possible because (1) humans can discover Truths of Reason through mere thinking and (2) the structure of the human mind mirrors the structure of the world. Let’s look at each of these claims in turn. First, humans can discover Truths of Reason through mere thinking. Truths of Reason, Leibniz believed, are principles that are based on the law of non-contradiction, as their negations are self-contradictory. Since Truths of Reason are based on the law of non-contradiction, they are necessarily true, as it is logically impossible for them to be false. Second, the structure of the human mind mirrors the structure of the world. Like the world, the human mind is structured rationally. Given that (1) we can know certain necessary truths by mere thinking and (2) the structure of the human mind mirrors the structure of the world, it follows that (3) we can know certain necessary truths about the world by mere thinking. In other words, since the mind mirrors the world, it follows that the necessary truths we learn by examining our minds are not just about our minds but also about the world. Therefore, we can have necessary knowledge about the world. Unfortunately, Leibniz’s claim that the human mind mirrors the world is an unproven assumption; therefore, his entire system is dogmatic.

Hume also embraced transcendental realism, believing that the constitution of the world is in no way dependent upon human thought or perception. Hume, however, rejected Leibniz’s dogmatic assumption that the human mind mirrors the world. Therefore, although Hume acknowledged that we are aware of certain necessary truths apart from experience (he called them Relations of Ideas), he believed, contrary to Leibniz, that these truths are merely truths about the structure of one’s mind and not about the external world. Hume believed that the only way we can have knowledge about the world is through our senses. Unfortunately, Hume conceded, the knowledge we gain about our senses is contingent, as it is not based on the law of non-contradiction. Our senses can merely tell us what happened in the past and what is happening in the present; they cannot tell us what will happen in the future. Since our senses cannot tell us what will happen in the future, it is always possible that the scientific laws that we observe at work today will cease to exist in the future; therefore, since it is possible that such laws may one day not exist, our knowledge of such laws is contingent. So, although unlike Leibniz’s systems, Hume’s system is not dogmatic, it is unfortunately skeptical.

Kant wants (1) to have necessary knowledge of the world and (2) to avoid dogmatism. However, he realizes that one who embraces transcendental realism cannot have both of these: either he or she must give up (1) and be a Humean skeptic or give up (2) and be a Leibnizean dogmatist. In order to have both (1) and (2), Kant realizes that he must reject transcendental realism. Rejecting transcendental realism, he embraces transcendental idealism.

Transcendental idealism claims that the world does not exist independently of human subjectivity. In other words, transcendental idealism claims that, to a certain extent, human thought or perception effects the constitution of the world. To put it yet another way, it claims that the world is determined by the way humans interpret it. In fact, Kant claims that “the world” would not exist at all if it were not for human subjectivity.

By embracing transcendental idealism, Kant is able to (1) have necessary knowledge of the world and (2) avoid dogmatism. He is able to have necessary knowledge of the world because, if the mind necessarily imposes certain structures on the world and if these structures are a part of the world, it follows that our experiences of the world reveal necessary truths about the world. He is able to avoid dogmatism because he does not make the dogmatic assertion that the mind mirrors the world.

Kant calls his turn from transcendental realism to transcendental idealism a “Copernican Revolution.” He calls it such for the following reason. The Copernican Revolution in astronomy switched the relationship between two objects, the sun and the earth. Specifically, this revolution rejected the traditional view that the sun revolved around the earth and, instead, claimed that the earth revolved around the sun. Similarly, Kant’s Copernican Revolution switches the relationship between two objects, knowledge and the world. Specifically, Kant’s revolution rejects the traditional view that knowledge revolves around subjects. In other words, his revolution claims that knowledge is determined by the world; to put it another way, that one can be said to have knowledge of the world because his or her beliefs conform to the world. Instead, Kant claims that objects revolve around knowledge. In other words, he claims that the world is determined by knowledge; to put it another way, one can be said to have knowledge to the world because the world conforms to his or her beliefs.


2. Explain Kant’s distinctions between the two types of knowledge (a priori and a posteriori) and the two types of judgments (analytic and synthetic). Which knowledge-judgment combinations are possible for the transcendental realist? Why? Which are possible for the transcendental idealist? Why?

According to Kant, a priori knowledge is knowledge that is both necessary and experientially irrefutable. To say that a type of knowledge is necessary is to say that it is logically impossible for it to be false, as its negation violates the law of non-contradiction. To say that a type of knowledge is experientially irrefutable is to say that it cannot be proven false by any possible experience. It should be noted that the experiential irrefutability of a priori knowledge follows from its necessity. In other words, if it is logically impossible for a given statement to be false, then it follows that it is impossible for any experience to ever prove that statement false. An example of a priori knowledge is the proposition, “All triangles have three sides.” This statement is necessarily true, as its negation violates the law of non-contradiction. In other words, since three-sidedness is an essential quality of a triangle, to negate this statement (and thus to say that “Not all triangles do have three sides”) is to essentially say that “Not all triangles are not triangles.” Since this statement is necessarily true, it is also experientially irrefutable: since it is logically impossible for a triangle to exist that does not have three sides, it follows that we could never experience a non-three-sided triangle.

Contrary to a priori knowledge, a posteriori knowledge is knowledge that is contingent and experientially refutable. To say that a type of knowledge is contingent is to say that it is logically possible for it be false, as its negation does not violate the law of non-contradiction. To say that a type of knowledge is experientially refutable is to say that it is possible for it to be proven false by experience. It should be noted that the experiential refutability of a posteriori knowledge follows from its contingency. In other words, if it is logically possible for a given statement to be false, then it follows that it is possible for an experience to prove that statement false. An example of a posteriori knowledge is the proposition, “This triangle is blue.” This statement is contingently true, as its negation does not violate the law of non-contradiction. In other words, since blueness is not an essential quality of triangularity, a logical contradiction does not occur when we negate this statement (and say that “This triangle is not blue”). Since this statement is contingently true, it is also experientially refutable: since it is logically possible for a triangle to exist that is blue, it follows that we many one day experience a blue triangle.

An analytic judgment is a judgment whose predicate is contained in its subject. For example, the following judgment is analytic: “Triangles have three sides.” To see why this is so, it is helpful to put the statement the Subject is Predicate form, which can be stated as follows: “Triangles (subject) are things with three sides (predicate).” In this case, we can see that the predicate is known if the subject is merely understood. In other words, if we knew the definition of triangle, we would know that triangles are necessarily three-sided; if a “triangle” did not have three sides, it would not be a triangle. One way to discern whether a judgment is analytic is to see whether its negation is self-contradictory; if so, then the judgment is analytic. We can see this in the above example. If we say that “Triangles are not things with three sides,” we are violating the law of non-contradiction and essentially saying that “Triangles are not triangles.”

Contrary to an analytic judgment, a synthetic judgment is a judgment whose predicate is not contained in its subject. For example, the following judgment is synthetic: “Every event has a cause.” To see why this statement is synthetic, let’s put it in the Subject is Predicate form. When we do so, the statement is rendered as follows: “Events (subject) are things that have causes (predicate).” It is clear that events cannot be defined as “things that have causes”; even if an event did not have a cause, it would still remain an event. Proof for this can be found in the fact that it is possible to imagine an uncaused event. (I cannot imagine a four-sided triangle, but I can imagine an uncaused event.) Unlike an analytic judgment, the negation of a synthetic judgment is not contradictory. As we just saw, it is not contradictory to negate the sentence “Events are things that have causes.” For when we say “Events are things that do not have causes,” we are not violating the law of non-contradiction and essentially saying that “Events are not events.”

Whereas transcendental realists believe that the constitution of the world is independent of subjectivity, transcendental idealists believe that the world, to some extent at least, is dependent of subjectivity. In other words, whereas transcendental realists believe that external objects would exist as they do even if humans thought about those objects differently than they do, transcendental idealists believes that objects external to themselves would not exist as they do if humans did not think about those objects as they do.

Given these definitions, it follows that transcendental realists can have two types of knowledge-judgment combinations, while transcendental idealists can have three types of knowledge-judgment combinations.

Both transcendental realists and idealists can have a priori knowledge of analytic judgments. In other words, whether or not subjectivity determines the world’s constitution, it is possible to have a priori knowledge of an analytic judgment. Analytic judgments will always be known a priori. This is so because an analytic judgment is a judgment whose contrary violates the law of non-contradiction and a priori knowledge is knowledge that is necessary and experientially irrefutable, and, as we saw earlier, if a statement’s contrary violates the law of non-contradiction (and is, thus, analytic), then that statement is known with necessity (and is, thus, known a priori)

Both transcendental realists and idealists can also have a posteriori knowledge that is synthetic. In other words, whether or not subjectivity determines the world’s constitution, it is possible to have a posteriori knowledge of a synthetic judgment. If one’s thinking does not determines the world’s constitution, then he or she can only have a posteriori knowledge of synthetic judgments, as these judgments are not based on the law of non-contradiction and, therefore, they cannot be known with necessity. If one’s thinking determines the world’s constitution, then it is still possible for him or her to have a posteriori knowledge of synthetic judgments, as it is possible that the world is only partially determined by his or her thinking.

Only transcendental idealists can have a priori knowledge that is synthetic. If the world’s constitution is not determined by human thought, then I can never have a priori knowledge of synthetic judgment. If my thought does not determine the world’s constitution, then a judgment whose negation is not contradictory cannot be necessary (as its negation does not violate the law of non-contradiction). For instance, if my thought does not effect the truth of the statement “Every event has a cause,” then it is logically possible for an uncaused event to occur. If the world’s constitution is determined by human thought, however, then I can have a priori knowledge of this judgment. For it might be that my thought necessarily effects the world so that events always have causes. If this is the case, then it is possible to have knowledge that “Every event has a cause” that is necessary (because it is impossible for my thought to not to effect the world in this way).


3. Explain Kant’s arguments to show that space is an a priori intuition (using both the metaphysical and transcendental expositions). How does this imply that space is transcendentally ideal?

In the Metaphysical Exposition on space, Kant gives four arguments that space is an a priori intuition. The first two show that space is known a priori and the second two show that space is an intuition. These arguments are based on the progressive method, as they begin with ordinary experience of spatial objects and show that this experience is only possible if space is an a priori intuition. In the Transcendental Exposition, Kant gives another argument that space is an a priori intuition. This argument is based on the regressive method, as it assumes the validity of geometry (the science of space) and shows that geometry is only possible if space is an a priori intuition. In what follows, we will look at all of these arguments in turn.

Before looking at these arguments, we should define a few terms. First, while a priori knowledge is knowledge that is necessary, a posteriori knowledge is knowledge that is contingent. Second, while intuition is essentially sense-experience and is of particulars, thought is essentially conceptualization and is of universals.

Kant’s first argument shows that space is known a priori by showing that, contrary to the claims of empiricism, we must have an idea of space prior to experiencing it. Empiricists claim that we are able to know the concept of a thing by experiencing many instances of that thing and extracting out what those instances have in common. With regards to space, empiricists claim that we have the concept of space because we have experienced different bits of space and have extracted out what these bits of space have in common—namely, spatiality. Contrary to empiricism, Kant claims that in order to experience bits of space, we must already have the idea of space itself. He claims that in order to know that I am experiencing space, I must first know what space is; if I did not first know what space was, then I would not be able to know that it’s space that I’m experiencing. Although this argument might make Kant sound like an innatist, argument three shows that such is not the case. (In argument three, he shows that we do not have innate knowledge of space, but become aware of space through experience; however, because space is a unique kind of individual, it only takes one experience of space to know about all of space.)

Kant’s second argument claims that space must be known a priori because we can conceive of space without outer objects, but cannot conceive of outer objects without space. (An outer object is an object outside one’s stream of consciousness.) This claim seems uncontroversial. We can easily imagine a universe in which nothing existed; however, if we imagine a universe in which at least one object existed, then we would also need to imagine space existing, as it is impossible to imagine a non-spatial object. Since we can conceive of space without outer objects, it follows that objects in space are known a posteriori. This follows because objects in space are contingent, as it is logically possible for them not to exist—as is evidenced by the fact that we can conceive of the world being void of all objects. Since we cannot conceive of outer objects without space, it follows that space is known a priori. This follows because space is necessary, as it is logically impossible for space to not exist—as is evidenced by the fact that we cannot conceive of objects existing without also conceiving of space existing.

Kant’s fourth argument proves that space is an intuition by noting that space is not a concept. Space cannot be a concept because the relationship of space to its particulars is different than the relationship of concepts to their particulars. The relationship of a concept to it particulars is one in which the particulars are under the concept. In other words, the concept is what all particulars have in common. For instance, all of the world’s triangles share the concept of triangularity. On the other hand, the relationship of space to its particulars is not one in which the particulars are under space. Spaces are not instances of space, but parts of space. If you take all spaces and put them together, you have space; on the other hand, if you take all the triangles and put them together, you do not have triangularity. Space, therefore, must be an individual thing. And since it is an individual thing, it must be something that is intuited.

Kant’s third argument shows that space is not only an individual, but a unique kind of individual. Space is different than other individuals because examining a part of it tells you about all of it. Examining a part of most individual things will only tell you about that part and not about the individual thing as a whole. For example, if I examine the leg of a table (i.e., a part of a table), I only learn about the table’s leg and not about other parts of the table—for instance, it’s top. Examining a part of space, on the other hand, tells you about all of space. For example, if I examine one patch of space, I will know what all of space is like—for every one patch of space is like every other patch of space.

In the Transcendental Exposition, Kant shows that space is an a priori intuition by appealing to geometry, the science of space. Everyone agrees that knowledge of geometrical propositions is a priori, as such knowledge is necessary. Unlike many thinkers, however, Kant assumes that geometrical propositions are synthetic and substantive, being discovered through experience and being about the world. (Such people as Hume have rejected this assumption and have claimed that knowledge of geometrical propositions is analytic and vacuous, being discovered through concept-analysis and being merely about one’s own mind.) Since geometry, the science of space, is a priori, it follows that space is a priori. Since geometry, the science of space, is synthetic, it follows that space is synthetic; moreover, since space is synthetic, it follows that it is an intuition. Space, therefore, is an a priori intuition.

Since space is an a priori intuition, it follows that judgments about it must be synthetic and that they must be known a priori: since space is known a priori, it follows that judgments about it will be known a priori and since space is an intuition, it follows that judgments about it are synthetic. (All intuitions are synthetic because one does not learn of them through concept-analysis.) Since judgments about space must be synthetic and must be known a priori, it follows that space is transcendentally ideal, as only transcendental idealists can have a priori knowledge of synthetic judgments.

In order to understand why only transcendental idealists can have a priori knowledge of synthetic judgments, we need to understand the difference between transcendental idealism and transcendental realism. Whereas transcendental realists believe that the constitution of the world is independent of subjectivity, transcendental idealists believe that the world, to some extent at least, is dependent on subjectivity. In other words, whereas transcendental realists believe that external objects would exist as they do even if humans thought about those objects differently than they do, transcendental idealists believes that objects external to themselves would not exist as they do if humans did not think about those objects as they do.

If the world’s constitution is not determined by human thought, then I can never have a priori knowledge of synthetic proposition—as it will be logically possible for any synthetic proposition to occur, as the negation of all such propositions does not violate the law of non-contradiction. For instance, if my thought does not effect the truth of the statement “Every event has a cause,” then it is logically possible for an uncaused event to occur. If the world’s constitution is determined by human thought, however, then I can have a priori knowledge of synthetic propositions. For it might be possible that my thought will necessarily effect the world so that events always have causes. If this is the case, then it is possible to have knowledge that “Every event has a cause” that is necessary (because it is impossible for my thought to not to effect the world in this way).


4. Explain Kant’s arguments to show that time is an a priori intuition (using both the metaphysical and transcendental expositions). How does this imply that time is transcendentally ideal?

In arguments one, two, four, and five, Kant gives four arguments that time is an a priori intuition. Arguments one and two show that time is known a priori and arguments four and five show that time is an intuition. These arguments are based on the progressive method, as they begin with ordinary experience of temporal objects and show that this experience is only possible if time is an a priori intuition. In argument three, Kant gives another argument that time is an a priori intuition. This argument is based on the regressive method, as it assumes the validity of what Kant calls temporal axioms and shows that temporal axioms are only possible if time is an a priori intuition. In what follows, we will look at all of these arguments in turn.

Before looking at these arguments, we should define a few terms. First, while a priori knowledge is knowledge that is necessary, a posteriori knowledge is knowledge that is contingent. Second, while intuition is essentially sense-experience and is of particulars, thought is essentially conceptualization and is of universals.

Kant’s first argument shows that time is known a priori by showing that, contrary to the claims of empiricism, we must have an idea of time prior to experiencing it. Empiricists claim that we are able to know the concept of a thing by experiencing many instances of that thing and extracting out what those instances have in common. With regards to time, empiricists claim that we have the concept of time because we have experienced different temporal objects and have extracted out what those objects have in common—namely, temporality. Contrary to empiricism, Kant claims that in order to experience temporal objects, we must already have the idea of temporality, or time itself. He claims that in order to know that I am experiencing a temporal object, I must first know what time is; if I did not first know what time was, then I would not be able to know that I’m experiencing an object existing in time. Although this argument might make Kant sound like an innatist, argument five shows that such is not the case. (In argument five, he shows that we do not have innate knowledge of time, but become aware of time through experience; however, because time is a unique kind of individual, it only takes one experience of timeto know about all of time.)

Kant’s second argument claims that time must be known a priori because we can conceive of time without objects, but cannot conceive of objects without time. This claim seems uncontroversial. We can easily imagine time existing without any objects; however, we cannot imagine objects existing timelessly. Since we can conceive of time without objects, it follows that objects in time are known a posteriori. This follows because objects in time are contingent, as it is logically possible for them not to exist—as is evidenced by the fact that we can conceive of time existing without any objects existing. Since we cannot conceive of objects existing timelessly, it follows that time is known a priori. This follows because time is necessary, as it is logically impossible for time to not exist—as is evidenced by the fact that we cannot conceive of objects existing timelessly.

Kant’s fourth argument proves that time is an intuition by noting that time is not a concept. Time cannot be a concept because the relationship of time to its particulars is different than the relationship of concepts to their particulars. The relationship of a concept to it particulars is one in which the particulars are under the concept. In other words, the concept is what all particulars have in common. For instance, all of the world’s triangles share the concept of triangularity. On the other hand, the relationship of time to its particulars is not one in which the particulars are under time. Times are not instances of time, but parts of time. If you take all times and put them together, you have time; on the other hand, if you take all the triangles and put them together, you do not have triangularity. Time, therefore, must be an individual thing. And since it is an individual thing, it must be something that is intuited.

Kant’s fifth argument shows that time is not only an individual, but a unique kind of individual. Time is different than other individuals because examining a part of it tells you about all of it. Examining a part of most individual things will only tell you about that part and not about the individual thing as a whole. For example, if I examine the leg of a table (i.e., a part of a table), I only learn about the table’s leg and not about other parts of the table—for instance, it’s top. Examining a part of time, on the other hand, tells you about all of time. For example, if I examine one bit of time, I will know what all of time is like—for every one patch of time is like every other patch of time.

Kant’s third argument shows that time is an a priori intuition by appealing to the temporal axioms, which give the basic characteristics of time. When put together, the two temporal axioms (that time is one-dimensional and that difference times are successive) tell us that it can only be one time at any given point. Everyone would agree that knowledge of the temporal axioms is a priori, as such knowledge is necessary. Kant also assumes that propositions about the temporal axioms geometrical are synthetic and substantive, being discovered through experience and being about the world. Since the temporal axioms are a priori, it follows that time is a priori. Since the temporal axioms are synthetic, it follows that time is synthetic; moreover, since time is synthetic, it follows that it is an intuition. Time, therefore, is an a priori intuition.

Since time is an a priori intuition, it follows that judgments about it must be synthetic and that they must be known a priori: since time is known a priori, it follows that judgments about it will be known a priori and since time is an intuition, it follows that judgments about it are synthetic. (All intuitions are synthetic because one does not learn of them through concept-analysis.) Since judgments about time must be synthetic and must be known a priori, it follows that time is transcendentally ideal, as only transcendental idealists can have a priori knowledge of synthetic judgments.

In order to understand why only transcendental idealists can have a priori knowledge of synthetic judgments, we need to understand the difference between transcendental idealism and transcendental realism. Whereas transcendental realists believe that the constitution of the world is independent of subjectivity, transcendental idealists believe that the world, to some extent at least, is dependent on subjectivity. In other words, whereas transcendental realists believe that external objects would exist as they do even if humans thought about those objects differently than they do, transcendental idealists believes that objects external to themselves would not exist as they do if humans did not think about those objects as they do.

If the world’s constitution is not determined by human thought, then I can never have a priori knowledge of synthetic proposition—as it will be logically possible for any synthetic proposition to occur, as the negation of all such propositions does not violate the law of non-contradiction. For instance, if my thought does not effect the truth of the statement “Every event has a cause,” then it is logically possible for an uncaused event to occur. If the world’s constitution is determined by human thought, however, then I can have a priori knowledge of synthetic propositions. For it might be possible that my thought will necessarily effect the world so that events always have causes. If this is the case, then it is possible to have knowledge that “Every event has a cause” that is necessary (because it is impossible for my thought to not to effect the world in this way).


5. Leibnizean dogmatism can be summarized as the belief that analytic propositions are substantive, while Humean skepticism can be summarized as the belief that all a priori knowledge is vacuous. Explain these statements.


An analytic judgment is a judgment whose predicate is contained in its subject. For example, the following judgment is analytic: “Triangles have three sides.” To see why this is so, it is helpful to put the statement the Subject is Predicate form, which can be stated as follows: “Triangles (subject) are things with three sides (predicate).” In this case, we can see that the predicate is known if the subject is merely understood. In other words, if we knew the definition of triangle, we would know that triangles are necessarily three-sided; if a “triangle” did not have three sides, it would not be a triangle. One way to discern whether a judgment is analytic is to see whether its negation is self-contradictory; if so, then the judgment is analytic. We can see this in the above example. If we say that “Triangles are not things with three sides,” we are violating the law of non-contradiction and essentially saying that “Triangles are not triangles.”

A priori knowledge is knowledge that is both necessary and experientially irrefutable. To say that a type of knowledge is necessary is to say that it is logically impossible for it to be false, as its negation violates the law of non-contradiction. To say that a type of knowledge is experientially irrefutable is to say that it cannot be proven false by any possible experience. It should be noted that the experiential irrefutability of a priori knowledge follows from its necessity. In other words, if it is logically impossible for a given statement to be false, then it follows that it is impossible for any experience to ever prove that statement false. An example of a priori knowledge is the proposition, “All triangles have three sides.” This statement is necessarily true, as its negation violates the law of non-contradiction. In other words, since three-sidedness is an essential quality of a triangle, to negate this statement (and thus to say that “Not all triangles do have three sides”) is to essentially say that “Not all triangles are not triangles.” Since this statement is necessarily true, it is also experientially irrefutable: since it is logically impossible for a triangle to exist that does not have three sides, it follows that we could never experience a non-three-sided triangle.

To say that a proposition is substantive is to say that it is useful and yields information about the world and not merely information about one’s own mind or thought processes. To say that a proposition is vacuous is to say that it is useless and does not yield information about the world, but only about one’s own mind or thought processes.

Leibniz believes that analytic propositions are substantive. In order to see why he believes this, we first need to understand two other beliefs of his. First, Leibniz believes that, through examining their minds, humans become aware of certain analytic propositions, or what he refers to as Truths of Reason. In other words, by examining our own minds, we become aware of numerous truths whose opposites are self-contradictory. For example, through thinking, I become aware of the fact that God is a necessary being. Leibniz believes this is an analytic proposition because necessity is contained within the concept of God; in other words, necessity is one of God’s essential attributes. Since necessity is contained within the concept of God, if I negate this statement (and say that “God is not a necessary being”) then I am violating the law of non-contradiction (and essentially saying that “God is not God”). Second, Leibniz also believes that the structure of the human mind mirrors the structure of the metaphysical world, which in turn mirrors the structure of the physical world. Specifically, the mind, the metaphysical world, and the physical world are all structured rationally. Therefore, it follows that we can discover the basic structure of the metaphysical and physical worlds if we understand the basic structure of our minds. This second belief, of course, is an unproven assumption; for this reason, such people as Hume and Kant call Leibniz a dogmatist.

Given these two beliefs, it follows that Leibniz believes that analytic propositions are substantive. Since we become aware of analytic propositions through examining our minds, it follows that analytic propositions are about our mind. But since the mind mirrors the metaphysical and physical worlds, it also follows that analytic propositions are about the metaphysical and physical worlds. In other words, when we discover a Truth of Reason, we discover a truth, not just about our own mind, but also about the universe.

An example will help to better understand Leibniz’s position. Leibniz believes that through mere thinking we can become aware of the principle of the equality of cause and effect. This principle, he holds, is based on the law of non-contradiction and is, therefore, an analytic proposition. This principle does not merely tell us about the mind’s constitution; it also tells us about the universe’s constitution. The universe runs according to this principle, which is corroborated by some of Isaac Newton’s empirically observed laws of motion (The Cambridge Dictionary of Philosophy, “rationalism,” 772).

Hume believes that all a priori knowledge is vacuous. He believes this for two reasons. First, unlike Leibniz, Hume does not believe that the structure of the mind mirrors the structure of the world. Therefore, when I examine my mind and discover a proposition that I know a priori, it follows that this proposition only tells me something about my mind and nothing about the world. Second, Hume believes that, since a priori knowledge is knowledge of propositions whose contraries violate the law of non-contradiction, such knowledge does not really tell us anything. For example, since the proposition that “All triangles have three sides” is essentially the same as the proposition that “All triangles are triangles,” knowledge is obvious and, therefore, does not tell us anything at all, or, at least, does not tell us anything that is useful.