Kant’s Illusion of Synthetic a Priori: Induction Still a Problem

One central problem in the history of philosophy that I find vibrant and unresolved is the problem of induction, generally attributed to the great David Hume. Kant said to have been awakened from his “dogmatic slumber” by the philosophy of Hume. But not all philosophers agree that after being awakened, Kant remained awake for long. At any rate, “What was Kant awakened to?” represents a fundamental question for the present discussion. And a provisional answer is that one of the aspects of philosophy and indeed a feature of the world, we might say, to which Kant was awakened, is causality. By “causality” or “causation” is meant the relation between two events, one being the cause and the other the effect. Hume denied that we can ever perceive cause and effect, nor can we prove it deductively. The reason we think we can, Hume maintained, is that our minds develop a habit whereby we feel impelled to see necessary connections between events in the world. These connections, however, Hume noted, are not as necessary as we might think. In fact, we make the assumption that every event has a cause based upon inductive reasoning. In other words, we assume that events in the future will necessary occur in the same way as we have experienced them in the past because that is the way we have experienced them in the past. This, however, begs the question. The problem is that inductive reasoning does not afford us conclusive proof of causal connections in the world. What we experience, Hume concludes, is but a series of constant conjunction between events. A more important conclusion of Hume’s doctrine is that habit is the foundation of all natural science, and indeed of all human knowledge. Kant’s response to the problem posed by Hume came in the form of an obscure concept known as “synthetic a priori.”

My intent here is to show that not only is there no such a thing as “synthetic a priori”, but that there is no reason to believe that such a concept exists. Perhaps, as I also hope to show in the course of my discussion, Kant arrived at the conclusion that synthetic a priori judgments are possible because he overlooked the relation between linguistic forms and the world, and additionally because he was mislead by the grand architecture of his own intricate philosophical system.  And at the end of this discussion, it will be appropriate to determine whether the problem of induction still stands.

Before we get into an analysis of the meaning and validity of synthetic a priori,   I find it useful to illustrate the philosophical background to which Kant was reacting. Kant saw the history of philosophy hitherto as an intellectual battle between two factions, between rationalists and empiricists. Very roughly, the former believed that thought is an independent source of knowledge, while the latter, conversely, believed that experience is the only way to acquire knowledge. One famous rationalist, Descartes, examined the question of the existence of an external world and the reliability of our senses to acquire knowledge of such a world. In his Meditations on the First Philosophy, Descartes doubts everything that can possibly be doubted to arrive at the one conclusive truth that cannot be denied, and that is the self—I must exist in some form or other because I think. He then uses his conclusion as an epistemological foundation. On the other hand, the empiricist Hume rejected this idea entirely by arguing as follows:

a)      If there is such a thing as the “self,” then we must have an impression or an idea of it—but neither do we have such an idea, nor such an impression. Furthermore, if we want to doubt everything that can possibly be doubted, then we must also doubt the existence of a thinking self. Therefore, we have no grounds to prove the existence of a thinking self, for these might just well be a bundle of perceptions, and

b)      We are wrong to assume that events or properties which occurred in the past will necessarily continue to happen or stay the same in the future, i.e., we have no logical grounds to claim that reason can tell us about causal connections between events and things in the world, and that the “laws” of nature will always be constant.

Hume’s philosophy leaves us with the problem of induction. The implications of Hume’s famous dictum are that metaphysics is impossible, that the possibility to acquire knowledge is impossible, doing philosophy is impossible. In other words, Hume takes empiricism to its logical conclusion.

Before I move to Kant’s response to Hume, I find it helpful to clarify the problem of induction, as Hume saw it. The problem of induction says we assume that all events in the world have causal connections. In other words, people believe that any given event in the world occurs as a result of a previous event, which causes a second event. We make this assumption, Hume proposes, not on logical grounds but out of mere habituation because our reasoning contains the hidden assumption that that events or properties that have occurred in the past will necessarily continue to happen or stay the same in the future; or we presuppose that nature is uniform. Consider gravity, for example. If an object is lifted in the air and then released, one will assume that the object will necessarily fall to the ground. But where do we get this necessity from, and why do we feel impelled to make this assumption? Imagine one who experiences the world for the first time. In the morning he sees the sun is rising at dawn and it is going down at dusk. Now, imagine explaining that the sun must rise every morning and set in the evening by telling him that the sun is rising and setting is an example of regularity. That man would not be convinced and would demand proof. He might ask what makes us so sure that things will not change the next day or even the next minute; that is, what faculty of the mind gives us the certainty of causality? How could we prove our claims? We could give examples such as that for millennia on earth, the sun always has risen in the morning and set in the evening, and gravity has always attracted bodies toward the ground.  We could also add that science can tell us precisely how gravity works. But neither past events, nor science can accurately predict how the future is going to be like. What scientists can do is to study past events and formulate hypotheses about the future. In fact, we might say that what we call knowledge is in reality a probability. Despite the great many observations we may have collected, we cannot know with certainty, or deduce, that the so-called laws of nature will remain constant in the future. Past experience—and not deductive reasoning—suggests to us that gravity will probably work the same way tomorrow.

With regard to knowledge, Hume would say that we set rules that apply to various circumstances, and these rules generate in us strong beliefs. For example, if we play billiards, we may notice that every time the cue ball is hit, we have an expectation or, better yet, a strong belief that upon collision the second ball will roll away. We make a judgment that whenever this happens (what we believe being the cause), a second event is produced, and that is, the cue ball will cause the second ball to move. This judgment arises through reason—and that is, through the application of our beliefs concerning past experiences of cause and effect. In other words, no matter how close we look we can never see or experience causation itself. We make this sort of judgment from past experience because it seems natural to us to assume that if we observe a billiard ball moving toward another, we presume that the only logical result is that ball A will hit ball B and cause it to roll away. But a person who has never been exposed to billiard balls collisions before could just imagine that ball B will not move at all upon collision or that ball A will take off toward the ceiling or stop in front of ball B or even disappear before it gets near ball B. Therefore, so long as there is no contradiction involved, if it is conceivable that ball A could behave differently from what we normally expect, so long as this behavior is not logically contradictory, we are not entitled to assume that the only possibility is that ball B will be moving away from ball A upon collision, and thus that A causes B. the only reason we make this judgment is that we have had numerous experiences of the like in the past and, as a result, we have formed a strong belief that A will always cause B in the future.

One might object that if it were not the case that future events behave like those we have observed in the past, we would not have that idea in the first place—after all, ideas are copied from impressions. But Hume would respond that we cannot possibly say that billiard ball A causing billiard ball B to roll away is necessary. In reality, our mind makes an association of two distinctive ideas; namely, idea 1: one ball rolls onto the table; and idea 2: a different ball rolls onto the table. Furthermore, if we consider idea 1, we may note that it is possible even to break it down into numerous sub ideas. For example, imagine that ball A moves along a distance of a foot onto the table. Now, we should not even assume that the ball continuously and uniformly rolls onto the table. It is possible that the ball performs tiny undetectable movements that we conceive as one uniform motion.  To take a different example, consider the proposition that bread nourishes us today. We still cannot rationally assume that it will do so tomorrow. Another objection that might be raised is that we do know that in the future bread will nourish us because if it did not, then bread would not be bread anymore—that is, we would call it by another name.

But Hume would reply that when one says that “if bread will change, it would not be bread anymore,” one is saying that for some reason bread might change—and that is still an assumption based upon what we are here questioning, causality. That is, one would assume that changing entails causation necessary to stop us from being nourished or for bread to lose its nourishing properties. Therefore, the only difference between a person who has never been exposed to bread or to billiard ball collisions and one who has are the person’s beliefs or expectations. It will not matter how many times and how close we look at events. We will not discover the secret force that caused ball A to move B or discover the property of bread that nourishes or the causal relation between two events. Therefore, this idea of causal relations comes from experience of constant conjunction.

Human belief starts with impressions, produced by direct experience. Thus, ideas are copies, less vivid, of impressions. Also, although we often think of certain concepts as if they were single ideas, in fact they are separate. For example, the idea of a pink unicorn forms in our mind from the idea of pink, the idea of a horse, and the idea of a horn. So, it is our mind that connects ideas and gives rise to resemblance, contiguity, and cause and effect. Therefore, what we call “knowledge” derives from a constant conjunction and association of ideas. The only two forms of knowledge for Hume are “relation of ideas” and “matters of fact.” Relations of ideas are a priori judgments that have no external referents, e.g., mathematical and logical knowledge are example of relations of ideas; they express empty truths, they are tautologies. And matters of fact are those judgments that derive from observations of existing things, i.e., from experience.

Now, since relations of ideas are empty truths, our knowledge derives from experience, which rests upon our belief in matters of fact. But because each idea in our mind is distinct, then the implication is that we cannot even speculate that there is a causal connection between ideas. It follows that we cannot learn even from experience. In fact, causal reasoning cannot be rationally justified. Kant agrees with Hume, on the one hand, that reason cannot help us understand the concept of cause and effect. In fact Kant goes so far as to say that there can be no doubt that knowledge begins with experience. But on the other hand, he does not agree with Hume that the causal relation between events or ideas is a mere result of habit, or an unintelligible stream of separate events. Rather, Kant suggests that this judgment is due to a third source or class of judgment that Hume fails to recognize, and that is the synthetic a priori. In other words, Kant believes that humans possess certain synthetic a priori cognitions, which are the result of the form of our mental apparatuses.

Now before we get deep into the heart of these synthetic a priori cognitions, let us review the traditional two classes of judgments recognized by philosophers until that point. Hume identifies two classes of judgments that Kant accept, though Kant renames them: what Hume refers to as “relation of ideas”, is what Kant calls analytic. The idea of an analytic judgment according to Kant is that by analyzing a statement we discover that the predicate of a sentence, A, belongs to the subject of the same sentence, B; for example, the predicate “unmarried man” is covertly contained in the concept of the subject “bachelor.” Analytic judgments are therefore tautologies, i.e., they are empty truths that do not extend our knowledge. The second type of judgment, which Hume calls “matters of fact”, is referred to by Kant as synthetic. The relevant feature of a synthetic judgments is that the predicate of a sentence, A, is not contained within the concept of the subject of the sentence, B; for example, in the proposition “All bodies are heavy” (A7/B11), Kant says that the predicate “heavy” is not contained in the concept of the subject “body”.  The term synthetic indicates that we perform a synthesis between two ideas, we unify, by taking two independent ideas, a “body” and the “weight”, forming a new concept that extends our knowledge.

But there is a third class of judgment, Kant argues, that Hume overlooked. This type of judgment explains causality—in fact, causality is itself this sort of judgment—and that is synthetic a priori. For Kant it is actually the mind that comes with the knowledge of causality; namely, the mind creates causal connections between objects and events in the world so that we can make sense of it. So, the mind, instead of being, as Locke would put it, a blank slate, is actually more like a furrowed field. Those “furrows” are a priori categories of the mind that produce causality and space and time. Kant believes that our minds contribute to the formation of relations of cause and effect, laws of nature, and the idea of necessary connection. I said “contributes” because our sensory perceptions are given to us by the nature of objects (things in themselves) and by the activity of our mind. But then the question is from what does Kant conclude that we have knowledge of synthetic a priori propositions?  And his answer is that that there exist instances of judgments that are not true by definition, they are synthetic, but at the same time are known prior to experience. This concept of “prior to experience” is taken for granted at this point, but I will need to clarify it in a later section of this paper. At present, let us assume for the sake of argument that it is possible to know something prior to experience.

Some examples of synthetic a priori for Kant are the following:

  1. “7 + 5 = 12” (B15-16) (Indeed for Kant all propositions of mathematics are synthetic a priori)
  2. “The shortest distance between two points is a straight line.” (B16-17)
  3. “Everything that happens has its cause.” (B13/A9)

Let us now see why Kant thinks that the above listed statements are synthetic a priori and determine whether, and why, Hume overlooked the possibility of synthetic a priori. To take proposition 2, for example, Kant maintained that the concept “straight line” is not contained within the concept “the shortest distance between two points”, yet when we think about it, we realize that “a straight line is the shortest distance between two points” is necessarily (analytically) true.  With regard to mathematical statements, Kant says that, for example, “7+5=12” is synthetic a priori. What Kant means is that the concept of 12 or of a dozen things is not contained in the idea of 7+5. Yet, it is necessarily true that “7+5=12.” This necessity, Kant claims, is not due to the fact that 7+5 is logically 12 as in the case of a proposition such as “A triangle is a three-sided figure” where the definition of a triangle is a geometric figure with three sides. Rather, 12 can be obtained in many ways, i.e., 13-1, 8+4, and so forth. According to Kant, what follows from all this is that synthetic a priori propositions are possible. Thus, the concepts of cause and effect, as well as time and space, are all synthetic a priori conditions and not external ideas that the mind strives to attain. They are the shape that the mind gives to experience. Kant agrees with Hume that we cannot form these concepts through experience precisely because we form experience through these concepts.

I think that the foregoing is a fair summary of Hume’s problem of induction and of Kant’s distinction between analytic, synthetic, and synthetic a priori. My next task is to determine whether such distinctions, as proposed and described by Kant, are viable. In the first place, I do not think that Kant’s examples provide any evidence that a dichotomy exists between analytic and synthetic judgments. Worse, I do not think that Kant proves the existence of synthetic a priori, nor do I think such judgments exist.

But let us first consider the alleged analytic/synthetic dichotomy. Consider proposition 1, “All bodies are extended”, which Kant regards as analytic. According to Kant, this is analytic “For I do not need to go outside the concept that I combine with the word ‘body’ in order to find that extension is connected with it.” (B11) In other words, according to Kant a statement is analytic when the statement is true by virtue of the meaning of the concepts of its terms and independently of experience. But how can anything be true independently of experience? “What are ‘concepts’? And in virtue of what are concepts true?” we may ask. In the first place, if one says that the concept of extension, i.e., occupying or taking up space, is contained within, or is synonymous with, the concept of body, we wonder who decides what is or what is not contained in the “concept” of a subject.  As Quine points out in “Two Dogmas of Empiricism”[1] if we rely upon the dictionary definition of a word, in this case the word “body”, we have not explained how the concept of the predicate is contained in the subject. A dictionary is a list of already established synonyms, which is itself hinging upon the notion of synonymy, and thus is circular.  And by the same token, if we look up the term “extension” we do not necessarily find contained within it the concept of “body”.

Secondly, Kant failed to realize that the admission that there are judgments about the world that can be known prior to experience is incompatible with his very definition of analytic judgments, which are judgments of facts about the world that are true independently of experience. That is to say, if an analytic statement or tautology is by definition a proposition devoid of factual content, then that proposition says nothing true or meaningful about the world. Consequently, we cannot speak of the meaning of one concept being contained within the meaning of another concept because the meanings of concepts rely upon experience of objects and events in the world. That is to say, there is a significant difference between the observation that all bodies in the world are extended or occupy space and the statement in quotation marks “All bodies are extended.” The first case is a fact whose meaning is grounded in the nature of the world and in the rules and usage of language. Namely, we observe certain objects in the world and then we ascribe a psychological meaning “body”. Consequently, we are able to make statements such as “All bodies are extended” which we deem analytic because we follow pre-established rules. But the second case, i.e., the bracketed “All bodies are extended” has the same sense, but not the same reference. In fact, the statement contained within the quotation marks does not refer to anything at all, and so it must be treated as a logical truth. In other words, the statement becomes a self-referential logical unit and its parts symbols that can be interchanged one for the other.

Consequently, to understand whether “All bodies are extended” is an analytic proposition, we must treat it as a logical truth. That is, we should be able to interchange its terms without changing its truth. But we have seen that in this kind of statement, the concept of analyticity depends upon the concept of synonymy, which in itself depends upon the concept of synonymy. That is, if “body” is the same as “extension” we should be able to say that this is equivalent to a logical statement of the form A=A, that is, “body” = “extension”. Now, a proposition of the form “A=A” is a mere repetition of the first term. That is, if I say “My book is a book” I merely repeat a statement twice. What I mean in fact—strictly speaking in logical terms—is simply that I have a book or that the object that lies on my desk is a book. Or, I could say that there are objects that we call books in the world or I can point at a book and say “That’s a book.” And there is a sense in which the sentence is synthetic if we take it outside the quotation marks, so to speak, and we say that all objects with pages and covers etc. that we encounter are books.

On the other hand, with a proposition such as “All bodies are extended” we cannot substitute “body” with “extension” because the terms do not refer to the same thing. In order to show that they are synonymous, I must take them outside the brackets and put them in context, and thus the truth or value of this statement would depend upon extra-linguistic factors, i.e., the experience of objects and the fact that objects occupy space, rather than, as Kant would say, upon the meaning of the terms. One may argue that once we have experienced those entities, a sentence such as “All bodies are extended” is immediately understood as a tautology. But if “body” is equal to “extension”, then I must be able to utter “body” to mean “extension”, or vice versa, in order for it to be a tautology. But this is not the case. I suggest that “All bodies are extended” is analytic only in a metaphorical sense because “extension” and “body” can refer to the same thing but differ in meaning.

An even clearer illustration of the problem of analytic statements as defined by Kant is the classic example of the alleged analytic statement “All bachelors are unmarried men.” To argue that this is an analytic statement I have to accept the statement as one that has no factual content. Thus I have to accept the meaning of the terms “bachelor” and “unmarried man” as logically equivalent.  But I can dispute this by saying that the statement is not true if we consider, for example, that a priest is an unmarried man but not a bachelor or a man who has a domestic relation but remains unmarried is not a bachelor. The point is that Kant did not put too much weight on the relationship between language and the world, that is, that if we treat a proposition as analytic we must relate it to the world, but upon doing so we no longer have an analytic proposition. Kant supposes that the sentence itself is true by virtue of the meaning of its concepts and that we need not experience bodies to know they occupy space. But the sentence to be understood requires that one have previous experience of the world and understand the concept of body and extension. So, if I use it to state the rule that equates meanings of bodies with being extended, then I am making an analytic assertion of the form A=A; but if I have to find out whether “body” and “extension” are equivalent, I must necessarily verify the statement empirically, which is contrary to the analytic concept. And as a result, there is a sense in which “All bodies are extended” extends our knowledge. For example, I could use it to assert that there are objects in my room. To reiterate the point of this section about analytic, I would put it as Quine did,

It is obvious that truth in general depends on both language and extra-linguistic fact. The statement “Brutus killed Caesar” would be false if the world had been different in certain ways, but it would also be false if the word “killed” happened rather to have the sense of “begat” hence the temptation to suppose in general that the truth of a statement is somehow analyzable into a linguistic component and a factual component. Given this supposition, it next seems reasonable that in some statements the factual component should be null; and these are the analytic statements. But, for all its a priori reasonableness, a boundary between analytic and synthetic statement simply has not been drawn. (Quine, Two Dogmas, §VI. EMPIRICISM WITHOUT THE DOGMAS)

We next move onto the concept of synthetic, which is also not uncontroversial; that is, based upon Kant’s definition, we also find the notion of synthetic to be obscure. As we have seen earlier, Kant defines a synthetic proposition as one in which the predicate of the subject is not contained at all in the concept of the subject; thus, synthetic statements extend our knowledge by the fact that the predicate of a proposition adds something new or informative to the subject, which cannot be known by virtue of the definition of terms involved. As an example of a synthetic proposition, Kant gives “All bodies are heavy.” A synthetic proposition we have noted is one that is true by virtue of experience and independent of the meaning of its terms. Kant says that in “‘All bodies are heavy’ the predicate is something different from that which I think in the mere concept of a body in general.” (B11)  But as I have indicated earlier with regard to analytic statements, we encounter the same difficulty here with regard to synthetic statements, i.e., who decides what goes into the concept of  “body?” If I say that the concept of extension is what I think when I think of a body, i.e., that a body is defined as that entity which occupy space, then why can’t I define bodies as those entities which have a weight? Could I say that in the world there are bodies that have no weight? The only way to make this statement true is if I take the concept of “body” in a metaphorical sense: “Monads are those bodies which have no weight.”

To be clear, let us use another example. Consider the statement “The Eiffel Tower is 300.65 meters high.” This, according to Kant, is a synthetic statement because I cannot derive the concept of 300.65 meters from the concept of the subject Eiffel Tower. I need to go to France and measure the tower and learn its height. Now, we said that analytic statements are such in virtue of the meaning of their terms. But in order to know the meaning of any term, one must be exposed to the world and learn its meaning. The objection there was that once one has learned the meaning of terms he will recognize that, say, “bachelor” always meant an unmarried man. But by the same token, we can say that once one has learned that the Eiffel Tower is 300.65 meters high, the height of the tower becomes an analytic fact by virtue of definition of Eiffel Tower—i.e., that tower which measures 300.65 meters in height. In other words, once we learn the height of the Eiffel Tower, we know by definition that the Eiffel Tower is that tower which measures 300.65 meters in height. Similarly, once one has learned and experienced bodies in the world, he will then recognize that—by definition—all bodies have weight.

At this point we have demonstrated that the distinction between analytic and synthetic statements is cloudier than Kant wants us to believe; analytic statements are dubiously analytic when they rely on synonymy, (e.g. “A bachelor is an unmarried man”). Also, we have shown that synthetic judgments are not objectively synthetic since no two people would agree upon how a given subject is defined, and therefore a synthetic statement, upon realization, can become an analytic one.  So after clearing the air, we are now ready to turn to the synthetic a priori. We now know what the meaning of “synthetic” entails. However, thus far I have used the term “a priori” without defining it. By and large, philosophers all agree that by “a priori” is meant prior to experience. Kant’s misapprehension on this matter, I believe, is due to his overlooking a simple fact, that is, nothing can be understood independently of previous experience.

Take the proposition “7 + 5 = 12” (B15-16), or any propositions of mathematics, which Kant considers synthetic a priori. Kant says that this proposition is synthetic because the concept of the predicate (7+5) is not covertly contained in the subject (12). At the same time, he also says that the statement is analytic because when 7 and 5 are added up, they necessarily make 12.  But we have to ask, “To what subject and what predicate is Kant referring?” If I put a proposition in quotation marks, as I have illustrated earlier, then there is no subject or predicate. The proposition becomes a self-referential logical unit. The proposition in quotation marks is necessarily analytic because it lacks factual context—it does not refer to entities in the world. In a sense, if I bracket a proposition it is as if I unify the terms as such: sevenplusfiveistwelve. The way to look at such a statement is that I create a singular logical symbol contained within quotation marks that refers to the number “12.” In fact, when I speak of it as a proposition, I do not say “‘Seven and five’ are…”, but rather “‘Seven and five’ is twelve”.

Thus, “5+7” and all mathematical propositions are analytic because they do not refer to anything—they are abstract entities.  Taken as abstract mathematical propositions, these kinds of statements are tautological. If we want to argue that they are synthetic since they extend our knowledge or that we need to count our fingers to find the answer, we must notice that we treat the terms in the sentence as real objects in the world. That is, we have to say something like Joe has a total of 12 apples because he has 7 apples in the bag and 5 apples in the basket. Another example of synthetic a priori judgment for Kant is this: “The shortest distance between two points is a straight line.” (B16-17)  And again, we see that when considered as a logical unit, the statement is analytic, and outside the brackets, i.e., referred to the world may seem synthetic, but it cannot be both at the same time. Similarly, if I say “Time is money” I could trick one into believing that I made a synthetic a priori proposition because the meaning of the concept of “time” is not contained in the meaning of the concept of “money”, and yet the proposition is known to be true by definition! It is clear now that the confusion which leads Kant to thinking that these types of statements are synthetic a priori stems from the fact that he did not realize that when we treat propositions as logical utterances devoid of factual content, we create a self-contained logical system that has no relation to observations of facts and events that occur in the world. Or, to put it another way, Kant overlooked the relation between the logical form of certain propositions and the way they relate to the physical world.

I believe that the propositions of mathematics are the propositions of geometry. Kant believed that geometry was synthetic a priori because it describes space, which for Kant is the form of intuition of our outer sense. But if the geometry considered is the Euclidian type, then a theorem such as “The area of a triangle is base times height divided by two,” which is logically synthetic, should not be confused with the proposition “The area of a Euclidean triangle is base times height divided by two,” which is an analytic proposition. The moral of the story here is that the axioms of a geometry are pre-established rules, and its theorems are the logical consequences of these rules. Thus, a given geometry is a self-contained logical system devoid of factual content, that is, it is not about physical space, but can be used to reason about physical space. Therefore, the axiom “A straight line is the shortest distance between two points,” which is logically synthetic, must not be confused with “A Euclidean straight line is the shortest distance between two points,” which is analytic.  The error that led Kant to believing in synthetic a priori judgments was to use both senses interchangeably. But a proposition can either have factual content, which makes it synthetic, or it can be a logical one, devoid of factual content, and be analytic, but not both.

Hume himself, it has to be noticed, made a similar mistake in his reasoning, in The Missing Shade of Blue. Hume unwittingly hurt his case by showing what he so vehemently tried to reject—that there are innate ideas. His example asks us to imagine a series of shades of blue from the deepest to the lightest, say, Blue-1 to Blue-10, and then remove one shade, e.g., remove Blue-8. Now expose this series of shades of blue to a person who is not acquainted with B-8, though he is acquainted with colors of all kinds. Hume considers it obvious that that person will instantly perceive a blank where B-8 is missing. But this is obviously not true. It is not true because an individual who has been exposed to the world and other colors possesses the experience that allows him to detect that a certain shade is missing. A person who has never experienced B-8, granted such a person exists, is one who has lived in the world and experienced other colors and understands the difference between shades and gradation and colors and missing or not missing. In other words, it does not make sense to speak of making judgments a priori when we operate within a realm of experience.

After having deconstructed Kant’s architecture, we are now able to see that the concept of synthetic a priori is a myth. We have come to a conclusion of this discussion, which, if correct, leaves us with Hume’s problem of induction still unsolved. Unfortunately, Hume’s solution is not very soothing. For if inductive reasoning is founded on the expectation that characteristics of our experience will persist in experience to come, we have no use for inductive reasoning to acquire knowledge of the world. Consequently, for Hume we have to accept that induction is but a mysterious trait of human nature, and as he puts it,

If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion. (David Hume, An Enquiry Concerning Human Understanding §IV, pt I)

Neither Kant nor Popper solved this problem. If anything, Popper tried to dissolve it. And others such as Nelson Goodman have simply discarded it. The positivists concluded that metaphysical propositions were neither true nor false but rather nonsensical; however, the positivists’ own dictum shot itself in the foot upon demonstrating that the propositions of logical positivism too were nonsensical. On the other hand, Karl Popper argued that metaphysical statements are not meaningless statements, but rather not testable or provable. And a further effect generated by the problem of induction is the rise of seriously extreme skepticism perpetrated by postmodernist philosophy.

Kant condemned transcendent metaphysics arguing that human understanding is made in such a way that it always tries to venture beyond the realm of possible experience and to grasp the nature of things in themselves—but our minds do not have the “power” to go beyond the empirical world. And it is for this reason that Kant saw an endless intellectual battle among philosophers. But while Kant admitted that our defective apparatuses constantly attempt to go beyond the limits of possible experience so we get lost in philosophical contradictions, he did not take a cue from this fact and fell back into speculative metaphysics, instead. The problem is, I believe, that Kant wanted to prove that certain concepts are necessary and known a priori; these a priori concepts are according to Kant a bridge between thought and perception. Causality is for Kant a necessary a priori condition for the possibility of experience. But the way Kant tries to prove this is by means of the illusion that synthetic a priori judgments are possible, which we have discounted as a misapprehension of the way language refers to the world. To use Nietzsche’s words,

Kant asked himself: How are synthetic judgments a priori possible?—And what really did he answer? By means of a faculty. “By means of a means (faculty)”—he had said, or at least meant to say. But, is that—an answer? An explanation? Or is it not rather merely a repetition of the question? (Beyond Good and Evil, section 11, Hollingdale translation, p. 23)

Kant showed us that we begin our investigations with an apparatus that is already defective, and yet he attempted to find a rational foundation upon which to base metaphysics, by using the same defective apparatus. A common assumption among philosophers is that Kant’s failure is due to his faith in the valid­ity of Euclidean geometry, Aristotelian logic, and Newtonian physics. But given the era in which he wrote, I think these mistakes are pardonable. One aspect of his philosophy for which we might not forgive Kant is that he was, as Alfred J. Ayer once put it, “duped by grammar”, into thinking that certain propositions that were tautological could also tell us something about the structure of the mind and the world. With regard to the problem of induction, Kant did not resolve it. Perhaps, his contribution inspired ways to dissolve it, and with regard to Kant’s transcendental idealism which purported to rescue metaphysics, I shall submit that it was due to linguistic confusion.

In conclusion, we find ourselves face to face with the uncomfortable implications generated by the problem of induction: that all human scientific knowledge lacks certainty. We also realize that there is no consensus over whether Kant’s response to Hume’s problem succeeds. At any rate, I think that Hume’s problem still stands, though we no longer have to worry so much about its implications. My way of looking at knowledge is to recognize that, as Quine puts it, is a “man-made fabric” that we constantly modify based on our experience. As circular as this may sound, we have no alternative but to find consolation in certain conceptual frames or in one or the other philosophical tradition. At the very least, I trust, the problem left by Hume, reframed by Wittgenstein and by Quine, serves to show the futility of any kind of Metaphysical speculation and the need to direct our philosophical efforts to pragmatism and a special attention to the usage of language and its relation to the world.

[1] Willard Van Orman Quine “Two Dogmas of Empiricism” §II. DEFINITION,


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Astronomical Poem

I was there. I know you don’t believe me, but I saw thousands and thousands of collapsing stars. I traveled fast—faster than light along with tachyons—in fact I was a tachyon. I felt the level of oxygen and I sped through the ozone layer and then up higher onto an unknown galaxy far away from our solar system where the fabric of time bent gently against my body. I took a nap on a large molecular cloud, and was awakened by a wave of gamma rays—and you don’t believe me? I washed my hands into the dark matter of the universe, and watched in awe the gravitational redshift moving upwards, caused by a giant white dwarf below me. I did not see those knobs, though the exquisite fine tuning of the universe would suggest so. I did not see the watch maker. I paused and contemplated the universe’s infinity. All around me, I saw billions of stars exploding and releasing the elements that made your big eyes: why do you think they are bright and beautiful? Each one is made of stardust. Each one is made of different elements from the explosion of stars that lived far away from one another. You are the universe because the universe is in you. And I was there, and I saw thousands and thousands of collapsing stars.