Kant’s Philosophical Method and the a Priori

Contents:

1. The Centrality of a priori Reasoning
2. Kant’s Description of the A Priori
3. Judgments: Analytic and Synthetic
4. A Priori Synthetic Propositions
5. The Methodology of the Copernican Turn as the Method of the Critique
6. Addenda
7. Hume and the A Priori
8. References
9. External Links
10. Notes

The Centrality of A Priori Reasoning

Many outstanding introductory books have been written on Kant and, in many cases, the notion of an a priori proposition or argument serves as an introductory concept for his entire philosophical program. Following the philosophical contributions of Locke, Hume, and Leibniz, the a priori came to be treated as a focal concept in relation to neighboring concepts such as necessity, universality, and deducibility; concepts that are, in turn, integral to the project of determining whether and to what extent knowledge and truth, central concepts in modern and classical philosophy, are truly possible. In Kant’s case, the a priori becomes an anchoring principle in the broader search for knowledge.

Kant begins Preface A (The First Edition) by laying out the central problem/question of the Critique: reason is, by its very nature, compelled to reach ever higher for the first principles of all things. But in doing so, it fnds itself reaching for principles that transcend our experience. Thus, in reaching ever higher on its path to bring unity to our understanding, it loses a necessary basis for doing so: the ready capacity to relate its concepts to objects in our experience. In another way of speaking, one might say that in its search for higher, more comprehensive principles, it inevitably enters the realm of ungrounded speculation.

A contemporary example is Freud’s theory of the unconscious mind. While the theory is tremendously useful and especially so inasmuch as it allows for an internally coherent theory of mental illness, it is nevertheless a speculative theory. One might always take a skeptical stance toward the unconscious and ask, as Popper did,¹ whether there is way to show that there isn’t an unconscious. So long as a theory cannot, in principle, be disproved, we may be in a position of being able to provide explanations, but because it is inaccessible to falsification, it cannot be taken on as a central concept of a scientifically grounded theory. In simple terms, while such a theory provides answers, it does not provide a genuine foundation since it must ultimately be taken on faith. As a second example, we might also bring forward the result of Hume’s skepticism about the immortality of the soul. Inasmuch as its existence is merely founded upon a “faint idea” of our “future condition” (see Hume’s Treatise on Human Nature, I, 3, 9)² it fails to give us an adequate grounding for any claim to truly know its future destiny.

These examples illustrate, as was said, the central problem of the Critique, that while reason is compelled to seek ever higher principes, it must inevitably do so by resorting to principles that transcend experience. This leaves the pretensions of Metaphysics toward being a science particularly in doubt. Kant conceived of Metaphysics as purely involving relationships between concepts.³ Yet, metaphysics has traditionally held out the claim that its conclusions structure and shape the nature of our experience itself, e.g. regarding the existence of the soul or of God or of a free will. The answers to such questions have historically deeply affected not merely our theoretical-scientific experience of the world, but also the ethical and political ideas that structure our social institutions. Perhaps of equally great or greater historical significance is the fact that such disagreements have been a perennial source of social and inter-societal conflict. Thus, it appears that clear, well founded answers to the questions Metaphysics poses should be regarded as a desirable; yet, the entire field of investigation as such may be called into question. Thus, the “critical” question poses itself: “Is metaphysics possible?” and if so, how? Inasmuch as metaphysics is properly the domain of pure reason the critique of pure reason is the critique of metaphysics.

His proposed answer lies in a change in methodology, which has come to be known as his “Copernican turn.” Its “maxim” or guiding precept runs as follows: “we can know a priori of things only what we ourselves put into them” (Bxviii). As Kant points out in Preface B, it is a method that originated in geometry before it was applied to physics. It is one that entirely does away with enumerative induction as a “way up” to principles. By formulating our (hypothetical) principles first and then running experiments to discover whether nature is consistent with them we are able to progress toward the confirmation of our theories of the natural world that can, in turn, be extended toward a consistent system of concepts—a “science” as the Aristotelian tradition would have it.

This procedure has as he writes, allowed Physics and Mathematics to find themselves on a sure path toward the advancement of knowledge (see Bxiii). Why not then apply it to Metaphysics? As he tells us, the opposite procedure, that of attempting to gather a priori concepts from the objects of our experience must end in failure (Bxvi) since (as Hume emphasized) experience by itself can never yield principles with a claim to universality or necessity.⁴

The guiding thread of the Critique as a whole is, in fact, to uncover whether Metaphysics might, in a way similar to physics and mathematics, be able to find itself on a reliable path, by the same method. The lesson Its application to physics teaches us is that any general ideas drawn from experience may, in fact, serve to mislead our intuitions about must be true. This was shown when Galileo famously dropped two balls of unequal weight from the Leaning Tower of Pisa and when Copernicus proposed that the sun does not go around the earth, but the earth around the sun. The lesson may be stated simply in different terms as the maxim that reason, in its attempt to bring unity to our experience, and not the senses must guide our way in the development of scientific knowledge.

Thus, we return to the theme of the centrality of a priori concepts since they alone can provide the basis for any assured progress along the path toward the continued growth of knowledge and understanding. Since the project of explicating how a priori concepts relate to our capacity to reason and understand in relation to the development of a science is central to the Critique, it becomes an important initial concept for acquiring a sense of its argument.

Kant’s Description of the A Priori

Kant gestures early on toward the a priori in the “Preface to the First Edition.” There his description of what he takes the Critique of Pure Reason to accomplish shows that it is motivated by a need for a renewal of the search for a truly reliable basis for knowledge; in fact, for the discovery of a justification of rationality in general, with all of its humanistic aspirations. The Critique is

…a call to reason to undertake anew the most difficult of all its tasks, namely, that of self-knowledge, and to institute a tribunal which will assure to reason its lawful claims, and dismiss all groundless pretensions, not by despotic decrees, but in accordance with its own eternal and unalterable laws. This tribunal is no other than the critique of pure reason. I do not mean by this a critique of books and systems, but of the faculty of reason in general, in respect of all knowledge after which it may strive independently of all experience.”

A xii

It may be noticed that Kant regards his critique in terms of the “self-knowledge” of reason, a term that may evoke the critical Socratic search for self-knowledge, Descartes’ methodical doubt, or even Kant’s own essay “What is Enlightenment“⁵ where he characterizes its spirit in terms of a willingness to use the light of one’s own reason in order to sift one’s beliefs. Certainly, knowledge founded on a priori principles could be used to underwrite such confidence. But Kant is not merely interested in the critique of books or systems as he tells us, but seeks a foundation for the use of one’s reason in “the faculty of reason in general.” with the phrase (at the end of the quotation ), “knowledge after which it may strive independently of all experience” we arrive at a preliminary definition of what Kant himself means by the term “a priori” that takes us directly into the connection between the a priori and the kind of knowledge that can be characterized as “a priori.”

Kant goes on to tell us that for anything we know to be qualified as a priori it must be “absolutely necessary” [A xv]. Futhermore, it must

serve as the measure, and therefore as the supreme example, of all apodeictic (philosophical) certainty.

Axv

The platinum-iridium bar stored in Paris that serves as the international standard of measurement for the meter was instituted in 1790 (the first edition of the Critique was published in 1781), but the concept may well have influenced Kant in writing this remark. But, of course, he will eventually appeal to a yet higher standard, the operation of our understanding itself. In either case, however, there is a sense of foundational knowledge to which Kant is driving us, especially where the project of a critique of reason in general is concerned.

In section II (B4) of the Introduction, he goes on to say that any a priori principle must also pass the test of strict universality and necessity:

Empirical universality is only an arbitrary extension of a validity holding in most cases to one which holds in all, for instance, in the proposition, ‘all bodies are heavy.’ When, on the other hand, strict universality is essential to a judgment, this indicates a special source of knowledge, namely a faculty of a priori knowledge. Necessity and strict universality are thus sure criteria of a priori knowledge, and are inseparable from one another.”

B4

These are the two touchstones of genuinely a priori knowledge. With necessity, it might be said, we are given the requirement that what is said must always be true if it is to count as a priori true; and with the condition of strict universality we are given the added condition that what is claimed must be true in every case/every instance of a subject. Because in some cases it may be easier to apply either strict universality or necessity as a criterion, Kant writes that it may be “advisable to use the two criteria separately, each by itself being infallible” [B4]. If either criterion for justification can be applied, the other will follow.

This criteria comes into their own once they are applied to arguments such as modus ponens and modus tollens. For example, consider the proposition, “if there is a line, there is a point.” In this example, we have a case of a statement that can be held to be necessarily true (always, in every case) because the proposition “All lines are made up of points” is universally true. By modus ponens, if we suppose that there is a line (that this is a true statement), it immediately follows that there must also be a point. Because of the way in which Euclidean geometry defines a line (as being made up of points, of requiring at least two points) the conclusion, that there is a point, will follow with certainty. Additionally, there is no need to go looking for instances of lines in our experience to confirm this result. It follows, as we might say, by virtue of the meaning of the terms alone. Its truth may be known independently of any experience and, indeed, prior to any experience to inasmuch as geometry is applied to our experience.

Furthermore, no appeal to experience is necessary to justify its claim to truth. Because it is based upon a particular definition of “line” introduced by Euclid himself (a line is a succession of points) the claim that where there is a line there is a point can hardly fail to be true with strict universality and necessity whenever the definition of line is assumed to be true. By contrrast, a statement such as “All swans are white,” an example of an a posteriori claim, is neither “absolutely necessary” nor justifiable prior to experience, nor even strictly universal, because the only appeal it makes for its justification is to our experience. The world of our experience cannot, because it is mutable, be used to justify statements of merely factual, empirical accuracy as strictly necessary or universal.

This naturally brings up the question of the ultimate basis for the justification of a priori claims. It appears from what has been said that experience will not suffice. Hence, it would seem that the creation of ad hoc definitions must be our best source. Nevertheless, such definitions, however useful they may be, do not, in turn, appear to have any justification beyond themselves, unless an appeal is made to some version of the Platonic forms. This is where the genius of Kant’s solution enters persuasively: the basis for our capacity to know anything a priori is finally based upon our very capacity to reason about the world in general. Regardless of the content of the proposition, any argument of the form

1. P —-> Q
2. P
3. /Q

Will necessarily generate for us the same response. Any denial of the conclusion would result in a contradiction, indicating something contrary to reason. This kind of result may well have been an intuitive “spark” or as he appears to phrase it, “clue” for Kant, motivting his attempt to discover whether our intellectual capacity has any internal principles of its own operation. Indeed, Kant does make his notion of a transcendental logic the foundation for his development of the “functions of the understanding” in relation to the possible forms a proposition might take in the opening sections of his Analytic of Concepts (see B94 in particular).

Judgments: Analytic and Synthetic

Let’s begin discussing this topic by looking at the concept of a judgment itself. A judgment for Kant is a proposition (a statement that may be either true or false) in subject-predicate form (A is B). the predicate might belong to the subject by virtue of an identity (all bachelors are unmarried men), a class-inclusion relationship (All cats are animals), or by virtue of being an observed property of the subject to which it is joined (All bovine creatures are hoofed animals). An a priori judgment will be a proposition in which the predicate belongs to its subject term necessarily and with strict universality (always and in every case).

An analytic judgment is formed when the predicate belongs to the subject by virtue of being contained in its “concept,” or intension (the meaning attributed to the subject). Returning to the example, “All lines have points,” a point may be regarded as contained in the intension of “line” since the term “line” is defined in Euclidean Geometry as a series of points. It is thus “analytically” true to say that all lines have points simply by virtue of an analysis of the meaning of the subject term.

Synthetic judgments are by contrast “ampliative”: their justification requires going beyond the mere concept of a term in forming a judgment about its truth value and thus an “extension our knowledge” in a real sense. For example, the truth value of a proposition such as “No Canadian Geese are found south of Mexico” could not be known simply by virtue of an analysis of the concept “Canadian Goose.” The fact is that the migratory patterns of Canadian Geese are variable and subject to chance. All judgments that are based upon experience or that may only be possibly true are ampliative in this sense and may be considered synthetic. Thus, “All swans are white” is a synthetic proposition. Thus, the distinction aligns with the Kant’s strict sense of the a priori since those that are synthetic must be non-analytic: because they involve a posteriori truth claims taken from experience. Nevertheless, Kant argues that some propositions may be both a priori true and nevertheless synthetic–an apparent contradiction in terms.

A Priori Synthetic Propositions

An apparent contradiction in terms? Yes, because anything that can be considered an priori true proposition must be always true and true in every case. But synthetic propositions are apparently propositions that are ampliative–they must involve some appeal to experience to certify their truth and, as was mentioned above, such propositions may not always be true and in every case.

Nevertheless, Kant argues that some propositions are both a priori and synthetic–whose justification requires that they be genuinely ampliative in the above sense of the term. One example is “The shortest distance between any two points is a straight line.” Another is, “Every alteration has its cause.” This proposition is intuitively true in every case: even if the empricist-skeptic feels inclined to wonder whether the sun will rise tomorrow, it would not suspend the law of causality. We would likely wonder what might have caused such an occurrence.

Furthermore, the statement is ampliative. Questioning its truth value takes us into the empirical world of facts and events and out of the realm of concepts and meanings. And yet it appears to make a certain and evident claim about the uncertain and inconstant world of facts and events. It somehow rises above the difficulty that besets any attempt to draw a universal principle from our observation of facts or events, the factual truth of their very universality. It is important to see what is at stake here: Kant is contesting his predecessors. He is contesting the line drawn between claims about facts and relations between ideas. He is attempting to point out a limitation in their reasoning, that of the recognition that some genuinely a priori ideas may be applied to experience. And if that is the case, we may ask how that may be so and in virtue of what capacity within us.

The Methodology of the Copernican Turn as the Method of the Critique

Kant’s discussion of the Copernican Turn primarily concerns a shift in methodology that brought about the scientific revolution: the technique of proposing our own answers to our questions about the natural world before testing them for confirmation. For the development of geometry, this meant stating clearly what was necessarily implied in concepts formed a priori, and then applying it to reasoning with figures. The procedure was sanctioned by the realization that if the geometer was “to know anything with a priori certainty he must not ascribe to the figure anything save what necessarily follows from what he himself has put into it in accordance with his concept.”⁶

It may be argued that this very method becomes the methodological underpinning of the Critique itself. We might reflect that, in a sense, the supposition that the mind has a priori (in the sense of being first in the order of knowledge) concepts that structure its operation is an operation Kant has performed upon the mind itself: he has formulated certain a priori concepts concerting our cognitive processes, giving structure to what would otherwise have been a mass of unstructured phenomena from an empirical point of view. Thus, he does to our understanding of the mind what he ascribes to his early geometer who enacted an “intellectual revolution–far more important than the discovery of the passage round the celebrated Cape of Good Hope.”⁷

The picture begins to attain even greater clarity and perspective once we compare what he says concerning the application of the same method to physics to his treatment of concepts. When Torricelli and Galileo performed their experiments, they did not do so in the spirit of empirical discovery–as if their experiments were furthering our experience of the world to help us reach more general conclusions about it; rather, as Kant writes, “They learned that reason has insight only into that which it produces after a plan of its own.”⁸ Thus far, Kant is being consistent in the application of what he rightly takes to the substance of the intellectual revolution he is describing. He does, however, take small step further toward what might be seen as a more distinctively Kantian direction. In Bxiii-xiv he writes,

Even physics, therefore, owes the beneficent revolution in its point of view entirely to the happy thought, that while reason must seek in nature, not fictitiously ascribe to it, whatever as not being knowable through reason’s own resources has to be learnt, if learnt at all, only from nature, it must adopt as its guide, in so seeking, that which it has itself put into nature.”

Critique of Pure Reason, Bxii-xiv

In terms of his own methodology, Kant follows the guidelines of the intellectual revolution discussed above when he goes on to discuss the forms of our perception and categories of our understanding in the Transcendental Aesthetic and Transcendental Logic. That is to say. he (Kant) supplies principles devised by his own reasoning in order to explain the phenomenon of our capacity for a priori knowledge and does so by the same conjectural method used by Galileo, Torricelli, and the geometers that preceded them. He first notices that we do, in fact, have a capacity to make a priori judgments and then provides what is in effect a hypothesis that explains how such judgments can be possible.

His answer is one based upon argumentation, but is nevertheless one devised by his own reason, just as Copernicus’ was. He conjectures that the categories of our understanding and forms of our perception are the ultimate bases of the intelligibility that the mind brings to sensory intuition and argues, in effect, that they are both necessary and conjunctively sufficient to explain our capacity for a priori knowledge. Read in this way, Kant may be seen as an advocate for his solution, but not one who has posed it in the spirit of dogmatism; rather, he poses the forms of perception and categories of understanding as a contribution to the process of conjecture and refutation.

Addenda

Hume and the A Priori

Section IV, Pt. 1, of Hume’s Enquiry Concerning Human Understanding explicates the relationship between relations of ideas and matters of fact to a priori reasoning. Relations of ideas and matters of fact align with the Leibnizian distinction in Monadology 33 between truths of reason and truths of fact. The interest in returning to Hume’s text in particular is the way in which it echoes many of the points discussed above. It shows a series of points in the dialectic to which Kant is directly responding in a way that shows him to have been well aware of Hume’s text.

Relationships between ideas encompass “every affirmation which is either intuitively or demonstratively certain.” Hume gives as an example of relations of ideas the relationship between numbers or an axiom of geometry. In the case of matters of fact, he notes a primary difference: the contrary of matters of fact is always possible, “because it can never imply a contradiction.” We cannot, he writes, any more infer a contradiction from the statement, “the sun will not rise tomorrow” than from the assertion that it will. He furthermore writes that “All reasonings concerning matters of fact seem to be founded on the relation of cause and effect” and that no a priori reasoning can be attained from our experience concerning matters of fact.

We have here the basis for a distinction between two ways of knowing based upon deducibility. That is, we can apply modus ponens as a test to discover whether a particular proposition is an a priori one based upon whether it implies a contradiction.

But the key to this distinction lies in the necessity or contingency that is held to attend the consequence of any statement assumed to be true. Thus, we might argue the contrary of the proposition “If a match is lit, it will produce heat,” without contradiction, since the consequent, “it will not produce heat” follows as a merely contingent, not a necessary truth and this has everything to do with the kind of truth that is expressed in the statement. Hume would argue that one statement is just as valid as the other because the truth value of the conditional expresses a merely factual, contingent truth, due to the fact that the antecedent and consequent are related as facts of experience. To make this explicit, one might write, “If P is factually true in relation to Q, then Q is contingently true.” From factual truths only contingent truths follow. This is another way of expressing the equally Humean claim that no a priori principle will result from any amount of reasoning regarding matters of fact.

Nor can we reason a priori from relations of ideas to matters of fact:

When we reason a priori, and consider merely any object or cause, as it appears to the mind, independent of all observation, it never could suggest to us the notion of any distinct object, such as its effect, much less show us the inseparable and inviolable connection between them. A man must be very sagacious who could discover by reasoning that crystal is the effect of heat, and ice of cold, without being previously acquainted with the operation of these qualities.

Section IV, Pt. 1, of Hume’s Enquiry Concerning Human Understanding

When we look at how these distinctions line up, the appearance of circularity rises to the surface: truths of fact are only contingently true, hence they cannot be necessary. They are not necessary because they involve matters of fact, which can only be contingently true. The ultimate reasoning behind this kind of argument is the reasoning that while ideas do not change, matters of fact, facts of experience can and do. Hence, if we are to look for the essential core of this distinction, it is probably to be found in the idea expressed at outset that what truly characterizes the a priori as such is not only its universality, but its claim to being always true.

References

• Immanuel Kant, Immanuel Kant’s Critique of Pure Reason (1929), trans. Norman Kemp Smith, Bedford/St. Martin’s Press, Boston, 1965. Available online here.
  • “What is Enlightenment?” in The Philosophy of Immanuel Kant, ed. Carl J. Friedrich, Random House, 1993 pp.145-154.
• Karl Popper, “The Problem of Demarcation (1974),” Popper Selections, ed. David Miller, Princeton University Press, NJ, 1985, pp. 118-130.
  • The Logic Of Scientific Discovery (1935), Routledge, 2002.
• David Hume, Treatise of Human Nature (1739), Oxford University Press, 1975.
  • An Enquiry Concerning Human Understanding, in The Empiricists, Anchor Books, 1974.
• Quine, W. V. O. (1961). “Two Dogmas of Empiricism”. The Philosophical Review. 60 (1): 20–43. Reprinted in his 1953 From a Logical Point of View. Harvard University Press.
• Locke, John. The Works, vol. 1 An Essay concerning Human Understanding Part 1. Rivington, 1689.

External links

• Kant’s The Critique of Pure Reason
• The German Edition of the Critique (Felix Meiner Verlag)
• “What is Enlightenment?“
• Popper’s The Logic of Scientific Discovery
• Quine’s Two Dogmas of Empiricism
• Locke’s Essay Concerning Human Understanding

Notes

1. See Popper’s further remarks in “The Problem of Demarcation” where we find him writing as follows: “There may be lots of people who are Freudian or Adlerian cases: Freud himself was clearly a Freudian case, and Adler an Adlerian case. But what prevents their theories from being scientific in the sense here described is, very simply, that they do not exclude any physically possible human behavior. Whatever anybody may do is, in principle, explicable in Freudian or Adlerian terms.” Perhaps the point may be illustrated by an anecdote that is sometimes attributed to Freud. Regarding the significance of his cigar smoking, he is supposed to have said, “Sometimes a cigar is just a cigar.” But indeed how would one properly demarcate the cases (taking Popper’s point into account)? When do we know we have encountered the symptoms of a neurotic fixation? ↩︎
2. In Hume’s Treatise, T 1.3.9.13, SBN 113-4, we find him writing the following concerning our true knowledge of the future state of the soul: “As belief is an act of the mind arising from custom, ’tis not strange the want of resemblance shou’d overthrow what custom has establish’d, and diminish the force of the idea, as much as that latter principle encreases it. A future state is so far remov’d from our comprehension, and we have so obscure an idea of the manner, in which we shall exist after the dissolution of the body, that all the reasons we can invent, however strong in themselves, and however much assisted by education, are never able with slow imaginations to surmount this difficulty, or bestow a sufficient authority and force on the idea. I rather choose to ascribe this incredulity to the faint idea we form of our future condition, deriv’d from its want of resemblance to the present life, than to that deriv’d from its remoteness.” ↩︎
3. In the Preface to the Second Edition, Bxiv, we read, “We come now to metaphysics, a purely speculative science, which occupies a completely isolated position and is entirely independent of the teachings of experience. It deals with mere conceptions—not, like mathematics, with conceptions applied to intuition—and in it, reason is the pupil of itself alone. It is the oldest of the sciences, and would still survive, even if all the rest were swallowed up in the abyss of an all-destroying barbarism. But it has not yet had the good fortune to attain to the sure scientific method” (Meikeljohn trans.) ↩︎
4. It is worth considering that Popper arrives at the same conclusion regarding statements that may be admitted into an empirical science. In The Logic of Scientific Discovery, p. 18 we find him writing, “Now in my view there is no such thing as induction. Thus inference to theories, from singular statements which are ‘verified by experience’ (whatever that may mean), is logically inadmissible. Theories are, therefore, never empirically verifiable. If we wish to avoid the positivist’s mistake of eliminating, by our criterion of demarcation, the theoretical systems of natural science,” then we must choose a criterion which allows us to admit to the domain of empirical science even statements which cannot be verified.
   
   But I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience. These considerations suggest that not the verifiability but the falsifiability of a system is to be taken as a criterion of demarcation. In other words: I shall not require of a scientific system that it shall be capable of being singled out, once and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific system to be refuted by experience.” Falsifiability is, in other words, another way to think about Kant’s strategy.” ↩︎
5. The opening paragraph of Kant’s “What is Enlightenment” runs as follows: “Enlightenment is man’s emergence from his self-imposed immaturity. Immaturity is the inability to use one’s understanding without guidance from another. This immaturity is self-imposed when its cause lies not in lack of understanding, but in lack of resolve and courage to use it without guidance from another. Sapere Aude! “Have courage to use your own understanding!”–that is the motto of enlightenment.” It should be remarked that there is much in the two prefaces to the Critique that exemplifies a humanistic faith in the light of reason to guide us beyond tradition and take us into new frameworks for understanding. Not least is the example of the Copernican turn itself, which is based upon a move to let reason, not the senses, to take the lead regardless of whatever the senses might appear to confirm as pre-theoretically intuitively true (see further remarks in the first section). ↩︎
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