Editorial Note:

This was the Senior Thesis of David Samra at the University of New Hampshire.

Popper on the A Priori

by David Samra

Karl Popper was both a lifelong student and advocate of Immanuel Kant. The chapter on Kant within Popper's Conjectures and Refutations (Ch. 7) is more than enough to prove Popper's admiration. However, included in this chapter and many of Popper's other works, he rejects Kant's concept of synthetic a priori knowledge on the grounds that Kant created an impossible category of unfalsifiable knowledge. Is this rejection of Kant's synthetic a priori knowledge justified? In the following, I evaluate Popper's position on synthetic a priori knowledge and reveal its difficulties. This essay is divided into three sections. The first section will elucidate Popper's position in detail, and describe its problems. The second will analyze Popper's criticisms of Kant and refute them. In the final section, I will offer an amendment to Popper's position, which will reconcile Popper's criticisms with Kantian philosophy, where the doctrine of falsification finds its origin.


Popper's critique of the synthetic a priori begins with his interpretation of the Critique of Pure Reason:    in response to Hume's devastating critique of induction (well-renowned for waking Kant from his "dogmatic slumber") and the apparent successes of Newtonian Mechanics, Kant strove to justify inductive inferences (and therefore scientific methods) via an argument that was not itself inductive. Popper does not believe Kant is successful in his project:

Kant tried to force his way out of this difficulty by taking the principle of induction (which he formulated as the 'principle of universal causation') to be 'a priori valid'. But I do not think that his ingenious attempt to provide an a priori justification for synthetic statements was successful. (Logic of Scientific Discovery, 29, emphasis mine 1)

How did Kant fail, according to Popper, and why? Popper's rejection of Kant's synthetic a priori claims comes from two sources:  Popper's own fallibilism doctrine and Kant's alleged (by Popper) a priori justification of Newton's laws. Fallibilism, at least according to Popper, is inconsistent with synthetic a priori knowledge in principle, and uses the a priori justification of Newton's laws in Kant's Metaphysical Foundations of Natural Science as evidence of unfalsifiable synthetic a priori statements.

The term 'fallibilism' generally refers to the theory that no belief can be so well justified or supported by good evidence and apposite circumstances that it could not be false. Popper's particular brand of fallibilism is not much different, except for his emphasis on the justification of beliefs through the scientific method.

Falsificationists (the group of fallibilists to which I belong) believe... that they have discovered logical arguments which show that the programme of the first group [the verificationists]2 cannot be carried out:  that we can never give positive reasons which justify the belief that a theory is true... we falsificationists believe that we have also discovered a way to realize the old ideal of distinguishing rational science from various forms of superstition... the rationality of science lies not in its habit of appealing to empirical evidence in support of its dogmas -- astrologers do so too -- but solely in the critical approach:  in an attitude which, of course, involves the critical use, among other arguments, of empirical evidence (especially in refutations). (Conjectures and Refutations, 310; bold emphasis mine)

In the above passage, Popper explains the rationale for his beliefs. Fallibilism, for him, is the epistemological doctrine that best explains how contemporary science provides knowledge without resorting to dogmatic beliefs (i.e. faith). All beliefs include falsehoods we may or may not be unaware of, which renders the quest for certainty impossible. When we become aware of a false belief, we consequently become aware of our capability for belief in falsehoods, and are reminded how much more we have to learn.

Popper's fallibilism can account for why Einstein's replacement of Newtonian Mechanics stimulated so much progress in physics, a field that some of his contemporaries had once thought nearly finished. Popper points to the beginning of World War I, when even physicists as renowned as Henri Poincaré believed Newton's theory was true and irrefutable (Conjectures and Refutations, 258). Fallibilism, for Popper, explains the existence of scientific progress - the continual discovery of our own ignorance and quest for the truth. Scientific progress is possible because new theories account for new (or sometimes, old) empirical evidence, which earlier scientific theories could not. In this fashion, Popper's fallibilism describes the gradual evolution of knowledge, where new knowledge is built upon the bedrock of old, falsified knowledge:

It so happens that the real linchpin of my thought about human knowledge is fallibilism and the critical approach; and that I see... that human knowledge is a very special case of animal knowledge. My central idea in the field of animal knowledge (including human knowledge) is that it is based on inherited knowledge. It is of the character of unconscious expectations. It always develops as the result of modification of previous knowledge.

...human knowledge... may be formulated in language, in propositions. This makes it possible for knowledge to become conscious and to be objectively criticizable by arguments and by tests. In this way we arrive at science. Tests are attempted refutations. All knowledge remains fallible, conjectural.

...we learn by refutations, i.e., by the elimination of errors, by feedback. (Realism and the Aim of Science, xxxv, bold emphasis mine)

Since humans can only eliminate errors, Popper believed all knowledge is an approximation to the truth. In his later years, he coined the term "verisimilitude" to express the idea of theories with greater (or lesser) degrees of correspondence with reality (Conjectures and Refutations, 315).

Additionally, in the above passages, Popper loosely defines "dogma" as a theory or belief accompanied by an attitude that denies or ignores counter-arguments and refuses criticism, especially contrary empirical arguments. Popper contrasts dogmas with "the rationality of science", which he believes concurs with his fallibilist doctrine. Thus, any belief considered infallible is a dogmatic belief, because the dogmatist refuses to allow any possibility of error within his belief. Even logical truths are fallible to the extent that we may err in judging whether a truth is analytic or demonstrated to be proof valid.

At first glance, fallibilism would appear to be consistent with the belief in synthetic a priori knowledge. A synthetic statement is one that can be denied without contradiction; an a priori proposition is one that can be justified independently of experience. It follows that false a priori propositions are necessarily false, and true a priori propositions are necessarily true. Analytically true statements, in contrast to synthetic statements, cannot be denied without contradiction; therefore, analytic a priori propositions are always necessarily true. A synthetic a priori statement makes a claim to the same kind of truth-value as analytic a priori statements (i.e., necessarily true), but synthetic statements are not true by definition and, for that reason, they must be demonstrated to be true. Since synthetic statements must be shown to be true outside of definitional knowledge (which is analytic), our synthetic knowledge is mediate and subject to error or revision. Therefore, it would seem that belief in synthetic a priori statements is not inherently dogmatic, even though their truth value is independent of experience.

So why does Popper reject synthetic a priori statements, if there is no inherent contradiction between fallibilism and synthetic a priori knowledge? Popper believes that the synthetic a priori is, at best, merely a disguise for induction:

...I found that it was not the principle of causation (as he [Kant] thought) among his synthetic principles a priori which was decisive [toward solving Hume's problem of causation], but the way he used it; for he used it as a principle of induction.

Induction, Hume had shown, was invalid because it led to an infinite regress. Now, in the light of Kant's analysis (and my rejection of a priori valid synthetic principles) I was led to the formulation:  induction is invalid because it leads either to an infinite regress or apriorism. (Objective Knowledge, 86)

It is worth noting here that Popper mentions his rejection of "a priori valid synthetic principles" before he formulated his own case against induction. This suggests Popper has other reasons for rejecting the synthetic a priori (which will be discussed in Section 2). However, as I will discuss shortly, Popper's criticism of Kant's attempt to give Newtonian Mechanics an a priori justification is still Popper's major motivation to reject the synthetic a priori. Still, it is not entirely clear how Popper reaches this conclusion. He does not adequately explain his assertion that the synthetic a priori is unfalsifiable dogma in all situations (in Section 2, I will point to this belief as Popper's mistake in his analysis of Kant). The most important hint from the above passage is Popper's claim that synthetic a priori knowledge is an epistemological fallacy (i.e. dogmatism), like infinite regress. He concludes that induction is invalid because it is caught in a dilemma between infinite regress and apriorism (a dogma within an a priori principle).

I claim fallibilism is not inherently inconsistent with synthetic a priori knowledge. Nevertheless, Popper rejects synthetic a priori knowledge on a charge of inconsistency with his particular fallibilist doctrine:

...the principle of induction would have in any case to be treated as a non-falsifiable statement. For if this principle - which is supposed to validate the inference of theories - were itself falsifiable, then it would be falsified with the first falsified theory, because this theory would then be a conclusion, derived with the help of the principle of induction... But this means that a falsifiable principle of induction would be falsified anew with every advance made by science. It would be necessary, therefore, to introduce a principle of induction assumed not to be falsifiable. But this would amount to the misconceived notion of a synthetic statement which is a priori valid, i.e. an irrefutable statement about reality. (Logic of Scientific Discovery, 254)

Popper claims synthetic a priori beliefs are dogmatic because they entail their own infallibility; which shows synthetic a priori statements to be absurd. Why does Popper make such an argument? Before answering this question in detail, I submit this interpretation of synthetic a priori knowledge is too narrow, and his focus on Kant's Metaphysical Foundations of Natural Science3 overlooks the notion of the regulative use of reason in the Critique of Pure Reason. As discussed later in this section, Popper uses Kant's attempt to give a priori validity to Newtonian Mechanics as a counterexample to the notion of synthetic a priori knowledge. Contrary to Popper's philosophical position, however, accepting synthetic a priori knowledge does not necessitate a dogmatic approach to science. I hope to make this point sufficiently clear.

Popper's first step toward rejecting any theory is to see if it is inconsistent with his fallibilism, as illustrated in this quote:

...if we adhere to our demand that scientific statements must be objective, then those statements which belong to the empirical basis of science must also be objective, i.e. inter-subjectively testable. Yet inter-subjective testability always implies that from the statements which are to be tested, other testable statements can be deduced. Thus if the basic statements in their turn are to be inter-subjectively testable, there can be no ultimate statements in science:  there can be no statements in science which cannot be tested, and therefore none which cannot in principle be refuted, by falsifying some of the conclusions which can be deduced from them. (Logic of Scientific Discovery, 47)

Popper's claim that science has no ultimate statements explains his rejection of inductivist procedures, since, by his own account, inductivist procedures rely on basic statements as ultimate statements. Basic statements, according to Popper, are

...those statements which are reducible to elementary (or 'atomic') statements of experience - to 'judgments of perception' or 'atomic propositions' or 'protocol-sentences' or what not. (ibid., 35)4

The process of induction requires these elementary statements because, by most accounts of the contemporary empirical positivists of Popper's time, scientific theories produced by induction must be based on5 elementary propositions of experience or else they are meaningless. Elementary propositions of experience ultimately provide the verification of scientific theories. Without empirical verification, a theory is non-scientific and, according to logical positivism, meaningless.

This 'shows itself' very clearly in the case of Wittgenstein, according to whom every meaningful proposition must be logically reducible to elementary (or atomic) propositions, which he characterizes as descriptions or 'pictures of reality' (a characterization, by the way, which is to cover all meaningful propositions). We may see from this that Wittgenstein's criterion of meaningfulness coincides with the inductivists' criterion of demarcation, provided we replace their words 'scientific' or 'legitimate' by 'meaningful'. (ibid., 36)6

However, positivists fail to see the implications of their own project:

For scientific laws, too, cannot be logically reduced to elementary statements of experience. If consistently applied, Wittgenstein's criterion of meaningfulness rejects as meaningless those natural laws the search for which, as Einstein says, is 'the supreme task of the physicists':  they can never be accepted as genuine or legitimate statements. (ibid., 36)

Popper's argument that scientific laws cannot be logically reduced to elementary statements of experience has been frequently used against logical positivist accounts of science. Carl Hempel, after the Logic of Scientific Discovery, would eloquently express this idea in Problems and Changes in the Empiricist Criterion of Meaning.

The verifiability requirement rules out all sentences of universal form and thus all statements purporting to express general laws; for these cannot be conclusively verified by any finite set of observational data. And since sentences of this type constitute an integral part of scientific theories, the verifiability requirement must be regarded as overly restrictive in this respect. (Problems and Changes in the Empiricist Criterion of Meaning, §2.1)

Thus elementary propositions of experience serve as ultimate statements for verificationist procedures, and are rejected by Popper.7

As noted above, Popper mistakenly believes "induction is invalid because it leads either to an infinite regress or apriorism." Kant sought to offer an alternative to the infinite regress resulting from the inductive justification for induction, according to Popper's reading, and believed he could save induction through the synthetic a priori. However, Popper has the same conclusion about synthetic a priori knowledge as knowledge provided by verificationist procedures. Therefore, for Popper, synthetic a priori statements appear to be more than just necessary propositions, independent of experience, which can be denied without contradiction. A synthetic a priori statement is another form of an ultimate statement, which has no validity in Popper's fallibilist doctrine. Popper refers to the synthetic a priori as "apriorism," to demonstrate its erroneous nature. Even claims like "every event must have its cause", the synthetic a priori conclusion reached at the end of the Second Analogy, should not be accepted as knowledge, according to Popper:

The belief in causality is metaphysical. It is nothing but a typical metaphysical hypostatization of a well justified methodological rule - the scientist's decision never to abandon his search for laws. (The Logic of Scientific Discovery, 248)

For Popper, metaphysical claims are not inherently false, but they cannot and do not represent knowledge. Metaphysical claims are merely conjectures about the world that cannot be tested.

Given Popper's method for rejecting theories, I will now elaborate his argument for the rejection of synthetic a priori knowledge. Popper begins his analysis with Kant's description for synthetic a priori statements:

...are there or are there not synthetic statements which could be valid a priori? Kant said yes, and claimed arithmetic, geometry, the principle of causality (and some major part of Newton's physics) as synthetic and a priori valid. (Objective Knowledge, 92)

By associating the synthetic a priori with the above subjects, Popper seems to assume that, should the synthetic a priori be unable to explain any one of these subjects, the synthetic a priori itself must be rejected. Such a requirement is a clear logical fallacy, but only if taken as a logical proof. In order to be charitable to Popper's views, we should interpret him, not offering a strict logical proof against the synthetic a priori, but instead as offering a rationale for rejecting the synthetic a priori. Popper considers Newtonian Mechanics to represent the failure of the synthetic a priori writ large.

Here Kant brought in his 'Copernican Revolution':  it was the human intellect which invented, and imposed, its laws upon the sensual morass, thus creating the order of nature...

This was a bold theory. But it collapsed once it was realized that Newtonian dynamics was not a priori valid but a marvelous hypothesis - a conjecture. (ibid., 92)

This quote points to Popper's fundamental rationale for his rejection of the synthetic a priori:  Newtonian Mechanics has since been replaced by Einstein's theories of relativity and Bohr's quantum mechanics. How does Popper's rejection of the synthetic a priori stem from the rejection of Newtonian Mechanics? The above quote explains how Kant's theory of the synthetic a priori "collapsed once it was realized that Newtonian dynamics was not a priori valid". With the failure of Newtonian Mechanics, Kant's belief that important aspects of Newton's theory, though synthetic, could be justified a priori, became suspect. Popper's philosophy impugns Kant's conception of the synthetic apriori itself.

Popper's use of Kant's a priori justification of Newton as his counter example to synthetic a priori knowledge in general could be a result of his interpretation and reconstruction of Kant's answer to the question:  "How is pure natural science possible?" Kant, Popper claims, attributes our knowledge and perception of the world to the cognitive faculties shaping knowledge and perception.

...we are not passive receptors of sense data, but their active digestors. By digesting and assimilating them we form and organize them into a Cosmos, the Universe of Nature. In this process we impose upon the material presented to our senses the mathematical laws which are part of our digestive and organizing mechanism. Thus our intellect does not discover universal laws in nature, but it prescribes its own laws and imposes them upon nature. (Conjectures and Refutations, 126-7)

Popper rejects Kant's explanation for the possibility of pure natural science on the grounds that it proves too much, because it implies we all need to discover the same scientific theories.

...if the fact of our attainment of epistêmê can be explained at all by the fact that our intellect legislates for nature, and imposes its own laws upon it, then the first of these two facts [our attainment of epistêmê] cannot be contingent any more than the second [that our intellect legislates and imposes its own laws upon nature]. Thus the problem is no longer how Newton could make his discovery but how everybody else could have failed to make it. How is it that our digestive mechanism did not work much earlier? (ibid., 127)

By Popper's account, Kant's theory of experience explains how humans, in general, can claim scientific knowledge, but it does not explain why certain individuals have knowledge while others do not, or why certain scientific knowledge appears at one point in history over another.

Popper saw the synthetic a priori as an all or nothing attempt at solving certain riddles of knowledge, such as arithmetic, geometry, the principle of causality, and Newtonian Mechanics. By Popper's account, Kant's theory of our cognitive faculties claimed:

a) Synthetic a priori knowledge is necessary in order to have 'pure natural science'.

b) Arithmetic, geometry, causality, and parts of Newtonian Mechanics are known synthetic a priori.

c) Synthetic a priori knowledge is based on the nature of our cognitive faculties.

Popper's objections to Kant's theory:

(1) If Newtonian Mechanics are part of an innate understanding required for our experience of the world, why was Newton, born in the 1600s, the first to arrive at any theory remotely resembling them?

(2) How can some parts of Newtonian Mechanics be true synthetic a priori, since we know (now) that Newtonian Mechanics is only one possible model for describing the physical world and is not the most accurate?

(3) Kant's theory of experience is wrong because he cannot account for (1) and (2). Our scientific conjectures will not all be the same; they differ from person to person and over time. Thus the theory of synthetic a priori knowledge is false.

Step (3) is expressed in the following passage.

According to Kant's theory, 'pure natural science' is not only possible; although he does not always realize this, it becomes, contrary to his intention, the necessary result of our mental outfit. This is a patently absurd consequence of Kant's idea. (ibid., 127)

Popper's reasoning is flawed because he takes what Kant holds to be necessary for experiential knowledge and misinterprets it as being sufficient for experiential knowledge.. For instance, would Popper believe it is necessary that we reason in similar ways for mathematics or logic? Just because all human beings are capable of mathematics and logic, does not mean we will all discover Gödel's proof. However, Kant would claim anyone who discovered Gödel's proof necessarily is capable of mathematics and logic. Likewise, Kant reasoned that if Newton could come up with scientific knowledge, it was because he experienced things. Moreover, Kant further reasoned, if anyone experienced anything at all, it could only be a result of certain cognitive faculties. Kant was trying to establish the necessary preconditions for experiential knowledge, and not the sufficient preconditions. Popper seems to make a major error here and reverse the order of conditional reasoning, interpreting Kant to claim that anyone who has experience must necessarily come up scientific theories.

Regardless, Popper concludes it would be absurd to take Kant's theory seriously, since we do not theorize about science in the same fashion. This is exemplified by the transition from Newtonian Mechanics to general relativity.

But we are more active and free than even you [Kant] believed; for similar observations or similar environmental situations do not, as your theory [of our cognitive faculties] implied, produce similar explanations in different men. (ibid., 128)

By this point, Popper's refutation of Kant is very problematic. There may be good reasons for this.

First, a brief historical backdrop helps one understand Popper's rejection of the synthetic a priori. Popper's claim against our synthetic a priori knowledge of Newtonian Mechanics is very similar to earlier arguments from other philosophers levied against Kant. The logicist projects from Frege and Russell provided arguments against Kant's intuitionalist mathematics. Poincaré had already made claims that the discovery of non-Euclidian geometry invalidated Kant's theory of geometry. For Popper to use the downfall of Newtonian Mechanics as the prime counter-example against synthetic a priori knowledge does not seem so unjustified in its philosophical context. ItII is natural to be skeptical, if not outright hostile, to a well-established idea that appears to be refutable on multiple grounds. It is, however, awkward that Popper does not mention these developments in his discussion of the synthetic a priori, because, without such background knowledge, Popper's arguments seem much weaker than they really are.

Another important clue explaining the absence of a rigorous refutation of the synthetic a priori in Popper's treatment of the topic is his belief that philosophical theories cannot be given any kind of rigorous refutation.

There have been thinkers who believed that the truth of a theory may be inferred from its irrefutability. Yet this is an obvious mistake, considering that there may be two incompatible theories which are equally irrefutable - for example, determinism and its opposite, indeterminism. To infer the truth of a theory from its irrefutability is therefore inadmissible, no matter how we interpret irrefutability. (Conjectures and Refutations, 264)

Popper describes two ways a theory can be irrefutable:  in a purely logical sense (an analytic truth) or in an empirical sense. In the former case, the theory is merely logically consistent, and in the latter, no empirical data exists that could possibly refute the theory (such as a "most real being"). In both cases, truth cannot be inferred from the fact that the theory is irrefutable (ibid., 264), so Popper concludes that "philosophical theories, or metaphysical theories, will be irrefutable by definition" (ibid., 266). In addition to this conclusion, Popper poses an important problem:

If philosophical theories are all irrefutable, how can we ever distinguish between true and false philosophical theories? (ibid., 266)

Popper's solution is to claim all theories are aimed at solving problems:

In other words, every rational theory, no matter whether scientific or philosophical, is rational in so far as it tries to solve certain problems. A theory is comprehensible and reasonable only in its relation to a given problem-situation, and it can be rationally discussed only by discussing this relation.

Now, if we look upon a theory as a proposed solution to a set of problems, then the theory immediately lends itself to critical discussion - even if it is non-empirical and irrefutable. For we can now ask questions such as, Does it solve the problem? Does it solve it better than other theories? Has it perhaps merely shifted the problem? Is the solution simple? Is it fruitful? Does it perhaps contradict other philosophical theories needed for solving other problems? Questions of this kind show that a critical discussion even of irrefutable theories may well be possible. (ibid., 268-9)

Popper's practice of evaluating philosophical ideas as attempts at solving problems sheds light on his treatment of the synthetic a priori. Popper was not concerned with proving synthetic a priori knowledge does not exist -- he did not think such a proof was necessary, or even possible -- but instead he wanted to demonstrate that synthetic a priori knowledge does not resolve the problems faced by science. In this respect, Popper's rejection of the synthetic a priori is most likely a result of his association between induction and the synthetic a priori, since Popper's rejection of the synthetic a priori always refers to concepts Kant claims we establish a priori but which are, as Popper sees it, actually contingent (a posteriori) or true by definition (analytic a priori). Such concepts in dispute include causation, geometry, arithmetic, and some parts of Newtonian Mechanics, and thus Popper focuses on the failure of explaining Newtonian Mechanics with the synthetic a priori. This supposedly shows how the synthetic a priori provides an inadequate explanation of our knowledge of the empirical world. Popper's criteria for judging a theory can be expressed by the question:  How many problems can a philosophical theory solve?

Clearly restated, Popper's argument against the synthetic a priori is:

I. Newtonian Mechanics is supposedly true synthetically and known a priori. Such knowledge cannot be revised or refuted on the basis of experience.

II. Scientific claims must be empirically falsifiable.

III. Newtonian Mechanics is incapable of explaining certain types of phenomena; it has been falsified.

By (1), (2), and (3), Popper infers,

IV. The synthetic a priori does not establish the truth of any part of Newtonian Mechanics. The synthetic a priori does not explain why we have scientific knowledge.


V. The category of the synthetic a priori should be rejected as a dogmatic response to Hume's problem of induction.

The rationale for each of Popper's steps is as follows. Premise I is from Kant's attempt to justify some of Newton's Laws a priori. Premise II expresses Popper's distinction between scientific theories and other theories (such as metaphysical theories). Step III expresses Einstein's conquest over the former authority of Newtonian Mechanics. Step V does not logically follow from step IV, but instead marks the point where Popper rejects the synthetic a priori as a bad philosophical theory.


In my critique of Popper, I reject Popper's argument that Kant's theory proves too much and his subsequent claim that the synthetic a priori should be rejected. I will defend the motivations behind Popper's attempt to refute the synthetic a priori, and explain how Popper's falsificationism is not much different from Kant's theory of science.

Premise II, above, is the weakest part of Popper's argument. To reiterate Popper's rationale for rejecting the synthetic a priori:

Thus the problem is no longer how Newton could make his discovery but how everybody else could have failed to make it. How is it that our digestive mechanism did not work much earlier? (Conjectures and Refutations, 127)

Besides Popper's logical error of misinterpreting Kant's necessary conditions for experience as sufficient ones, the real philosophical problem with Popper's reasoning is his assumption that we are completely aware of how our cognitive capacities work. It seems apparent that, even if Newtonian Mechanics is a requisite part of the cognitive apparatus governing our experience, we would not necessarily observe the Newtonian laws as differentiated from our normal, everyday experience. Indeed, Kant seems to share Plato's theory of recollection (that we have knowledge we are not aware of):  "If we only knew what we know... we would be astonished by the treasures contained in our knowledge" (Wiener Logik, p. 843). It is not implausible that Kant believed Newtonian Mechanics to be one of these treasures.

Popper crosses over into dangerous territory when he emphasizes the differences among subjective experiences instead of the similarities among inter-subjective experiences. Without inter-subjective experience, science would be impossible. The precept that statements can be tested by criteria observable by everyone is based on the assumption that we share similar experiences of the world. So Kant's claim that we come hardwired with knowledge does not prove too much at all, as Popper asserts. Kant wants to explain the success of Newtonian Mechanics despite the fact that we are all subjective beings with no special access to each other's experience, by emphasizing how our cognition is constructed to produce similar experiences (cause and effect, for example).

Popper's misreading of Kant prohibits him from realizing his own mistake:

According to Kant's theory, 'pure natural science' is not only possible; although he does not always realize this, it becomes, contrary to his intention, the necessary result of our mental outfit (Conjectures and Refutations, 127)

Popper stresses how absurd it is that we all should think the same, but Kant's emphasis is on the possibility of science, given the construction of our cognitive faculties. Kant is not claiming we will all think the same, down to the last particular, but merely that our experiential framework is the same. Popper cannot claim that we experience things differently; because then it is unclear how inter-subjectivity is possible, since we would never know whether we were experiencing the same world. Popper fails to recognize the distinction between having a different experience of things, which is dependent upon the cognitive faculties that structure experience, and experiencing different things, which is dependent upon the subject's spatiotemporal positioning in the world. Kant's focus is on the former, though Popper interprets Kant through the lens of the latter. The degree to which our experiences differ is irrelevant for science -- what Kant focuses on, and what Popper ignores, are the similarities in our experience that universal statements depend upon. Due to our similar experiences of the world, Kant believed some aspects of Newtonian Mechanics are necessary characteristics of the cognitive faculties that make experience possible.

Although Popper's argument against Kant's synthetic a priori does not work, Popper does have a legitimate concern. Popper wishes to stress the growth of knowledge's dependency upon empirically falsifiable claims (i.e. scientific claims). Consequently, if components of science can be justified a priori, that is, independently of experience, they present an obvious challenge to Popper's fallibilist doctrine. As a result Popper argued against the a priori for his entire life, even if the arguments he used were unsound.

There is a large degree of merit in Popper's defense of the vital role science plays in the construction of our knowledge. However, as stated above, emphasizing the importance of science in the construction of our knowledge through inter-subjective criteria was nothing new to Kant. Popper himself claims,

My use of the terms 'objective' and 'subjective' is not unlike Kant's. He uses the word 'objective' to indicate that scientific knowledge should be justifiable, independently of anybody's whim:  a justification is 'objective' if in principle it can be tested and understood by anybody. (Logic of Scientific Discovery, 44)

This passage refers to A821/B849, where Kant says,

...the ground of the agreement of all judgments, regardless of the difference among the subjects, rests on the common ground, namely the object, with which they therefore all agree and through which the truth of the judgment is proved. (Critique of Pure Reason, A821/B849)

Popper recognizes that he and Kant share the similar requirement of a common experience between subjects (i.e., the object) to serve as the basis for objective knowledge, and yet Popper believes synthetic a priori knowledge is inconsistent with science, while synthetic a priori knowledge is central to Kant's conception of science. Popper tries to distance himself from Kant by rejecting the synthetic a priori, but on closer analysis, Popper's theory of science does not differ greatly from Kant's.

What are the differences between Kant and Popper's theory of science? Kant's theory of science relies on the regulative and constitutive use of reason in addition to the conjectural nature of scientific theories. In the latter respect, Kant's theory of science is not much different from Popper's. The main differences between the two thinkers are Popper's reliance on falsification to distinguish science from non-science and Kant's dependence on the regulative use of reason.

Kant defines the regulative use of reason as "a principle of the greatest possible continuation and extension of experience, in accordance with which no empirical boundary would hold as an absolute boundary" (A509/B537). In contrast, the constitutive use of reason is "for extending the concept of the world of sense beyond all possible experience" (A509/B537). The constitutive use of reason projects concepts of the empirical world ("world of sense") beyond all possible sense experience (theorizing that everything is composed of atoms, for example). The regulative use of reason maintains the uniformity of the non-empirical, general rules of experience, such as cause and effect, which are all a priori and denied by Popper. Moreover, regulative principles of reason are never true in virtue of being postulated (A179/B222), and serve for practical uses (A569/B597). Kant claims reason is the "faculty of unity of the rules of understanding under principles" (B356), which means our cognition will always seek to unite appearances under common principles. As a result,

Reason presupposes those cognitions of the understanding which are first applied to experience, and seeks the unity of these cognitions in accordance with ideas that go much further than experience can reach. (A662/B690)

Reason works to unify existing knowledge provided by sense experience into a more systematic theory of our experience, maintained by the regulative use of reason, and to extend that unification beyond the world of our experience.8 This is the essence of human science.

The next part of Kant's theory of science is to explain how we distinguish good theories from bad. He presents two types of proofs:  apagogic and ostensive. An ostensive proof is "combined with the conviction of truth and simultaneously with insight into its sources" (A789/B817) and an apagogic proof "can produce certainty" (A789/B817) by proving "a single false one [ground] among the consequences flowing from its contrary, and then the contrary is also false" (A791/B819). The ostensive proof uses multiple conditional proofs (assumes the antecedent and then proves its consequents) to demonstrate its assumed premise ("its sources") is true, whereas the apagogic proof uses an indirect proof to show its assumed premise produces a contradiction. Thus, the "real cause for the use of apagogic proofs in various sciences" is that "the grounds from which a certain cognition should be derived are too manifold or lie too deeply hidden" (A790/B818). That is, the ostensive proof is not used for the "various sciences" (Kant refers here to mathematics, natural science, and formal logic), "because to have insight into all possible consequences of any proposition that is assumed exceeds our powers...", and "for this reason a hypothesis can never be transformed into a demonstrated truth by this path" (A790/B818). On the contrary, with an apagogic proof,

...if even only a single false consequence can be derived from a proposition, then this proposition is false. Now instead of having to run through the entire series of the grounds in an ostensive proof that can lead to the truth of a cognition, by means of complete insight into its possibility, one need only find a single false one... (A791/B819)

It may seem Kant has premeditated Popper's falsification, but Kant does not appreciate the apagogic proof as Popper does. Surprisingly, although Kant notices how useful the apagogic proof is within the "various sciences", on the very next page he dismisses the use of the apagogic proof in natural science:

In natural science, since everything there is grounded on empirical intuitions, such false pretenses can frequently be guarded against through the comparison of many observations; but this kind of proof [apagogic] itself is for the most part unimportant in this area. (A792/B820, bold emphasis mine)

It can be informative, in this case, to view Popper as a student of Kant, emphasizing a neglected part of his forerunner's theory of reason. To restate the above Kantian quotations, using today's philosophical vocabulary:  Kant understood falsification could be used in the empirical sciences, but did not think it played any important role in the discovery of scientific knowledge. In contrast, Popper sees falsification as indisputably important for developing new scientific theories about the world.

Regardless, Popper still makes incongruous claims like this one:

According to Kant's theory, 'pure natural science' is not only possible; although he does not always realize this, it becomes, contrary to his intention, the necessary result of our mental outfit. (Conjectures and Refutations, 127)

Kant's theory of experience does not necessarily require scientific knowledge. For if we postulate a scientific theory, then

...the universal is assumed only problematically, and it is a mere idea, the particular being certain while the universality of the rule for this consequent is still a problem... This I will call the "hypothetical" use of reason. (A646/B674)

Scientific knowledge employs the hypothetical use of reason, but the hypothetical use of reason does not guarantee the acquisition of scientific knowledge, because the grounds of empirical laws are, to use Kant's language, too manifold or too deeply hidden. Since reason is compelled to seek "the unity of these cognitions in accordance with ideas that go much further than experience can reach" (A662/B690), the universal empirical laws that reason seeks must be assumed before they are known. Kant emphasizes the word "problematically" because the hypothetical use of reason has its limits:

...how is one to know all possible consequences, which would prove the universality of the assumed principle if they followed from it? Rather, this use of reason is only regulative, bringing unity into particular cognitions as far as possible and thereby approximating the rule to universality. (A647/B675)

Again, Kant did not understand the problem posed by assuming universal claims as Popper does. According to Popper, our knowledge includes universals, which cannot be proven -- only falsified. However, Popper does not seem to appreciate that Kant did not regard scientific knowledge as a necessary and predetermined, but rather as approximate, given how the regulative use of reason may never be certain that a rule universally applies to all consequences.

The final point to make clear is that Popper is wrong to suggest, that, because Kant believed some parts of Newtonian Mechanics were true a priori, Kant did not believe experience serves as the touchstone of science. Popper insinuates this claim through his repeated insistence on Kant's attempt to prove certain aspects of Newtonian Mechanics a priori. However, this example is an exception, which can be viewed as an inconsistency on Kant's part.

By nature (in the empirical sense) we understand the combination of appearances as regards their existence, in accordance with necessary rules, i.e., in accordance with laws. There are therefore certain laws, and indeed a priori, which first make a nature possible; the empirical laws can only obtain and be found by means of experience, and indeed in accord with its original laws, in accordance with which experience itself first becomes possible. (A216/B263, emphasis mine)

Empirical laws are found only through experience. However, they still require the "original laws" that make empirical laws, as well as experience, possible. In the above quotation, Kant is referring to synthetic a priori transcendental laws, which Popper himself could use to address a problem in his own philosophy (I will address this in the next section).

Although Popper may believe he is avoiding dogmatism by rejecting the synthetic a priori, this is simply not the case, as shown above, because one may believe in the synthetic a priori and still believe that scientific knowledge rest on experience.


Merely to prove synthetic a priori knowledge and fallibilism are consistent is not enough. It is my argument that Popper's falsification is incomplete without the synthetic a priori. Popper's falsification arguments do not prove that scientific statements are, in fact, rational. They only specify which scientific theories we should believe in. In this sense, Popper's account of falsification is merely normative:  he describes the process through which we select our scientific theories -- we believe in those theories that survive falsification attempts and discard those we have falsified -- but Popper does not prove the theories which do survive actually correspond to reality. Indeed, Popper believes that falsification points to the theories that are most true, or most approximate to reality.

I uphold the ancient theory of truth (almost explicit in Xenophanes and Democritus and Plato, and quite explicit in Aristotle) according to which truth is the agreement with the facts of what is being asserted. (Realism and the Aim of Science, xxxi)

The term "truth", more specifically, refers to the correspondence of human theories to reality, as defined by Alfred Tarski.9

That we may operate, without getting involved in antinomies, with the idea of objective truth in the sense of correspondence to the facts, has been shown by the work of Alfred Tarski. (Conjectures and Refutations, 36)

Although Popper presents his theory as a realist explanation of scientific knowledge, the concept of testing theories that attempt to explain something about the world does not make sense unless there is some reason to believe beforehand that the world corresponds to our tests. Popper does not recognize this point. He believed that his demarcation of falsifiability between science and metaphysics was rational, since, in light of Hume who had established induction as irrational, his description of the scientific method was not induction, nor did it fail to Hume's criticism, and can yet explain how science works on a normative level; hence, Popper concludes, not irrational. Popper's conclusion is not sound, because proving one theory rational involves more than showing it is normative, but that our normative acts also correspond to reality. I believe Popper can solve his problem of ultimate justification using Kant's own aforementioned "original laws" of experience.

These "original laws" are described in the analogies of experience, in the Critique of Pure Reason, as the transcendental laws that make experience possible. The transcendental law useful for Popper's dilemma is the conclusion resulting from Kant's second analogy of experience:  every event must have a cause. In this famous analogy, Kant asserts that nature, as we experience it, is necessarily composed of regularities (operates according to laws). However, the synthetic a priori statement that nature, in general, is uniform, cannot explain why some scientific theories are to be rationally preferred over another, since there needs to be a determination of which particular regularities will continue. As one skeptic, J.D. Kenyon, has written, even if we accept the uniformity of nature, the

...truth [of the uniformity of nature] would in no way narrow the range of possible courses of nature, and it would be compatible with any specific conclusion from experience, however unnatural to us. (Aristotelian Society, "Doubts about the Concept of Reason", 255)

What Kenyon overlooks is how falsification can help us approximate the truth by ruling out those theories that cannot explain observed phenomena, once uniformity of nature has been established. It is therefore possible for Popper to agree with Kenyon that we do not yet know the possible courses of nature, but still believe scientists can continue to focus and define the ranges of possible courses of nature by eliminating possible hypotheses about the world. Through this process, we establish what Popper called "verisimilitude", or truth-likeness, where theories, through falsification, become better a more accurate description of the world.

I would like to present two counter-arguments to my amendment of Popper's theory of science. The first counter-argument consists of two objections. To start, it could be argued that there is no reason to prefer falsification over induction, should the uniformity of nature be established. A proponent of induction may claim that a thinker is perfectly justified in accepting one theory over another, because his theory can explain more regularities than another theory. Hume's challenge is to attack the uniformity of nature upon which induction rests, but if we accept Kant's theory of experience, then induction is no longer vulnerable to Hume. However, as Kenyon points out above (and as Popper believed), it is impossible to know for certain that Newtonian Mechanics does not explain as many regularities as general relativity (or another theory), since it is impossible to count all the times a theory is verified. Induction still fails even with the uniformity of nature established, according to this critique.

The second objection attacks verisimilitude, which seems to be a common criticism of Popper. There are two general arguments against verisimilitude. One argues that falsifying one theory will not bring us any closer to the truth, since there are an infinite number of theories. According to this objection, all theories have the same verisimilitude, rendering verisimilitude incomprehensible. This criticism is an extension of Popper's own fallibilism, according to which we do not know the truth. Yet falsification, by Popper's own account, attempts to eliminate false hypotheses and bring us closer to the truth. This objection is too strong for Popper's own philosophy. But with Kantian premises combined with Popper's falsification, the belief in falsification remains consistent with the belief that we cannot obtain the truth because there are an infinite number of possible theories and falsification is only the method of eliminating false theories to move toward the truth. The diagram of a logarithmic function approaching a pre-established limit, below, visually illustrates how the two beliefs are consistent:

The green horizontal line on the y-axis represents truth obtainable by scientific procedures, or the lawfulness of nature as established by Kant, and the limit of the logarithmic function. The red line, expressed as a logarithmic function, represents the growth of scientific knowledge:  each falsified theory brings our theoretical understanding of reality closer to the truth line. In other words, the green line is reality, and the red line is our knowledge. And yet, no matter how many theories we falsify, we still never reach the truth. A logarithmic function like this one will only approach, but never meet, its limit. Thus, this second objection fails to unravel my theory of verisimilitude. We can understand verisimilitude if we remember, since nature is uniform and every event necessarily has its cause, falsifying possible causes eliminates possible causes and rules out possible courses of nature but always leaves something for future discovery. That is to say, the possible causes of nature are infinitely subtle, so with each new theory more observations are explained. However, new theories will always have more observations they cannot explain because they lack the sophistication to do so.

A possible response to my above diagram is the incommensurability response:  That the theories we construct are merely one of many possible historical sequences of theories. So what appears to us as scientific progress is merely an illusion. The following diagram, presented in Jay F. Rosenberg's article Comparing the Incommensurable, illustrates how such scenario is possible. Each theory is represented by t, with the associated number representing its historical sequence.

Here 't4a' and 't4b' are presumed to represent two equally-qualified but incommensurable successors to T3, that is, two competing theories, each of which satisfies its epistemological responsibilities vis-à-vis their common predecessor as well as does the other. The question, then, is this:  Must there in principle exist a single qualified successor, T5, which reconciles such a split, or could such a splitting prove to be perpetually irreconcilable? (Wilfrid Sellars:  Fusing the Images, "Comparing the Incommensurable:  Another Look at Convergent Realism", p.97)

According to my theory of a combined Kant-Popper philosophy of science, the idea that theories may converge back onto the same theory is a necessary result. This is because all theorizing will be constrained by reality10. Even if competing theories are incompatible, as new theories are created and old theories falsified, new theories will be progressively similar because the range of possible true theories is limited to what reality permits. As such the incommensurability response cannot sink my Kant-Popper fusion.

The second counter-argument against verisimilitude is a result of refutations of Popper's formal definition of verisimilitude, first offered in his Conjectures and Refutations11, by Miller and Tichý independently from each other in 1974 (Stanford Encyclopedia of Philosophy, §5). The lack of a formal definition for verisimilitude does not, however, mean it is invalid.

...a formal definition of verisimilitude is not needed for talking sensibly about it.

...the widely held view that scrapping this definition weakens my theory is completely baseless.

...nobody has ever shown that my theory of knowledge... is shaken in the least by this unfortunate mistaken definition, or why the idea of verisimilitude (which is not an essential part of my theory) should not be used further within my theory as an undefined concept. (Realism and the Aim of Science, xxxvi-xxxvii)12

Popper's own defense is more than adequate in this case.

Even though these particular criticisms are not fatal to Popper's philosophy, falsification is not without its problems. For example, it is still unclear how many falsifying instances it takes to reject a theory and even what counts as a satisfactory falsifying instance. These problems do pose serious challenges to Popper's theory, but they are not grave enough to reinstantiate induction. Although I cannot discuss these difficulties here, they remain an interesting topic for further investigation. My goal was to invalidate Popper's unsatisfactory rejection of the synthetic a priori and to show the merits of including the synthetic a priori within a falsificationist framework. To this end I have shown that Popper is unsuccessful at establishing the synthetic a priori as a dogmatic approach to science; that Kant believed, like Popper, science is always revisable to experience; and that Popper's theory of truth and science is incomplete without Kant.


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Carnap, Rudolf. Philosophy and Logical Syntax. London:  Kegan Paul, Trench, Trubner & Co. Ltd., 1935.

Coffa, J A. The Semantic Tradition From Kant to Carnap:  to the Vienna Station. Ed. Linda Wessels. Cambridge / New York / Port Chester / Melbourne / Sydney:  Cambridge UP, 1991.

Fernandes, Sergio L. De C. Foundations of Objective Knowledge. Dordrecht/Boston/Lancaster:  D. Reidel Company, 1985.

Hempel, Carl G. "Problems and Changes in the Empiricist Criterion of Meaning." 11 Rev. Intern. De Philos. 41 (1950):  41-63. 16 Mar. 2008 http://www.lawrence.edu/fast/boardmaw/Hempel_Emp_Crit.html.

Kant, Immanuel. Critique of Judgement. Trans. James C. Meredith. Ed. Nicholas Walker. Oxford and New York:  Oxford UP, 2007.

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Kants gesammelte Schriften, vols. 1-29. Königlich Preussischen Akademie der Wissenschaftlicher und Deutsche Akademie der Wissenschaften zu Berlin, eds. De Gruyter & Reimer, Berlin, 1910-83.

Kenyon, J D. "Doubts About the Concept of Reason." Aristotelian Society 59 (1985):  249-267.

Popper, Karl R. Conjectures and Refutations. London and New York:  Routledge, 2002.

Popper, Karl R. Realism and the Aim of Science. Totowa, NJ:  Rowman and Littlefield, 1983.

Popper, Karl R. The Logic of Sceintific Discovery. London:  Hutchinson, 1959.

Popper, Karl R. The Myth of the Framework. Ed. M A. Notturno. London and New York:  Routledge, 1994.

Rosenberg, Jay F. Wilfrid Sellars:  Fusing the Images. New York:  Oxford UP, 2007.

Ross, Kelley L. "Sir Karl Popper." The Proceedings of the Friesian School, Fourth Series. 2003. 12 Apr. 2007 http://friesian.com/hermenut.htm.

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1. Popper uses "a priori" as shorthand for "synthetic a priori" throughout his works. It is my opinion that this shorthand reflects Popper's indifference toward contesting the validity of analytic truths, which rests upon the principle of non-contradiction.

2. By verificationists, Popper is loosely referring to logical positivists and their ilk.

3. Popper refers to the eight theorems of chapter 2, especially proposition 7, remark 2 of the Metaphysical Foundations of Science for Kant's a priori justification of Newtonian Mechanics. (Conjectures and Refutations, 128)

4. As a small disclaimer, Popper does not mean atomic sentences here, but atomic claims (i.e. judgments of experience:  "red chair here now"). Popper has very little interest in atomic sentences (he does not deal with linguistic usage and grammar) and his interest is almost exclusively in the latter, which has to do with science.

5. Popper says "reducible to", but "based on" is more accurate since he does not mean that all statements can be converted to some elementary form, but that statements rest upon some irreducible tenet of experience.

6. Popper's quote predates the Philosophical Investigations. Wittgenstein had only written the Tractatus when this passage was written.

7. Although Hempel and Popper both reject the verificationist criterion of meaning, Hempel did not believe falsification could provide a demarcation between scientific and non-scientific claims. Moreover, as not to misrepresent Hempel, he did not also necessarily believe there were no ultimate statements in science. The reasoning expressed by Hempel is used both by Popper and Hempel to reach different conclusions.

8. Take note, however, that Popper believes reason attempts to explain the world outside of possible experience also. He writes, "Almost every statement we make transcends experience. There is no sharp dividing line between an 'empirical language' and a 'theoretical language':  we are theorizing all the time, even when we make the most trivial singular statement." Even the statement, 'All swans are white' "transcends experience - not because of the word 'white', but because of the word 'swan'. For by calling something a 'swan', we attribute to it properties which go far beyond mere observation" because the word 'swan' is a universal, "and universals always entail a law-like behaviour" (Logic of Scientific Discovery, 423).

9. Note:   Popper's interpretation of Tarski was commonplace at the time, but Tarski has since denied that his work was on metaphysics (correspondence theory of truth) but merely on semantics (meaning of truth).

10. See:  http://friesian.com/hermenut.htm and http://friesian.com/rudwick.htm.

11. See pages 316-317.

12. This passage is ambiguous where Popper claims verisimilitude is not "an essential part of my theory"; for I would argue verisimilitude is not essential to his normative theory of science, which relies upon falsifiability of theories, but verisimilitude is completely essential to his theory of truth, as verisimilitude seems to be a direct consequence of Popper's fallibilism and realism.