Why the Objectivist Interpretation of Falsification Matters

1. Introduction

The World 3 introduced by K. R. Popper in his later writings consists of objective knowledge, besides other things, that is, of “problems, theories, and arguments as such” (Popper 1972, 109), which Popper distinguished sharply from subjective knowledge, that is, from “a state of mind or of consciousness or a disposition to behave or to react” (Popper 1972, 108). Indeed, he went so far as to claim the uselessness of studying traditional as well as “a large part of contemporary” epistemology, as “while intending to study scientific knowledge, they [students] studied in fact something which is of no relevance to scientific knowledge” (Popper 1972). One of the aims of this article is to argue that Popper was right: subjectivism is a byproduct of justificationism, ¹ the doctrine completely repudiated by Popper (1983, chapter I, section 2), and it is of no importance for our understanding of science. Another aim, the main one, is to apply the distinction between subjectivism and objectivism to the ways in which scientific method is interpreted, and to explain why the objectivist interpretation of the method of falsification matters.

The ambition of the article is thus to clarify some crucial issues within the Popperian tradition. Section 2 introduces and explains the distinction between subjectivist and objectivist interpretations of scientific method, which is not as familiar as the distinction between subjective and objective knowledge. It argues that the subjectivist approach does not help us to understand science. Section 3 applies the objectivist approach to the method of falsification, and proposes its main advantages. It presents a simple argument that saves Popper’s method of falsification from the constantly repeated objections known as the Duhem–Quine thesis and/or the problem of underdetermination. The gravest difficulty is, however, discussed in Section 4 with regard to the deductive character of the method of falsification. According to Popper, “the falsifying mode of inference . . . is the modus tollens of classical logic” (Popper [1934] 1959, section 18). But as the content of a conclusion of every valid argument is included in the content of its premises taken together, it seems that modus tollens faces the problem of begging the question, like any deductive argument. The answer to be provided will also shed some light on the so-called paradox of inference, and on the key difference between justificatory and critical arguments, the difference highlighted, but not properly explained, by Popper himself (see Popper 1983, 19-28).

2. Subjectivist versus Objectivist Interpretation of Scientific Method

Before I introduce the difference between subjectivist and objectivist interpretations of scientific method, I shall explain what sources inspired me to come up with terminology that is not so common. One source springs directly from critical rationalism. By “objectivism,” David Miller refers to “the doctrine that our knowledge is a public matter and has little to do with what we as individuals believe” (Miller 2006, 83). It is evident that Miller’s view follows accurately Popper’s distinction between subjective and objective knowledge mentioned above. The second inspiration comes from the domain of post-analytic philosophy, and is related to what Donald Davidson called “epistemic” and “non-epistemic” views of truth. The epistemic view of truth “introduces a dependence of truth on what can be verified by finite rational creatures, while the denial of such dependence makes truth objective,” so to describe these conflicting views one can “well hit on the words ‘subjective’ and ‘objective’” (Davidson 2001, 177). Davidson’s aim was not to reconcile these views “but to question their clarity,” as he believed them to be “fundamentally mistaken” as “both invite skepticism”:

Subjective theories are skeptical in the way idealism or many versions of empiricism are skeptical; they are skeptical not because they make reality unknowable, but because they reduce reality to so much less than we believe there is. Objective theories, on the other hand, seem to throw in doubt not only our knowledge of what is “evidence-transcendent,” but all the rest of what we think we know, for such theories deny that there is any link between belief and truth. (Davidson 2001, 178)

However, it is doubtful whether a proponent of the objective view of truth must deny that there is any link between belief and truth. Indeed, my belief that I am now reading Davidson’s book may be perfectly true (or false), regardless of what I think about the belief. It turns out rather that the trouble is whether we know that our beliefs are true, and in this way, we face the question of what method, if any, can be used to find out that our beliefs are true. I shall argue that it is not the absence of a link between beliefs and their truth (if they are true) that distinguishes the subjectivist approach to scientific method from the objectivist one, but rather the absence of any link between justificatory arguments on one hand and our knowledge of the truth of what they are supposed to justify on the other.

To keep the matters simple, let T stand for a scientific theory and let us ask by what method, if any, scientists may know that T is true. ² Almost all contemporary philosophers of science agree that the truth of T cannot be proved conclusively but “only” supported by evidence. From the point of view of deductive logic, if T passes a test, or even millions of tests, it does not follow that T is true but only that T can be either true or false, these possibilities being equal. So, although the fact that T passed tests cannot provide good reasons in favor of T’s truth, perhaps it can influence a scientist S to believe in T, and thus to involve S in invalid reasoning. In that case, S would reason invalidly from (T → p) and p to T, and end up with believing, not knowing, that T is true.

But what if S reasons from (T → p) and p to “It is probable that T?” Does he reason validly and does he know that T is true? Well, one of the theorems of probability calculus says that if T implies p, then Pr(T) ≤ Pr(T|p), where “Pr” means “probability.” But there can be another statement q that is consistent with p, and such that Pr(T|p.q) is low. Here is an example given by Watkins (1984, 62): let T say of a randomly chosen integer that it is odd, let p say that it is a prime number, and let q say that it is the number 2. Although T does not imply p, the point is that all depends on the evidence that is taken as a basis for determining the probability of T, as Pr(T|p) ≈ 1 while Pr(T|p.q) = 0. Many thinkers (e.g., Bolzano, Carnap, Keynes) introduced therefore the requirement of total evidence: S should include in his evidence E everything he knows, as omissions might significantly affect the probability of T.

Watkins showed that we cannot know that the requirement of total evidence has been met. Let E be a large conjunction of singular observation statements and let m be a meta-statement saying that E contains all evidence known by S at the time t. For S to verify m, he would need to check that (1) every statement in E is relevant to the tested theory T and known by him to be true, and that (2) every statement not in E is either not relevant to T or not known by him. Evidently, this is an impossible task to accomplish hence the status of m, that is, of the presupposition that E describes all the evidence in S’s possession that is relevant to T, will be indeterminate (Watkins 1984, 67). A scientific theory T cannot be established therefore as “probably true by being related by probability logic to evidence that is certain” (Watkins 1984, 58).

However, one could argue that the notion of inductive support works well even without the requirement of total evidence. J. Norton (2014, 672), for instance, claims that his material theory of induction “so alters things that the traditional problem of induction can no longer be set up.” ³ This is because the “problem of justifying some particular induction is replaced by the straightforward task of justifying the facts that warrant it” (Norton 2014) and Norton believes that his idea of a non-hierarchical empiricism explains how the task is accomplished. The idea is that “the relations of inductive support in mature science form . . . [a] non-hierarchical structure” (Norton 2014, 686), the inductive cogency of which “arises from the requirement that each proposition in it has strong inductive support, where the support for the proposition may be drawn from other propositions of generality both lesser and greater than it” (Norton 2014, 689). The non-hierarchical structure is self-supporting (Norton 2014, 686), no requirement of total evidence is needed, and the regress problem, typical of any formal attempts at solving the problem of induction, does not even arise.

Let us grant that Norton’s approach is immune to the traditional problem of induction. Yet, there are more arguments against the idea of inductive support than those already discussed above. I shall mention just one of them, the so-called Popper–Miller theorem, as I believe that it so universal and so formal that it destroys Norton’s material theory of induction as well.

According to Norton (2014, 674), the relevant inductive support is not governed by inductions, which are (deductively valid) enthymemes, but by true inductive inferences, which use “general facts” as “warrants for an inference.” Let there be a scientific theory T and an evidence statement E including Norton’s general facts, which as we are told supports T inductively. As we were assured by Norton that T does not follow deductively from E, we can ask with Popper and Miller (1987) what is the part of the excess content of T by which T goes beyond or transcends E. Their (not entirely uncontroversial) ⁴ suggestion is that this part of the content of T can be identified with the conditional E → T because it is the deductively weakest proposition that is sufficient, in the presence of E, to yield T (Popper and Miller 1987, 569). Now we can ask (Q), “What is the effect of E on E → T?” Miller (1994, 73) answered (Q) by two formulas of probability calculus. The first was already mentioned four paragraphs above. It is the theorem inferred from the multiplication law which says that

The second is a weak form of the law of complementation, and it says that

As E & ~ T logically implies E, we get by (1)

and as E & ~ T is the negation of E → T, it must hold by (2) that

The answer to (Q) is given by (4) for it says that the effect of E on E → T is never positive, that is E can never support T inductively, contrary to what Norton and others claim.

As (4) is deduced from the axioms of probability calculus, it seems that there are just two ways in which to question it. One was already mentioned in Footnote 4, and I shall say no more about it here. The second is to claim that inductive support still can exist but is not expressible in probabilistic terms. Perhaps E can inductively support T even if E lowers (<) or does not affect (=) the probability of E → T? It is difficult to imagine that the proponents of inductive support would embrace this suggestion. ⁵ So until there is a clear-cut counterexample against the Popper–Miller theorem, it seems to be fair to conclude that the theorem deprives all non-deductive arguments of their justificatory power. More precisely, it explains why they never had such power. The so-called no-miracles arguments, for instance, cannot justify the truth or at least the near truth of a scientific theory by the claim that its empirical adequacy cannot be a mere coincidence. If their conclusions go beyond their premises, the Popper–Miller theorem applies. But if their conclusions follow deductively from their premises, then they commit the fallacy of begging the question, which is to be described in Section 4 below.

It follows that whatever justificatory arguments do, they do not establish the truth of what has been, supposedly, justified by their use. The truth of our ordinary beliefs as well as of scientific theories can be neither deductively proved nor inductively supported. So even if our beliefs or scientific theories are true, we cannot know it by the use of justificatory arguments. A subjectivist may be satisfied by this result since he interprets a method or an argument as a tool of recasting the subject’s mental states. Scientists use their methods, especially the gathering of evidence, to change the epistemic qualities of their beliefs, he may argue, not to find out that their beliefs are true. To this I would reply that it is a logically consistent opinion, of course, but one that has feet of clay. It saves good reasons by confining them to the subject’s mental states, but says nothing about scientific knowledge that is open to the public. Indeed, it gives no account of how scientific knowledge can be explored by the use of reason and public discussion.

All philosophers of science agree that today’s scientific theories can be refuted tomorrow and none of them denies that scientific knowledge changes. So what must be considered in turn is the objectivist interpretation of scientific method, which ties a method or an argument to the content of a belief itself, especially to the truth value of the sentence that is believed. Subjectivists interpret methods and arguments as tools for recasting the subject’s mental states while objectivists interpret them as tools for adjudicating the truth value of an investigated sentence. ⁶ As I have argued that there are no arguments by means of which scientists learn that an investigated sentence is true, it is high time to consider the question whether there are arguments by means of which they may learn that such a sentence is false. And as my concern is primarily with Popper’s method of falsification, I shall proceed to discuss this method.

3. The Conjectural Character of Falsification, and the Duhem–Quine Thesis

The difference between subjectivist and objectivist interpretations of scientific method can be applied to the method of falsification as well. The method of falsification is seen by subjectivists as a method by use of which a scientist S becomes suspicious of a theory T believed so far, as the method brings good reasons against p, and hence weakens S’s belief in T. Objectivists think that the method of falsification helps S to falsify T, and thus to change his opinion, that is, to start to believe not-T, as the method displays T’s falsity. Now it may look as if there is no difference between subjectivist and objectivist views of the method of falsification. According to both of them, the method ends up with a denial of what has been put to the test at the beginning of investigation. But there is at least one key difference. According to objectivists, the method of falsification cannot influence the epistemic quality of S’s belief. It does not weaken S’s belief in T, as it gives S no good reasons against T. Yet, the method helps S to start to believe not-T. There is no contradiction here because S can start to believe not-T even without having good reasons against T. ⁷ Popper’s theory of basic statements, which is summarized in the next paragraph, explains how it is possible.

The falsification of T is conjectural because falsifying basic statements are unjustified. Contrary to what psychologism claims, the basic statement B, comprising a counterexample to T, cannot be justified by “immediate experience” as it contains general terms denoting physical entities that exhibit law-like behavior, and these terms cannot be reduced to experience. But B can neither be justified by statements, as that would lead to infinite regress. Thus, it seems that B must be accepted dogmatically. The unpleasant situation in which one is advised to choose from the three alternatives just mentioned is described by Popper ([1934] 1959, section 25) as Fries’s trilemma. Popper ([1934] 1959, section 29) proposed to solve it by replacing the need for the justification of B by the requirement of B’s testability. To accept B as a falsifying statement of T, B must describe a reproducible effect explained by a low-level empirical (i.e., falsifiable) hypothesis that has passed tests (i.e., has been corroborated). If doubts about B persevere, it can be tested further still, but nothing compels scientists to accept it—a decision is needed to accept B as tested to their satisfaction. The acceptance of B is thus unjustified and conjectural, and the falsification of T is such as well. To falsify T, we need “a false consequence of it; not . . . a reason to suppose that we have identified a false consequence” (Miller 1994, 70). In this sense, one can start to believe not-T even without good reasons against T.

Having clarified the conjectural status of falsification, I must stress that scientific knowledge is no less conjectural. In the second section of the article, we have seen that scientists can have good reasons to believe something but it does not thus constitute objective knowledge. Now we have to recall Popper’s distinction between subjective and objective knowledge. Subjective knowledge is represented by the states of subjects’ minds while objective knowledge consists of the contents of theories that are open to the public. Popper’s anti-justificationism leads thus directly to objectivism. Scientists can be sure about many things, but what matters is the truth of what they are sure about. The truth of a scientific theory, if true, can be reduced neither to subjective nor to intersubjective feelings of being in possession of good reasons in favor of the theory’s truth. What goes for truth goes for falsity too: the falsity of a scientific theory T cannot be known with good reasons. However, scientists may use the method of falsification to find out that T is false, and thus not only to change their opinions but also objective scientific knowledge. ⁸ In the rest of the article, I shall try to explain this optimistic view of the method of falsification.

It is often claimed that the method of falsification is discredited by the Duhem–Quine thesis or by the underdetermination thesis. What I claim is that if falsification is interpreted in the objectivist way, this is no longer the case. The Duhem–Quine thesis is usually stated like this: empirical evidence cannot even falsify a theory, as “any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system” (Quine [1951] 1961, 43). This argument can be read strongly or in a weaker sense. The strong reading is fishy. Let us suppose that to test a large scientific system T against experience, we derive a prediction p from T, and that p fails in tests. And let us say that we read Quine strongly, so that, for example, we decide to sacrifice modus tollens instead of other parts of T. This is, at least, what some philosophers permit, claiming that Quine’s holism is radical because it

argues that the Duhem problem can be extended so that mathematics and logic are included in the theoretical system, and that it may be reasonable to regard an experiment as falsifying them rather than the empirical part of the system. (Ladyman 2002, 170)

But what Duhem taught us is that the failure of p does not indicate the falsity of any specific part of T. It means that the Duhem–Quine thesis implies neither the reasonableness of regarding any specific part of T as falsified ⁹ nor the impossibility of T’s falsification. To see what it implies, we have to take into account its weak reading.

To read the Duhem–Quine thesis in a weaker sense is to claim with Duhem ([1906] 1954, 185) that the failure of p does not say which part of the tested system T is refuted. But this is just a fact of logic that Popper (1976, section 32) calls the law of retransmission of falsity: the falsity of a conclusion validly derived from a set of premises is retransmitted to at least one of those premises. And Quine was, of course, aware of it:

Sometimes also an experience implied by a theory fails to come off; and then, ideally, we declare the theory false. But the failure falsifies only a block of theory as a whole, a conjunction of many statements. The failure shows that one or more of those statements is false, but it does not show which. (Quine 1969, 79)

Now it seems that the method of falsification is just another instance of the problem of underdetermination, as a negative test result cannot show which part of the tested system has been falsified. But this reading is one of the most common misunderstandings in the philosophy of science: yes, the Duhem–Quine thesis is right, but falsification is not underdetermined.

To see why this is so, we must distinguish two readings of falsification. According to the subjectivist reading, to falsify a system T means to give the subject S good reasons for rejecting T or a part of T. If that was the purpose of falsification, it would be impossible. There are never good reasons to reject T, as the falsifying evidence is conjectural. ¹⁰ And even if it could be established, the Duhem–Quine thesis still holds. According to the objectivist reading, to falsify a system T means to derive its falsity validly from a set of premises that contains essentially statements of the results of empirical tests of T. As Popper says, “the falsifying mode of inference . . . is the modus tollens of classical logic” (Popper [1934] 1959, section 18). Duhem and Quine are right that a refuted prediction p indicates the falsity of the system T as a whole, and not of any particular part of it. But this fact does not make falsification impossible as the question what particular part of T should be rejected arises only after the falsification of T as a whole system. The Duhem–Quine thesis is thus no longer a problem for falsification: if the prediction p derived from a system T fails in tests, its falsity is retransmitted to T as a whole. And there is no problem of underdetermination either: the question of what part of T should be refuted in turn comes only after the falsification of T as a whole.

I do not claim of course that the Duhem–Quine thesis and the problem of underdetermination are no problems at all. I claim only that they are not problems for falsification, and that the obsession to think contrariwise reveals how many thinkers read falsification in the subjectivist way, which is incompatible with Popper’s intentions. For instance, Rosenberg (2000, 196) says that “if statements can only be tested by employing auxiliary hypotheses, strict falsification is impossible, for it is the set of auxiliary hypotheses and the hypothesis under test which is falsified, and not any one particular statement among them.” What Rosenberg should have added, however, is that the set as a whole is strictly falsified. Another author, J. Leplin (2004, 124), went even as far as to write,

The indispensability of auxiliary hypotheses in generating observable predictions from theories belies the apparent logical asymmetry between verification and falsification. If empirical evidence cannot establish theories, neither can it refute them. For the refutation of a theory requires that theoretical auxiliaries assumed in testing it be independently established.”

However, the truth is that Duhem’s insight that scientists always test large systems cannot destroy the asymmetry between verification and falsification: basic statements may falsify the tested system but under no condition could they verify or confirm it (see Popper 1983, section 22). ¹¹

Indeed, the tables could be fairly turned on those who are adverse to falsification by stressing that the Duhem–Quine thesis does in fact demonstrate the usefulness of falsification, as it recognizes the falsity of the tested system T and thus raises the question what part of T should be rejected in turn. As already acknowledged, the last question cannot be answered through the falsification of T, but this does not mean that it cannot be resolved. There are at least two ways to confront radical holism. One is to try to derive p from a subsystem of T (call it X, for example). If this is accomplished, the rest of T is cleared of all guilt, and X is rejected, although no auxiliaries are established (as Leplin asserts to be necessary for successful refutation). If it does not succeed, another standard method may still help: advancing a falsifiable conjecture about what part of T is “responsible” for the falsity of p, and subsequently testing it. ¹² Unless the conjecture is itself falsified, that part is guessed to be false. Both strategies help scientists to locate the error although neither does so unerringly.

4. Critical Arguments, the Fallacy of Begging the Question, and the Paradox of Inference

So far, I have argued that the method of falsification is immune to the famous Duhem–Quine thesis. But now comes the key problem: modus tollens is a deductive mode of falsifying inference but the content of the conclusion of every valid deductive argument is included in the premises. So how can modus tollens be a tool for adjudicating the falsity of an investigated sentence (i.e., of T as a whole), if its conclusion (i.e., not-T) is asserted in its premises? Can an investigator who reasons via modus tollens find out that T is false by that very argument? To ask these questions is to confront critical arguments with the fallacy of begging the question. Here is how Miller (1994, 56) describes the problem with regard to sufficient reasons (“proofs”):

Suppose that e is offered as a sufficient reason in favour of the proposition h. Then e will fail to establish or prove h unless e logically implies h. But if e logically implies h, h will not actually have been proved to be true, even though it may have been validly derived from e; for the derivation rests on an assumption, namely e, that itself asserts the truth of h (and perhaps more). As a proof of the truth of h the argument will be shamelessly circular. In an attempt to justify h the very question at issue will have been begged.

It would be too easy and hasty to suggest that the method of falsification is immune to the problem of begging the question because it makes no attempt to establish or to prove the falsity of the tested theory. Although Section 3 made clear that I accept the suggestion, it must be inferred from some premises, otherwise there would be no informative account of it, and the rescue of falsification from the problem of begging the question would remain verbal. We can see that there is indeed trouble when we rephrase the above quotation as follows ¹³ :

Suppose that E is offered as a conjectural counterexample to T. Then E will fail to falsify T unless E logically implies the falsity of T. But if E logically implies the falsity of T, T will not actually have been falsified, even though its falsity may have been validly derived from E; for the derivation rests on an assumption, namely E, that itself asserts the falsity of T (and perhaps more). As a falsification of T the argument will be shamelessly circular. In an attempt to falsify T the very question at issue will have been begged, namely the falsity of T.

Let E stand for not-p and let T imply p. Then we get the modus tollens of classical logic and the last two sentences of the rephrasing reveal the trouble: the falsifying mode of inference is circular because it begs the question at issue, namely, the falsity of what has been, supposedly, falsified by the argument. It seems that we can rightly ask whether it is the argument that shows the falsity of T to a subject S who investigates T by the use of that argument.

To my mind, modus tollens does show to S the falsity of T, whence something must be wrong with the rephrasing. I suppose that it is the third sentence, which is simply false. ¹⁴ As we have seen in Section 3, according to objectivists, the falsification is conjectural, and to falsify T is to derive validly its falsity from a set of premises that contains essentially the results of empirical tests of T. As E (or not-p, respectively) reports just those results, the fact stated in the rephrasing that “the derivation rests on an assumption, namely, E, that itself asserts the falsity of T” does no harm to conjectural falsification. There is no attempt to justify either the assumption or the falsity of T. Never mind that the falsification of T is unjustified, the important thing is that it can be done.

What still has not been provided, however, is an explanation of how it can happen that the investigating subject S who reasons via modus tollens finds out at the end of his reasoning that T is false, if T’s falsity is included in premises from the start. To ask this question is to confront critical arguments no longer with the fallacy of begging the question but with the so-called paradox of inference. I shall describe the paradox shortly and then, as I think it makes sense to claim that we can utilize deductive arguments to find out that some sentences are false but not that they are true, I shall try to say more about the contrast between the use of justificatory and critical deductive arguments.

The above argument that critical arguments do not beg the question at issue is in agreement with J. N. Keynes who claimed that the fallacy of begging the question is “a fallacy of proof, rather than a fallacy of inference; that is to say, it arises when we ask how a given thesis is to be established, rather than when we ask what follows from a given hypothesis” (Keynes [1884] 1906, 425). So an investigator S, who explores the theory T by deriving a prediction p from it, and by confronting the prediction with the results of empirical tests, may proceed—if the results display p’s falsity—to infer not-T. His reasoning does not beg the question, unless he thinks that the falsity of T has been proved this way. Nonetheless, one may begin to sense a paradox here, for “on the one hand, we are to advance to something new; the conclusion of an inference must be different from the premises, and hence must go beyond the premises” while “on the other hand, the truth of the conclusion necessarily follows from the truth of the premises, and the conclusion must therefore in some sense be contained in the premises” (Keynes [1884] 1906, 414). In short, it seems that an inference, to be useful, must advance us to something new but, at the same time, a deductively valid inference cannot do that. So the subject S who reasons through a deductively valid argument becomes stuck in the paradox of inference. ¹⁵

I deny S’s stagnation. If we look closer at the falsifying mode of inference, we shall see that it indeed moves S forward, though it does not enlarge his knowledge. If S reasons via modus tollens, it is the argument that displays to him the falsity of T. He finds out that T is false because he validly infers the conclusion not-T, ¹⁶ so it is the argument that changes his opinion from T to not-T. To be sure, to end up with not-T, S must discover something that contradicts his original opinion T, but this discovery, this “advance to something new”—to use Keynes’s words quoted above—is not made by reasoning. Modus tollens just declares that the discovery has already been made and expresses it in the second premise by not-p. At this stage of his reasoning, S has abandoned p as a result of experience, not in response to any argument. If he proceeds further and infers not-T from premises, his job is done: T is eliminated in response to the argument. It is therefore no surprise to conclude that as far as objective knowledge is concerned, there is no discovery of new knowledge. By falsifying the theory T, the set of proposed theories, that is, scientific knowledge, is diminished. Of course, T still inhabits World 3, though not one of its subsets, the subset reserved for objective knowledge.

Now imagine, in contrast, that S wants to determine not the falsity but the truth of T. In this case, he can use no deductive argument at all. Of course, S may think he knows that T is true because it follows from a set of true premises, but he is wrong as the content of T was included in the premises from the start, so to think that it is the argument, what establishes the truth of T is to commit the fallacy of begging the question. This way, we can question the common view that S augments at least his subjective knowledge by reasoning through a valid argument, that is, by deducing a conclusion not previously seen by him from already known premises. ¹⁷ For, we can ask what S, who reasons validly, let us say, from Y to T, learns about T subjectively. Surely, he does not learn that T is true, as for knowing that he would have to know that Y is true, and this is not what the argument tells him. We are thus led back again to the problem of begging the question that blocks justificatory arguments.

In brief, the contrast between justificatory and critical deductive arguments relates neither to the context of discovery, nor to the context of justification, but to the issue what can be achieved by valid arguments. I have argued that neither justificatory nor critical deductive arguments can augment or justify our knowledge, but that we can use critical arguments to reduce our knowledge. Although I am ready to agree that this result is questionable with regard to subjective knowledge, simply because it is not clear what subjective knowledge is about, the result is evidently true as far as objective knowledge is concerned. Despite what justificationists claim, scientific knowledge is left perfectly intact by justificatory arguments.

5. Conclusion

There is a sense in which objective knowledge needs an investigating subject. It needs him to change, as it does not change itself. If there was nobody to investigate scientific theories, there would be no change in objective knowledge at all. However, the change cannot be rendered by any arguments or methods. Only critical arguments help. One among them is the falsifying mode of inference, modus tollens, by which the method of falsification proceeds. The objectivist interpretation of this method holds that the falsification of a theory T is a valid derivation of T’s falsity from a set of premises that contains essentially the results of empirical tests of T. The famous Duhem–Quine thesis does not affect the method because if a prediction p derived from a complex system T fails in tests, its falsity is retransmitted to T as a whole. The often repeated objection that falsification is threatened by the problem of underdetermination does no harm either. In fact, the question of what part of T should be refuted comes only after the falsification of T as a whole. The objectivist interpretation deals also with the problem of begging the question by regarding falsification as completely free of any attempt at justification. It is agreed that to falsify T is to derive its falsity from conjectural assumptions that themselves assert the falsity of T, but this is exactly how it should be. Finally, the deductive way in which falsification proceeds is not blocked by the paradox of inference as the falsifying mode of inference moves us forward, not to enlarge our knowledge but to reduce it.