withdrawing unfalsifiable hypotheses

Following Quine’s line of argument against the distinction between necessary and contingent truths (Quine, 1951), when a contradiction arises, consistency can be restored by rejecting or modifying any assumption which contributes to the derivation of contradiction: no hypothesis is immune from possible alteration. Of course there are epistemological and pragmatic limitations: some hypotheses contribute to the derivation of useful consequences more often than others, and some participate more often in the derivation of contradictions than others. For example it might be useful to abandon, among the hypotheses which lead to contradiction, the one which contributes least to the derivation of useful consequences; if contradictions continue to exist and the assessed utility of the hypotheses changes, it may be necessary to backtrack, reinstate a previously abandoned hypothesis and abandon an alternative instead.

Hence, the derivation of inconsistency contributes to the search for alternative, and possibly new hypotheses: for each assumption which contributes to the derivation of a contradiction there exists at least one alternative new system obtained by abandoning or modifying the assumption. The classical example of a theoretical system that is opposed by a contradiction is the case in which the report of an empirical observation or experiment contradicts a scientific theory. Whether it is more beneficial to reject the report or the statement of the theory depends on the whole effect on the theoretical system. It is also possible that many alternatives might lead to non-comparable, equally viable, but mutually incompatible, systems. As Lakatos argues, in a mature theory with a history of useful consequences, it is generally better to reject an anomalous conflicting report than it is to abandon the theory as a whole. The cases in which we have to abandon a whole theory are very rare: a theory may be considered as a complex information system in which there is a collection of cooperating individual statements some of which are useful and more firmly held than others; propositions that belong to the central core of a theory are more firmly held than those which are located closer to the border, where instead rival hypotheses may coexist as mutually incompatible alternatives. Accumulating reports of empirical observations can help in deciding in favor of one alternative over another.

We may conclude by asserting that contradiction, far from damaging a system, helps to indicate regions in which it can be changed (and improved). It is always better to produce mistakes and then correct them than to make no progress at all. We have to remember that even without restoring consistency, an inconsistent system can still produce useful information. Of course from the point of view of classical logic we are compelled to derive any conclusion from inconsistent premises, but in practice efficient proof procedures infer only "relevant" conclusions with varying degrees of accessibility, as stated by the criteria of non-classical relevant entailment (Anderson & Belnap, 1975).

Many attempts have also been made to model abduction by developing some formal tools in order to illustrate its computational properties and the relationships with the different forms of deductive reasoning. Some of these formal models of abductive reasoning are based on the theory of the epistemic state of an agent, where the epistemic state of an individual is modeled as a consistent set of beliefs that can change by expansion and contraction. The nature of the kinds of inconsistencies captured by these formalisms and the fact that they do not adequately account for some roles played by anomalies, conflicts, and contradictions in many forms of explanatory reasoning are discussed in (Magnani, 1999a).

The framework of belief revision is sometimes called coherence approach (Doyle, 1992). In this approach it is important that the agent holds some beliefs just as long as they are consistent with the agent’s remaining beliefs. Inconsistent beliefs do not describe any world, and so are unproductive; moreover, the changes must be epistemologically conservative in the sense that the agent maintains as many of its beliefs as possible when it adjusts its beliefs to the new information. It is contrasted to the foundations approach, according to which beliefs change as the agent adopts or abandons satisfactory reasons (or justifications). This approach is exemplified by the well-known "reason maintenance systems" (RMS) or "truth maintenance systems" (TMS) (Doyle, 1979), elaborated in the area of artificial intelligence to cooperate with an external problem solver. In this approach the role of inconsistencies is concentrated on the negations able to invalidate justifications of beliefs; moreover, as there are many similarities between reasoning with incomplete information and acting with inconsistent information, the operations of RMS concerning revision directly involve logical consistency, seeking to solve a conflict among beliefs. The operations of dependency-directed backtracking (DDB) are devoted to this aim: RMS informs DDB whenever a contradiction node (for instance a set of beliefs) becomes believed, then DDB attempts to remove reasons and premises, only to defeat nonmonotonic assumptions: "If the argument for the contradiction node does not depend on any of these (i.e., it consists entirely of monotonic reasons), DDB leaves the contradiction node in place as a continuing belief" (Doyle, 1979, p. 36), so leaving the conflicting beliefs intact if they do not depend on defeasible assumptions, and presenting a paraconsistent behavior.

We may also see belief change from the point of view of conceptual change, considering concepts either cognitively, like mental structures analogous to data structures in computers, or, epistemologically, like abstractions or representations that presuppose questions of justification. Belief revision - even if extended by formal accounts such as cited above is able to represent cases of conceptual change such as adding a new instance, adding a new weak rule, adding a new strong rule (see Thagard, 1992, pp. 34-39, for details), that is, cases of addition and deletion of beliefs, but fails to take into account cases such as adding a new part-relation, adding a new kind-relation, adding a new concept, collapsing part of a kind-hierarchy, reorganizing hierarchies by branch jumping and tree switching, in which there are reorganizations of concepts or redefinitions of the nature of a hierarchy. These last cases are the most evident changes occurring in many kinds of creative reasoning, for example in science. Related to some of these types of conceptual change are different varieties of inconsistencies (Magnani, 1999a).

Moreover, the logical accounts of abduction certainly elucidate many kinds of inconsistency government, which nevertheless reduce to the act of finding contradictions able to generate the withdrawal of some hypotheses, beliefs, reasons, etc.: these contradictions always emerge at the level of data (observations), and consistency is restored at the theoretical level. This view may distract from important aspects of other kinds of reasoning that involve intelligent abductive performances. For example, empirical anomalies are not alone in generating impasses, there are also the so-called conceptual anomalies. In science, first and foremost, empirical anomaly resolution involves the localization of the problem at hand within one or more constituents of the theory. It is then necessary to produce one or more new hypotheses to account for the anomaly, and finally, these hypotheses need to be evaluated so as to establish which one best satisfies the criteria for theory justification. Hence, anomalies require a change in the theory, yet once the change is successfully made, anomalies are no longer anomalous but in fact are now resolved. General strategies for anomaly resolution, as well as for producing new ideas and for assessing theories, have been studied by Darden (1991).

The so-called conceptual problems represent a particular form of anomaly. In addition, resolving conceptual problems may involve satisfactorily answering questions about the nature of theoretical entities. Nevertheless such conceptual problems do not arise directly from data, but from the nature of the claims in the principles or in the hypotheses of the theory. It is far from simple to identify a conceptual problem that requires a resolution, since, for example, a conceptual problem concerns the adequacy or the ambiguity of a theory, and yet also its incompleteness or (lack of) evidence. Some examples derived from the historical discovery of non-Euclidean geometries which illustrate the relationships between strategies for anomaly resolution and explanatory and productive visual thinking are illustrated in (Magnani 1999b): it is shown how visual thinking is relevant to hypothesis formation and scientific discovery and explored the first epistemological and cognitive features of visual abduction.

The fact that inconsistencies may occur also at the theoretical level is further emphasized if we consider that in science or in legal reasoning (Thagard, 1992), hypotheses are mainly layered. Hence, the organization of hypotheses is more complex than the one illustrated in formal models, and abduction is not only a matter of mapping from sets of hypotheses to a set of data. In many abductive settings there are hypotheses that explain other hypotheses so that the selection or creation of explanations is related to these relationships. This kind of hierarchical explanations has also been studied in the area of probabilistic belief revision (Pearl, 1988). Moreover, when a scientist introduces a new hypothesis, especially in the field of natural sciences, he is interested in the potential rejection of an old theory or of an old knowledge domain. Consistency requirements we described in the framework of deductive models, governing hypothesis withdrawal in various ways, would arrest further developments of the new abduced hypothesis. In the scientist’s case there is not the deletion of the old concepts, but rather the coexistence of two rival and competing views. Other cognitive and epistemological situations present a sort of paraconsistent behavior: a typical kind of inconsistency maintenance is the well-known case of scientific theories that face anomalies. Explanations are usually not complete but only furnish partial accounts of the pertinent evidence: not everything has to be explained. Newtonian mechanics is forced to cohabit with the anomaly of perihelion of Mercury until the development of the theory of relativity, but it also has to stay with its false prediction about the motion of Uranus.

In conclusion, contradiction has a preference for strong hypotheses which are more easily falsified than weak ones; and moreover, hard hypotheses may more easily weakened than weak ones, which prove difficult subsequently to strengthen. It is always better to produce mistakes and then correct them than to make no progress at all. Hypotheses may be unfalsifiable. In this case it is impossible to find a contradiction in some area of the conceptual systems in which they are incorporated. Notwithstanding this fact, it is sometimes necessary to construct ways of rejecting the unfalsifiable hypothesis at hand by resorting to some external forms of negation, external because we want to avoid any arbitrary and subjective elimination, which would be rationally or epistemologically unjustified.

Let us now consider a kind of "weak" (unfalsifiable) hypotheses that are hard to negate and the ways for making it easy. In these cases the subject can rationally decide to withdraw his hypotheses even in contexts where it is impossible to find "explicit" contradictions; more than that, thanks to the new information reached simply by finding this kind of negation, the subject is free to form new hypotheses. I will explore whether negation as failure can be employed to model hypothesis withdrawal in Poincaré’s conventionalism of the principles of physics and in Freudian analytic reasoning.

There is a kind of negation, studied by researchers into logic programming, which I consider to be very important also from the epistemological point of view: negation as failure. It is active as a "rational" process of withdrawing previously-imagined hypotheses in everyday life, but also in certain subtle kinds of diagnostic (analytic interpretations in psychoanalysis) and epistemological settings. Contrasted with classical negation, with the double negation of intuitionistic logic, and with the philosophical concept of Aufhebung, negation as failure shows how a subject can decide to withdraw his hypotheses, while maintaining the rationality of his reasoning, in contexts where it is impossible to find contradictions.

The statements of a logical data base are a set of Horn clauses which take the form:

R(t₁, ... ,t_n) ¬ L₁ Ù L₂ Ù ... Ù L_m

(m ³ 0, n ³ 0, where R(t₁, ... ,t_n) - conclusion - is the distinguished positive literal and L₁ Ù L₂ Ù ... Ù L_m - conditions - are all literals, and each free variable is implicitly universally quantified over the entire implication). In more conventional notation this would be written as the disjunction

R(t₁, ... ,t_n) Ú Ø L_1Ú Ø L₂ Ú .. Ú Ø L_m

where any other positive literal of the disjunctive form would appear as a negated precondition of the previous implication.

Let us consider a special query evaluation process for a logical data base that involves the so-called negation as failure inference rule (Clark, 1978). We can build a Horn clause theorem prover augmented with this special inference rule, such that we are able to infer Ø P when every possible proof of P fails.

We know that a relational data base only contains information about true instances of relations. Even so, many queries involve negation and we can answer them by showing that certain instances are false. For example, let’s consider this simple case: to answer a request for the name of a student not taking a particular course, C, we need to find a student, S, such that the instance (atomic formula) Takes(S,C) is false. For a logical data base, where an atomic formula which is not explicitly given may still be implied by a general rule, the assumption is that an atomic formula is false if we fail to prove that it is true. To prove that an atomic formula P is false we do an exhaustive search for a proof of P. If every possible proof of P fails, we can infer Ø P. The well-known PROLOG programming language (Roussel, 1975) uses this method of manipulating negation.

We have to deal with a proof such as the following:

where the "proof that P is not provable" (Clark, 1978, p. 120) is the exhaustive but unsuccessful search for a proof of P. Here the logical symbol Ø acquires the new meaning of "fail to prove" Clark proposes a query evaluation algorithm based essentially on ordered linear resolution for Horn clauses (SLD) augmented by the negation as failure inference rule "Ø P may be inferred if every possible proof of P fails" (SLDNF).

Clark (1978) has shown that for every meta-language proof of Ø P obtained by a Horn clause theorem prover (query evaluation) augmented with negation as failure there exists a structurally similar object-language proof of Ø P. He has proved that a query evaluation with the addition of negation as failure will only produce results that are implied by first order inference from the completed data-base, that is, the evaluation of a query should be viewed as a "deduction" from the completed data base (correctness of query evaluation). Consequently negation as failure is a sound rule for deductions from a completed data base.

Although the query evaluation with negation as failure process is in general not complete, its main advantage is the efficiency of its implementation. There are many examples in which the attempt to prove neither succeeds nor fails, because it goes into a loop. To overcome these limitations it is sufficient to impose constraints on the logical data base and its queries, and add loop detectors to the Horn clause problem solver: by this method the query evaluation process is guaranteed to find each and every solution to a query. However, because of the undecidability of logic, no query evaluator can identify all cases in which a goal in unsolvable. A best theorem prover does not exist and there are no limitations on the extent to which a problem solver can improve its ability to detect loops and to establish negation as failure.

I will explore whether negation as failure can be employed to model hypothesis withdrawal in Poincaré’s conventionalism of the principles of physics and in Freudian analytic reasoning. The first case shows how conventions can be motivationally abandoned; the second one explains how the questioned problem of the probative value of clinical findings can be solved.

First of all we will consider some aspects dealing with Poincaré’s famous conventionalism of the principles of physics and the possibility of negating conventions. An extension of Poincaré’s so-called geometric conventionalism, according to which the choice of a geometry is only justifiable by considerations of simplicity, in a psychological and pragmatic sense ("commodisme"), is the generalized conventionalism, expressing the conventional character of the principles of physics: "The principles of mathematical physics (for example, the principle of conservation of energy, Hamilton’s principle in geometrical optics and in dynamics, etc.) systematize experimental results usually achieved on the basis of two (or more) rival theories, such as the emission and the undulation theory of light, or Fresnel’s and Neumann’s wave theories, or Fresnel’s optics and Maxwell’s electromagnetic theory, etc. They express the common empirical content as well as (at least part of) the mathematical structure of such rival theories and, therefore, can (but need not) be given alternative theoretical interpretations" (Giedymin, 1982, pp. 27-28).

From the epistemological point of view it is important to stress that the conventional principles usually survive the demise of theories and are therefore responsible for the continuity of scientific progress. Moreover, they are not empirically falsifiable; as stated by Poincaré in Science and Hypothesis:

The conventional principles of mechanics derive from experience, as regards their "genesis", but cannot be falsified by experience because they contribute to "constitute" the experience itself, in a proper Kantian sense. The experience has only suggested their adoption because they are convenient: there is a precise analogy with the well-known case of geometrical conventions, but also many differences, which pertain the "objects" studied.

Conventional principles survive the demise (falsification) of theories in such a way that they underlie the incessant spectacle of scientific revolutions: "It is the mathematical physics of our fathers which has familiarized us little by little with these various principles; which has habituated us to recognize them under the different vestments in which they disguise themselves" (Poincaré, 1958, p. 95). Underlying revolutions of physics, conventional principles guarantee the historicity and the growth of science itself. Moreover the conventional principles surely imply "firstly, that there has been a growing tendency in modern physics to formulate and solve physical problems within powerful, and more abstract, mathematical systems of assumptions [...]; secondly, the role of conventional principles has been growing and our ability to discriminate experimentally between alternative abstract systems which, with a great approximation, save the phenomena has been diminishing (by comparison to the testing of simple conjunctions of empirical generalizations)" (Giedymin, 1982, p. 28). Moreover, as stated above, they are not empirically falsifiable: "The principles of mechanics [...] reduce in final analysis to a simple convention that we have a right to make, because we are certain beforehand that no experiment can contradict it" (Poincaré, 1905, p. 135).

Although arbitrary and conventional the conventional principles too can be substituted by others. This is the main problem treated by Poincaré in the last passages of Chapter IX, "The Future of Mathematical Physics", in The Value of Science. Already the simple case of "linguistic" changes in science "suffices to reveal generalizations not before suspected" (Poincaré, 1958, p. 78). By means of the new discoveries scientists arrive at a point where they are able to "admire the delicate harmony of numbers and forms; they marvel when a new discovery opens to them an unexpected perspective" (Poincaré, 1958, pp. 75-76), a new perspective that is always provisional, fallible, open to further confirmations or falsifications when compared to rival perspectives.

We have seen how the conventional principles of physics guarantee this continuous extension of experience thanks to the various perspectives and forms expressed by experimental physics. However, because conventional, "no experiment can contradict them". The experience only suggested the principles, and they, since absolute, have become constitutive just of the empirical horizon common to rival experimental theories.

Poincaré observes:

Poincaré appeals to a form of weak negation: let us follow the text. To pursue his point, Poincaré illustrates the attempts to reconcile the "calorimetric experiment of Curie" with the "principle of conservation of energy":

At this point Poincaré resolutely asserts: "What an advantageous explanation, and how convenient! First, it is unverifiable and thus irrefutable. Then again it will serve to account for any derogation whatever to Mayer’s principle; it answers in advance not only the objection of Curie, but all the objections that future experimenters might accumulate. This new and unknown energy would serve for everything" (p. 110). Now Poincaré can show how this ad hoc hypothesis can be identified with the non falsificability of the conventional principle of the conservation of energy:

Finally, Poincaré’s argumentation ends by affirming negation as failure: "and, as I have written in ‘Science and Hypothesis’, if a principle ceases to be fecund, experiment without contradicting it directly will nevertheless have condemned it"(ibid.).

Let us now analyze this situation from the epistemological point of view: the conventional principle has to be withdrawn when it "ceases to be fecund", or when it seems that we have failed to prove it. Remember that for a logic data base the assumption is that an atomic formula is false if we fail to prove that it is true. More clearly: as stated above, every conventional principle, suitably underlying some experimental laws, generates expectations with regard to the subsequent evidences of nature. We consider as proof of a conventional principle the fact that we can increasingly extend and complete the experimental laws related to it, adding the new (expected) evidence that "emerges" from the experimental research. If, after a finite period of time, nature does not provide this new "evidence" that is able to increase the fecundity of the conventional principle, this failure leads to its withdrawal: "experiment without contradicting it directly will nevertheless have condemned it". Analogously to the Freudian case of constructions I will illustrate in the following section, the "proof that a principle is not provable" is the unsuccessful search for a proof of the principle itself. Here too, the logical symbol Ø acquires the new meaning of "fail to prove" in the empirical sense.

Let us resume: if the old conventional principle does not produce new experimental "evidence" to underpin it, it is legitimate to abandon the principle, when convenient: the opportunity to reject the old principle will happen just by exploiting the experimental evidence which, even if not suitable for contradicting it (that is, it is "unassailable by experiment"), is nevertheless suitable as a basis for conceiving a new alternative principle.

Moreover, in the light of Poincaré’s theory of the principles of physics that we have just illustrated, the nominalistic interpretation of conventionalism given by Popper (Popper, 1963) appears to be very reductive. Moreover, Popper’s tendency to identify conventions with ad hoc hypotheses is shown to be decidedly unilateral, since, as is demonstrated by the passages, immediately above, the adhocness is achieved only in a very special case, when the conventional principle is epistemologically exhausted.

We will now illustrate how it is possible to explain the epistemological status of Freud’s method of clinical investigation in terms of a special form of negation as failure. We are not dealing here with the highly controversial problem of the epistemological status of psychoanalytic clinical theories (comprehensively analyzed in Grünbaum, 1984): it is well-known that clinical data have no probative value for the confirmation or falsification of the general hypotheses of psychoanalytic clinical theories of personality, because, given that they depend completely on the specific nature of the clinical setting, they are devoid of the independence that characterizes observations endowed with scientific value.

Furthermore, because of the lack of probative value in the patient’s clinical data with regard to the analyst’s interpretations, any therapeutic gains from analysis may be considered to have been caused not by true insightful self-discovery but rather by placebo effects induced by the analyst’s powers of suggestion. If the probative value of the analysand’s responses is negated, then Freudian therapy might reasonably be considered to function as an emotional corrective (performed by a positive "transference" effect) and not because it enables the analysand to acquire self-knowledge; instead he or she capitulates to proselytizing suggestion, which operates the more insidiously since under the pretense that analysis is nondirective. Suggestion is indeed responsible for the so-called epistemical contamination of the patient’s responses.

Freud asks the patient to believe in the analyst’s theoretical retrodictions of significant events in his early life and these theoretical retrodictions are communicated to him as constructions:

The aim is to provoke the previously-cited true insightful self-discovery that guarantees the cure (Freud, cit., 1920, vol. 18, 1920, p. 18). A single construction is built as a "sequence" of the interpretations that issue from clinical data found in the clinical setting, epistemologically characterized by "transference" and "countertransference":

A construction can be considered as a kind of "history" or "narrative" of the analysand’s significant early life events, which is never complete, but can be rendered more and more comprehensive by adding new interpretations.

Freudian clinical reasoning refers to a kind of abductive reasoning, which is called selective (Magnani, 1992): its uncertainty is due to nonmonotonicity, the analyst may always withdraw his or her interpretations (constructions) when new evidence arises. Every construction is generated by a "double" abduction: first of all the analyst has to select a suitable general psychoanalytic hypothesis, apply it to some "single element of the material" to produce an interpretation, then he has to select each of these general hypotheses in such a way that the sequence of the generated interpretations can give rise to a significant and consistent construction. Every "abduced" construction, suitably connected with some other clinical psychoanalytical hypotheses, generates expectations with regard to the analysand’s subsequent responses and remarks.

Of course the analyst aims to build the most complete construction. The problem here is the analyst cannot propose to the analysand any construction he wants, without some form of external testing. As stated above, the objection most often raised against psychoanalysis is that "therapeutic success is nonprobative because it is achieved not by imparting veridical insight but rather by the persuasive suggestion of fanciful pseudoinsights that merely ring verisimilar to the docile patient" (Grünbaum, 1984, p. 138). In one of his last papers, Constructions in analysis (Freud, cit., vol. 23, 1937, pp. 257-269), Freud reports that "a certain well-known man of science" had been "at once derogatory and unjust" because

Freud looks for a criterion for justifying, in the clinical setting, the abandonment of constructions that have been shown to be inadequate (it is interesting to note that in the cited article Freud emphasizes the provisional role of constructions referring to them also as "hypotheses" or "conjectures"). This is the fundamental epistemological problem of the method of clinical investigation: Freud is clear in saying that therapeutic success will occur only if incorrect analytic constructions, spuriously confirmed by "contaminated" responses from the patient, are discarded in favor of new correct constructions (that are constitutively provisional) derived from clinical data not distorted by the patient’s compliance with the analyst’s communicated expectations.

Freud then proceeds "to give a detailed account of how we are accustomed to arrive at an assessment of the ‘Yes’ or ‘No’ (considered as "direct evidences") of our patients during analytic treatment - of their expression of agreement or of denial" (p. 257).

Analytic constructions cannot be falsified by dissent from the patient because "it is in fact true that a ‘No’ from one of our patients is not as a rule enough to make us abandon an interpretation as incorrect" (p. 257). It might seem to Freud that patient dissent from an interpretation can be always discounted as inspired by neurotic resistance. It is only "in some rare cases" that dissent "turns out to be the expression of legitimate dissent" (p. 262). A "patient’s ‘No’ is no evidence of the correctness of a construction, though it is perfectly compatible with it" (p. 263). Rather, a patient’s ‘No’ might be more adequately related to the "incompleteness" of the proposed constructions: "the only safe interpretation of his ‘No’ is that it points to incompleteness" (p. 263).

Even if a patient’s verbal assent may result from genuine recognition that the analyst’s construction is true, it may nevertheless be spurious because it derives from neurotic resistance, as already seen in his or her dissent. Assent is "hypocritical" when it serves "to prolong the concealment of a truth that has not been discovered" (p. 262). On the other hand, assent is genuine and not hypocritical when patient’s verbal assent will be followed and accompanied by new memories: "The ‘Yes’ has no value unless it is followed by indirect confirmations, unless the patient, immediately after his ‘Yes’, produces new memories which complete and extend the construction" (p. 262)

Since "Yes" and "No" do not have any importance to test a construction it is necessary to see other facts, such as "the material" that has "come to light" after having proposed a construction to the patient:

Let us now analyse this situation from the epistemological point of view: the analyst has to withdraw the construction (hypothesis) when has failed to prove it. Remember that for a logic data base the assumption is that an atomic formula is false if we fail to prove that it is true. More precisely: as stated above, every construction, suitably connected with some other clinical psychoanalytical hypotheses, generates expectations with regard to the analysand’s subsequent responses and remarks. We consider the fact that we can continuously extend and complete a construction by adding the new (expected) material that "has come to light" from the patient as proof of the construction validity. If the patient does not provide this new "material" which is able to extend the proposed construction, this failure leads to the withdrawal of the construction itself. So the "proof that a construction is not provable" is the unsuccessful search for a proof of the construction itself. Here the logical symbol Ø acquires the new meaning of "fail to prove" in the empirical sense.

Let us resume: if the patient does not provide new "material" which extends the proposed construction, "if", as Freud declares, "nothing further develops we may conclude that we have made a mistake and we shall admit as much to the patient at some suitable opportunity without sacrificing any of our authority". The "opportunity" of rejecting the proposed construction "will arise" just

A new cycle very similar to the one previously started with the assumption of the first construction takes place: a new construction (derived by applying new clinical psychoanalytical hypotheses and schemes) is provisionally conceived on the basis of the new material that came to light when the analyst was seeking to extend the old one ("we often get an impression as though [...] our bait of falsehood had taken a carp of truth").

The inferential process is clearly nonmonotonic: in an initial phase we have some material coming from the patient and which provides the background for an initial abduced construction; in a second phase we have to add to the initial material what emerges after having communicated to the patient the first construction. If in this second phase the new material is not suitable for extending the first construction, the negation as failure compels the analyst to withdraw and reject the construction. The whole process is nonmonotonic because the increase of material does not generate an increase in (the number of) constructions: the old construction is abandoned ("the false construction drops out, as if it has never been made").

I should stress that the epistemological role of what Freud calls "indirect confirmations" or disconfirmations of analytic constructions is in my opinion negligible. These patient responses, other than verbal assent or dissent, Freud declares, "are in every respect trustworthy" (p. 263). Examples are when a patient has a mental association whose content is similar to that of the construction, or when a patient commits a parapraxis as part of a direct denial. Moreover, when a masochistic patient is averse to "receiving help from the analyst", an incorrect construction will not affect his symptoms, but a correct one will produce "an unmistakable aggravation of his symptoms and of his general condition" (p. 265). The indirect confirmations, in Freud’s opinion, provide a "valuable basis for judging whether the construction is likely to be [further] confirmed in the course of analysis" (p. 264).

We should not confuse the kind of transformations of "No" in "Yes" (or viceversa) that pertains to the "indirect confirmations" or disconfirmations, with the above-described extension of constructions toward the most complete one on the basis of new (expected) material that emerges. In conclusion, a patient’s "Yes" or "No", whether direct or indirect, has no role to play in withdrawing constructions. I think that these cases do not have any function in the process of abandoning a construction because they always keep open the possibility of extending it: moreover, the indirect confirmations or disconfirmations do not increase the acceptability of constructions. In my opinion we should not consider Freud as an inductivist, despite his emphasis on these kind of indirect evidence.

Moreover, as stated by Grünbaum, who tends to consider Freudian analysis of clinical method as inductive, this presumption of the consilience of clinical inductions is "spurious" because

The second section of Constructions in analysis concludes with a very explicit affirmation of nonmonotonicity: "Only the further course of the analysis enables us to decide whether our constructions are correct or unserviceable. [...] an individual construction is anything more than a conjecture which awaits examination, confirmation or rejection. We claim no authority for it, we require no direct agreement from the patient, nor do we argue with him if at first he denies it. In short, we conduct ourselves on the model of a familiar figure in one of Nestroy’s farces - the manservant who has a single answer on his lips to every question or objection: ‘It will all become clear in the course of future developments’" (p. 265).

But we have shown that Freud considers important only the rejection achieved by negation as failure. The epistemological aim is not to validate a construction by extensions provided by new material or by indirect confirmations or disconfirmations. Freud aims to reject it. Perhaps in Freud’s considerations there are some ambiguities in perceiving the asymmetry between falsification and confirmation, but it would seem that my interpretation of Freud as a special falsificationist can be maintained without fear of distorting his methodological intention. Freud is a special type of "falsificationist" because negation as failure guarantees the possibility of freely withdrawing a construction and substituting it with a rival and better one. In the computational case, negation as failure is achieved by suitable algorithms related to the knowledge that is handled (see above, section 2.). In the human and not computational case, negation as failure is played out in the midst of the analyst-analysand interaction, where transference and countertransference are the human epistemological operators and "reagents". Negation as failure is therefore a limitation on the dogmatic and autosuggestive exaggerations of (pathological) countertransference.