Testability and Ockham’s Razor: How Formal and Statistical Learning Theory Converge in the New Riddle of Induction

Nelson Goodman’s new riddle of induction forcefully illustrates a challenge that must be confronted by any adequate theory of inductive inference: provide some basis for choosing among alternative hypotheses that fit past data but make divergent predictions. One response to this challenge is to distinguish among alternatives by means of some epistemically significant characteristic beyond fit with the data. Statistical learning theory takes this approach by showing how a concept similar to Popper’s notion of degrees of testability is linked to minimizing expected predictive error. In contrast, formal learning theory appeals to Ockham’s razor, which it justifies by reference to the goal of enhancing efficient convergence to the truth. In this essay, I show that, despite their differences, statistical and formal learning theory yield precisely the same result for a class of inductive problems that I call strongly VC ordered, of which Goodman’s riddle is just one example.     

Verisimilitude and Content

Popper’s original definition of verisimilitude in terms of comparisons of truth content and falsity content has known counter-examples. More complicated approaches have met with mixed success. This paper uses a new account of logical content to develop a definition of verisimilitude that is close to Popper’s original account. It is claimed that Popper’s mistake was to couch his account of truth and falsity content in terms of true and false consequences. Comparison to a similar approach by Schurz and Wiengartner show certain advantages of this new approach.     

Zwart and Franssen’s impossibility theorem holds for possible-world-accounts but not for consequence-accounts to verisimilitude

Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts, content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, but in agreement. We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic (object-language) versus semantic (meta-language) formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence (Sect. 6).     

Psychoanalyzing Historicists?: The Enigmatic Popper

The paper shows how Karl Popper’s critique of ‘historicism’ is permeated by psychoanalytic discourse regardless of his critique that psychoanalysis is one of the exemplars of pseudoscience. Early on, when he was formulating his philosophy of science, Popper had an apparently stringent criterion, viz. falsifiablity, and painstaking analysis. The central argument of this paper is that despite his representation of psychoanalysis as the principal illustration of the category he dubs as ‘pseudoscience’, Popper’s analysis has been infused with psychoanalysis when it comes to his social and political philosophy. Besides, not only was his interpretation of the proponents of ‘historicism’ and the ‘closed’ society mediated by the very concepts of a field which he indicted as pseudoscientific but also he frequently slipped into vacuous and unverifiable accusations forgetting the jurisdiction he formerly accorded to empirical adequacy and logical consistency when examining and assessing theories.     

Point-Free Geometry and Verisimilitude of Theories

A metric approach to Popper’s verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some of the difficulties arising from the known definitions of verisimilitude.     

Popper’S Evolutionary Epistemology Revamped

In a paper entitled “Revolution in Permanence”, published in the collection “Karl Popper: Philosophy and Problems”, John Worrall (1995) severely criticised several aspects of Karl Popper’s work before commenting that “I have no doubt that, given suffi-cient motivation, a case could be constructed on the basis of such remarks that Popper had a more sophisticated version of theory production......” (p. 102). Part of Worrall’s criticism is directed at a “strawpopper”: in his “Darwinian Model” emphasising the similarities and differences between genetic mutation, variation in animal behaviour and the gestation of scientific theories, Popper (1975, 1981, 1994) never stated that tentative scientific conjec-tures “while more or less random, are not completely blind.” He was referring to variation in animal species behaviour, and about tentative scientific conjectures he said nothing, although common sense would indicate that presumably he regarded them as being less blind and less random. In Popper (1977, 1983), giving a summary of his “Darwinian Model”, he repaired this omission about tentative scientific conjectures by inserting the sentence “On a level of World 3 theory formation they are of the character of planned gropings into the unknown.” Recent developments in the field of genetics (see for example Raff (1996), Lewis (1999), Korn (2002)) indicate that Popper’s intuitions were along the modern lines while Worrall’s intuitions are old fashioned. Therefore Popper’s “Darwinian Model” remains both viable and fruitful.     

Automatically deriving readers’ knowledge structures from texts

Latent semantic analysis (LSA) serves as both a theory and a method for representing the meaning of words based on a statistical analysis of their contextual usage (Foltz, 1996; Landauer & Dumais, 1997). In experiments in the domains of psychology and history, we compared the representation of readers’ knowledge structures of information learned from texts with the representation generated by LSA. Results indicated that LSA’s representation is similar to readers’ representations. In addition, the degree to which the reader’s representation is similar to LSA’s representation is indicative of the amount of knowledge the reader has acquired and of the reader’s reading ability. This approach has implications both as a model of learning from text and as a practical tool for performing knowledge assessment.     

The Implication of Popper’s Anti-inductive Theory for the Development of Indigenous Psychologies

Echoing Kumar’s advocacy that psychologists should not ignore Popper, this article received the methodological strategies for attaining the epistemological goal of universal psychology or global psychology as suggested by previous indigenous psychologists and argued that it is impossible for them to attain this goal by the inductive method. The significant implications of Popper’s anti-inductive theory for solving this dilemma are emphasized for future progress of indigenous psychologies.     

On the Possibility of Inference to the Best Explanation

Various proposals have suggested that an adequate explanatory theory should reduce the number or the cardinality of the set of logically independent claims that need be accepted in order to entail a body of data. A (and perhaps the only) well-formed proposal of this kind is William Kneale’s: an explanatory theory should be finitely axiomatizable but it’s set of logical consequences in the data language should not be finitely axiomatizable. Craig and Vaught showed that Kneale theories (almost) always exist for any recursively enumerable but not finitely axiomatizable set of data sentences in a first order language with identity. Kneale’s criterion underdetermines explanation even given all possible data in the data language; gratuitous axioms may be “tacked on.” Define a Kneale theory, T, to be logically minimal if it is deducible from every Kneale theory (in the vocabulary of T) that entails the same statements in the data language as does T. If they exist, minimal Kneale theories are candidates for best explanations: they are “bold” in a sense close to Popper’s; some minimal Kneale theory is true if any Kneale theory is true; the minimal Kneale theory that is data equivalent to any given Kneale theory is unique; and no Kneale theory is more probable than some minimal Kneale theory. I show that under the Craig-Vaught conditions, no minimal Kneale theories exist.     

Performance and learning goals for emotion regulation

Goal orientation theory is concerned with performance and learning goals in academic, athletic, and other ability areas. Here we examine performance and learning goals for emotion regulation. We define performance goals for emotion regulation as seeking to prove one’s ability to manage emotions; learning goals for emotion regulation are defined as seeking to improve one’s ability to manage emotions. In two studies, we tested the hypothesis that performance goals for emotion regulation would be associated with greater use of defensive emotion regulation strategies and depressive symptoms. Results from both studies showed that individuals with greater performance goals for emotion regulation reported higher levels of rumination and thought suppression and greater depressive symptoms, while individuals with greater learning goals reported greater use of cognitive reappraisal. The findings suggest that goals for emotion regulation may help explain individual differences in use of defensive versus constructive emotion regulation strategies.     

To Believe in Belief

Summary  Take the following version of scientific realism: we have good reason to believe that (some of the) current scientific theories tell us something specific about the underlying, i.e. unobservable, structures of the world, for instance that there are electrons with a certain electric charge, or that there are viruses that cause certain diseases. Popper, the rationalist, would not have adhered to the proposed formulation of scientific realism in terms of the rationality of existential beliefs concerning unobservables. Popper did not believe in belief. According to Van Fraassen, the empiricist, one may yet have a rational existential belief concerning unobservables, given a liberal notion of rationality of belief. In this paper I will investigate to what extent a reassessment of both Popper’s rejection of the rationality of belief and Van Fraassen’s reformulation of the rationality of belief, points towards a new and pragmatist dissolution of the ‘problem of scientific realism’.     

Tracing the Development of Thought Experiments in the Philosophy of Natural Sciences

Summary  An overview is provided of how the concept of the thought experiment has developed and changed for the natural sciences in the course of the 20th century. First, we discuss the existing definitions of the term ‘thought experiment’ and the origin of the thought experimentation method, identifying it in Greek Presocratics epoch. Second, only in the end of the 19th century showed up the first systematic enquiry on thought experiments by Ernst Mach’s work. After the Mach’s work, a negative attitude towards thought experiments came in the beginning of the 20th century, which went on until the Thomas Kuhn’s and Karl Popper’s work on thought experiments. Only from the mid-1980s did thought experiments begin to be considered relevant to scientific enterprise. Finally, we show the existing empirical and ‘functional’ theories which have developed about the nature and purpose of thought experiments.     

牟宗三先生以"自律道德"的理论诠释儒学之蠡测

Mou Zongsan uses the highest moral principle “autonomy” to interpret Confucius’ benevolence and Mencius’ “inherent benevolence and righteousness”, focuses on the self-rule of the will. It does not do any harm to Mencius’ learning, on the contrary, it is conducive to the communication between Chinese and Western philosophies. If we stick to Kant’s moral self autonomy and apply it to interpreting Zhu Xi’s moral theory, similarly we will discover the implications of Zhu Xi’s “autonomy” in his moral learning. Therefore, it is inappropriate for Mou Zongsan to say that Zhu Xi’s ethics belongs to the autonomous one. __________ Translated from Zhexue Yanjiu 哲学研究 (Philosophical Researches), 2005, (6): 33–39     

On the role of beliefs in observational flavor conditioning

In previous research (Baeyens, Vansteenwegen et al., 1996) we demonstrated that when observers consume a series of CS+ and CS−flavored drinks while simultaneously watching a videotaped model who synchronically drinks identical drinks and facially expresses his evaluation (dislike to CS+, neutral to CS−) of the liquids, the observers acquire a dislike for CS+ flavored relative to CS−flavored drinks. The aim of the present experiments was to test some predictions derived from a “direct conditioning” theory of such observational flavor learning. Using the same observational flavor conditioning procedure, we investigated (Exp. 1) the effect of manipulating the observers’ belief concerning the relationship between the drinks that they and the model were consuming (same/different/no information). Observational flavor conditioning was obtained when observers were led to believe that they were drinking the same drinks as the model did, and when they were not informed about this relationship, but not when told to be drinking different drinks. At the same time, however, the observers were not able to correctly identify the source of the model’s expression of dislike: They showed no CS-US contingency-awareness. Whereas the former finding suggests the causal involvement of conscious beliefs and cognitive inference processes in observational learning, the latter is more in line with the idea that the model’s facial expressions may act like a US’ which is automatically associated with the paired flavor CS+, without any involvement of conscious beliefs or cognitive inferences. These two crucial findings were replicated in Exp. 2. Also, we obtained evidence in this study that the belief manipulation affected learning through its influence on the observers’ attention for the model’s facial evaluative expressions. These results can be integrated either by a cognitive theory allowing the beliefs on which the inferences are based to be of an implicit nature, or by a “direct conditioning” theory that conceives of the US’ as an interpreted event, rather than as a mechanistically and invariantly acting physical entity.     

On the role of beliefs in observational flavor conditioning

In previous research (Baeyens, Vansteenwegen et al., 1996) we demonstrated that when observers consume a series of CS+ and CS−flavored drinks while simultaneously watching a videotaped model who synchronically drinks identical drinks and facially expresses his evaluation (dislike to CS+, neutral to CS−) of the liquids, the observers acquire a dislike for CS+ flavored relative to CS−flavored drinks. The aim of the present experiments was to test some predictions derived from a “direct conditioning” theory of such observational flavor learning. Using the same observational flavor conditioning procedure, we investigated (Exp. 1) the effect of manipulating the observers’ belief concerning the relationship between the drinks that they and the model were consuming (same/different/no information). Observational flavor conditioning was obtained when observers were led to believe that they were drinking the same drinks as the model did, and when they were not informed about this relationship, but not when told to be drinking different drinks. At the same time, however, the observers were not able to correctly identify the source of the model’s expression of dislike: They showed no CS-US contingency-awareness. Whereas the former finding suggests the causal involvement of conscious beliefs and cognitive inference processes in observational learning, the latter is more in line with the idea that the model’s facial expressions may act like a US’ which is automatically associated with the paired flavor CS+, without any involvement of conscious beliefs or cognitive inferences. These two crucial findings were replicated in Exp. 2. Also, we obtained evidence in this study that the belief manipulation affected learning through its influence on the observers’ attention for the model’s facial evaluative expressions. These results can be integrated either by a cognitive theory allowing the beliefs on which the inferences are based to be of an implicit nature, or by a “direct conditioning” theory that conceives of the US’ as an interpreted event, rather than as a mechanistically and invariantly acting physical entity.     

Kepler’s optics without hypotheses

This paper argues that Kepler considered his work in optics as part of natural philosophy and that, consequently, he aimed at change within natural philosophy. Back-to-back with John Schuster’s claim that Descartes’ optics should be considered as a natural philosophical appropriation of innovative results in the tradition of practical and mixed mathematics the central claim of my paper is that Kepler’s theory of optical imagery, developed in his Paralipomena ad Vitellionem (1604), was the result of a move similar to Descartes’ by Kepler. My argument consists of three parts. First, Kepler borrowed a geometrical model and experiment of optical imagery from the mélange of mixed and practical mathematics provided in the works of the sixteenth-century mathematicians Ettore Ausonio and Giovanni Battista Della Porta. Second, Kepler criticized the Aristotelian theory of light and he developed his own alternative metaphysics. Third, Kepler used his natural philosophical assumptions about the nature of light to re-interpret the model of image formation taken from Della Porta’s work. Taken together, I portray Kepler’s theory of optical imagery as a natural philosophical appropriation of an innovative model of image formation developed in a sixteenth-century practical and mixed mathematical tradition which was not interested in questioning philosophical assumptions on the nature of light.     

Roger Swyneshed’s Obligationes: A Logical Game of Inference Recognition?

In [Dutilh Novaes, Medieval-obligations as logical Games of Consistency maintenance, synthese, (2004)], I proposed a reconstruction of Walter Burley’s theory of obligationes, based on the idea that Burley’s theory of obligationes could be seen as a logical game of consistency maintenance. In the present paper, I intend to test the game hypothesis on another important theory of obligationes, namely Roger Swyneshed’s theory. In his treatise on obligationes [edited by P.V. Spade, cf. Spade History and philosophy of Logic 3(1982) 1-32], Swyneshed introduced significant modifications to the general framework of obligationes. To compare the two theories, I apply the same formal apparatus used in the previous paper. It will become patent that Swyneshed’s theory is considerably different from Burley’s, among other reasons because the dynamic aspects that play a major role in the latter are simply not present in the former. My conclusion is that Swyneshed’s version of obligationes is not directed towards consistency maintenance, but rather towards inference recognition, and that it is, from a game-theoretical perspective, less interesting a theory than Burley’s.     

The Relation of Personal Epistemology to Parenting Style and Goal Orientation in College Mothers

This study sought to establish the relevance of mothers’ epistemic beliefs to their parenting style and preferred academic goals for their child. College mothers (N = 163) from primarily working class families completed a variety of self-report measures including a modified version of Schommer’s [(1990). Journal of Educational Psychology, 82, 498–504] Epistemological Beliefs Questionnaire, the Parental Attitudes Questionnaire-Revised [Reitman, Rhode, Hupp, & Altobello (2002). Journal of Psychopathology and Behavioral Assessment, 24(2), 119–127], and several goal orientation scales. Results indicated that a view of learning as effortful and under the learner’s control and a view of knowledge as actively constructed were associated with an authoritative parenting style and with a preference for their child to focus on learning, improvement, and effort in approaching academic tasks. By contrast, a view of learning as quick, straightforward, relatively passive and as based in innate constraints and a view of knowledge as consisting of discreet, unambiguous facts were associated with authoritarian and permissive styles and the adoption of performance goals for one’s child. Portions of this study were presented at the annual meeting of the Society for Research in Child Development in Atlanta, April, 2005.     

The ‘Gray’s Elegy’ Argument, and The Prospects for the Theory of Denoting Concepts

Russell’s new theory of denoting phrases introduced in “On Denoting” in Mind 1905 is now a paradigm of analytic philosophy. The main argument for Russell’s new theory is the so-called ‘Gray’s Elegy’ argument, which purports to show that the theory of denoting concepts (analogous to Frege’s theory of senses) promoted by Russell in the 1903 Principles of Mathematics is incoherent. The ‘Gray’s Elegy’ argument rests on the premise that if a denoting concept occurs in a proposition, then the proposition is not about the concept. I argue that the premise is false. The ‘Gray’s Elegy’ argument does not exhaust Russell’s ammunition against the theory of denoting concepts. Another reason Russell rejects the theory is, as he says, that it cannot provide an adequate account of non-uniquely denoting concepts. In the last section of the paper, I argue that even though Russell was right in thinking that the theory of denoting concepts cannot provide an adequate account of non-uniquely denoting concepts, Russell’s new theory does not succeed in eliminating the occurrence of all denoting concepts, as it requires a commitment to the existence of variables that indirectly denote their values. However, the view that variables are denoting concepts is unproblematic once the ‘Gray’s Elegy’ argument is blocked.     

Colour, world and archimedean metaphysics: stroud and the quest for reality

This paper proposes a fundamentally opposite conception of the possibility of metaphysics to that of Barry Stroud in The Quest for Reality and other writings. I discuss Stroud’s views on everyday ‚truth’ and metaphysics (Section 1), on interpretation (Section 2 – replying with a theory of ‚quasi-understanding’), and his ‚no threat’ claim (Section 3). But the main argument (Section 4) is a response to Stroud’s claim that we have no right either to affirm or to deny the metaphysical reality of colours. Stroud’s view resembles Carnap’s (1950, Revue Internationale de Philosophie 4, 20–40), that experience can in some sense never settle the metaphysical issue between e.g. materialism, idealism and phenomenalism; though we can allow everyday ‚knowledge’ e.g. that there is a fallen tree in the garden outside, as something available on all three views. (Carnap takes the undecidability as a sign that the metaphysical issue is a pseudo-question; Stroud insists it is factual, but places it beyond our ken, ‚external’.) I argue, instead, that metaphysical argument is possible from within our conceptual scheme and epistemic situation (as in Gareth Evans’s arguments for realism over phenomenalism); that ‚external’ and ‚internal’ questions cannot be separated as Stroud wishes; and that if we really were denied knowledge on ‚metaphysical’ matters, that would infect our right to claim knowledge of ‚observational’ matters too. And I sketch a theory of colour that would allow us to conclude (at once ‚metaphysically’ and ‚internally’) that things are indeed ‚really’ coloured. For all his expressions of sympathy for Wittgenstein, Stroud’s metaphysics is remarkably Cartesian.