Justification of Induction

Il problema apparentemente insolubile di una giustificazione non circolare dell’induzione diverrebbe più abbordabile se invece di chiederci solo cosa ci assicura che un fenomeno osservato si riprodurrà in modo uguale in un numero potenzialmente infinito di casi futuri, ci chiedessimo anche come si spiega che esso si sia manifestato fin qui in modo identico e senza eccezioni in un numero di casi finito ma assai alto. E’ questa l’idea della giustificazione abduttiva dell’induzione, avanzata in forme diverse da Armstrong, Foster e (...) BonJour: serie talmente regolari di fenomeni sono da un punto di vista logico talmente improbabili che se il mondo fosse puramente casuale (se cioè gli eventi si presentassero con frequenza proporzionale alla loro probabilità logica) esse non potrebbero verificarsi se non per una coincidenza miracolosa. Pertanto, tali regolarità si spiegano solo assumendo che siano prodotte da meccanismi o necessità nomiche; ma se questo è il caso, è corretto concludere che tali regolarità persisteranno anche in futuro senza eccezioni, e dunque le inferenze induttive su di esse sono giustificate. Anche Kornblith argomenta dall’effettivo successo delle inferenze induttive all’esistenza di regolarità oggettive in natura; mentre Sankey parte dall’ uniformità della natura per giustificare l’induzione. Congiungendo le due argomentazioni, dunque, si ottiene di nuovo una giustificazione dell’induzione in base all’argomento del “se non è un miracolo …”. Un ostacolo su questa via è specificare in che senso la natura sia uniforme (dato che ovviamente non lo è in ogni suo aspetto) e di quali regolarità possiamo aspettarci che persistano senza eccezione anche in futuro (dato che evidentemente non tutte lo fanno: l’acqua non bolle sempre a 100°, la pressione non è sempre funzione della temperatura, e così via). Entrano qui in gioco le conoscenze di sfondo e la ripetizione delle osservazioni in condizioni diverse, che ci mostrano quali circostanze siano rilevanti al verificarsi del fenomeno dato. In tal modo, le nostre descrizioni delle regolarità naturali convergono su descrizioni che specificano sia le condizioni individualmente necessarie e congiuntamente sufficienti, sia tutti gli argomenti delle funzioni che costituiscono tali regolarità. Ciò consente di formulare i principi di Uniformità della Natura e di Induzione in modo non generico (e dunque, a seconda della formulazione, vuoto o eccessivo), ma circostanziato: così essi asseriscono, rispettivamente, che la natura è uniforme negli aspetti evidenziati dalle descrizioni su cui convergiamo grazie alle osservazioni ripetute, e che solo queste descrizioni possono essere induttivamente generalizzate. Ciò consente anche di risolvere enigmi alla Goodman, quali: poiché le osservazioni ci hanno mostrato (solo) il verificarsi di una data regolarità fino al momento presente t, come possiamo presumere che essa si verificherà anche dopo t? La risposta è che osservazioni e conoscenza di sfondo non ci dicono che vi sia alcun limite temporale tra le condizioni necessarie della regolarità data. (shrink)

In a recent Philosophy of Science article Gerhard Schurz proposes meta-inductivistic prediction strategies as a new approach to Hume's. This comment examines the limitations of Schurz's approach. It can be proven that the meta-inductivist approach does not work any more if the meta-inductivists have to face an infinite number of alternative predictors. With his limitation it remains doubtful whether the meta-inductivist can provide a full solution to the problem of induction.

Watkins proposes a neo-Popperian solution to the pragmatic problem of induction. He asserts that evidence can be used non-inductively to prefer the principle that corroboration is more successful over all human history than that, say, counter-corroboration is more successful either over this same period or in the future. Watkins's argument for rejecting the first counter-corroborationist alternative is beside the point. However, as whatever is the best strategy over all human history is irrelevant to the pragmatic problem of induction since we (...) are not required to act in the past, and his argument for rejecting the second presupposes induction. (shrink)

In 1955, Goodman set out to 'dissolve' the problem of induction, that is, to argue that the old problem of induction is a mere pseudoproblem not worthy of serious philosophical attention. I will argue that, under naturalistic views of the reflective equilibrium method, it cannot provide a basis for a dissolution of the problem of induction. This is because naturalized reflective equilibrium is -- in a way to be explained -- itself an inductive method, and thus renders Goodman's dissolution viciously (...) circular. This paper, then, examines how the old problem of induction crept back in while nobody was looking. (shrink)

Abstract: According to Laurence BonJour, the problem of induction can be solved by recognizing the a priori necessity that inductive conclusions constitute the best explanations of inductive premises. I defend an interpretation of the key probability claims BonJour makes about inductive premises and show that they are not susceptible to many of the objections that have been lodged against them. I then argue that these purportedly necessary probability claims nevertheless remain deeply problematic and that, as a result, BonJour's proposal fails (...) to provide a satisfactory resolution of the problem of induction. (shrink)

Jin Yuelin (1895?1984), a Chinese logician and philosopher, is greatly influenced by Hume's and Russell's philosophies. How should we respond to Hume's problem of induction? This is an important clue to understand Jin's whole philosophical career. The first section of this paper gives a brief historical review of Russell and Jin. The second section outlines Hume's skeptical arguments against causality and induction. The third section expounds Russell's justification of induction by discussing his views on Hume's skepticism, causality, principle of induction, (...) and empirical postulates. The fourth section clarifies Jin's justification of induction by discussing his critique of Hume's epistemology and his arguments for the reliability of causality and the eternal truth and apriority of the principle of induction. The final section compares Jin's justification of induction with Russell's and concludes that there are similarities and differences between their projects and that both their attempts fail. This paper takes the similar responses to the problem of induction by Jin and Russell to demonstrate the communication that there has been between Chinese philosophers and the Western ones. (shrink)

In this paper I offer a straight solution to Hume's problem of induction by defusing the assumptions on which it is based. I argue that Hume's problem only arises if we accept (i) that there is no necessity but logical necessity, or (ii) that it is unreasonable to believe that there is any form of necessity in addition to logical necessity. I show that Hume's arguments in favour of (i) and (ii) are unsound. I then offer a suggestion as to (...) how the weakness of his arguments has escaped detection. Finally, having claimed that there remains a surmountable problem with inductive arguments, I end by characterising that problem and a possible approach to its solution. (shrink)

In 1947 Donald Cary Williams claimed in The Ground of Induction to have solved the Humean problem of induction, by means of an adaptation of reasoning first advanced by Bernoulli in 1713. Later on David Stove defended and improved upon Williams’ argument in The Rational- ity of Induction (1986). We call this proposed solution of induction the ‘Williams-Stove sampling thesis’. There has been no lack of objections raised to the sampling thesis, and it has not been widely accepted. In our (...) opinion, though, none of these objections has the slightest force, and, moreover, the sampling thesis is undoubtedly true. What we will argue in this paper is that one particular objection that has been raised on numerous occasions is misguided. This concerns the randomness of the sample on which the inductive extrapolation is based. (shrink)

No one doubts that philosophers have discussed at length ‘the problem of induction’, but it would also be generally recognized that there would be disagreement as to precisely what that problem is. Rather than tackle the formulation problem, I will borrow from a popular text: Our existence as well as science itself is based on the principle of induction that tells us to reason from past frequencies to future likelihoods, from the limited known of the past and present to the (...) unknown of the past, present, and future ... But though inductive probability is psychologically inescapable, we have trouble providing a rational justification for it. We might say, then, that there is such a practice as induction, and a problem associated with it is that of justifying engaging in it. We engage in reasoning from things we know about the past and present to conclusions about the past, present and future. We can't resist doing this but we have trouble finding a rational justification for doing so. This problem suggests a generalization. We engage in reasoning, reaching new conclusions. It would be hard to resist engaging in this practice. How do we provide a rational justification for it? (shrink)

Induction is ‘the glory of science and the scandal of philosophy’. I diagnose why. I call my solution a “disappearance theory of induction”: inductive inferences are not themselves arguments, but they synthesise manifold reasons that are. Yet the form of all these underlying arguments is not inductive at all, but rather deductive. Both in science and in the wider practical sphere, responsible people seek the most measured way to understand their situation. The most measured understanding possible is thick with arguments (...) in support of every last belief. To achieve such an understanding is richly synthetic. Science has become systematically good at progressing towards this aim. But by virtue of their analytical orientation many philosophers are predisposed to misunderstand the nature of measurement, and thus to fall into confusion about the reasonableness of science. In considering an inductive inference, philosophers have expected to see one argument, rather than many; supposing that there is one argument, they have sought to describe its form; and then they have even attempted to establish a general kind of warrant for such a form of argument. Actually some significant philosophical contributions have issued from such work, but the worth, I argue, of these contributions, is best appreciated when they are all comprehended within the perspective that I defend. I also discuss how much more natural it is from the standpoint of synthetic philosophy (of the rationalists) rather than analytic philosophy (of the empiricists) to embrace the ideal of a most measured understanding, and in its light understand the integrity of both scientific and everyday beliefs. (shrink)

Chattopadhyaya (philosophy, Jadavpur U., Calcutta) examines the epistemological and methodological implications of induction and probability.

Hume's sceptical arguments regarding induction have not yet been successfully answered. However, I shall not in this paper discuss the important attempts to answer Hume since that would be too lengthy a task. On the supposition that Hume's sceptical arguments have not been met, the empirical world is a place where, as the popular metaphor goes, all the glue has been removed. For the Humean sceptic, the only empirical knowledge that we can have is given to us in immediate perception. (...) We have no reason to believe that the patterns of future events will in any way resemble patterns of events in the present or past. We have no reason to believe even that present events not observed resemble present events that are observed, or that knowledge of past and present can be any guide in making new discoveries about what took place in the past. What we have is an ideal setting for the calculation of a priori probabilities. We have a field of distinct events having no logical or evidential ties to one another. The attempt to justify induction that I wish to present is an appeal to a priori probability. (shrink)

Note on Howard Sankey's "Induction and Natural Kinds".

This paper is an attempt at a vindication of induction. The point of departure is that induction requires a justification and that the only kind of justification possible is a vindication. However traditional vindications of induction have rested on unjustified assumptions about the aim of induction. This vindication takes the end pursued in induction simply to be correct prediction. It is argued that induction is the only reasonable way of pursuing this end because induction is the only objective method of (...) predicting. While objectivity is not a necessary condition for successful predicting, it is a sufficient condition for the possession of a property that is, in turn, a necessary condition for correct predicting; and further there could be no reason to expect any non-objective method to possess this necessary condition for success. Induction is the only objective method of predicting for it alone uses facts which must be identified by any predicting method based on rules; and it alone uses these facts according to a relationship that must hold between facts and any meaningful empirical statement. Any alternative to induction must assume that the factual regularities that have been detected will alter in the future and the way they are expected to alter must be arbitrary. It is further claimed that this vindication is proof against the criticisms that have been advanced against practicalist justifications of induction. (shrink)

Claims to have solved the problem of induction are always stimulating, and especially so when the claim is put forward with the wit and sparkle of Professor Mellor's inaugural lecture The Warrant of Induction (Cambridge: Cambridge University Press, 1988). Unfortunately, however, Mellor's proposed solution is inadequate to its task.

An improvement on Horwich's so-called pseudo-proof of Russell 's principle of induction is offered, which, we believe, avoids certain objections to the former. Although strictly independent of our other work in this area, a connection can be made and in the final section we comment on this and certain questions regarding rationality, etc.

The dissertation is a detailed critique of the main elements of Hans Reichenbach's pragmatic treatment of the problem of induction. In the introductory Chapter I we give a broad overview of Reichenbach's theory of probability and induction, indicating that he approaches the problem of justifying inductive inference in general by attempting first to reduce all kinds of non-deductive reasoning to combinations of inferences in accordance with the rules of deductive logic together with RRI -- the "rule of induction." Having thus (...) reduced inductive inference to its elementary components, he then proposes to solve the problem of justification by providing independent pragmatic justifications for those components. In Chapter II we show that Reichenbach's analysis of inductive inference involves a second non-deductive elementary component, a rule of application (RRA), which he fails to integrate properly into his theory of induction. RRI is a rule for "inferring" statistical probability statements from observed relative frequencies -- a rule of inverse inference. RRA is a rule for "predicting" individual events on the basis of statistical probability statements -- a rule of direct inference. We show that Reichenbach construes elementary inductive "inference" in such a way that only a pragmatic justification of the _combined_ use of RRI and RRA will suffice for a Reichenbachian solution to the problem of induction. It is further argued that there is no reasonable pragmatic point of view from which RRI alone could be justified. In Chapter III we find that RRA, when suitably modified to avoid a certain defect in Reichenbach's version of it, can justifiably be used by an agent only if he has (a) knowledge of a certain probability, (b) knowledge that he is going to deal with almost all of the members of a certain sequence, and (c) knowledge about the sizes of the utility stakes associated with the sequence in question. Reichenbach makes no provision for (c), while his attempt to satisfy the requirement (b) by appeal to Poisson sequences turns out to be fundamentally unsatisfactory. The knowledge required by (a) is presumably to be supplied through the use of RRI. In Chapter IV we consider the combination of RRI and RRA, which yields a rule for "predicting" individual events on the basis of observed relative frequencies -- i.e., a rule of predictive inference. The task of justifying such predictive inference is the heart of the problem of induction as it arises for Reichenbach. Yet we argue that RRI does not yield the probability knowledge required for the statistically justified use of RRA, while an alternative approach to the justification of predictive inference suggested by Reichenbach's reply to an old objection of Paul Hertz is shown to require a conception of predictive inference which is pragmatically unacceptable. Reichenbachian predictive inference thus remains unjustified. In Chapter V we consider in detail Reichenbach's "method of correction," which lies at the foundation of both his theory of higher-level probabilities and his attempted epistemological reduction of all scientific inference to a combination of deductive logic with his elementary inductive rule(s). His justificatory arguments in this connection concerning earliness of probability-finding are found to be grossly unsatisfactory, while the prospects for an alternative statistical justification are shown to be nil. Thus, the method of correction and the reductive developments which depend on it appear to be quite groundless. In Chapter VI, we draw the earlier results together and conclude that Reichenbach's attempt to provide pragmatic foundations for an empiricist theory of knowledge falls far short of its goal in ways which have not generally been recognized. Finally, we offer some brief reflections on the pragmatic rationale which underlies the Reichenbachian program. (shrink)

An improvement on Horwich's so-called "pseudo-proof" of Russell's principle of induction is offered, which, we believe, avoids certain objections to the former. Although strictly independent of our other work in this area, a connection can be made and in the final section we comment on this and certain questions regarding rationality, etc.

This paper defines the form of prior knowledge that is required for sound inferences by analogy and single-instance generalizations, in both logical and probabilistic reasoning. In the logical case, the first order determination rule defined in Davies (1985) is shown to solve both the justification and non-redundancy problems for analogical inference. The statistical analogue of determination that is put forward is termed 'uniformity'. Based on the semantics of determination and uniformity, a third notion of "relevance" is defined, both logically and (...) probabilistically. The statistical relevance of one function in determining another is put forward as a way of defining the value of information: The statistical relevance of a function F to a function G is the absolute value of the change in one's information about the value of G afforded by specifying the value of F. This theory provides normative justifications for conclusions projected by analogy from one case to another, and for generalization from an instance to a rule. The soundness of such conclusions, in either the logical or the probabilistic case, can be identified with the extent to which the corresponding criteria (determination and uniformity) actually hold for the features being related. (shrink)

I critically examine an evolutionary debunking argument against moral realism. The key premise of the argument is that there is no adequate explanation of our moral reliability. I search for the strongest version of the argument; this involves exploring how ‘adequate explanation’ could be understood such that the key premise comes out true. Finally, I give a reductio: in the sense in which there is no adequate explanation of our moral reliability, there is equally no adequate explanation of our inductive (...) reliability. Thus, the argument that would debunk our moral views would also, absurdly, debunk all inductive reasoning. (shrink)

In this essay, I take the role as friendly commentator and call attention to three potential worries for John D. Norton’s material theory of induction. I attempt to show that his “principle argument” is based on a false dichotomy, that the idea that facts ultimately derive their license from matters of fact is debatable, and that one of the core implications of his theory is untenable for historical and fundamental reasons.

If one believes, as Hume did, that all events are loose and separate, then the problem of induction is probably insoluble. Anything could happen. But if one thinks, as scientific essentialists do, that the laws of nature are immanent in the world, and depend on the essential natures of things, then there are strong constraints on what could possibly happen. Given these constraints, the problem of induction may be soluble. For these constraints greatly strengthen the case for conceptual and theoretical (...) conservatism, and rule out Goodmanesque inferences based on alternative descriptions of the world. This may not, in itself, solve the problem, but it significantly changes its nature. (shrink)

This article offers a simple technical resolution to the problem of induction, which is to say that general facts are not always inferred from observations of particular facts, but are themselves sometimes defeasibly observed. The article suggests a holistic account of observation that allows for general statements in empirical theories to be interpreted as observation reports, in place of the common but arguably obsolete idea that observations are exclusively particular. Predictions and other particular statements about unobservable facts can then appear (...) as deductive consequences of such general observation statements, rather than inductive consequences of other particular statements. This semantic shift resolves the problem by eliminating induction as a basic form of inference, and folding the justification of general beliefs into the more basic problem of perception. (shrink)

In this paper I argue that Norton's case against Brown's rationalism about thought experiments suffers from serious shortcomings, which relate to the nature of induction.