Induction, Misc

I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act as (...) if one has substantive information about the world when one does not. I sketch the outlines of a solution in part I, showing how it differs from others, with full details to follow in subsequent parts. The solution is pragmatic in sentiment (though differs in specifics to arguments from, for example, William James); the conceptions we use to guide our actions are and should be at least partly determined by preferences. This is cashed out in a reformulation of decision theory motivated by a non-reductive formulation of hypotheses and logic. A distinction emerges between initial assumptions--that can be non-dogmatic--and effective assumptions that can simultaneously be substantive. An explanation is provided for the plausibility arguments used to explain assigned probabilities in BCT. -/- In subsequent parts, logic is constructed from principles independent of language and mind. In particular, propositions are defined to not have form. Probabilities are logical and uniquely determined by assumptions. The problems considered fatal to logical probabilities--Goodman's `grue' problem and the uniqueness of priors problem are dissolved due to the particular formulation of logic used. Other problems such as the zero-prior problem are also solved. -/- A universal theory of (non-linguistic) meaning is developed. Problems with counterfactual conditionals are solved by developing concepts of abstractions and corresponding pictures that make up hypotheses. Spaces of hypotheses and the version of Bayes' theorem that utilises them emerge from first principles. -/- Theoretical virtues for hypotheses emerge from the theory. Explanatory force is explicated. The significance of effective assumptions is partly determined by combinatoric factors relating to the structure of hypotheses. I conjecture that this is the origin of simplicity. (shrink)

It is generally accepted among philosophers of science that hypothesis testing is a key methodological feature of science. As far as philosophical theories of confirmation are con...

I examine what the mathematical theory of random structures can teach us about the probability of Plenitude, a thesis closely related to David Lewis's modal realism. Given some natural assumptions, Plenitude is reasonably probable a priori, but in principle it can be (and plausibly it has been) empirically disconfirmed—not by any general qualitative evidence, but rather by our de re evidence.

Hope is an attitude with a distinctive epistemological dimension: it is incompatible with knowledge. This chapter examines hope as it relates to knowledge but also to probability and inductive considerations. Such epistemic constraints can make hope either impossible, or, when hope remains possible, they affect how one’s epistemic situation can make hope rational rather than irrational. Such issues are especially relevant to when hopefulness may permissibly figure in practical deliberation over a course of action. So I consider cases of second-order (...) inductive reflection on when one should, or should not, be hopeful for an outcome with which one has a long record of experience: in other words, what is the epistemology behind when one should, if ever, stop hoping for outcomes which have failed one many times in the past? (shrink)

This paper argues that philosophers of science have before them an important new task that they urgently need to take up. It is to convince the scientific community to adopt and implement a new philosophy of science that does better justice to the deeply problematic basic intellectual aims of science than that which we have at present. Problematic aims evolve with evolving knowledge, that part of philosophy of science concerned with aims and methods thus becoming an integral part of science (...) itself. The outcome of putting this new philosophy into scientific practice would be a new kind of science, both more intellectually rigorous and one that does better justice to the best interests of humanity. (shrink)

There are a bewildering variety of claims connecting Darwin to nineteenth-century philosophy of science—including to Herschel, Whewell, Lyell, German Romanticism, Comte, and others. I argue here that Herschel’s influence on Darwin is undeniable. The form of this influence, however, is often misunderstood. Darwin was not merely taking the concept of “analogy” from Herschel, nor was he combining such an analogy with a consilience as argued for by Whewell. On the contrary, Darwin’s Origin is written in precisely the manner that one (...) would expect were Darwin attempting to model his work on the precepts found in Herschel’s Preliminary Discourse on Natural Science. While Hodge has worked out a careful interpretation of both Darwin and Herschel, drawing similar conclusions, his interpretation misreads Herschel’s use of the vera causa principle and the verification of hypotheses. The new reading that I present here resolves this trouble, combining Hodge’s careful treatment of the structure of the Origin with a more cautious understanding of Herschel’s philosophy of science. This interpretation lets us understand why Darwin laid out the Origin in the way that he did and also why Herschel so strongly disagreed, including in Herschel’s heretofore unanalyzed marginalia in his copy of Darwin’s book. (shrink)

Sosa, Pritchard, and Vogel have all argued that there are cases in which one knows something inductively but does not believe it sensitively, and that sensitivity therefore cannot be necessary for knowledge. I defend sensitivity by showing that inductive knowledge is sensitive.

As it is standardly conceived, Inference to the Best Explanation (IBE) is a form of ampliative inference in which one infers a hypothesis because it provides a better potential explanation of one’s evidence than any other available, competing explanatory hypothesis. Bas van Fraassen famously objected to IBE thus formulated that we may have no reason to think that any of the available, competing explanatory hypotheses are true. While revisionary responses to the Bad Lot Objection concede that IBE needs to be (...) reformulated in light of this problem, reactionary responses argue that the Bad Lot Objection is fallacious, incoherent, or misguided. This paper shows that the most influential reactionary responses to the Bad Lot Objection do nothing to undermine the original objection. This strongly suggests that proponents of IBE should focus their efforts on revisionary responses, i.e. on finding a more sophisticated characterization of IBE for which the Bad Lot Objection loses its bite. (shrink)

Philosophy of science is seen by most as a meta-discipline – one that takes science as its subject matter, and seeks to acquire knowledge and understanding about science without in any way affecting, or contributing to, science itself. Karl Popper’s approach is very different. His first love is natural philosophy or, as he would put it, cosmology. This intermingles cosmology and the rest of natural science with epistemology, methodology and metaphysics. Paradoxically, however, one of his best known contributions, his proposed (...) solution to the problem of demarcation, helps to maintain the gulf that separates science from metaphysics, thus fragmenting cosmology into falsifiable science on the one hand, untestable philosophy on the other. This has damaging repercussions for a number of issues Popper tackles, from the problem of induction to simplicity of theory and quantum theory. But his proposed solution to the demarcation problem is untenable. Metaphysical assumptions are an integral part of scientific knowledge, inherent in the persistent acceptance of unified theories against the evidence. Once this is appreciated, it becomes obvious that natural philosophy, a synthesis of science and philosophy, is both more rigorous and of greater intellectual value than the two dissociated components we have today. What Popper sought for could come to full fruition. Problems that Popper tackled, from the problem of induction, to the problem of unity of theory, problems of quantum theory, and problems concerning the scope and limits of physics, all receive more adequate resolution within the new, fully-fledged natural philosophy. (shrink)

Formal and empirical work on the Wisdom of Crowds has extolled the virtue of diverse and independent judgment as essential to the maintenance of ‘wise crowds’. In other words, com-munication and imitation among members of a group may have the negative effect of decreasing the aggregate wisdom of the group. In contrast, it is demonstrable that certain meta-inductive methods provide optimal means for predicting unknown events. Such meta-inductive methods are essentially imitative, where the predictions of other agents are imitated to (...) the extent that those agents have proven successful in the past. Despite the (self-serving) optimality of meta-inductive methods, their imitative nature may undermine the ‘wisdom of the crowd’, since these methods recommend that agents imitate the predictions of other agents. In this paper, I present a replication of selected results of Thorn and Schurz, illustrating the effect on a group’s performance that may result from having members of a group adopt meta-inductive methods. I then expand on the work of Thorn and Schurz by considering three simple measures by which meta-inductive prediction methods may improve their own performance, while simultaneously mitigating their negative impact on group performance. The effects of adopting these maneuvers are investigated using computer simulations. (shrink)

State of the art paper on the problem of induction: how to justify the conclusion that ‘all Fs are Gs’ from the premise that ‘all observed Fs are Gs’. The most prominent theories of contemporary philosophical literature are discussed and analysed, such as: inductivism, reliabilism, perspective of laws of nature, rationalism, falsificationism, the material theory of induction and probabilistic approaches, according to Carnap, Reichenbach and Bayesianism. In the end, we discuss the new problem of induction of Goodman, raised by the (...) grue predicate. (shrink)

The applicability of Bayesian conditionalization in setting one’s posterior probability for a proposition, α, is limited to cases where the value of a corresponding prior probability, PPRI(α|∧E), is available, where ∧E represents one’s complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one’s personal probability in a proposition by conditioning on a proposition that represents a (...) proper subset of one’s complete body of evidence. While defeasible conditionalization has wider applicability than standard Bayesian conditionalization (since it may be used when the value of a relevant prior probability, PPRI(α|∧E), is unavailable), there are circumstances under which some instances of defeasible conditionalization are unreasonable. To address this difficulty, I outline the conditions under which instances of defeasible conditionalization are defeated. To conclude the article, I suggest that the prescriptions of direct inference and statistical induction can be encoded within the proposed system of probability updating, by the selection of intuitively reasonable prior probabilities. (shrink)

Many people argue that history makes a special difference to the subjects of biology and psychology, and that history does not make this special difference to other parts of the world. This paper will show that historical properties make no more or less of a difference to biology or psychology than to chemistry, physics, or other sciences. Although historical properties indeed make a certain kind of difference to biology and psychology, this paper will show that historical properties make the same (...) kind of difference to geology, sociology, astronomy, and other sciences. Similarly, many people argue that nonhistorical properties make a special difference to the nonbiological and the nonpsychological world. This paper will show that nonhistorical properties make the same difference to all things in the world when it comes to their causal behavior and that historical properties make the same difference to all things in the world when it comes to their distributions. Although history is special, it is special in the same way to all parts of the world. (shrink)

Meta-induction, in its various forms, is an imitative prediction method, where the prediction methods and the predictions of other agents are imitated to the extent that those methods or agents have proven successful in the past. In past work, Schurz demonstrated the optimality of meta-induction as a method for predicting unknown events and quantities. However, much recent discussion, along with formal and empirical work, on the Wisdom of Crowds has extolled the virtue of diverse and independent judgment as essential to (...) maintenance of 'wise crowds'. This suggests that meta-inductive prediction methods could undermine the wisdom of the crowd inasmuch these methods recommend that agents imitate the predictions of other agents. In this article, we evaluate meta-inductive methods with a focus on the impact on a group's performance that may result from including meta-inductivists among its members. In addition to considering cases of global accessibility (i.e., cases where the judgments of all members of the group are available to all of the group's members), we consider cases where agents only have access to the judgments of other agents within their own local neighborhoods. (shrink)

Applying good inductive rules inside the scope of suppositions leads to implausible results. I argue it is a mistake to think that inductive rules of inference behave anything like 'inference rules' in natural deduction systems. And this implies that it isn't always true that good arguments can be run 'off-line' to gain a priori knowledge of conditional conclusions.

The problem of rational prediction, launched by Wesley Salmon, is without doubt the Achilles heel of the critical method defended by Popper. In this paper, I assess the response given both by Popper and by the popperian Alan Musgrave to this problem. Both responses are inadequate and thus the conclusion of Salmon is reinforced: without appeal to induction, there is no way to make of the practical prediction a rational action. Furthermore, the critical method needs to be vindicated if one (...) pretends that its application be suitable for the preference of hypothesis. I argue that the nature of this vindication is such that it may be applied also to induction. Thus, to be a popperian is a good reason also to be an inductivist. (shrink)

The hard problem of induction is to argue without begging the question that inductive inference, applied properly in the proper circumstances, is conducive to truth. A recent theorem seems to show that the hard problem has a deductive solution. The theorem, provable in zfc, states that a predictive function M exists with the following property: whatever world we live in, M correctly predicts the world’s present state given its previous states at all times apart from a well-ordered subset. On the (...) usual model of time a well-ordered subset is small relative to the set of all times. M’s existence therefore seems to provide a solution to the hard problem. My paper argues for two conclusions. First, the theorem does not solve the hard problem of induction. More positively though, it solves a version of the problem in which the structure of time is given modulo our choice of set theory. (shrink)

In this book the analysis of the relationship between Whewell and Mill is extended from the theme of induction, the topic the author starts with, to the comparison between the two projects of an overall reform of knowledge. These programmes announce themselves to the general public as proclamations of war for or against the academic, political and religious establishment; however, when viewed from the inside, they more or less consciously share very similar objectives. This applies both to the scientific method (...) and to ethics and politics. (shrink)

Even though evidence underdetermines theory, often in science one theory only is regarded as acceptable in the light of the evidence. This suggests there are additional unacknowledged assumptions which constrain what theories are to be accepted. In the case of physics, these additional assumptions are metaphysical theses concerning the comprehensibility and knowability of the universe. Rigour demands that these implicit assumptions be made explicit within science, so that they can be critically assessed and, we may hope improved. This leads to (...) a new conception of science, one which we need to adopt in order to solve the problem of induction. (shrink)

This paper constitutes one extended argument, which touches on various topics of Critical Rationalism as it was initiated by Karl Popper and further developed in his aftermath. The result of the argument will be that critical rationalism either offers no solution to the problem of induction at all, or that it amounts, in the last resort, to a kind of Critical Rationalist Inductivism as it were, a version of what I call Good Old Induction. One may think of David Miller (...) as a contemporary representative of what I consider as the ‘no solution’ version of critical rationalism, while Alan Musgrave stands for the version of ‘critical rationalist induction’. Popper’s own writings admit of either interpretation. (shrink)

We ordinarily assume that we have reliable knowledge of our immediate surroundings, so much so that almost all the time we entrust our lives to the truth of what we take ourselves to know, without a moment’s thought. But if, as Karl Popper and others have maintained, all our knowledge is conjectural, then this habitual assumption that our common sense knowledge of our environment is secure and trustworthy would seem to be an illusion. Popper’s philosophy of science, in particular, fails (...) to do justice to the distinction we ordinarily draw between secure knowledge and mere conjecture. But Popper’s philosophy of science, in particular his attempted solution to the problem of induction, is defective. It fails to take into account that physics, in only accepting unified theories, even though endlessly empirically more successful disunified rivals are always available, makes the persistent metaphysical assumption that all disunified theories are false. Once this point is acknowledged, it becomes clear that a new conception of scientific method is required which sees science as making a hierarchy of metaphysical assumptions concerning the comprehensibility and knowability of the universe. This provides a framework of relatively unproblematic assumptions and associated methods of science within which much more problematic assumptions and associated methods can be critically assessed and improved. This hierarchical view seems at first to intensify the problem of distinguishing certainty from conjecture, in that it emphasizes that scientific knowledge, and even humble common sense knowledge, contain usually unacknowledged cosmological conjectures. But actually it explicates the basis we have for drawing the distinction between trustworthy knowledge and mere conjecture, and even goes some way towards providing a rationale for this distinction, in so far as one exists. (shrink)

This paper contends that some of the recent critical appraisals of universals theories of natural laws, namely, van Fraassen's analysis of Armstrong's probabilistic laws, are largely ineffective since they fail to disclose the incompatibility of universals and any realistic natural law setting. Rather, a more profitable line of criticism is developed that contests the universalists' claim to have resolved the induction problem (i.e., the separation of natural laws from mere accidental regularities), and thereby reveals the universals' philosophically inadequate concept of (...) a physical property. (shrink)

Geoffrey Stokes's introduction to Karl Popper's work portrays it as an evolving system of ideas and aims to explore the little-understood intricate logical relationships between Popper's work on scientific method and his philosophy of politics. It is one of the few books to cover the debate between Popper and the Frankfurt School. Characteristic of many of Stokes's "criticisms" is that they are presented as Popper "admitting" or "granting" them - as if Popper was not the one who originally raised and (...) dealt with them in the systematic elaboration of his philosophy. A refreshing exception is that Stokes acknowledges (but only in a footnote) that the idea that Popper was originally a "dogmatic falsificationist" is merely a Lakatosian myth. (shrink)

The word ‘induction’ is derived from Cicero’s ‘inductio’, itself a translation of Aristotle’s ‘epagôgê’. In its traditional sense this denotes the inference of general laws from particular instances, but within modern philosophy it has usually been understood in a related but broader sense, covering any non-demonstrative reasoning that is founded on experience. As such it encompasses reasoning from observed to unobserved, both inference of general laws and of further particular instances, but it excludes those cases of reasoning in which the (...) conclusion is logically implied by the premises, such as induction by complete enumeration. (shrink)