First I employ Bayes's Theorem to give some precision to the atheologian's thesis that it is improbable that God exists given the amount of evil in the world (E). Two arguments result from this: (1) E disconfirms God's existence, and (2) E tends to disconfirm God's existence. Secondly, I evaluate these inductive arguments, suggesting against (1) that the atheologian has abstracted from and hence failed to consider the total evidence, and against (2) that the atheologian's evidence adduced to support (...) his thesis regarding the relevant probabilities is inadequate. (shrink)

According to a familiar argument, iterated prisoner's dilemmas of known finite lengths resolve for ideally rational and well-informed players: They would defect in the last round, anticipate this in the next to last round and so defect in it, and so on. But would they anticipate defections even if they had been cooperating? Not necessarily, say recent critics. These critics "lose" the backward-induction paradox by imposing indicative interpretations on rationality and information conditions. To regain it I propose subjunctive interpretations. (...) To solve it I stress that implications for ordinary imperfect players are limited. (shrink)

A simple summary of the difference between induction and deduction.

In philosophy, an argument consists of a set of statements called premises that serve as grounds for affirming another statement called the conclusion. Philosophers typically distinguish arguments in natural languages (such as English) into two fundamentally different types: deductive and inductive. Each type of argument is said to have characteristics that categorically distinguish it from the other type. The two types of argument are also said to be subject to differing evaluative standards. Pointing to paradigmatic examples (...) of each type of argument helps to clarify their key differences. The distinction between the two types of argument may hardly seem worthy of philosophical reflection, as evidenced by the fact that their differences are usually presented as straightforward, such as in many introductory philosophy textbooks. Nonetheless, the question of how best to distinguish deductive from inductive arguments, and indeed whether there is a coherent categorical distinction between them at all, turns out to be considerably more problematic than commonly recognized. This article identifies and discusses a range of different proposals for marking categorical differences between deductive and inductive arguments while highlighting the problems and limitations attending each. Consideration is also given to the ways in which one might do without a distinction between two types of argument by focusing solely on the application of evaluative standards to arguments instead. (shrink)

The backward induction argument purports to show that rational and suitably informed players will defect throughout a finite sequence of prisoner's dilemmas. It is supposed to be a useful argument for predicting how rational players will behave in a variety of interesting decision situations. Here, I lay out a set of assumptions defining a class of finite sequences of prisoner's dilemmas. Given these assumptions, I suggest how it might appear that backward induction succeeds and why it is actually (...) fallacious. Then, I go on to consider the consequences of adopting a stronger set of assumptions. Focusing my attention on stronger sets that, like the original, obey the informedness condition, I show that any supplementation of the original set that preserves informedness does so at the expense of forcing rational participants in prisoner's dilemma situations to have unexpected beliefs, ones that threaten the usefulness of backward induction. (shrink)

Many philosophers and game theorists have been struck by the thought that the backward induction argument (BIA) for the finite iterated pris- oner’s dilemma (FIPD) recommends a course of action which is grossly counter-intuitive and certainly contrary to the way in which people behave in real-life FIPD-situations (Luce and Raiffa 1957, Pettit and Sugden 1989, Bovens 1997).1 Yet the backwards induction argument puts itself forward as binding upon rational agents. What are we to conclude from this? Is it (...) that people in real-life FIPD-situations tend to act irrationally and that our own intuitions about what to do in such situations reveal us to be irra- tional? Alternatively, should we abandon game theory and decision theory as a guide to rationality? Or are there other ways in which the apparent disparity between the dictates of rationality and the reality of reasoning can be accommodated? (shrink)

There are two curious features about the backward induction argument (BIA) to the effect that repeated non-cooperation is the rational solution to the finite iterated prisoner’s dilemma (FIPD). First, however compelling the argument may seem, one remains hesitant either to recommend this solu- tion to players who are about to engage in cooperation or to explain cooperation as a deviation from rational play in real-life FIPD’s. Second, there seems to be a similarity between the BIA for the FIPD (...) and the surprise exam paradox (SEP) and one cannot help but wonder whether the former is indeed no more than an instance of the latter. I argue that there is an important difference between the BIA for the FIPD and the SEP, but that a comparison to the SEP can help us understand why the conclusion of the BIA for the FIPD strikes us as a counterintuitive solution to real-life FIPD’s. (shrink)

Metaphysical problems may be solved by the methods of inference employed in the empirical sciences. So we are told by many realists and pragmatists, among whom may be mentioned Professors J. B. Pratt, William Savery, and Donald Williams. Mr. Williams and Mr. Pratt have argued for the use of inductive methods in establishing the existence of an external world. Mr. Savery has asserted that all philosophical inference as to matter of fact is inductive. This naturalistic attitude is by (...) no means unusual—in fact it is so common in this age in which the speculations of scientists as well as their achievements have captivated the popular imagination, that even philosophers have for the most part failed to examine its validity and presuppositions. It is the purpose of this paper to present such an examination, not of the philosophic employment of inductive methods in general, but in regard to one specific problem; namely, that of the existence of an external world. What I purpose then is to present and evaluate the view that the existence of an external world may be established by inductive methods as employed in the empirical sciences. (shrink)

The traditional form of the backward induction argument, which concludes that two initially rational agents would always defect, relies on the assumption that they believe they will be rational in later rounds. Philip Pettit and Robert Sugden have argued, however, that this assumption is unjustified. The purpose of this paper is to reconstruct the argument without using this assumption. The formulation offered concludes that two initially rational agents would decide to always defect, and relies only on the weaker (...) assumption that they do not believe they will not be rational in later rounds. The argument employs the idea that decisions justify revocable presumptions about behaviour. (shrink)

This essay discusses and criticizes Richard Swinburne's inductive argument for the existence of God. In his The Existence of God, Swinburne aims at showing that the existence of God is more probable than not. This is an argument taking into consideration the premises of all traditional arguments for the existence of God. Swinburne uses the phenomena and events that constitute the premises of these arguments as evidence in an attempt to show that his hypothesis is more probably (...) true than nor. Swinburne pursues this task by way of applying Bayes' theorem. The aim of this essay is normative - to judge the strength of Swinburne's argument for the existence of God. My primary objections towards Swinburne is that he professes a subjective concept of probability, that he relies too heavily on simplicity as a virtue of plausible and probable hypotheses and that his concept of God involves an incoherent picture of God's nature. I question not only the actual success of Swinburne's project but what his argument, if it had been successful, would have been able to establish. (shrink)

C-Inductive arguments are arguments that increase the probability of a hypothesis. This can be contrasted with what is called a P-Inductive argument. A P-inductive argument is an argument that shows the overall probability of a hypothesis to be more probable than not. In this paper, we put forth a C-inductive argument for the truth of the Catholic hypothesis (CH). Roughly, we take CH to be the hypothesis that the core creedal beliefs found (...) within the Catholic Tradition are true. Specifically, we argue that we would expect the Miracle of Fátima on CH, but, we wouldn’t expect it as much on ~CH. In order to establish this thesis, we first discuss the basics of confirmation theory. Second, we give the historical context of the Miracle of Fátima. Third, we briefly survey and then reject two possible non-supernatural explanations of the apparent miracle. Doing this will help make plausible that the Miracle of Fátima is actual evidence that a hypothesis needs to predict. Fourth, we give the details as to why we should expect the Miracle of Fátima more on CH than ~CH. Finally, we argue that miracles that occur in Protestant contexts, generally don’t carry the same evidential weight for a Protestant hypothesis as the Miracle of Fátima carries for CH. (shrink)

In recent years there have been several attempts to construct inductive arguments for some version of scientific realism. Neither the characteristics of what would count as inductive evidence nor the conclusion to be inferred have been specified in ways that escape sceptical criticism. By introducing the pragmatic criterion of manipulative efficacy for a good theory and by sharpening the specification of the necessary inductive principle, the viability of a mutually supporting pair of argument forms are defended. (...) It is shown that by the use of these forms, taken together, a sequence of inductive arguments could be constructed, given suitable cases histories to serve as evidence. It also shown that the best inductive argument for the most daring realist claim is the weakest when compared with similarly structured arguments for less daring claims. (shrink)

In this paper, I discuss how Newton’s inductive argument of the Principia can be defended against criticisms levelled against it by Duhem, Popper and myself. I argue that Duhem’s and Popper’s criticisms can be countered, but mine cannot. It requires that we reconsider, not just Newton’s inductive argument in the Principia, but also the nature of science more generally. The methods of science, whether conceived along inductivist or hypothetico-deductivist lines, make implicit metaphysical presuppositions which rigour requires (...) we make explicit within science so that they can be critically assessed, alternatives being developed and assessed, in the hope that they can be improved. Despite claiming to derive his law of gravitation by induction from phenomena without resource to hypotheses, Newton does nevertheless acknowledge in the Principia that his rules of reasoning make metaphysical presuppositions. To this extent, Newton has a more enlightened view of scientific method than most 20th and 21st century scientists and historians and philosophers of science. (shrink)

In a priori analogies, the analogue is constructed in imagination, sharing certain properties with the primary subject. The analogue has some further property clearly consequent on those shared properties. Ceteris paribus the primary subject has that property also. The warrant involves non-empirical, e.g., moral intuition but is also defeasible. The argument is thus neither deductive nor inductive, but an additional type. In an inductive analogy, the analogues back the warrant from below. Distinguishing these two types of arguments (...) by analogy gives epistemic evaluative factors primacy over resemblance factors in classifying arguments—a prescient insight on Govier’s part. (shrink)

Roy Harrod; III—The General Structure of Inductive Argument, Proceedings of the Aristotelian Society, Volume 61, Issue 1, 1 June 1961, Pages 41–56, https://doi.

Studies on so-called Change Blindness and Inattentional Blindness have been taken to establish the claim that conscious perception of a stimulus requires the attentional processing of that stimulus. One might contend, against this claim, that the evidence only shows attention to be necessary for the subject to have access to the contents of conscious perception and not for conscious perception itself. This “Methodological Argument” is gaining ground among philosophers who work on attention and consciousness, such as Christopher Mole. I (...) find that, without the supporting evidence of inaccessible consciousness, this argument collapses into an indefensible form of inductive parsimony. The Methodological Argument is thus shown to be unsuccessful when used against the claim that attention is required for conscious perception, though I suggest that it may be successful against the more ambitious claim that attention is necessary for all conscious experience. (shrink)

Abstract In order to be a general theory of human cognition, the theory of mental models needs to accommodate a variety of forms of reasoning in addition to deduction. The mental model theory of induction is a crucial step in establishing generality. After suggesting that the theory of mental models can also account for abduction and analogy, the paper points out that inductive performance is likely to be constrained both by the nature of the representation used and by strategic (...) factors. Since human cognition involves the communication of arguments, a final section explores the relationship between the theory of mental models and the notion of an argument. It proposes that models can contain tokens of inductive arguments which can be referred to in the course of other arguments. (shrink)

A thorough and practical introduction to inductive logic with a focus on arguments and the rules used for making inductive inferences.

In this paper, I consider the pessimistic induction construed as a deductive argument (specifically, reductio ad absurdum) and as an inductive argument (specifically, inductive generalization). I argue that both formulations of the pessimistic induction are fallacious. I also consider another possible interpretation of the pessimistic induction, namely, as pointing to counterexamples to the scientific realist’s thesis that success is a reliable mark of (approximate) truth. I argue that this interpretation of the pessimistic induction fails, too. If (...) this is correct, then the pessimistic induction is an utter failure that should be abandoned by scientific anti-realists. (shrink)

The argument from inductive risk, as developed by Rudner and others, famously concludes that the scientist qua scientist makes value judgments. The paper aims to show that trust in the soundness of the argument is overrated – that philosophers who endorse its conclusion fail to refute two of the most important objections that have been raised to its soundness: Jeffrey’s objection that the genuine task of the scientist is to assign probabilities to hypotheses, and Levi’s objection that (...) the argument is ambiguous about decisions about how to act and decisions about what to believe, that only the former presuppose value judgments, and that qua scientist, the scientist only needs to decide what to believe. (shrink)

Hume’s argument concerning induction is the foundation stone of his philosophical system, and one of the most celebrated and influential arguments in the entire literature of western philosophy. It is therefore rather surprising that the enormous attention which has been devoted to it over the years has not resulted in any general consensus as to how it should be interpreted, or, in consequence, how Hume himself should be seen. At one extreme is the traditional view, which takes the (...) class='Hi'>argument to be thoroughly sceptical, leading to the sweeping conclusion that all “probable reasoning” or “reasoning concerning matter of fact and existence” is utterly worthless, so that Hume is portrayed as a negative Pyrrhonian intent on undermining the credentials of all our would-be knowledge of the world. But at the other extreme a number of very prominent commentators, particularly in recent years, have put forward a strikingly contrasting view, that Hume’s intentions here are entirely non-sceptical, and that so far from advancing a negative thesis himself, he is merely intent on showing the implausible consequences of the “rationalist” position taken by some of his philosophical opponents. (shrink)

Developing the ideas presented in Jacquette (2011), the paper presents an indispensability argument aimed at justification of induction. First, Hume’s problem of induction is introduced via slightly different reconstructions. Second, several traditional attempts to solve Hume’s problem are presented. Finally, Jacquette’s(2011) proposal to justify induction by an indispensability argument is developed. I conclude with presenting a kind of indispensability argument for induction.

Three experiments examined the influence of argument length on plausibility judgements, in a category-based induction task. The general results were that when arguments were logically invalid they were considered stronger when they were longer, but for logically valid arguments longer arguments were considered weaker. In Experiments 1a and 1b when participants were forewarned to avoid using length as a cue to judging plausibility, they still did so. Indeed, participants given the opposite instructions did not follow those instructions either. In (...) Experiment 2 arguments came from a reliable or unreliable speaker. This manipulation affected accuracy as well as response bias, but the effects of argument length for both reliable and unreliable speakers replicated Experiments 1a and 1b. The results were analysed using receiver operating characteristic (ROC) curves and modelled using multidimensional signal detection theory (SDT). Implications for models of category-based inductive reasoning, and theories of reasoning more generally, are discussed. (shrink)

In the middle of a conference on the logic of science, an eminent biologist once said: “Does it not bother you guys that we scientists do not use any logic at all.” This statement was meant to be a friendly provocation, but there also was a serious message. Scientists often say that the logical analyses are exercises in formal logic and fail to illuminate what the scientists are doing, actual scientific practice. This recurring complaint, although not completely as I will (...) suggest, has not gone unnoticed in the philosophy of science. Indeed, the current trend in analytic philosophy of science as well as in teaching the method of science has been away from logic as a means of illuminating scientific inquiry. (shrink)

It is widely agreed that Hume's description of human inductive reasoning is inadequate. But many philosophers think that this inadequacy in no way affects the force of Hume's argument for the unjustifiability of inductive reasoning. I argue that this constellation of opinions contains a serious tension, given that Hume was not merely pointing out that induction is fallible. I then explore a recent diagnosis of where Hume's sceptical argument goes wrong, due to Elliott Sober. Sober argues (...) that Hume committed a quantifier-shift fallacy, i.e. inferred a statement of ?? form from one of ?? form. The implications of this diagnosis for the traditional problem of induction are briefly examined. (shrink)

Our reasoning evolved not for finding the truth, but for social bonding and convincing. This book highlights the consequences of these facts for scientific practice, and suggests how to correct the mistakes we still make.

Havstad (2022) argues that the argument from inductive risk for the claim that non-epistemic values have a legitimate role to play in the internal stages of science is deductively valid. She also defends its premises and thus soundness. This is, as far as we are aware, the best reconstruction of the argument from inductive risk in the existing literature. However, there is a small flaw in this reconstruction of the argument from inductive risk which (...) appears to render the argument invalid. This flaw is superficial, and a small amendment to it rescues the claim of validity. (shrink)