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)

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)

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)

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)

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)

A simple summary of the difference between induction and deduction.

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)

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)

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)

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)

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 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.

Is it possible to have moral knowledge? ‘Moral justification skeptics’ hold it is not, because moral beliefs cannot have the sort of epistemic justification necessary for knowledge. This skeptical stance can be summed up in a single, neat argument, which includes the premise that ‘Inductive arguments from non-moral premises to moral conclusions are not possible.’ Other premises in the argument may rejected, but only at some cost. It would be noteworthy, therefore, if ‘inductive inferentialism’ about morals (...) were shown to be at least possible. Some philosophers may suppose that inductive moral arguments from non-moral premises cannot get off the ground, but I show that a perfectly legitimate inductive moral argument exists. This argument has non-moral premises and a moral conclusion, its premises are related to its conclusion in the right way, and it avoids some of the problems of other, better-known arguments from ‘Is’ to ‘Ought’. (shrink)

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)

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)

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)

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

Since the mid-1970s, scholars have recognized that the skeptical interpretation of Hume's central argument about induction is problematic. The science of human nature presupposes that inductive inference is justified and there are endorsements of induction throughout "Treatise" Book I. The recent suggestion that I.iii.6 is confined to the psychology of inductive inference cannot account for the epistemic flavor of its claims that neither a genuine demonstration nor a non-question-begging inductive argument can establish the uniformity principle. (...) For Hume, that inductive inference is justified is part of the data to be explained. Bad argument is therefore excluded as the cause of inductive inference; and there is no good argument to cause it. Does this reinstate the problem of induction, undermining Hume's own assumption that induction is justified? It does so only if justification must derive from "reason", from the availability of a cogent argument. Hume rejects this internalist thesis; induction's favorable epistemic status derives from features of custom, the mechanism that generates inductive beliefs. Hume is attracted to this externalist posture because it provides a direct explanation of the epistemic achievements of children and non-human animals — creatures that must rely on custom unsupplemented by argument. (shrink)

Disputants in the debate regarding whether Hume's argument on induction is descriptive or normative have by and large ignored Hume’s positive argument (that custom is what determines inferences to the unobserved), largely confining themselves to intricate debates within the negative argument (that inferences to the unobserved are not founded on reason). I believe that this is a mistake, for I think Hume’s positive argument to have significant implications for the interpretation of his negative argument. In (...) this paper, I will argue that Hume’s positive and negative arguments should be read as addressing the same issues, whether normative or causal. I will then focus on the Enquiry version of Hume’s positive argument, arguing that it carries a significant normative conclusion: there, Hume argues that custom plays a normative role in justifying our inductive inferences. Given that Hume’s positive argument should be read as addressing the same issues as his negative argument, we should correspondingly read Hume’s negative argument in the Enquiry as having a normative conclusion. (shrink)

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)

Discussion on whether Hume's treatment of induction is descriptive or normative has usually centred on Hume's negative argument, somewhat neglecting the positive argument. In this paper, I will buck this trend, focusing on the positive argument. First, I argue that Hume's positive and negative arguments should be read as addressing the same issues . I then argue that Hume's positive argument in the Enquiry is normative in nature; drawing on his discussion of scepticism in Section 12 (...) of the Enquiry, I explain a framework by which he provides what I call consequent justification for our inductive practices in his positive argument. Based on this, I argue that his negative argument in the Enquiry should similarly be read as normative in nature. (shrink)

Related Works: Part II: C. T. Chong, Yue Yang. $\Sigma_2$ Induction and Infinite Injury Priority Argument, Part II: Tame $\Sigma_2$ Coding and the Jump Operator. Ann. Pure Appl. Logic, vol. 87, no. 2, 103--116. Mathematical Reviews : MR1490049 Part III: C. T. Chong, Lei Qian, Theodore A. Slaman, Yue Yang. $\Sigma_2$ Induction and Infinite Injury Priority Argument, Part III: Prompt Sets, Minimal Paries and Shoenfield's Conjecture. Mathematical Reviews : MR1818378.

Critics of the ideal of value‐free science often assume that they must reject the distinction between epistemic and nonepistemic values. I argue that this assumption is mistaken and that the distinction can be used to clarify and defend the argument from inductive risk, which challenges the value‐free ideal. I develop the idea that the characteristic feature of epistemic values is that they promote, either intrinsically or extrinsically, the attainment of truths. This proposal is shown to answer common objections (...) to the distinction and provide a principled basis for separating legitimate from illegitimate influences of nonepistemic values in scientific inference. *Received June 2009; revised September 2009. †To contact the author, please write to: 503 S. Kedzie Hall, Michigan State University, East Lansing, MI 48824‐1032; e‐mail: [email protected]. (shrink)