Demonstrative Induction and the Skeleton of Inference

It has been common wisdom for centuries that scientific inference cannot be deductive; if it is inference at all, it must be a distinctive kind of inductive inference. According to demonstrative theories of induction, however, important scientific inferences are not inductive in the sense of requiring ampliative inference rules at all. Rather, they are deductive inferences with sufficiently strong premises. General considerations about inferences suffice to show that there is no difference in justification between an inference construed demonstratively or ampliatively. The inductive risk may be shouldered by premises or rules, but it cannot be shirked. Demonstrative theories of induction might, nevertheless, better describe scientific practice. And there may be good methodological reasons for constructing our inferences one way rather than the other. By exploring the limits of these possible advantages, I argue that scientific inference is neither of essence deductive nor of essence inductive.     

CAN RATIONALIST ABDUCTIVISM SOLVE THE PROBLEM OF INDUCTION?

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.     

Argument by Analogy

In this essay I characterize arguments by analogy, which have an important role both in philosophical and everyday reasoning. Arguments by analogy are different from ordinary inductive or deductive arguments and have their own distinct features. I try to characterize the structure and function of these arguments. It is further discussed that some arguments, which are not explicit arguments by analogy, nevertheless should be interpreted as such and not as inductive or deductive arguments. The result is that a presumed outcome of a philosophical dispute will have to be reconsidered.     

Is inferential reasoning just probabilistic reasoning in disguise?

Oaksford, Chater, and Larkin (2000) have suggested that people actually use everyday probabilistic reasoning when making deductive inferences. In two studies, we explicitly compared probabilistic and deductive reasoning with identical if-then conditional premises with concrete content. In the first, adults were given causal premises with one strongly associated antecedent and were asked to make standard deductive inferences or to judge the probabilities of conclusions. In the second, reasoners were given scenarios presenting a causal relation with zero to three potential alternative antecedents. The participants responded to each set of problems under both deductive and probabilistic instructions. The results show that deductive and probabilistic inferences are not isomorphic. Probabilistic inferences can model deductive responses only using a limited, very high threshold model, which is equivalent to a simple retrieval model. These results provide a clearer understanding of the relations between probabilistic and deductive inferences and the limitations of trying to consider these two forms of inference as having a single underlying process.     

归纳推理和演绎推理的关系理论及其模型

推理是人类高级认知过程的一种,相关的心理学研究一般将其分为归纳推理和演绎推理两个方面。归纳推理是从特殊到一般的推理过程,与之相对的演绎推理则是从一般到特殊的过程。归纳推理和演绎推理的关系问题是当前心理推理研究领域的一个重点问题。这一问题主要有两种理论解释：一种是单过程理论,该理论认为归纳推理和演绎推理本质上是同一个认知过程,以单过程理论为基础构建的推理模型称为单维模型;另一种是双过程理论,认为归纳推理和演绎推理是两个不同的认知过程,并不同程度地受到启发和分析过程的影响。未来研究可多关注推理的时间进程,以及采用不同的研究方法对各自理论提供数据支持。     

A relevance theory of induction

A framework theory, organized around the principle of relevance, is proposed for category-based reasoning. According to the relevance principle, people assume that premises are informative with respect to conclusions. This idea leads to the prediction that people will use causal scenarios and property reinforcement strategies in inductive reasoning. These predictions are contrasted with both existing models and normative logic. Judgments of argument strength were gathered in three different countries, and the results showed the importance of both causal scenarios and property reinforcement in categorybased inferences. The relation between the relevance framework and existing models of category-based inductive reasoning is discussed in the light of these findings.     

论“演绎”和归纳-演绎区分(英文)

几乎所有逻辑学导论教科书对"演绎"的定义都鼓励我们相信,归纳-演绎的区分存在于各种论证中,而且"演绎"的外延是明确的论证类。这篇论文中我们论证这种思路是错误的。特别地,我们辩护以下观点:为得到归纳-演绎区分而使用的典型的"演绎"之定义,要么太狭隘,要么不够充分。基于一个对归纳-演绎区分的收缩式理解,我们得到以下结论:该区分的内容没有超出批判性思维的两类核心问题。     

Relativism, Absolutism, and Tolerance

Abstract: A common view is that relativism requires tolerance. We argue that there is no deductive relation between relativism and tolerance, but also that relativism is not incompatible with tolerance. Next we note that there is no standard inductive relation between relativism and tolerance—no inductive enumeration, argument to the best explanation, or causal argument links the two. Two inductive arguments of a different sort that link them are then exposed and criticized at length. The first considers relativism from the objective point of view ‘of the universe’, the second from the subjective point of view of the relativist herself. Both arguments fail. There is similarly no deductive relation between absolutism and tolerance—neither entails the other—and no inductive connection of any sort links the two. We conclude that tolerance, whether unlimited or restricted, is independent of both relativism and absolutism. A metaethical theory that says only that there is one true or valid ethical code, or that there is a plurality of equally true or valid ethical codes, tells us nothing about whether we should be tolerant, much less how tolerant we should be.     

Logic, reasoning, and verbal behavior

This paper analyzes the traditional concepts of logic and reasoning from the perspective of radical behaviorism and in the terms of Skinner's treatment of verbal behavior. The topics covered in this analysis include the proposition, premises and conclusions, logicality and rules, and deductive and inductive reasoning.     

Problem-solving in general practice

Objective: To identify problem solving strategies in general practice. Basic procedures: Three styles of scientific reasoning were defined and modelled on the medical environment. These models were tested in a simulated doctor-patient encounter. Main findings: According to the definitions contained in the models a deductive or hypotheticodeductive strategy could not be discovered. All participants used exclusively the inductive method and, more specifically, the speculative variant. This variant may be best described as a process of iterative pattern recognition. Conclusions: The manifest utilization of the inductive method carries many implications among which are the irretraceability and irreproducibility of the process. The speculative form approaches the conception of art rather than science. This is exactly what most doctors try to tell: medicine is an art. The strategy allows for flexibility and quick response to the patient's needs.     

Measures of national stereotypes as predictors of the latencies of inductive versus deductive stereotypic judgements

According to Taifel's accentuation theory, national stereotypes can be thought of as the correlation between trait dimensions and national affiliations, This correlation is high when the trait shows high homogeneity within and high distinctiveness between the national groups. The present study tested the hypothesis that a trait's distinctiveness would facilitate inductive stereotypic judgements (inferences from trait to nationality) whereas homogeneity would facilitate deductive stereotypic judgements (inferences from nationality to trait). The latencies of inductive and deductive stereotypic judgements of 48 German subjects were assessed for 39 traits and three foreign nationalities (English, French, Italian). Multiple regression analyses using latencies for both types of judgements us criterion variables and both distinctiveness and homogeneity as predictor variables were conducted. The stereotype measures of Katz and Braly and McCauley and Stitt served as additional predictor variables. As expected from accentuation theory, distinctiveness predicted inductive but not deductive latencies, whereas homogeneity predicted deductive but not inductive latencies. For the latencies of deductive stereotypic judgements, the stereotype measure of Katz and Braly as well as that of McCauley and Stitt also proved to be significant predictors. The results are discussed and recommendations are given with respect to the assessment of national stereotypes.     

The ontomystical argument revisited

I argue that Alexander Pruss’s ontomystical arguments should not be endorsed without further argumentative support of their premises. My specific targets are his claims that (i) Śamkara’s principle is true and (ii) the high mystics had phenomenal experiences of radical dependence and as of a maximally great being. Against (i), I urge a host of counterexamples. The only ways I can see for Pruss to respond to these counterexamples end up falsifying (ii). The key problem which leads to this conclusion is that Pruss needs a criterion for distinguishing phenomenal experiences from non-phenomenal experiences according to which the experiences of the high mystics were phenomenal experiences while the experiences of those persons I discuss in my counterexamples to Śamkara’s principle are not. There appears to be no such criterion. I suggest that the future of the ontomystical arguments lies in developing them as inductive rather than deductive arguments.     

Induction,Normality and Reasoning with Arbitrary Objects

This paper concerns the apparent fact — discussed by Sinan Dogramaci (2010) and Brian Weatherson (2012) — that inductive reasoning often interacts in disastrous ways with patterns of reasoning that seem perfectly fine in the deductive case. In contrast to Dogramaci's and Weatherson's own suggestions, I argue that these cases show that we cannot reason inductively about arbitrary objects. Moreover, as I argue, this prohibition is neatly explained by a certain hypothesis about the rational basis of inductive reasoning — namely, the hypothesis that inductive reasoning is fundamentally reasoning about what normally happens (in a non‐statistical sense).     

The Context of Inference

There is an ambiguity in the concept of deductive validity that went unnoticed until the middle of the twentieth century. Sometimes an inference rule is called valid because its conclusion is a theorem whenever its premises are. But often something different is meant: The rule's conclusion follows from its premises even in the presence of other assumptions. In many logical environments, these two definitions pick out the same rules. But other environments are context-sensitive, and in these environments the second notion is stronger. Sorting out this ambiguity has led to profound mathematical investigations with applications in complexity theory and computer science. The origins of this ambiguity and the history of its resolution deserve philosophical attention, because our understanding of logic stands to benefit from their details.

I am eager to examine together with you, Crito, whether this argument will appear in any way different to me in my present circumstances, or whether it remains the same, whether we are to abandon it or believe in it.—Plato Crito, 46d     

Deductively Definable Logics of Induction

A broad class of inductive logics that includes the probability calculus is defined by the conditions that the inductive strengths [A|B] are defined fully in terms of deductive relations in preferred partitions and that they are asymptotically stable. Inductive independence is shown to be generic for propositions in such logics; a notion of a scale-free inductive logic is identified; and a limit theorem is derived. If the presence of preferred partitions is not presumed, no inductive logic is definable. This no-go result precludes many possible inductive logics, including versions of hypothetico-deductivism.     

The Possibility of Inductive Moral Argumets

Abstract

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, eat 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 show to be at least possible. Some philosophers may suppose that inductive moral argumets from non-moral premises cannot get off the ground, but I show that a perfectly legitimate inductive moral argument exists. This argument has on-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-know argumets from ‘Is’ to ‘Ought’.     

Is Induction Epistemologically Prior to Deduction?

Most philosophers hold that the use of our deductive powers confers an especially strong warrant on some of our mathematical and logical beliefs. By contrast, many of the same philosophers hold that it is a matter of serious debate whether any inductive inferences are cogent. That is, they hold that we might well have no warrant for inductively licensed beliefs, such as generalizations. I argue that we cannot know that we know logical and mathematical truths unless we use induction. Our confidence in our logical and mathematical powers is not justified if we are inductive sceptics. This means that inductive scepticism leads to a deductive scepticism. I conclude that we should either be philosophical sceptics about our knowledge of deduction and induction, or accept that some of our inductive inferences are cogent.     

The pessimistic induction: a bad argument gone too far

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.     

Mathematical statistics and metastatistical analysis

This paper deals with meta-statistical questions concerning frequentist statistics. In Sections 2 to 4 I analyse the dispute between Fisher and Neyman on the so called logic of statistical inference, a polemic that has been concomitant of the development of mathematical statistics. My conclusion is that, whenever mathematical statistics makes it possible to draw inferences, it only uses deductive reasoning. Therefore I reject Fisher's inductive approach to the statistical estimation theory and adhere to Neyman's deductive one. On the other hand, I assert that Neyman-Pearson's testing theory, as well as Fisher's tests of significance, properly belong to decision theory, not to logic, neither deductive nor inductive. I then also disagree with Costantini's view of Fisher's testing model as a theory of hypothetico-deductive inferences.In Section 5 I disapprove Hacking₁'s evidentialists criticisms of the Neyman-Pearson's theory of statistics (NPT), as well as Hacking₂'s interpretation of NPT as a theory of probable inference. In both cases Hacking misses the point. I conclude, by claiming that Mayo's conception of the Neyman-Pearson's testing theory, as a model of learning from experience, does not purport any advantages over Neyman's behavioristic model.     

Belief,Credence, and the Preface Paradox

Many discussions of the ‘preface paradox’ assume that it is more troubling for deductive closure constraints on rational belief if outright belief is reducible to credence. I show that this is an error: we can generate the problem without assuming such reducibility. All that we need are some very weak normative assumptions about rational relationships between belief and credence. The only view that escapes my way of formulating the problem for the deductive closure constraint is in fact itself a reductive view: namely, the view that outright belief is credence 1. However, I argue that this view is unsustainable. Moreover, my version of the problem turns on no particular theory of evidence or evidential probability, and so cannot be avoided by adopting some revisionary such theory. In sum, deductive closure is in more serious, and more general, trouble than some have thought.