What inductive explanations could not be

Marc Lange argues that proofs by mathematical induction are generally not explanatory because inductive explanation is irreparably circular. He supports this circularity claim by presenting two putative inductive explanantia that are one another’s explananda. On pain of circularity, at most one of this pair may be a true explanation. But because there are no relevant differences between the two explanantia on offer, neither has the explanatory high ground. Thus, neither is an explanation. I argue that there is no important asymmetry between the two cases because they are two presentations of the same explanation. The circularity argument requires a problematic notion of identity of proofs. I argue for a criterion of proof individuation that identifies the two proofs Lange offers. This criterion can be expressed in two equivalent ways: one uses the language of homotopy type theory, and the second assigns algebraic representatives to proofs. Though I will concentrate on one example, a criterion of proof identity has much broader consequences: any investigation into mathematical practice must make use of some proof-individuation principle.     

HOW TO ANALYSE SUBSTANCE: A REPLY TO SCHNIEDER

In a recent issue of this journal, Benjamin Schnieder has presented an objection to the account of individual substance that we have developed and put to various uses in our works on metaphysics. According to Schnieder's objection, our proposal to analyse this notion of substantiality suffers from a special kind of circularity. In this paper, we give two replies to Schnieder's objection. The first is that a successful analysis is not, in fact, required to avoid the sort of circularity about which Schnieder complains. The second is that our analysis does not involve the alleged circularity.     

Sosa’s Reflective Knowledge: How damaging is epistemic circularity?

The problem of epistemic circularity maintains that we cannot know that our central belief-forming practices (faculties) are reliable without vicious circularity. Ernest Sosa??s Reflective Knowledge (2009) offers a solution to this problem. Sosa argues that epistemic circularity is virtuous rather than vicious: it is not damaging. Contra Sosa, I contend that epistemic circularity is damaging. Section 1 provides an overview of Sosa??s solution. Section 2 focuses on Sosa??s reply to the Crystal-ball-gazer Objection. Section 2 also contends that epistemic circularity does not prevent us from being justified in (e.g.) perceptual beliefs, or from being justified in believing that (e.g.) sense perception is reliable. But, Sect. 3 argues that it does prevent us from being able to satisfactorily show that our central belief-forming practices (faculties) are reliable. That is, epistemic circularity prevents us from distinguishing between reliable and unreliable practices, from guiding ourselves to use reliable practices and avoid unreliable ones, and from defending reliable practices against skepticism. Hence, epistemic circularity is still damaging. The concluding section suggests that this has repercussions for Sosa??s analysis of the value of reflective knowledge.     

Arcs in perceptual space--going off at a tangent

Underestimating the curvature of an arc may result from our tendency to view it as prolonged in the direction of the tangent to its ends. Support is given here for this hypothesis, but evidence is also provided that tangent deviation may alter an arc's circularity along its whole length.     

Why worry about theory‐dependence? Circularity,minimal empiricality and reliability

It is a widely shared view among philosophers of science that the theory‐dependence (or theory‐ladenness) of observations is worrying, because it can bias empirical tests in favour of the tested theories. These doubts are taken to be dispelled if an observation is influenced by a theory independent of the tested theory and thus circularity is avoided, while (partially) circular tests are taken to require special attention. Contrary to this consensus, it is argued that the epistemic value of theory‐dependent tests has nothing to do with the circularity or non‐circularity of the test, but is instead based on the minimal empiricality and reliability of observations. Since theory‐dependence does not in general prevent observations fulfilling these requirements, it should not be regarded as a phenomenon that is basically detrimental, but as neutral with respect to successful scientific knowledge gathering.     

Truth,Meaning, and Circularity

It is often argued that the combination of deflationism about truth and the truth-conditional theory of meaning is impossible for reasons of circularity. I distinguish, and reject, two strains of circularity argument. Arguments of the first strain hold that the combination has a circular account of the order in which one comes to know the meaning of a sentence and comes to know its truth condition. I show that these arguments fail to identify any circularity. Arguments of the second strain hold that the combination has a circular explanation of the ideas or concepts of meaning and truth. I show that these arguments identify a genuine, but acceptable, circularity.     

SOSA ON EPISTEMIC CIRCULARITY AND REFLECTIVE KNOWLEDGE

Abstract: Ernest Sosa has done important work on epistemic circularity, epistemic virtue, and reflective knowledge. He holds that epistemic circularity need not be vicious and need not prevent us from knowing that our ways of forming beliefs are reliable. In this article, I briefly explore Sosa's defense of this view and raise some questions about what is required for reflective knowledge.     

Outflanking the vicious circle

Sir Michael Dummett unfairly criticises Frank Ramsey for advocating full-fledged realism as a way to escape the problem of vicious circularity. Instead Ramsey uses a more moderate approach that only requires a thin commitment to theoretical terms. In ‘Theories’, Ramsey details a method to substitute observational terms for the theoretical terms appearing in a theory, but its early advocates, Rudolf Carnap and Carl Hempel, recognised that the resulting ‘ramsey-sentence’ does not intend to fully remove the theoretical content of the original theory. Through a model-theoretic approach, Jaakko Hintikka clarifies how the ramsey-sentence is embedded in the original theory, and, thereby, retains a commitment to the theoretical content that governs the substituted observable terms. By understanding how ramsey-sentences relate to the original theory, we will see that Ramsey need not assert a full-fledged realism to address vicious circularity. Instead of committing to the existence of all theoretical concepts involved in the original theory, ramsey-sentences assert the existence of an unspecified object that satisfies the substituted observable terms, and this commitment is sufficient to escape vicious circularity. Through this process of definition, Ramsey sidesteps Dummett's charge of full-fledged realism, and suggests a more moderate position that is consistent with Dummett's emphasis on domain specification.     

A COMPARISON OF TECHNIQUES WHICH TEST FOR JOB DIFFERENCES

There has been a recent trend in research seeking the most appropriate statistical technique for determining job similarities/differences. Monte Carlo methods were used to analyze more closely the repeated measures analysis of variance and the multivariate analysis of variance in order to add further insight into the viability of these techniques for this purpose. The conventional univariate analysis of variance, the ε-adjusted univariate F test, and the ε-adjusted univariate F test were compared to three multivariate tests (Roy's largest-root criterion, Wilk's likelihood ratio, and the Pillai-Barlett trace) in terms of power and control for Type I error when (1) circularity and homogeneity were met, (2) homogeneity was met but circularity was violated, (3) homogeneity was violated but circularity was met, and (4) both homogeneity and circularity were violated. The efficacy of the techniques was shown to be contingent upon whether the assumptions were met or not. The univariate test proved to be the better technique when circularity was met. The multivariate technique proved to be the better test when homogeneity was met while circularity was violated. The results were mixed when both circularity and homogeneity were violated. Guidelines for selecting a statistical technique which tests for job differences are offered.     

Undermining, circularity, and disagreement

Sometimes we get what seem to be good reasons for believing that we’ve misevaluated our evidence for a proposition P. In those cases, can we use our evidence for P itself to show that we haven’t misevaluated our evidence for P? I show why doing so appears to employ viciously circular reasoning. However, I then argue that this appearance is illusory in certain cases and that we sometimes can legitimately reason in that way. This claim sheds new light on the nature of epistemic undermining and epistemic circularity. In addition, it has implications for the current debate about the epistemic significance of disagreement. An important and influential position in that debate says that disagreement with others dramatically undermines our justification for a wide range of our opinions (e.g., political, religious, moral, economic, and philosophical opinions). My view on undermining and circularity implies that this position on disagreement rests on a mistake.     

Finite Reasons Without Foundations

This article develops a theory of reasons that has strong similarities to Peter Klein's infinitism. The view it develops, Framework Reasons, upholds Klein's principles of avoiding arbitrariness (PAA) and avoiding circularity (PAC) without requiring an infinite regress of reasons. A view of reasons that holds that the “reason for” relation is constrained by PAA and that PAC can avoid an infinite regress if the “reason for” relation is contextual. Moreover, such a view of reasons can maintain that skepticism is false by the maintaining that there is more to epistemic justification than can be expressed in any reasoning session. One crucial argument for Framework Reasons is that justification depends on a background of plausibility considerations. The final section of the article applies this view of reasons to Michael Bergmann's argument that any nonskeptical epistemology must embrace epistemic circularity.     

Deconstructing Hermes: A Critique Of The Hermeneutic Turn In Psychoanalysis

In this brief essay, I attempt to critique some of the philosophical problematics inherent with the hermeneutic turn in psychoanalysis. The proposition that “there are only interpretations of interpretations” leads to an inescapable circularity because interpretation ultimately lacks a referent or criterion for which to anchor meaning. If we follow this proposition through to its logical end, this ultimately collapses into relativism because meaning is relative to its interpretive scheme, which further relies on other interpretative schemata for which there are no definitive definitions, conclusive consensus, or universal laws governing interpretation. How can hermeneutics escape the charge of circularity, infinite regress, disavowal of universals, its tacit relativism, and the failure to provide a consensus or criteria for interpretation? How is psychoanalysis able to philosophically justify interpretative truth claims when they potentially inhere to a recalcitrant subjectivism while claiming to be objectively valuative?     

ESSENTIALISM AND RIGIDITY

Michael Della Rocca has recently argued that Kripkean essentialism is subtly self-defeating: to defend it, certain modal intuitions must be reconstrued in terms of similarity, but reconstruing them in this way threatens the principled rejection of similarity comparisons on which Kripke's essentialism depends. Della Rocca holds that Kripke's strategy must assume the necessity of identity, and that the necessity of identity already presupposes essentialism, which renders the defence circular. Against this, I argue that the necessity of identity may be accepted independently; therefore no circularity need arise. I also argue that Della Rocca fails to rebut an objection raised by Stephen Yablo.     

On the puzzle of language, pragmatics, and schizophrenia

The nature of circularity in thinking about language in schizophrenia is described, and initial observations by Byrne, et al. appropriate for breaking that circularity identified.     

Standard errors and confidence intervals in within-subjects designs: Generalizing Loftus and Masson (1994) and avoiding the biases of alternative accounts

Repeated measures designs are common in experimental psychology. Because of the correlational structure in these designs, the calculation and interpretation of confidence intervals is nontrivial. One solution was provided by Loftus and Masson (Psychonomic Bulletin & Review 1:476-490, 1994). This solution, although widely adopted, has the limitation of implying same-size confidence intervals for all factor levels, and therefore does not allow for the assessment of variance homogeneity assumptions (i.e., the circularity assumption, which is crucial for the repeated measures ANOVA). This limitation and the method's perceived complexity have sometimes led scientists to use a simplified variant, based on a per-subject normalization of the data (Bakeman & McArthur, Behavior Research Methods, Instruments, & Computers 28:584-589, 1996; Cousineau, Tutorials in Quantitative Methods for Psychology 1:42-45, 2005; Morey, Tutorials in Quantitative Methods for Psychology 4:61-64, 2008; Morrison & Weaver, Behavior Research Methods, Instruments, & Computers 27:52-56, 1995). We show that this normalization method leads to biased results and is uninformative with regard to circularity. Instead, we provide a simple, intuitive generalization of the Loftus and Masson method that allows for assessment of the circularity assumption.     

The oldest solution to the circularity problem for Humeanism about the laws of nature

According to Humeanism about the laws, the laws of nature are nothing over and above certain kinds of regularities about particular facts (the “Humean mosaic”). Humeanism has often been accused of circularity: according to scientific practice laws often explain their instances, but on the Humean view they also reduce to the mosaic, which includes those instances. In this paper I formulate the circularity problem in a way that avoids a number of controversial assumptions routinely taken for granted in the literature, and against which many extant responses are therefore ineffective. I then propose a solution that denies the alleged Humean commitment that laws are explained by their instances. The solution satisfies three desiderata that other solutions don’t: it provides independent motivation against the idea that Humean laws are explained by their instances; it specifies the sense in which Humean laws are nonetheless “nothing over and above” their instances; and it gives an alternative account of what does explain the laws, if not their instances. This solution, I will argue, is not only the simplest but also the oldest one: it appeals only to tools and theses whose first appearance predates the earliest statements of the circularity problem itself.

     

Knowledge, doubt, and circularity

Ernest Sosa??s virtue perspectivism can be thought of as an attempt to capture as much as possible of the Cartesian project in epistemology while remaining within the framework of externalist fallibilism. I argue (a) that Descartes??s project was motivated by a desire for intellectual stability and (b) that his project does not suffer from epistemic circularity. By contrast, Sosa??s epistemology does entail epistemic circularity and, for this reason, proves unable to secure the sort of intellectual stability Descartes wanted. I then argue that this leaves Sosa??s epistemology vulnerable to an important kind of skepticism.     

悖论的自指性与循环性

本文使用语义网分析悖论与自指性和循环性。主要结论是证明了有穷悖论都是自指的,同时其矛盾性必定基于循环性。我们还证明存在非自指但基于循环性的(无穷)悖论,比如亚布鲁悖论及其一般变形;又证明了存在自指但不基于循环性的(无穷)悖论,比如超穷赫兹伯格悖论和麦基悖论。这表明自指性与循环性对悖论而言是两个不同的概念。