Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...) is demonstrated that any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction. We conclude that our mathematical frame work is inappropriate for Theory of Computation. Furthermore, the result provides us a reason that many problems in Complexity Theory resist to be solved.(This work is completed in 2017 -5- 2, it is in vixra in 2017-5-14, presented in Unilog 2018, Vichy). (shrink)

Debunking arguments are arguments that seek to undermine a belief or doctrine by exposing its causal origins. Two prominent proponents of such arguments are the utilitarians Joshua Greene and Peter Singer. They draw on evidence from moral psychology, neuroscience, and evolutionary theory in an effort to show that there is something wrong with how deontological judgments are typically formed and with where our deontological intuitions come from. They offer debunking explanations of our emotion-driven deontological intuitions and dismiss complex deontological theories (...) as products of confabulatory post hoc rationalization. Through my discussion of Greene and Singer’s empirically informed debunking of deontology, I introduce the distinction between two different types of debunking arguments. The first type of debunking argument operates through regular undercutting defeat, whereas the second type relies on higher-order evidence. I argue that the latter type of debunking argument, of which the argument from confabulation is an example, is objectionably sloppy and therefore inadmissible in academic discussion. (shrink)

This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and (...) may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align. (shrink)

Recent work on conditional reasoning argues that denying the antecedent [DA] and affirming the consequent [AC] are defeasible but cogent patterns of argument, either because they are effective, rational, albeit heuristic applications of Bayesian probability, or because they are licensed by the principle of total evidence. Against this, we show that on any prevailing interpretation of indicative conditionals the premises of DA and AC arguments do not license their conclusions without additional assumptions. The cogency of DA and AC inferences rather (...) depends on contingent factors extrinsic to, and independent of, what is asserted by DA and AC arguments. arguments do not license their conclusions without additional assumptions. The cogency of DA and AC inferences rather depends on contingent factors extrinsic to, and independent of, what is asserted by DA and AC arguments. (shrink)

The article outlines a general epistemological theory of argument: a theory that regards providingjustified belief as the principal aim of argumentation, and defends it instrumentalistically. After introducing some central terms of such a theory (2), answers to its central questions are proposed: the primary object and structure of the theory (3), the function of arguments, which is to lead to justified belief (4), the way such arguments function, which is to guide the addressee's cognizing (5), objective versus subjective aspects of (...) argumentation (6), designing different types of argument (7). Then the notion of '(argumentatively) valid argument' is defined and criteria for the adequate use of such arguments are introduced (8). Finally, this conception is justified as, among others, leading to more true beliefs than competing conceptions (9). (shrink)

Norms—that is, specifications of what we ought to do—play a critical role in the study of informal argumentation, as they do in studies of judgment, decision-making and reasoning more generally. Specifically, they guide a recurring theme: are people rational? Though rules and standards have been central to the study of reasoning, and behavior more generally, there has been little discussion within psychology about why (or indeed if) they should be considered normative despite the considerable philosophical literature that bears on this (...) topic. In the current paper, we ask what makes something a norm, with consideration both of norms in general and a specific example: norms for informal argumentation. We conclude that it is both possible and desirable to invoke norms for rational argument, and that a Bayesian approach provides solid normative principles with which to do so. (shrink)

The article outlines a general epistemological theory of argument: a theory that regards providingjustified belief as the principal aim of argumentation, and defends it instrumentalistically. After introducing some central terms of such a theory, answers to its central questions are proposed: the primary object and structure of the theory, the function of arguments, which is to lead to justified belief, the way such arguments function, which is to guide the addressee's cognizing, objective versus subjective aspects of argumentation, designing different types (...) of argument. Then the notion of ' valid argument' is defined and criteria for the adequate use of such arguments are introduced. Finally, this conception is justified as, among others, leading to more true beliefs than competing conceptions. (shrink)

In this article, we argue for the general importance of normative theories of argument strength. We also provide some evidence based on our recent work on the fallacies as to why Bayesian probability might, in fact, be able to supply such an account. In the remainder of the article we discuss the general characteristics that make a specifically Bayesian approach desirable, and critically evaluate putative flaws of Bayesian probability that have been raised in the argumentation literature.

The aim of this paper is to rebut two major criticisms of the No-Miracles Argument for Realism. The first comes from Musgrave. The second comes from Colin Howson. Interestingly enough, these criticisms are the mirror image of each other. Yet, they both point to the conclusion that NMA is fallacious. Musgrave’s misgiving against NMA is that if it is seen as an inference to the best explanation, it is deductively fallacious. Being a deductivist, he tries to correct it by turning (...) it into a valid deductive argument. Howson’s misgiving against NMA is that if it is seen as an inference to the best explanation, it is inductively fallacious. Being a subjective Bayesian, he tries to correct it by turning it into a sound subjective Bayesian argument. I will argue that both criticisms are unwarranted. (shrink)

Everyday life reasoning and argumentation is defeasible and uncertain. I present a probability logic framework to rationally reconstruct everyday life reasoning and argumentation. Coherence in the sense of de Finetti is used as the basic rationality norm. I discuss two basic classes of approaches to construct measures of argument strength. The first class imposes a probabilistic relation between the premises and the conclusion. The second class imposes a deductive relation. I argue for the second class, as the first class is (...) problematic if the arguments involve conditionals. I present a measure of argument strength that allows for dealing explicitly with uncertain conditionals in the premise set. (shrink)

Argumentation is pervasive in everyday life. Understanding what makes a strong argument is therefore of both theoretical and practical interest. One factor that seems intuitively important to the strength of an argument is the reliability of the source providing it. Whilst traditional approaches to argument evaluation are silent on this issue, the Bayesian approach to argumentation (Hahn & Oaksford, 2007) is able to capture important aspects of source reliability. In particular, the Bayesian approach predicts that argument content and source reliability (...) should interact to determine argument strength. In this paper, we outline the approach and then demonstrate the importance of source reliability in two empirical studies. These experiments show the multiplicative relationship between the content and the source of the argument predicted by the Bayesian framework. (shrink)

The history of fallacy theory is long, distinguished and, admittedly, checkered. I offer a bird eye view on it, with the aim of contrasting the standard conception of fallacies as attractive and universal errors that are hard to eradicate with the contemporary preoccupation with “non-fallacious fallacies”, that is, arguments that fit the bill of one of the traditional fallacies but are actually respectable enough to be used in appropriate contexts. Godden and Zenker have recently argued that reinterpreting alleged fallacies as (...) non-fallacious arguments requires supplementing the textual material with something else, e.g. probability distributions, pragmatic considerations, dialogical context. Thus fallacies remain gappy on all accounts, and this is the hallmark of their failure. However, I argue that such gappiness is typically unproblematic, and thus no more flawed than enthymematic argumentation in general. This, in turn, calls into question the usefulness of the very notion of fallacy. (shrink)

The notion of “the burden of proof” plays an important role in real-world argumentation contexts, in particular in law. It has also been given a central role in normative accounts of argumentation, and has been used to explain a range of classic argumentation fallacies. We argue that in law the goal is to make practical decisions whereas in critical discussion the goal is frequently simply to increase or decrease degree of belief in a proposition. In the latter case, it is (...) not necessarily important whether that degree of belief exceeds a particular threshold (e.g., ‘reasonable doubt’). We explore the consequences of this distinction for the role that the “burden of proof” has played in argumentation and in theories of fallacy. (shrink)

An overview of the epistemological approach to argumentation, explaining what it is, justifying it as better than a rhetorical or a consensual ist approach.systematizing the main directions and theories according to their criteria for good argumentation and presenting their contributions to major topics of argumentation theory. Also. an introduction to the articles of the two special issues of Informal Logic about the epistemological approach to argumentation.

Some arguments are good; others are not. How can we tell the difference? This article advances three proposals as a partial answer to this question. The proposals are keyed to arguments conditioned by different degrees of uncertainty: mild, where the argument’s premises are hedged with point-valued probabilities; moderate, where the premises are hedged with interval probabilities; and severe, where the premises are hedged with non-numeric plausibilities such as ‘very likely’ or ‘unconfirmed’. For mild uncertainty, the article proposes to apply a (...) principle referred to as ‘Jeffrey’s rule’, for the principle is a generalization of Jeffrey conditionalization. For moderate uncertainty, the proposal is to extend Jeffrey’s rule for use with probability intervals. For severe uncertainty, the article proposes that even when lack of probabilistic information prevents the application of Jeffrey’s rule, the rule can be adapted to these conditions with the aid of a suitable plausibility measure. Together, the three proposals introduce an approach to argument evaluation that complements established frameworks for evaluating arguments: deductive soundness, informal logic, argumentation schemes, pragma-dialectics, and Bayesian inference. Nevertheless, this approach can be looked at as a generalization of the truth and validity conditions of the classical criterion for sound argumentation. (shrink)

This article provides a brief selective overview and discussion of recent research into natural language argumentation that may inform the study of human reasoning on the assumption that an episode of argumentation issues an invitation to accept a corresponding inference. As this research shows, arguers typically seek to establish new consequences based on prior information. And they typically do so vis-à-vis a real or an imagined opponent, or an opponent-position, in ways that remain sensitive to considerations of context, audiences, and (...) goals. Deductively valid inferences remain a limiting case of such reasoning. In view of these insights, it may appear less surprising that allegedly “irrational” behavior can regularly be produced in experimental settings that expose subjects to standardized reasoning tasks. (shrink)

Cross-cultural differences in argumentation may be explained by the use of different norms of reasoning. However, some norms derive from, presumably universal, mathematical laws. This inconsistency can be resolved, by considering that some norms of argumentation, like Bayes theorem, are mathematical functions. Systematic variation in the inputs may produce culture-dependent inductive biases although the function remains invariant. This hypothesis was tested by fitting a Bayesian model to data on informal argumentation from Turkish and English cultures, which linguistically mark evidence quality (...) differently. The experiment varied evidential marking and informant reliability in argumentative dialogues and revealed cross-cultural differences for both independent variables. The Bayesian model fitted the data from both cultures well but there were differences in the parameters consistent with culture-specific inductive biases. These findings are related to current controversies over the universality of the norms of reasoning and the role of normative theories in the psychology of reasoning. (shrink)

ABSTRACTIn everyday situations, people regularly receive information from large groups of people and from single experts. Although lay opinions and expert opinions have been studied extensively in isolation, the present study examined the relationship between the two by asking how many laypeople are needed to counter an expert opinion. A Bayesian formalisation allowed the prescription of this quantity. Participants were subsequently asked to assess how many laypeople are needed in different situations. The results demonstrate that people are sensitive to the (...) relevant factors identified for determining how many lay opinions are required to counteract a single expert opinion. People's assessments were fairly good in line with Bayesian predictions. (shrink)

An essential step to evaluating arguments is moving from the weight of individual premises to the weight of the conclusion. In order to perform this step, one must understand the relationship between the premises in the argument. In the past, analyzing premise relations in informal logic has been limited primarily to the linked-convergent distinction. This distinction has failed to resolve some of the basic problems in finding a definition because it has underestimated the degree to which premises interact with each (...) other in some complicated way. Embracing concepts from holistic epistemology, I argue that evaluating a premise involves considering a wide set of presuppositions and implications that that premise, if accepted, carries. I call this wide set the premise/world. The relationship between premises is then essentially just the relationship between these two premise/worlds. (shrink)