When Deduction leads to Belief

T h e paper questions the common assumption that rational individuals believe all propositions which they know to be logical consequences of their other beliefs: although we must acknowledge the truth of a proposition which is a deductive consequence ofour beliefs, we may not genuinely believe it. This conclusion is defended by arguing that some familiar counter- examples to the claim that knowledge isjustified true belief fail because they involve propositions which are not really believed. Beliefs guide conduct or issue in assertion by answering questions which arise in the course of deliberation and conversation, but the troublesome cases present proposi- tions which do not present the agent's answer to any question. The paper concludes by sketching the conditions under which the deductive conse- quences of our beliefs can be believe

Recent Work in Relevant Logic

This paper surveys important work done in relevant logic in the past 10 years

A SIMPLE SEQUENT SYSTEM FOR MINIMALLY INCONSISTENT LP

Minimally inconsistent LP (MiLP) is a nonmonotonic paraconsistent logic based on Graham Priest’s logic of paradox (LP). Unlike LP, MiLP purports to recover, in consistent situations, all of classical reasoning. The present paper conducts a proof-theoretic analysis of MiLP. I highlight certain properties of this logic, introduce a simple sequent system for it, and establish soundness and completeness results. In addition, I show how to use my proof system in response to a criticism of this logic put forward by J. C. Beall

Remarks on Logic and Critical Thinking

This work is compiled for the students, research scholars, academicians, who are interested in logic, philosophy, mathematics and critical thinking. The main objective of this book is to provide basics or fundamental knowledge for those who have chosen logic as their subject in order to develop analytical and critical ideas. It has been primarily developed to serve as an introductory piece of work which includes explanatory notes on different courses like Inductive logic, Deductive logic, propositional logic, Symbolic logic, Quantification logic, Modal logic and Critical thinking. Besides this, it also includes illustrations in decision making and scientific research methods in logic. This book is mainly devised to clear fundamental problems of logic. It contains eight chapters which are simply described and elaborated

Reflective Argumentation

Theories of argumentation usually focus on arguments as means of persuasion, finding consensus, or justifying knowledge claims. However, the construction and visualization of arguments can also be used to clarify one's own thinking and to stimulate change of this thinking if gaps, unjustified assumptions, contradictions, or open questions can be identified. This is what I call "reflective argumentation." The objective of this paper is, first, to clarify the conditions of reflective argumentation and, second, to discuss the possibilities of argument visualization methods in supporting reflection and cognitive change. After a discussion of the cognitive problems we are facing in conflicts--obviously the area where cognitive change is hardest--the second part will, based on this, determine a set of requirements argument visualization tools should fulfill if their main purpose is stimulating reflection and cognitive change. In the third part, I will evaluate available argument visualization methods with regard to these requirements and talk about their limitations. The fourth part, then, introduces a new method of argument visualization which I call Logical Argument Mapping (LAM). LAM has specifically been designed to support reflective argumentation. Since it uses primarily deductively valid argument schemes, this design decision has to be justified with regard to goals of reflective argumentation. The fifth part, finally, provides an example of how Logical Argument Mapping could be used as a method of reflective argumentation in a political controversy

Deductive Systems in Traditional and Modern Logic

The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic

Basic characteristics to achieve common sense reasoning

Not Include

Advanced mathematics and deductive reasoning skills: testing the Theory of Formal Discipline

This thesis investigates the Theory of Formal Discipline (TFD): the idea that studying mathematics develops general reasoning skills. This belief has been held since the time of Plato (2003/375B.C), and has been cited in recent policy reports (Smith, 2004; Walport, 2010) as an argument for why mathematics should hold a privileged place in the UK's National Curriculum. However, there is no rigorous research evidence that justifies the claim. The research presented in this thesis aims to address this shortcoming. Two questions are addressed in the investigation of the TFD: is studying advanced mathematics associated with development in reasoning skills, and if so, what might be the mechanism of this development? The primary type of reasoning measured is conditional inference validation (i.e. `if p then q; not p; therefore not q'). In two longitudinal studies it is shown that the conditional reasoning behaviour of mathematics students at AS level and undergraduate level does change over time, but that it does not become straightforwardly more normative. Instead, mathematics students reason more in line with the `defective' interpretation of the conditional, under which they assume p and reason about q. This leads to the assumption that not-p cases are irrelevant, which results in the rejection of two commonly-endorsed invalid inferences, but also in the rejection of the valid modus tollens inference. Mathematics students did not change in their reasoning behaviour on a thematic syllogisms task or a thematic version of the conditional inference task. Next, it is shown that mathematics students reason significantly less in line with a defective interpretation of the conditional when it is phrased `p only if q' compared to when it is phrased `if p then q', despite the two forms being logically equivalent. This suggests that their performance is determined by linguistic features rather than the underlying logic. The final two studies investigated the heuristic and algorithmic levels of Stanovich's (2009a) tri-process model of cognition as potential mechanisms of the change in conditional reasoning skills. It is shown that mathematicians' defective interpretation of the conditional stems in part from heuristic level processing and in part from effortful processing, and that the executive function skills of inhibition and shifting at the algorithmic level are correlated with its adoption. It is suggested that studying mathematics regularly exposes students to implicit `if then' statements where they are expected to assume p and reason about q, and that this encourages them to adopt a defective interpretation of conditionals. It is concluded that the TFD is not supported by the evidence; while mathematics does seem to develop abstract conditional reasoning skills, the result is not more normative reasoning