scholarly journals Informalizing Formal Logic

2019 ◽  
Vol 39 (2) ◽  
pp. 169-204
Author(s):  
Antonis Kakas
Keyword(s):  
Classical Logic ◽  
Deductive Reasoning ◽  
Formal Logic ◽  
Human Reasoning ◽  
Informal Reasoning ◽  
Logical Entailment

This paper presents a way in which formal logic can be understood and reformulated in terms of argumentation that can help us unify formal and informal reasoning. Classical deductive reasoning will be expressed entirely in terms of notions and concepts from argumentation so that formal logical entailment is equivalently captured via the arguments that win between those supporting concluding formulae and arguments supporting contradictory formulae. This allows us to go beyond Classical Logic and smoothly connect it with human reasoning, thus providing a uniform argumentation-based view of both informal and formal logic.

scholarly journals Inverse probability and the use of Likelihood

1932 ◽  
Vol 28 (3) ◽  
pp. 257-261 ◽  
Author(s):  
R. A. Fisher
Keyword(s):  
Large Class ◽  
Classical Theory ◽  
Deductive Reasoning ◽  
Inductive Reasoning ◽  
Human Reasoning ◽  
Inverse Probability ◽  
Observational Material ◽  
Statistical Work

Logicians have long distinguished two modes of human reasoning, under the respective names of deductive and inductive reasoning. In deductive reasoning we attempt to argue from a hypothesis to its necessary consequences, which may be verifiable by observation; that is, to argue from the general to the particular. In inductive reasoning we attempt to argue from the particular, which is typically a body of observational material, to the general, which is typically a theory applicable to future experience. In statistical language we are attempting to argue from the sample to the population, from which it was drawn. Since recent statistical work has shown that this type of argument can be carried out with exactitude in a usefully large class of cases(2, 3), by means of conceptions somewhat different from those of the classical theory of probability, it may be useful briefly to restate the logical and mathematical distinctions which have to be drawn.

Understanding reasoning: Let's describe what we really think about

2011 ◽  
Vol 34 (5) ◽  
pp. 269-270 ◽  
Author(s):  
Robert J. Sternberg
Keyword(s):  
Decision Making ◽  
Everyday Life ◽  
Deductive Reasoning ◽  
Inductive Reasoning ◽  
Real Life ◽  
Human Reasoning ◽  
Ecological Relevance ◽  
Target Article ◽  
Life Decision

AbstractI suggest psychologists would more profitably study a totally different area of human reasoning than is discussed in the target article – the inductive reasoning people use in their everyday life that matters in consequential real-life decision making, rather than the deductive reasoning that psychologists have studied meticulously but that has relatively less ecological relevance to people's lives.

Why Philosophy Needs Logical Psychologism

Dialogue ◽  
2013 ◽  
Vol 51 (4) ◽  
pp. 575-586 ◽  
Author(s):  
Vanessa Lehan-Streisel
Keyword(s):  
Deductive Reasoning ◽  
Human Reasoning ◽  
Formal Systems ◽  
Normative System

In this paper, I argue that social psychologism is the most philosophically appealing form of psychologism. I present two arguments in support of social psychologism. The first is that this form of psychologism allows philosophers to justify normative claims about human reasoning. In the second part of this paper I argue that social psychologism ameliorates historical concerns with psychologism in general. The conclusion I draw from this discussion is that a need to outline and justify a normative system for deductive reasoning requires some discussion of how formal systems and human minds connect to one another.

scholarly journals On the interplay between interpretation and reasoning in compelling fallacies

2020 ◽  
Author(s):  
Léo Picat ◽  
Salvador Mascarenhas
Keyword(s):  
Deductive Reasoning ◽  
Broad Class ◽  
Task Design ◽  
Judgment Task ◽  
Human Reasoning ◽  
Value Judgment ◽  
Psychology Of Reasoning ◽  
The Core ◽  
The Past ◽  
Illusory Inferences

We investigate the articulation between domain-general reasoning and interpretive processes in failures of deductive reasoning. We focus on illusory inferences from disjunction-like elements, a broad class of deductive fallacies studied in some detail over the past 15 years. These fallacies have received accounts grounded in reasoning processes, holding that human reasoning diverges from normative standards. A subset of these fallacies however can be analyzed differently: human reasoning is not to blame, instead the premises were interpreted in a non-obvious, yet perfectly predictable and reasonable way. Once we consider these interpretations, the apparent fallacious conclusion is no mistake at all. We give a two-factor account of these fallacies that incorporates both reasoning-based elements and interpretive elements, showing that they are not in real competition. We present novel experimental evidence in favor of our theory. Cognitive load such as induced by a dual-task design is known to hinder the interpretive mechanisms at the core of interpretation-based accounts of the fallacies of interest. In the first experiment of its kind using this paradigm with an inferential task instead of a simpler truth-value-judgment task, we found that the manipulation affected more strongly those illusions where our theory predicts that interpretive processes are at play. We conclude that the best way forward for the field to investigate the elusive line between reasoning and interpretation requires combining theories and methodologies from linguistic semantics and the psychology of reasoning.

Human Reasoning: Deduction Rules or Mental Models, or Both?

1993 ◽  
Vol 46 (4) ◽  
pp. 569-589 ◽  
Author(s):  
Maxwell J. Roberts
Keyword(s):  
Individual Differences ◽  
Mental Models ◽  
Deductive Reasoning ◽  
Good Deal ◽  
Human Reasoning ◽  
Unified Theory ◽  
Grand Unified Theory ◽  
Deduction Rules ◽  
Reasoning Mechanism ◽  
And Task

A good deal of energy is currently being expended into discovering the fundamental machinery underlying deductive reasoning. Is it based upon mental models (arrays) or deduction rules (propositions)? The appeal of finding a “grand unified theory” of reasoning is obvious, but the likelihood of achieving this must also be considered. This paper discusses the use of experimental psychology in attempts to discover the processes associated with the fundamental reasoning mechanism. One particular problem is that individuals can use different strategies to solve reasoning problems. The consequences of this are assessed in relation to: (1) the assumptions underlying the experiments, (2) the choice of tasks and task presentations intended to enable the fundamental reasoning processes to be viewed directly, and (3) the power status of the theories and the nature of the evidence required to show that either theory is superior. Under close scrutiny the debate appears to be unresolvable by using empirical techniques. However, although the main conclusions are negative, it is suggested that approaches that directly investigate individual differences are likely to be useful alternatives.

Précis ofBayesian Rationality: The Probabilistic Approach to Human Reasoning

2009 ◽  
Vol 32 (1) ◽  
pp. 69-84 ◽  
Author(s):  
Mike Oaksford ◽  
Nick Chater
Keyword(s):  
Probabilistic Reasoning ◽  
Deductive Reasoning ◽  
Human Life ◽  
Probabilistic Approach ◽  
Formal Theory ◽  
Logical Reasoning ◽  
Point Of View ◽  
Human Reasoning ◽  
Rational Animal ◽  
Bayesian Rationality

AbstractAccording to Aristotle, humans are the rational animal. The borderline between rationality and irrationality is fundamental to many aspects of human life including the law, mental health, and language interpretation. But what is it to be rational? One answer, deeply embedded in the Western intellectual tradition since ancient Greece, is that rationality concerns reasoning according to the rules of logic – the formal theory that specifies the inferential connections that hold with certainty between propositions. Piaget viewed logical reasoning as defining the end-point of cognitive development; and contemporary psychology of reasoning has focussed on comparing human reasoning against logical standards.Bayesian Rationalityargues that rationality is defined instead by the ability to reason aboutuncertainty. Although people are typically poor at numerical reasoning about probability, human thought is sensitive to subtle patterns of qualitative Bayesian, probabilistic reasoning. In Chapters 1–4 ofBayesian Rationality(Oaksford & Chater 2007), the case is made that cognition in general, and human everyday reasoning in particular, is best viewed as solving probabilistic, rather than logical, inference problems. In Chapters 5–7 the psychology of “deductive” reasoning is tackled head-on: It is argued that purportedly “logical” reasoning problems, revealing apparently irrational behaviour, are better understood from a probabilistic point of view. Data from conditional reasoning, Wason's selection task, and syllogistic inference are captured by recasting these problems probabilistically. The probabilistic approach makes a variety of novel predictions which have been experimentally confirmed. The book considers the implications of this work, and the wider “probabilistic turn” in cognitive science and artificial intelligence, for understanding human rationality.

Is There a Scientific Method?

2021 ◽  
pp. 21-35
Author(s):  
Steven L. Goldman
Keyword(s):  
Subjective Experience ◽  
Deductive Reasoning ◽  
A Priori ◽  
Inductive Reasoning ◽  
Modern Science ◽  
Francis Bacon ◽  
Human Reasoning ◽  
The World ◽  
Innate Ideas ◽  
External Causes

Modern science relies largely on method or, rather, on the claim that by employing a systematic, impersonal method, human reasoning can transcend the mind’s subjective experience of reality and discover the true, external causes of experience. In the early stages of modern science’s emergence out of medieval and Renaissance nature philosophy, Francis Bacon argued that this method was to be based on induction and experiment, without a priori mental input and with a minimum of mathematics. Rene Descartes argued that the required method was to be based on deduction, mathematics, and a priori and innate ideas, with a minimum of experiment. For Descartes, experiment served primarily as a check on deductive reasoning; for Bacon, experiment was a source of knowledge and constrained our inductive reasoning about empirical facts. Despite their differing styles, Descartes and Bacon together concretized the idea that a systematic method of reasoning could give us knowledge of the world.

Neuroanatomical Correlates of Human Reasoning

1998 ◽  
Vol 10 (3) ◽  
pp. 293-302 ◽  
Author(s):  
Vinod Goel ◽  
Brian Gold ◽  
Shitij Kapur ◽  
Sylvain Houle
Keyword(s):  
Pet Imaging ◽  
Right Hemisphere ◽  
Deductive Reasoning ◽  
Inferior Frontal Gyrus ◽  
Building Blocks ◽  
Middle Temporal Gyrus ◽  
Human Reasoning ◽  
General Terms ◽  
Brodmann Areas ◽  
Left Middle

One of the important questions cognitive theories of reasoning must address is whether logical reasoning is inherently sentential or spatial. A sentential model would exploit nonspatial (linguistic) properties of representations whereas a spatial model would exploit spatial properties of representations. In general terms, the linguistic hypothesis predicts that the language processing regions underwrite human reasoning processes, and the spatial hypothesis suggests that the neural structures for perception and motor control contribute the basic representational building blocks used for high-level logical and linguistic reasoning. We carried out a [15O] H2O PET imaging study to address this issue. Twelve normal volunteers performed three types of deductive reasoning tasks (categorical syllogisms, three-term spatial relational items, and three-term nonspatial relational items) while their regional cerebral blood flow pattern was recorded using [15O] H2O PET imaging. In the control condition subjects semantically comprehended sets of three sentences. In the deductive reasoning conditions subjects determined whether the third sentence was entailed by the first two sentences. The areas of activation in each reasoning condition were confined to the left hemisphere and were similar to each other and to activation reported in previous studies. They included the left inferior frontal gyrus (Brodmann areas 45, 47), a portion of the left middle frontal gyrus (Brodmann area 46), the left middle temporal gyrus (Brodmann areas 21, 22), a region of the left lateral inferior temporal gyrus and superior temporal gyrus (Brodmann areas 22, 37), and a portion of the left cingulate gyrus (Brodmann areas 32, 24). There was no significant right- hemisphere or parietal activation. These results are consistent with previous neuroimaging studies and raise questions about the level of involvement of classic spatial regions in reasoning about linguistically presented spatial relations.

scholarly journals Inconsistency Measurement for Improving Logical Formula Clustering

2020 ◽  
Author(s):  
Yakoub Salhi
Keyword(s):  
Classical Logic ◽  
Logical Consequence ◽  
Main Idea ◽  
Heterogeneous Data ◽  
Formal Logic ◽  
Clustering Methods ◽  
Logical Formula

Formal logic can be used as a tool for representing complex and heterogeneous data such as beliefs, knowledge and preferences. This study proposes an approach for defining clustering methods that deal with bases of propositional formulas in classical logic, i.e., methods for dividing formula bases into meaningful groups. We first use a postulate-based approach for introducing an intuitive framework for formula clustering. Then, in order to characterize interesting clustering forms, we introduce additional properties that take into consideration different notions, such us logical consequence, overlapping, and consistent partition. Finally, we describe our approach that shows how the inconsistency measures can be involved in improving the task of formula clustering. The main idea consists in using the measures for quantifying the quality of the inconsistent clusters. In this context, we propose further properties that allow characterizing interesting aspects related to the amount of inconsistency.

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