Online research in philosophy

We propose probability logic as an appropriate standard of reference for evaluating human inferences. Probability logical accounts of nonmonotonic reasoning with system p, and conditional syllogisms (modus ponens, etc.) are explored. Furthermore, we present categorical syllogisms with intermediate quantifiers, like the “most . . . ” quantifier. While most of the paper is theoretical and intended to stimulate psychological studies, we summarize our empirical studies on human nonmonotonic reasoning.

This paper describes a model of legal reasoning and a logic for reasoning with rules, principles and goals that is especially suited to this model of legal reasoning. The paper consists of three parts. The first part describes a model of legal reasoning based on a two-layered view of the law. The first layer consists of principles and goals that express fundamental ideas of a legal system. The second layer contains legal rules which in a sense summarise the outcome of the interaction of the principles and goals for a number of case types. Both principles, goals and rules can be used in legal arguments, but their logical roles are different. One characteristic of the model of legal reasoning described in the first part of the paper is that it takes these logical differences into account. Another characteristic is that it pays serious attention to the phenomena of reasoning about the validity and acceptance of rules, respectively principles and goals, and about the application of legal rules, and the implications of these arguments for the use of rules, principles and goals in deriving legal conclusions for concrete cases.The second part of the paper first describes a logic (Reason-Based Logic) that is especially suited to deal with legal arguments as described in terms of the previously discussed model. The facilities of the logic are illustrated by means of examples that correspond to the several aspects of the model.

Gilbert Harman, in Logic and Reasoning (Synthese 60 (1984), 107–127) describes an unsuccessful attempt ... to develop a theory which would give logic a special role in reasoning. Here reasoning is psychological, a procedure for revising one''s beliefs. In the present paper, I construe reasoning sociologically, as a process of linguistic interaction; and show how both reasoning in the psychologistic sense and logic are related to that process.

Pt. I. Writings on the theory of logic: I. Pure logic or the logic of quality apart from quantity. II. The substitution of similars. III. On the mechanical performance of logical inference. IV. On a general system of numerically definite reasoning.--Pt. II. John Stuart Mill's philosophy tested: I. On geometrical reasoning. II. On resemblance. III. The experimental methods. IV. Utilitarianism. V. On the method of difference.

Reasoning is a goal-oriented activity. The logical steps are at best the median part of a full reasoning: before them, a language has to be defined, and a model of the goal in this language has to be developed; after them, their result has to be checked in the real world with respect to the goal. Both the prior and the subsequent steps can be conducted rationally; none of them has a logical counterpart. Furthermore, Logic aims at prescribing what a correct reasoning is. But correct with respect to what? If the answer is: with respect to truth, the next question is whether the truth in everyday life, physics, economy, is the same as the truth that logicians have in mind. Resorting to Logic is justified only if an idealization in terms of true propositions in the logical sense is compatible with the goal. If such an idealization is legitimate, so is the use of classical Logic. If not, there is no authority forbidding to skew Logic in order to better reflect the nature of the reasoning required for the task.

Mental probability logic is a psychological competence theory about how humans interpret and reason about common-sense conditionals. Probability logic is proposed as an appropriate standard of reference for evaluating the rationality of human inferences. Common-sense conditionals are interpreted as “high” conditional probabilities, P(B|A) > .5. Probability logical accounts of nonmonotonic reasoning and inference rules like the modus ponens are explored. Categorical syllogisms with comparative and quantitative quantifiers are investigated. A series of eight experiments on human probabilistic reasoning in the framework of the basic nonmonotonic system p corroborate the psychological plausibility of the proposed approach.

, David Bloor suggests that logical reasoning is radically relativistic in the sense that there are incompatible ways of reasoning logically, and no culturally transcendent rules of correct logical inference exist which could allow for adjudication of these different ways of reasoning. Bloor cites an example of reasoning used by the Azande as an illustration of such logical relativism. A close analysis of this reasoning reveals that the Azande's logic is in fact impeccably Aristotelian. I argue that the conclusions Bloor can legitimately draw from his case study are not controversial and do nothing to make plausible the thesis of logical relativism.

I interpret Mill?s view on logic as the instrumentalist view that logical inferences, complex statements, and logical operators are not necessary for reasoning itself, but are useful only for our remembering and communicating the results of the reasoning. To defend this view, I first show that we can transform all the complex statements in the language of classical first-order logic into what I call material inference rules and reduce logical inferences to inferences which involve only atomic statements and the material inference rules. Then I explain why we introduce logical operators and logical inference rules into a system of the latter kind. In the end I determine what kind of negation is justified from this point of view.

The current paper details a restricted semantics for active logic, a time-sensitive, contradictiontolerant logical reasoning formalism. Central to active logic are special rules controlling the inheritance of beliefs in general, and beliefs about the current time in particular, very tight controls on what can be derived from direct contradictions (P &¬P ), and mechanisms allowing an agent to represent and reason about its own beliefs and past reasoning. Using these ideas, we introduce a new definition of model and of logical consequence, as well as a new definition of soundness such that, when reasoning with consistent premises, all classically sound rules are sound for active logic. However, not everything that is classically sound remains sound in our sense, for by classical definitions, all rules with contradictory premises are vacuously sound, whereas in active logic not everything follows from a contradiction.

What is the relationship between logic and reasoning? How do logical norms guide inferential performance? This paper agrees with Gilbert Harman and most of the psychologists that logic is not directly relevant to reasoning. It argues, however, that the mental model theory of logical reasoning allows us to harmonise the basic principles of deductive reasoning and inferential perfomances, and that there is a strong connexion between our inferential norms and actual reasoning, along the lines of Peacocke’s conception of inferential role.