Search results for "Syllogism"

The Syllogistic with Unity

2011

We extend the language of the classical syllogisms with the sentence-forms “At most 1 p is a q” and “More than 1 p is a q”. We show that the resulting logic does not admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete, even when reductio ad absurdum is allowed.

Probabilistic semantics for categorical syllogisms of Figure II

2018

A coherence-based probability semantics for categorical syllogisms of Figure I, which have transitive structures, has been proposed recently (Gilio, Pfeifer, & Sanfilippo [15]). We extend this work by studying Figure II under coherence. Camestres is an example of a Figure II syllogism: from Every P is M and No S is M infer No S is P. We interpret these sentences by suitable conditional probability assessments. Since the probabilistic inference of \(\bar{P}|S\) from the premise set \(\{M|P,\bar{M}|S\}\) is not informative, we add \(p(S|(S \vee P))>0\) as a probabilistic constraint (i.e., an “existential import assumption”) to obtain probabilistic informativeness. We show how to propagate the…

Mental Models vs Integrated Models: Explanations of Syllogistic Reasoning

1996

To compare mental versus integrated models explanations of syllogistic reasoning, we administered a multiple-choice questionnaire containing 19 pairs of syllogistic premises with valid conclusions (given in a C-A order) to 72 psychology undergraduates. Association between our integrated models classification and the empirical difficulty of items was strong.

Content and context effects in children's and adults' conditional reasoning

2002

We have recently shown that children interpret conditional sentences with binary terms (e.g., male/female) in both the antecedent and the consequent as biconditionals (Barrouillet & Lecas, 1998). We hypothesized that the same effect can be obtained with conditionals that do not contain binary terms provided that they are embedded in a context that restricts to only two the possible values on both the antecedent and the consequent. In the present experiment, we asked 12-year-old children, 15-year-old children, and adults to draw conclusions from conditional syllogisms that involved three types of conditional sentence: (1) conditionals with binary terms (BB), (2) conditionals with non-bi…

Probabilistic interpretations of the square of opposition

We investigate the square of opposition from a probabilistic point of view. Probability allows for dealing with exceptions and uncertainty. We will interpret the corners of the square by means of (precise or imprecise) conditional probability assessments. They will be defined within the framework of coherence, which originally goes back to de Finetti. In this framework probabilities are conceived as degrees of belief, where conditional probability is defined as a primitive concept. Coherence allows for dealing with partial and imprecise assessments. Moreover, the coherence approach is especially suitable for dealing with zero antecedent probabilities (i.e., here conditioning events may have…

Transitive Reasoning with Imprecise Probabilities

2015

We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent \(\text{ p-consistent }\) sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Finally, we present the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases.

Chronometric evidence for memory retrieval in causal conditional reasoning: The case of the association strength effect

2005

According to many models of conditional reasoning, correct responses to the uncertain forms affirmation of consequent (AC) and denial of antecedent (DA) rely on the retrieval of an alternative antecedent from semantic memory. The main prediction issuing from this hypothesis of online retrieval is that the associative strength of the relevant information in long-term memory affects the latency of its retrieval and then of the correct response of uncertainty to AC and DA. This prediction was tested in 64 adults who performed a syllogism evaluation task with familiar causal conditional premises. As predicted, correct responses of uncertainty to AC and DA were not only more frequent but also fa…

Transitivity in coherence-based probability logic

2016

We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study selected probabilistic versions of classical categorical syllogisms and construct a new version of the squa…

The Third Theory of Legal Objectivity

2013

The question of the objectivity of law rotates around the determination of the status of the norms that constitute the major premise of the practical syllogism representing the formal scheme of the justification of judicial decisions. Those who deny the objectivity of law believe that the existence and meaning of legal norms depend on the opinion of judges and jurists considered individually. The different versions of the objectivity of law reject this sceptical conclusion. The strongest versions of objectivity accepted by the different doctrines of natural law presuppose metaphysical realism and rule out the idea that what seems correct to someone can determine what is effectively correct;…

Taking Aim and Hitting the Target. Some Remarks on the Aristotelian Notion of eustoichia

2018

L’articolo è dedicato alla nozione aristotelica di eustochia (la capacità di fare buone congetture), nella convinzione che essa possa contribuire al ripensamento della nostra costitutiva precarietà. Diversamente da una lettura tradizionale che vede Aristotele principalmente come il filosofo del ragionamento deduttivo, l’articolo sostiene invece l’importanza di questa capacità cognitiva nel pensiero aristotelico. Con questo scopo, vengono analizzati i tre principali contesti in cui Aristotele fa riferimento all’eustochia: la costruzione del sillogismo (APo, 89b 10), il raggiungimento della virtù (EN, 1106b 16) e la creazione di metafore ((Rh. 1412a 13). Nonostante le evidenti differenze, que…