Conditional Syllogisms Research Articles

The Status of Conditional Syllogism in Syllogistics

Abstract The form of the conditional syllogism resembles that of the categorical syllogism, while its subject matter is at least a conditional premise, but its conclusion is always conditional conjunctive or disjunctive. This mixed structure to which we apply the rules of the categorical syllogism, is a structure of which Aristotle did not have an idea, and which the Stoics did not conceive, and which the non-Arabian logicians did not know until in modern times. But what we have to notice here is the putting of a conditional matter in the form of the categorical syllogism, and it is this kind of hybridization, if we dare to say, which generated this mixed structure which appeared for the first time in the history of logic in the treatise on the logic of Ibn Sina and which can be considered a discovery by this author until proof to the contrary, and that the ancient Arabian logicians have taken the habit of exhibiting in their treatises.

Stabilnost efekata pristranosti i efekta tematskog materijala u Wasonovom izbornom zadatku

The aim of this paper was to demonstrate bias effects (Evans, 1989) and the effect of thematic material (Griggs and Cox, 1982) on reasoning in Wason’s selection task and also, to investigate the stability of diese effects in respect to experience got in the same and similar types of tasks. Bias effects influence some typical errors in reasoning, and the effect of thematic material is the phenomena that bias effects are stronger in the situation of abstract tasks solving than in the situation of concrete tasks solving. Different theories of deductive reasoning try to explain these phenomena. In the experiment the subjects' task was to select two cards out of four of them that describe states of affairs, to check the validity of a given conditional sentence. Both kinds of effects (bias and thematic material) were found and were shown to be stable, in respect to experience acquired in previous conditional syllogisms solving, and also in respect to the order of selecting tasks solving (abstract-concrete and vice versa). It seems that none of the theories of reasoning give a complete explanation of these phenomena, so all explanations were considered.

La Contribution des Anciens Logiciens Arabes à l’Extension des Formes de la Déduction : La Théorie du Syllogisme Connectif Conditionnel

Logique Arabe | Déduction | Syllogisme Attributif | Syllogisme Hypothétique | Syllogism Connectif Conditionnel | Arabic Logic | Deduction | Predicative Syllogism | Hypothetical Syllogism | Connective Conditional Syllogism | منطق عربي | إستنتاج | قياس إقتراني حملي | قياس إقتراني شرطي | قياس شرطي متصل

CONDITIONALS AND DISJUNCTIONS IN MENTAL-LOGIC THEORY: A RESPONSE TO LIU AND CHOU (2012) AND TO LÓPEZ ASTORGA (2013)

Liu and Chou (2012) presented a two-step theory to describe reasoning both on the four traditional conditional syllogisms and on four parallel syllogisms tha...

Reality of cognitive pregnance in conditional syllogism problem

Reality of cognitive pregnance in conditional syllogism problem

ALFARABI ON CONDITIONALS

AbstractI examine the theory of conditional propositions (qaḍāyā šarṭiyya muttaṣila) and conditional syllogisms (qiyāsāt šarṭiyya) in the logical works of Alfarabi (d. 950). I contextualize Alfarabi's logical doctrines related to conditional reasoning against the backdrop of the context-theory of logic, which was developed by Aristotle's ancient commentators. I show that Alfarabi thought that conditional propositions have truth-conditions. I provide conjectural truth-conditions for conditional propositions, and conjectural validity-conditions for connective conditional syllogisms. These truth-conditions and validity-conditions are shown to be sensitive to the pragmatic conditions in which conditional propositions and arguments are deployed. I end by suggesting that Alfarabi's logical pragmatism is a consequence of his adoption of the late antique context-theory of logic rather than a result of his developing Aristotle's formal syllogistic theory adumbrated in thePrior Analytics.

Probability and Instruction Effects in Syllogistic Conditional Reasoning

Abstract — The main aim of this study was to examine whether people understand indicative conditionals on the basis of syntactic factors or on the basis of subjective conditional probability. The second aim was to investigate whether the conditional probability of q given p depends on the antecedent and consequent sizes or derives from inductive processes leading to establish a link of plausible co-occurrence between events semantically or experientially associated. These competing hypotheses have been tested through a 3 x 2 x 2 x 2 mixed design involving the manipulation of four variables: type of instructions (“Consider the following statement to be true”, “Read the following statement” and condition with no conditional statement); antecedent size (high/low); consequent size (high/low); statement probability (high/low). The first variable was between-subjects, the others were within-subjects. The inferences investigated were Modus Ponens and Modus Tollens. Ninety undergraduates of the Second University of Naples, without any prior knowledge of logic or conditional reasoning, participated in this study. follows that “if Results suggest that people understand conditionals in a syntactic way rather than in a probabilistic way, even though the perception of the conditional probability of q given p is at least partially involved in the conditionals’ comprehension. They also showed that, in presence of a conditional syllogism, inferences are not affected by the antecedent or consequent sizes. From a theoretical point of view these findings suggest that it would be inappropriate to abandon the idea that conditionals are naturally understood in a syntactic way for the idea that they are understood in a probabilistic way.

A Mixed Rasch Model of Dual-Process Conditional Reasoning

A fine-grained dual-process approach to conditional reasoning is advocated: Responses to conditional syllogisms are reached through the operation of either one of two systems, each of which can rely on two different mechanisms. System1 relies either on pragmatic implicatures or on the retrieval of information from semantic memory; System2 operates first through inhibition of System1, then (but not always) through activation of analytical processes. It follows that reasoners will fall into one of four groups of increasing reasoning ability, each group being uniquely characterized by (a) the modal pattern of individual answers to blocks of affirming the consequent (AC), denying the antecedent (DA), and modus tollens (MT) syllogisms featuring the same conditional; and (b) the average rate of determinate answers to AC, DA, and MT. This account receives indirect support from the extant literature and direct support from a mixed Rasch model of responses given to 18 syllogisms by 486 adult reasoners.

THE FACILITATING EFFECT OF THE HIERARCHICAL ORGANISATION OF CONCEPTS TO THE SYLLOGISTIC REASONING

1. Introduction The traditional tasks of logical reasoning can be both strikingly easy and extremely difficult for adults as well as children. From the four possible conditional reasoning problems, modus ponens (if p then q, p, therefore q) seldom invokes errors starting from six-year old children (Staudenmayer, Bourne 1977, Wildman, Fletcher 1977). However, even adults are reluctant to draw a perfectly valid conclusion from modus tollens (if p then q, not q, therefore not p), or are prone to make invalid conclusions with the conditional problems of the form denial of the antecedent (if p then q, not p, therefore not q) and affirmation of the consequent (q, therefore p). The amount of correct answers to the latter three tasks gradually increases with age, although adults' performance is far from perfect (see Overton 1990 for a review). Another group of tasks of traditional logic, categorical-syllogisms, appear to be more difficult. Similarly to the conditional problems, some of the possible 64 categorical syllogisms are solved correctly by preschoolers (e.g. All A are B, All B are C, therefore all C are A) (Dias, Harris 1988, Hawkins et al. 1984), however many other syllogisms are frequently solved incorrectly. The developmental data provided for the easier subset of 28 syllogisms regarding 9-year-old children and adults indicates that children solve correctly approximately one-third and adults one-half of the syllogisms (Bara et al. 1995). Thus, both in case of conditional syllogisms and categorical syllogisms, some development seems to occur. Several ideas about the origins of the development of logical reasoning have been suggested. According to the theory of mental models, children's deficiencies in syllogistic reasoning stem from their yet limited working memory abilities and skills in searching for counterexamples (in finding several alternative mental models for a particular syllogism) (Bara et al. 1995). Thus, according to this view, the growth of logical reasoning has nothing inherently logical about it (these are not the inferential rules that matter), instead the development is rooted in the increase of working memory abilities and knowledge base to interpret particular premises (Johnson-Laird et al. 1986). The theory of mental logic developed by Braine (1978, 1990) takes a different route. It divides logical skills into primary and secondary skills. Primary skills consist of inferential rules that are either innate or develop very early and are available to all of us. An example of one primary inferential rule is the above mentioned modus ponens; it is automatic and universally obvious to all people. Secondary skills, although based on the primary skills, are considered to be the result of education and have more academic nature. The correct answers to modus tollens would require some secondary skills; here it is necessary to construct a longer chain of reasoning where the primary rule of modus ponens and the reductio ad absurdum rule are applied. Therefore, fallacies with modus tollens are frequent and they gradually diminish with the cognitive development of a child. These longer reasoning chains impose greater demands on memory and often the use of written language is necessary. Another characteristic feature of secondary skills is the requirement to accept the strategy of minimal commitment--focus is not on what the speaker means, however imprecisely and elliptically it might have been expressed (as is the case with everyday reasoning), but on what the sentence is committed to (Braine 1978). Additionally, in non-academic everyday reasoning situations people use all the information available, whereas in case of more advanced logical tasks they should compartmentalise information, i.e. use only the information contained in the premises. Hence, Braine's theory, in contrast to the theory of mental models, proposes that specific skills that are introduced in school may be the constituent factors for the development logical reasoning. …

On the nature of mental models of conditional: The case of If, If then, and Only if

It has recently been reported that forward inferences from if p then q sentences (i.e., from antecedent to consequent) were faster than backward inferences from consequent to antecedent (Barrouillet, Grosset, & Lecas, 2000). The standard mental model theory assumes that this directionality effect is a figural effect due to the order the information enters working memory, whereas we claim that it results from the nature of the mental models that represent oriented relations from hypothetical values introduced by the word If. We tested these hypotheses in an experiment in which adult participants evaluated conditional syllogisms from either if p then q, p only if q, or p if q statements. Contrary to the predictions resulting from the standard theory, the three forms of the conditional provoked a reversed directionality effect and denial inferences took longer to endorse than affirmative inferences for all the forms of conditionals. We argue from these results that mental models of the conditional represent oriented relations instead of mere co-occurrences between events.

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

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-binary terms (NN), and (3) conditionals with non-binary terms embedded in a restrictive context (NNR). As we predicted, BB conditionals elicited more biconditional response patterns than did NN conditionals in all age groups. On the other hand, manipulating the context had the same effect in children but not in adults. Content and context constraints on conditional reasoning along with developmental issues are discussed within the framework of the mental models theory.

Markers of social group membership as probabilistic cues in reasoning tasks

Reasoning about social groups and their associated markers was investigated as a particular case of human reasoning about cue-category relationships. Assertions that reasoning involving cues (group markers) and associated categories (social groups) elicits specific probabilistic assumptions are supported by the results of three experiments. This phenomenon remains intact across the use of categorical syllogisms (Experiment 1), conditional syllogisms (Experiment 2), and the use of social groups that vary in their perceived cohesiveness, or entitativity (Experiment 3). Implications are discussed for various theories of reasoning, and additional aspects of social group/coalitional reasoning are also discussed.

The effect of explicit negatives and of different contrast classes on conditional syllogisms.

One experiment tested the effects of systematically negating the constituents of four fundamental inferences based on conditionals: Modus Ponens (i.e. inferences of the form: if p then q; p therefore q), Modus Tollens (if p then q; not-q therefore not-p); Affirmation of the Consequent (if p then q; q therefore p), and Denial of the Antecedent (if p then q; not-p therefore not-q). The latter two inferences are valid only for bi-conditionals (if, and only if, p then q). The participants drew their own conclusions from premises about letters and numbers on cards. We observed a significant effect of explicit negatives on Modus Tollens and Denial of the Antecedent problems: The inferences were drawn more often for conditionals that yield a negative conclusion (e.g. if p then not q; q therefore not p) than for conditionals that yield an affirmative conclusion (e.g. if not p then q; not q therefore p). Additionally, we observed a similar, but smaller effect on Affirmation of the Consequent problems. Furthermore, we observed a significant effect of the categorical premise (affirmative or negative), especially on Affirmation of the Consequent problems. Finally, we observed an effect of the magnitude of the contrast class. If the contrast is larger (a set of three, five or nine values), then the making of a double negation or the production of an affirmative conclusion is more difficult for Denial of the Antecedent inferences. We discussed the results in relation to a negative categorical premise bias, an affirmative premise bias, a negative conclusion bias and a double negation effect.

The Popperian framework, statistical significance, and rejection of chance

That Haig and Sohn find the hypothetico-deductive approach wanting in different ways shows that multiple conditional syllogisms are being used in different stages of theory corroboration in the Popperian approach. The issues raised in the two commentaries assume a different complexion when certain distinctions are made.

Ordering of information in conditional reasoning

Two experiments are reported in which participants are asked to evaluate computer‐presented conditional syllogisms consisting of a major premise (conditional rule), a minor premise and a conclusion. As an example the modus tollens inference with an affirmative conditional has the form if p then q, not‐q therefore not‐p. In these experiments, participants were asked to judge the validity of four types of conditional syllogisms with four types of conditional rule in which the presence and absence of negated components was varied. In Expt 1, half of the participants received problems with the conclusion presented prior to the premises, and half in the usual order. Experiment 2 combined this variable with a second: standard or reversed order of major and minor premises. Both manipulations substantially reduced the effects of the negative conclusion bias which is typically observed in this paradigm. The findings are discussed with respect to the debate between mental models and mental logic accounts of conditional inference.

Is everyday experience dysfunctional for the development of conditional reasoning?

According to “Comprehension theory” improved performance on invalid conditional syllogisms is a function of the ability to dissociate from a biconditional interpretation. Given that biconditional interpretation is typically used in inferring from everyday conditionals (i.e., circumstantial conditionals), the accumulation of everyday experience should reinforce its usage rather than weaken it and, hence, be dysfunctional in solving invalid conditional syllogisms. This study examines the hypothesis that certain kinds of experiences that are unique to schooling account for improved performance on invalid problems with age. The study estimated the independent effects of age and schooling in Grades 5 and 6 on scores obtained on invalid conditional and class syllogisms. The results point to a negative, albeit very small effect of out-of-school experience and to a considerable positive effect of schooling. Hence, contrary to other cognitive tasks in which schooling operates in the same direction as out-of-school experience, in this case, it apparently breaks daily-life interpretational habits and therefore is crucial for the developmental process.

Logic in conversation: Comparative studies of deduction in children and adults

Study 1 contains analyses of the conditional syllogisms produced during conversation by 4 1 2 -year-olds with adults, clients with therapists, and college students interviewed about causal theories. Because their conversational partners attempted to guide their behavior, a comparison of child and client inferences enabled evaluation of the relative influence of conversational role and age on deduction. Comparison of adult conversations enabled assessment of the role of differing contexts on inferential content. The speakers were similar except that the children made fewer independent inferences and shifts in taxonomic level and responded more frequently to socially controlling statements. Clients and children responded more to self-referential content. In Study 2, longitudinal corpora of conversations between adults and five children from 27 to 63 months of age were analyzed. By the time the children produced their own ifs, their inferences resembled adults'.

The New Rhetoric's Argument Schemes: A Rhetorical View of Practical Reasoning

In a lecture delivered in 1957, Chaim Perelman (1958) described the workings of practical reasoning and compared them to the structures of formal logic: Why envisage proof always in terms of a single model? . . . |A~ final convergence |of a number of indications~ can lead to conclusions so sure that only a lunatic would ever think of doubting them. . . . When we to reconstruct the past |for example~ the arguments which we use seem to me very much more like a piece of cloth, the total strength of which will always be vastly superior to that of any single thread which enters into its warp and woof. In The New Rhetoric, Perelman and Olbrechts-Tyteca (1969) developed a description of the various threads making up this cloth; these include the starting points for argument, the conventions governing argument practices, and the mechanisms or schemes for making inferences.(1) Each of these dimensions of argument is tied in Perelman and Olbrechts-Tyteca's (1969) theory to a conception of what the arguer believes that the audience will accept, since is in terms of an audience that an argumentation develops. For instance, the starting points of argument--facts, truths, presumptions, values, hierarchies, and the loci of the preferable--are derived from premises to which the arguer's anticipated audience presumably subscribes. The conventions for conducting arguments also grow out of practices and norms mutually accepted by interlocutors who participate together in a common culture. Likewise, the inferential schemes that move the audience to accept the arguer's claims are generated through commonplaces and structures recognized and accepted by Western society. Over two-thirds of The New Rhetoric was devoted to describing these agreed-upon liaisons that make inferences possible, for Perelman and Olbrechts-Tyteca believed that in practical reasoning, inferential moves are made possible rhetorically. Yet The New Rhetoric's system of argument schemes has not received attention proportionate to its significance. While numerous studies focused on the concepts of universal audience (Scult, 1976; Ray, 1978; Perelman, 1984; Golden, 1986), presence (Karon, 1976), and the rationality/reasonableness distinction (McKerrow, 1982; Laughlin & Hughes, 1986), attention to the argument schemes themselves has been infrequent, despite the fact that Perelman and Olbrechts-Tyteca (1969) devoted the bulk of their treatise to the rhetorical nature of inference forms. Quasi-logical, analogical, and dissociative scheme types been individually studied (Dearin, 1982; Measell, 1985; Schiappa, 1985). One critique of the system has appeared (van Eemeren, Grootendorst, & Kruiger, 1984), and various critics made partial or tentative efforts to apply the schemes to argument practices (Siebold, McPhee, Poole, Tanita, & Canary, 1981; Farrell, 1986). While argument textbooks make general use of the scheme typology to describe argument practices (Katula, 1983; Herrick, 1991), precise study of the individual schemes has been sporadic and indeterminate. Two decades after The New Rhetoric was published, Olbrechts-Tyteca (1979) expressed disappointment at the lack of attention given to the study of specific schemes. And in 1986, Thomas Farrell could claim that The New Rhetoric's descriptions of practical reasoning practices have been the singularly most neglected feature of Perelman's rhetorical theory. The scheme typology is nonetheless of singular importance because it provides us with a rhetorical account of the operation of argument schemes. Prior to The New Rhetoric, our vocabulary for describing inference patterns was limited to formal logical patterns (e.g., categorical, disjunctive, and conditional syllogisms) and the standard classifications of inductive reasoning (analogy, generalization, cause, and sign). Perelman and Olbrechts-Tyteca (1969) generated their schemes through a careful empirical process in which they collected discursive arguments for over ten years, typed them, and added new categories (dissociations, symbolic liaisons, and double hierarchy arguments, among others), thus providing a richer vocabulary for describing reasoning structures. …

Speaking deductively: Preschoolers' use of If in conversation and in conditional inference.

Conversations taped in the homes and preschools of 39 four-year-olds were used to determine whether children and adults spoke the type of if sentence found in conditional syllogisms, whether children made conditional deductions during conversation, and whether adult speech influenced children's use of if in conversation and deduction.

The Development of Conditional Reasoning: An Iffy Proposition

Publisher Summary This chapter attempts to make some sense of the competing claims concerning conditional-reasoning competence. The competence model is based on the natural deduction approach to standard logic; modus ponens and the schema for conditional proof provide inference rules for simple conditionals and, together with the recognition of the constraints imposed by universal quantification, they provide a model for reasoning with universally quantified conditionals. Piaget's account of conditional reasoning is inadequate on logical grounds, that is, it confuses simple and quantified conditionals, but it is possible to make fairly clear empirical predictions when quantifiers are assumed. Ennis and Brainerd have argued that Piaget's account of formal operational thought is wrong because children have some ability to evaluate conditional syllogisms correctly. However, Piaget argued that successful performances on many conditional reasoning tasks can be obtained without a formal operational appreciation of the conditional. Given that the class-inclusion logic structure of concrete operational thought should be sufficient for reasoning with simple conditionals; this does not appear to be a warranted dismissal of the theoretical expectations. Rather, the appropriate assessment of formal operational competency with conditionals appears to concern performances in judging universally quantified conditionals.