Minor Premise Research Articles

The Army’s Dilemma

Given its performance in Operation Iraqi Freedom, the Army's stock should be at an all-time high. It carried out a bold plan that was both operationally and logistically challenging against a larger if unmotivated force. It routed the Iraqi army and adapted well to the unexpected attacks by the fedayeen. It also fought well in the cities, often a killing field for attackers. It took few casualties, just over 100 dead before the declared end of hostilities. More impressively, it reversed the historical ratio of battle to non-battle injuries. Typically, the latter outnumber the former significantly, but in Iraq non-battle deaths were about one-third of those caused by combat. (1) Few non-battle injuries are widely seen as a characteristic of a well-trained and disciplined force. By any measure, the Army performed superbly. Additionally, the Army has embarked on what is arguably the most dramatic and radical transformation of any of the services. The current Army plan calls for a dramatic shift away from heavy armor to a family of 16 to 20-ton vehicles that will rely heavily on a networked system of information and situational awareness for battlefield success as opposed to heavy armor plate. The Army's rapid deployment goals are truly daunting (a brigade-sized force anywhere in the world in 96 hours, followed by the rest of a division by 120 hours). These ambitious goals are taxing all aspects of the Army's combat and support organizations to streamline to an unprecedented degree to even come close to meeting those timelines. How is it, then, that according to many reports the Army is perceived by senior defense policymakers as unimaginative, obstructionist, and wedded to concepts of warfare that are increasingly irrelevant to the current geopolitical environment? The Army's diminished status reflects in the filling of high-level joint billets by officers from the other services, including the Supreme Allied Commander, Europe, which had been held by an Army officer for more than 40 years. (2) This article suggests an explanation for this perception and ways the Army might alter it. How the Army Sees Itself The Army has long seen itself as the service, the one with the primary responsibility to win the nation's wars. Indeed, the Army's vision statement describes fighting and winning our nation's as its nonnegotiable contract with the American people. (3) It does not qualify the vision by indicating that it wins the wars in conjunction with the other services. This view finds more formal expression in Field Manual 3-0, Operations, the Army's capstone doctrinal manual: Land operations determine the outcome of major theater wars (MTWs). In an MTW, the nation employs large joint and multinational forces in major combat operations to defeat an enemy nation, coalition, or alliance. The Gulf War of 1991 is an example of an MTW. Army forces are the decisive forces for sustained land combat, war termination, and postwar stability. JFCs [joint force commanders] normally designate the land component as the supported force during those phases of a campaign. (4) The logic is clear: land operations are decisive in major theater wars, and Army forces are the decisive ones in land combat. Cast as a syllogism, it would read as follows: * Major premise: Land operations determine the outcome of major theater wars. * Minor premise: Army forces determine the outcome of land operations. * Conclusion: Army forces determine the outcome of major theater wars. The logic is impeccable. But as with all syllogisms, the validity hinges on the major and minor premises. This view has important implications. Chief among them is that the Army, a believer in joint operations, perceives the role of the other services as being, fundamentally, to support the Army. The Air Force and Navy get the Army to the theater and provide it such important combat support as naval gunfire, interdiction, and close air support. …

Ternary relations and relevant semantics

Modus ponens provides the central theme. There are laws, of the form A→ C. A logic (or other theory) L collects such laws. Any datum A (or theory T incorporating such data) provides input to the laws of L. The central ternary relation R relates theories L, T and U, where U consists of all of the outputs C got by applying modus ponens to major premises from L and minor premises from T. Underlying this relation is a modus ponens product (or fusion) operation ∘ on theories (or other collections of formulas) L and T, whence RLTU iff L∘ T⊆ U. These ideas have been expressed, especially with Routley, as (Kripke style) worlds semantics for relevant and other substructural logics. Worlds are best demythologized as theories, subject to truth-functional and other constraints. The chief constraint is that theories are taken as closed under logical entailment, which clearly begs the question if we are using the semantics to determine which theory L is Logic itself. Instead we draw the modal logicians’ conclusion—there are many substructural logics, each with its appropriate ternary relational postulates. Each logic L gives rise to a Calculus of L-theories, on which particular candidate logical axioms have the combinatorial properties expected from the well-known Curry–Howard isomorphism (with improvements by Dezani and her fellow intersection type theorists.). We apply their bubbling lemma, updating the Fools Model of Combinatory Logic at the pure → level for the system B ∧ T . We make fusion ∘ an explicit connective, proving a combinator correspondence theorem. Having taken relevant → as a left residual for ∘, we explore its right residual mate → r. Finally we concentrate on and prove a finite model property for the classical minimal relevant logic CB, a conservative extension of the minimal positive relevant logic B + .

Causal conditional reasoning and strength of association: The disabling condition case

Cummins (1995) has shown that reasoning with conditionals involving causal content is affected by the relative number of available alternative and disabling conditions. More recent evidence (Quinn & Markovits, 1998) indicates that, beside the number of stored conditions, the relative strength of association of the alternative conditions with the consequent term is another important factor that affects causal conditional reasoning. In this study we examined the effect of the strength of association for the disabling conditions. We identified causal conditionals for which there exists only one highly associated disabler. With these conditionals we constructed conditional inference problems in which the minor premise was expanded with the negation of a strongly or weakly associated disabler. Results of two experiments indicate that strength of association of stored disabling conditions is affecting reasoning performance: Acceptance of Modus Ponens and Modus Tollens increased when there was no strongly associated disabler available.

Developmental and Content Effects in Reasoning with Causal Conditionals

Two predictions derived from Markovits and Barrouillet's (2001) developmental model of conditional reasoning were tested in a study in which 72 twelve-year-olds, 80 fifteen-year-olds, and 104 adults received a paper-and-pencil test of conditional reasoning with causal premises (“if cause P then effect Q”). First, we predicted that conditional premises would induce more correct uncertainty responses to the Affirmation of the consequent and Denial of the antecedent forms when the antecedent term is weakly associated to the consequent than when the two are strongly associated and that this effect would decrease with age. Second, uncertainty responding to the Denial of the antecedent form (“P is not true”) should be easier when the formulation of the minor premise invites retrieval of alternate antecedents (“if something other than P is true”). The results were consistent with the hypotheses and indicate the importance of retrieval processes in understanding developmental patterns in conditional reasoning with familiar premises.

Pragmatic Method and Its Rhetorical Lineage

Pragmatic Method and Its Rhetorical Lineage

Obligation and the Conditional in Stit Theory

In this paper, we consider two different ways in which modus-ponens type reasoning with conditional obligations may be formalized. We develop necessary and sufficient conditions for the validity of each, and make some philosophical observations about the differences between the minor premises that each formalization requires. All this is done within the context of the Belnap-Perloff stit theory.

Daubert and Litigation-Driven Econometrics

PROFESSOR D.H. Kaye's paper raises interesting and important questions.1 The central issue that his paper tackles is when expert testimony employing statistics, particularly econometrics, should get to the jury. Based on the case study he discusses, his answer appears to be if it's not up to snuff. Kaye nonetheless emphasizes that the answer also must not exclude too much. In other words, we should admit studies that are less than ideal but still within the range of reasonable debate by experts.2 Kaye argues that the admissibility of evidence based on a statistical theory or technique should turn on whether the statistical method has been subjected to sufficient study to establish its validity as applied to a class of problems that includes the one being investigated in the litigation3 (i.e., the major premise, or overarching scientific theory4). The question [w]hether such a method is being applied properly to the problem at hand5 (the minor premise, or case-specific claims6) would generally be left to the jury. While as a conceptual matter this approach is appealing, we are less optimistic than Kaye is about its prospects for providing trial courts with principled guidance about the admissibility of statistical evidence. He concedes that the line between method and specific application can sometimes be difficult to fix,7 but we are afraid that in the case of econometric evidence and social science statistics, drawing that line will usually be problematic. Of course, there will be extreme cases in which the expert cannot justify the use of one model rather than an apparently reasonable alternative, or where

Reasoning from uncertain premises: Effects of expertise and conversational context

Four experiments investigated uncertainty about a premise in a deductive argument as a function of the expertise of the speaker and of the conversational context. The procedure mimicked everyday reasoning in that participants were not told that the premises were to be treated as certain. The results showed that the perceived likelihood of a conclusion was greater when the major or the minor premise was uttered by an expert rather than a novice (Experiment 1). The results also showed that uncertainty about the conclusion was higher when the major premise was uttered by a novice and an alternative premise by an expert, compared to when the major premise was uttered by an expert and the alternative by a novice (Experiment 2). Similarly, the believability of a conclusion was considerably lower when the minor premise was uttered by a novice and denied by an expert, as opposed to when an expert uttered the minor premise and a novice denied it (Experiment 3). Experiment 4 showed that the nature of the uncertainty induced by a denial of the minor premise depended on whether or not the context was a conversation. These results pose difficult problems for current theories of reasoning, as current theories are based on the results of experiments in which the premises are treated as certain. Our discussion of the results emphasises the importance of pragmatics in reasoning, namely, the role of general knowledge about the world in assessing the probability of a premise uttered by an expert or a novice and the role of interpretations of the premise based on pragmatic inferences in revising these initial probabilities.

Claims Analysis: Law, Logic, and Risk

Theme: Application of traditional logic and adaptation of methods from risk analysis enable the law to successfully resolve disputes. A claim to ownership may appear wherever some combination of cultural values assures reliability and exclusivity to the individual's decision. A valid claim must fit somewhere within the social contract to obtain recognition. The social contract is an agreement on risk and opportunity. There are two possibilities: either a person accepts opportunity and risk alone, or she shares them with others. Each society defines the specifics of the contract, but each uses the same general framework. 1. Each person has an exclusive claim to the fruits of her own labor. 2. No one holds an exclusive claim to wealth that has come to her through some method for which she is not responsible. There exists the possibility that the holder must share this wealth with others. 3. Each person must bear alone any losses that result from her independent actions. 4. Each person may demand that others help cover losses when the losses result from events outside her control. The four causes of change are the analytical method that links the client to an area of the social contract. Most commonly, the four causes are used to show that some area of human activity has become subject to rights legitimately held by the client. The four causes describe the situation before the client's problem started (material cause); the process that created the problem (efficient cause); the situation when this process was finished (formal cause); and the purpose of this change (final cause). The techniques of risk analysis measure the probability that the client's claim is valid. For example, the null hypothesis in science becomes the presumption of innocence in law. The law sets the limits of behavior that is so far from society's expectations that the behavior is illegal; here, the law applies the idea of a standard deviation. The burden of proof performs the same function as a level of confidence. But the law takes this technique a step farther. If the jury is persuaded to the relevant burden of proof, then a statement is accepted not merely within a range of probability, but as a certainty. That statement becomes the finding of fact. Comparing this finding to the pertinent legal standard creates the familiar syllogism where the law is the major premise, the finding of fact is the minor premise, and the judgment is the conclusion. A syllogism is a statistical comparison where the level of confidence is set at 100%. Developments in legal theory have paralleled developments in the natural sciences. The writing of John Locke and Sir William Blackstone (absolutes in law) paralleled the work of Sir Isaac Newton (absolutes in space and time). As Albert Einstein published his theories of relativity, Wesley Hohfeld identified eight fundamental legal relationships, each of which transformed itself in relation to the others. By century's end, Laurence Tribe wrote of the curvature of constitutional space much as gravity curves physical space.

A mental model analysis of young children's conditional reasoning with meaningful premises

Mental model theory has been used to explain many differing phenomena in adult reasoning, including the extensively studied case of conditional reasoning. However, the current theory makes predictions about the development of conditional reasoning that are not consistent with data. In this article, young children's performance on conditional reasoning problems and the justifications given are analysed. A mental model account of conditional reasoning is proposed that assumes that (1) young children can reason with two models and (2) the fleshing out of conditionals involves activation of information in semantic memory that uses the minor premise as a retrieval cue.

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.

Reasoning From Uncertain Premises

Previous studies have shown that 1 participants are reluctant to accept a conclusion as certainly true when it is derived from a valid conditional argument that includes a doubtful premise, and 2 participants typically link the degree of uncertainty found in a given premise set to its conclusion. Two experiments were designed to further investigate these phenomena. Ninety adult participants in Experiment 1 were first asked to judge the validity of three conditional arguments Modus Ponens, Denial of the Antecedent, and Affirmation of the Consequent. They were then required to evaluate conclusion uncertainty as a function of two degrees of asserted uncertainty in the major conditional premise (If p then it is very probable that q and if p then it is not very probable that q) of the arguments from the first task that were otherwise unchanged. Results revealed an effect for asserted-uncertainty in two of the three argument forms. Marginal support was found for the hypothesis that perceived argument validity would be a predictor of performance. Experiment 2 investigated the way 40 adult participants combined two sources of asserted uncertainty, one in the major premise and another in the minor premise, when they had to score the uncertainty of the conclusion. The two most prominent kinds of responses were to choose the same likelihood as the weaker of the two expressed in the premises, or a lower one. However, the within-subject consistency was poor. Theoretical implications are discussed.

Factors Contributing to Declines in Cardiac Mortality

To the Editor. —Dr Hunink and colleagues 1 are to be commended for their effort in attempting to model the various contributions of preventive and secondary modalities on the observed decline in mortality associated with coronary heart disease (CHD) from 1980 through 1990. However, their application of the model extends too far into the realm of causal inference, in which mathematical models have a limited role. We believe that their inferential procedures and logical stance are in error. The authors' argument may be summarized in the following syllogism: Their major premise is that reductions in CHD mortality are caused either by changes in risk factors or by changes in treatment; their minor premise is that only 50% of the reduction in CHD mortality can be attributed directly to risk factor changes; and their conclusion is that a large portion of prevented deaths are attributable to improvements in treatment. The major

The effect of premise order in conditional reasoning: a test of the mental model theory

The difference in difficulty between modus ponens ( if p then q; p; therefore q) and modus tollens ( if p then q; not-q; therefore not-p) arguments has been traditionally explained by assuming that the mind contains a rule for modus ponens, but not for modus tollens. According to the mental model theory, modus tollens is a more difficult deduction than modus ponens because people do not represent the case not-q in their initial model of the conditional. On the basis of this theory, we predicted that conditions in which reasoners are forced to represent the not-q case should improve correct performance on modus tollens. In particular, we predicted that the presentation of the minor premise ( not-q ) as the initial premise should produce facilitation. Experiment 1 showed that this is the case: whereas the inversion of the premise order did not affect modus ponens, it produced a significant increase of valid conclusions for modus tollens. Experiment 2 showed that this facilitation does not depend on the negative form (contrary vs. contradictory) of the minor premise. Experiments 3 and 4 (and/or some of their replications) demonstrated that facilitation also occurs when participants are asked to find the cases compatible with not-q or to evaluate a p conclusion. No premise order effect was found for sentences which make explicit the not-q case right from the start, i.e. p only if q conditionals and biconditionals (Experiments 5 and 6). Finally, Experiments 7 and 8 showed that the conditional fallacies are not significantly affected by the premise order.

Ibn Rušd et lesPremiers Analytiquesd'Aristote: Aaperçu sur un problème de syllogistique modale

Ibn Rušd devoted a certain number of works to Aristotle'sPrior Analytics. In a series ofopusculeswritten over a period of twenty years and following upon hisMiddle Commentary on Aristotle's Prior Analytics, he faced a problem particular to the modal syllogism – that of the mood of the conclusion in mixed syllogisms.The problem can be stated as follows: At the beginning of thePrior Analytics, Aristotle established a formal deductive principle – that of universal attribution (Pr. An.I.1.24b26–30). Applied to the modal syllogism, this principle is inadequate as stated. It is too general to be applied in a univocal manner in all modal syllogisms. To preserve a sense of coherence in Aristotle's declarations, the commentators had to interpret it. Presenting the interpretations of the commentators, primarily al-Fārābī and Alexander, on the basis of al-Fārābī'sLarge Commentary on Aristotle's Prior Analytics, Averroes criticizes them. Applied according to Alexander's interpretation, the principle of universal attribution is valid only for modal syllogisms one of whose premises is necessary and the other assertoric; according to al-Fārābī's interpretation, it is verified only when the minor premise is possible. Averroes proposes two preliminary solutions. Either this formal deductive principle must be applied differently according to the modal differences of the minor premises in mixed syllogisms (first solution) or would be used in two ways, generally or in keeping with each mood (second solution). These solutions are not satisfactory, for they call into question the unity and universality of the principle of universal attribution as established by Aristotle. What is the utility, Averroes asks, of a principle which does not hold for all modalities or does not apply to all the premises when thePr. An.ought to furnish formal and universal principles of deduction? And why did Aristotle define the principle of universal attribution without distinguishing its application according to each of the three modal premises? Returning at the end of his career to a literal exegesis of Aristotle's propositions and without harkening back to the earlier solutions, he proposes a theory of making the terms modal (fourth solution) in order to save Aristotle's declarations with respect to the principle of universal attribution and the mood of the conclusion of mixed syllogisms (Pr. An.I. 9.30al5–20). Though formally inadequate, this solution, which had a continued history, proposes a new way of looking at the classification of modal propositions.

Are "Gap-Fillers" Missing Premisses?

Identifying the missing or unstated premisses of arguments is important, because their logical quality depends on them. Textbook authors regard enthymematic syllogisms (e.g., "Elvis is a man, so Elvis is mortal") as having an unstated premiss - the major premiss (e.g., "All men are mortal"). They are said to be such because these syllogisms become formally valid when the major premiss is added (i.e., it is a gap-filler). I argue that unstated major premises are not gap-fillers: they support a part of the argument that is already given implicitly - the inference claim ("If the premisses are true then the conclusion is true"). As such, their logical status is the same as that of an unstated proposition that supports the minor premiss, which is not part of the argument. Therefore, the so-called "major premiss" is not an unstated premiss of the enthymeme.

Validation of causal bridging inferences in discourse understanding

We proposed that the causal bridging inference that links the sentences of Mary poured the water on the bonfire. The fire went out, must be validated against general knowledge. The two sentences were hypothesized to respectively serve as the minor premise and conclusion in a mental structure analogous to a syllogism. We posited that the missing premise, “Water extinguishes fire,” is computed, and validated against world knowledge. Subjects answered questions such as Does water extinguish fire? after reading either causal sequences; or control temporal sequences, such as Mary placed the water by the bonfire. The fire went out. Answer time was faster in the causal than the temporal condition for sentence pairs and for brief passages; and when causal analysis was complicated by greater inferential distance, and by the surface reversal of cause and effect. These findings clarify bridging inference processes, and provide an instance of readers' comprehension monitoring.

Theory Corroboration and Football: Measuring Progress

How a theory is assessed depends partly on the objective of the appraisal and partly on how the evidence is collected. P1 is a good prescription for using nonexperimental data to appraise whether or not an empirical statistic is as expected on the basis of a theory in an ex post facto fashion. The Popperian falsification prescription is still required to choose between incompatible theories. P4 is used as the major premise of the syllogistic argument form implicated when a theory is being tested experimentally. A significance test is used to make a statistical decision regarding which minor premise to use in the syllogistic argument. The conclusion drawn evaluates the tenability of a theory vis-a-vis a set of experimental data. A theory's verisimilitude depends on a series of experimental converging operations.

Significance tests and the duplicity of binary decisions.

Robert FolgerA. B. Freeman School of Business, Tulane UniversityPresents a justification for following statements and discusses their implications: It isduplicitous (misleading) to use significance tests for making binary (either/or) decisions regardingthe validity of a theory; binary choice between calling results significant or not significant shouldnot govern confidence placed i n a theory, because such confidence cannot be gained in either/or fashion characterizing deductive certainty. The implications include grounds for describing waysthat effect size estimates become useful in makingjudgments about value of theories.Charles Sanders Peirce, who some say was America's greatestphilosopher of science, wrote that science can only rest on ex-perience; he then added that experience can never result inabsolute certainty, exactitude, or universality (Buchler, 1955,p. 47). Hypothesis-testing procedures make explicit science'slack of certainty. In particular, inferential statistics provide esti-mates of whether a finding reflects merely random variation, anoutcome owing to chance rather than to causal mechanismshypothesized by theories. I contend that such procedures canbe used in a manner that would deserve label of duplicity(i.e., an attempt to dupe unsuspecting) it were actuallyintentional. Inferential statistics can be especially misleadingwhen carelessly applied logic suggests an unwarranted degreeof deductive certainty.Chow's (1988, Tabl e 2) syllogistic description of hypothesistesting (see my Table 1) illustrates how unwarranted conclu-sions can be reached by seemingly steps. Syllogisms areeither valid or invalid, hence logical validity is an all-or-noneproperty of an (Chow, 1988, p. 109). Chow therebymirrors common practice by emphasizing binary choice be-tween rejecting or not rejecting a theory. Researchers followingcommon practice can dupe themselves and others, however, be-cause neither a theory's validity nor its invalidity is a matter ofdeductiv e certainty.Chow's (1988) idea that the role of a statistical analysis. . .is to supply investigator with minor premise for syl-logistic (p. 108) also raises issues about use ofeffect sizes:All that is required of a statistical analysis is a binary decision.. . .because validity of syllogistic argument requires only thatinformation. Even a quantitatively more informative index isavailable (e.g., effect size, amount of variance accounted for, orthe power of test), it will still be used in a binary manner.. . .Nothing is gained by using an effect-size estimate.. . .(p. 108)Chow claimed that significance tests are superior to effect sizesI thank Bill Dunlap and Irving LaValle for comments.Correspondence concerning this article should be addressed to Rob-ert Folger, A. B. Freeman School of Business, Tulane University, NewOrleans, Louisiana 70118.on basis of logic of syllogistic argument. I interpret thesame syllogism differently, making role of effect sizes oncemore an open issue.No Proof of Validity: Problems inAffirming ConsequencesTh e heading of third colum n i Tabl 1 (Affirming conse-quent) is also e nam of a fallacy, which should imme-diately raise suspicions about imposing either/or (binary) deci-sions when judging theories. The fallacy of affirming conse-quent involves reasoning backward from validity ofconclusions to e presumed validity of their premises. Suppossomeone claims that if we follow principles of supply-sideeconomics, economy will prosper becaus th election ofa supply-side President caused economic prosperity. Amongother interpretive problems (e.g., what does it mean to imple-ment supply-side policies; what measure reveals degree towhich President had in fact done so; and how should eco-nomic prosperity b e measured?), ther is a clea r dange of spuri-ous correlation: How can one be sure that prosperity was notcaused by something else? It is also easy to see danger ofaffirmin g consequent from example s of fallaciou reasoninsuch a s following: If Hitler i still alive, sun hot.The sun is hot. Therefore Hitler is still alive.Chow argued for all-or-nothing, dichototnous choices, evenwhil e using wor d probably twic i n thir colum f Ta-ble 1, yet reference to probability rather than to certaintyis demanded by fallacious nature of consequence-affirmingarguments: Because it is logically false to conclude with deduc-tive certainty that true premises are entailed by true conse-quences, then at best any evidence for consequences' valid-ity provides only arguments consistent with validity of thepremises. It is more accurate to say that experimental resultsare consistent with a hypothesis than to say that they con-firm it.

Significance test or effect size?

I describe and question the argument that in psychological research, the significance test should be replaced (or, at least, supplemented) by a more informative index (viz., effect size or statistical power) in the case of theory-corroboration experimentation because it has been made on the basis of some debatable assumptions about the rationale of scientific investigation. The rationale of theory-corroboration experimentation requires nothing more than a binary decision about the relation between two variables. This binary decision supplies the minor premise for the syllogism implicated when a theory is being tested. Some metatheoretical considerations reveal that the magnitude of the effect-size estimate is not a satisfactory alternative to the significance test.