Validity, the Squeezing Argument and Alternative Semantic Systems: the Case of Aristotelian Syllogistic

We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran’s deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the goal is to offer a general discussion of the relations between informal notions—in this case, an informal notion of deductive validity—and logical apparatuses such as deductive systems and (model-theoretic or other) semantic systems that aim at offering technical, formal accounts of informal notions. Specifically, we will be interested in Kreisel’s famous ‘squeezing argument’; we shall ask ourselves what a plurality of semantic systems (understood as classes of mathematical structures) may entail for the cogency of specific applications of the squeezing argument. More generally, the analysis brings to the fore the need for criteria of adequacy for semantic systems based on mathematical structures. Without such criteria, the idea that the gap between informal and technical accounts of validity can be bridged is put under pressure.     

The interaction of temporal generalization gradients predicts the context effect

In a temporal double bisection task, animals learn two discriminations. In the presence of Red and Green keys, responses to Red are reinforced after 1-s samples and responses to Green are reinforced after 4-s samples; in the presence of Blue and Yellow keys, responses to Blue are reinforced after 4-s samples and responses to Yellow are reinforced after 16-s samples. Subsequently, given a choice between Green and Blue, the probability of choosing Green increases with the sample duration-the context effect. In the present study we asked whether this effect could be predicted from the stimulus generalization gradients induced by the two basic discriminations. Six pigeons learned to peck Green following 4-s samples (S(+)) but not following 1-s samples (S(-)) and to peck Red following 4-s samples (S(+)) but not following 16-s samples (S(-)). Temporal generalization gradients for Green and Red were then obtained. Finally, the pigeons were given a choice between Green and Red following sample durations ranging from 1 to 16 s. Results showed that a) the two generalization gradients had the minimum at the S(-) duration, an intermediate value between the S(-) and the S(+) durations, and the maximum at the S(+) as well as more extreme durations; b) on choice trials, preference for Green over Red increased with sample duration, the context effect; and c) the two generalization gradients predicted the average context effect well. The Learning-to-Time model accounts for the major trends in the data.     

Reassessing logical hylomorphism and the demarcation of logical constants

The paper investigates the propriety of applying the form versus matter distinction to arguments and to logic in general. Its main point is that many of the currently pervasive views on form and matter with respect to logic rest on several substantive and even contentious assumptions which are nevertheless uncritically accepted. Indeed, many of the issues raised by the application of this distinction to arguments seem to be related to a questionable combination of different presuppositions and expectations; this holds in particular of the vexed issue of demarcating the class of logical constants. I begin with a characterization of currently widespread views on form and matter in logic, which I refer to as ‘logical hylomorphism as we know it’—LHAWKI, for short—and argue that the hylomorphism underlying LHAWKI is mereological. Next, I sketch an overview of the historical developments leading from Aristotelian, non-mereological metaphysical hylomorphism to mereological logical hylomorphism (LHAWKI). I conclude with a reassessment of the prospects for the combination of hylomorphism and logic, arguing in particular that LHAWKI is not the only and certainly not the most suitable version of logical hylomorphism. In particular, this implies that the project of demarcating the class of logical constants as a means to define the scope and nature of logic rests on highly problematic assumptions.     

Cardiovascular reactivity in hypertensives: differential effect of expressing and inhibiting emotions during moments of interpersonal stress

This study investigated cardiovascular reactivity of hypertensive adults during periods of emotional stress. Two types of instructions were given at different moments, to the same subject, either to express or to suppress feelings during role-play. Expressing, but not inhibiting, emotions elicited significantly higher reactivity during responding to negative scenes, followed by responding during the positive interactions. Blood pressure increases in both expressing and inhibiting conditions, were also found during the instruction periods. Results indicated that socially demanding situations represent a stressor whose effects may vary depending on whether or not respondents regulate expression of emotions. It is suggested that the difficulty in expressing emotions found in some hypertensive individuals may have the function of controlling or reducing blood pressure reactivity.     

The Different Ways in which Logic is (said to be) Formal

I argue that, in the Prior Analytics, higher and above the well-known ‘reduction through impossibility’ of figures, Aristotle is resorting to a general procedure of demonstrating through impossibility in various contexts. This is shown from the analysis of the role of adunaton in conversions of premises and other demonstrations where modal or truth-value consistency is indirectly shown to be valid through impossibility. Following the meaning of impossible as ‘non-existent’, the system is also completed by rejecting any invalid combinations of terms in deductions or conversions. The notion of impossibility reaches the core of Aristotle's system in the Prior Analytics. On the one hand, the use of adunaton shows that he is following one of the two requisites for demonstrative science formulated in the Posterior Analytics, i.e. to demonstrate that it is impossible for things to be otherwise than stated. On the other hand, that demonstrations through impossibility are rooted in the notion of contradiction supports the claim that Aristotle might have been trained to use this specific procedure in the context of dialectical exercises in the academy. This need not rule out other influences on Aristotle's preferred procedures of proving or counter-proving, but it paves a way to a better understanding of Aristotle's logic under the light of Plato's dialectic.     

The Buridanian Account of Inferential Relations between Doubly Quantified Propositions: a Proof of Soundness

On the basis of passages from John Buridan's Summula Suppositionibus and Sophismata, E. Karger has reconstructed what could be called the ‘Buridanian theory of inferential relations between doubly quantified propositions’, presented in her 1993 article ‘A theory of immediate inference contained in Buridan's logic’. In the reconstruction, she focused on the syntactical elements of Buridan's theory of modes of personal supposition to extract patterns of formally valid inferences between members of a certain class of basic categorical propositions. The present study aims at offering semantic corroboration—a proof of soundness—to the inferential relations syntactically identified by E. Karger, by means of the analysis of Buridan's semantic definitions of the modes of personal supposition. The semantic analysis is done with the help of some modern logical concepts, in particular that of the model. In effect, the relations of inference syntactically established are shown to hold also from a semantic point of view, which means thus that this fragment of Buridan's logic can be said to be sound.     

Health‐adjusted neuropsychological test norms based on 463 older Swedish car drivers

There is a need for improved normative information in particular for older persons. The present study provides neuropsychological test norms on seven cognitive tests used in a sample representing the general older driving population, when uncontrolled and controlled for physical health. A group of 463 healthy Swedish car drivers, aged 65 to 84 years, participated in a medical and neuropsychological examination. The latter included tests of visual scanning, mental shifting, visual spatial function, memory, reaction time, selective attention, and simultaneous capacity. Hierarchical regression analyses demonstrated that, when uncontrolled for health, old age was associated with significant impairment on all seven tests. Education was associated with a significant advantage for all tests except most reaction time subtests. Women outperformed men on selective attention. Controlling for health did not consistently change the associations with education, but generally weakened those with age, indicating rises in normative scores of up to 0.36 SD (residual). In terms of variance explained, impaired health predicted on average 2.5%, age 2.9%, education 2.1% and gender 0.1%. It was concluded (1) that individual regression‐based predictions of expected values have the advantage of allowing control for the impact of health on normative scores in addition to the adjustment for various demographic and performance‐related variables and (2) that health‐adjusted norms have the potential to classify functional status more accurately, to the extent that these norms diverge from norms uncontrolled for physical health.     

Does Happiness Predict Medication Adherence among African Americans with Hypertension?

Poor medication adherence is a leading cause of excessive cardiovascular morbidity among African Americans. Many adherence-promoting interventions have addressed economic barriers, improved the patient-provider relationship, simplified regimens, and used reminder systems; however, the problem of low adherence remains intractable. Meanwhile, positive psychological attributes that might serve to promote medication adherence have not been fully explored. To address this gap, we examined the association between happiness and medication adherence among low-income African Americans with hypertension treated in a safety-net setting. Data were obtained from the Alabama Collaboration for Cardiovascular Equality, 2007?C2008. Happiness was measured using the 4-item scale of Lyubomirsky and Lepper; low, moderate, and high happiness were defined by tertiles because of the non-normal distribution. Medication adherence was assessed with the Morisky Medication Adherence Scale. Associations were quantified with ordinal logistic regression. Our sample of 573 African Americans was 71.6?% female and had an average age?±?SD of 53.6?±?9.7?years and a median happiness score of 5.2. Compared to participants with low happiness, the odds (OR; 95?% CI) of being in a better medication adherence category were greater for those with moderate (1.53; 1.02?C2.27) and high (2.26; 1.52-3.37) happiness, after adjusting for age, sex, income, education, and difficulty paying for medical care. Within this cohort of low-income African Americans with hypertension, participants with greater happiness exhibited better medication adherence. Although one interpretation of our study is that more adherent patients are naturally happier, our findings raise the possibility that adding happiness-boosting components may increase the effectiveness of more traditional adherence interventions.     

A phase transition model for the speed-accuracy trade-off in response time experiments

Most models of response time (RT) in elementary cognitive tasks implicitly assume that the speed-accuracy trade-off is continuous: When payoffs or instructions gradually increase the level of speed stress, people are assumed to gradually sacrifice response accuracy in exchange for gradual increases in response speed. This trade-off presumably operates over the entire range from accurate but slow responding to fast but chance-level responding (i.e., guessing). In this article, we challenge the assumption of continuity and propose a phase transition model for RTs and accuracy. Analogous to the fast guess model (Ollman, 1966), our model postulates two modes of processing: a guess mode and a stimulus-controlled mode. From catastrophe theory, we derive two important predictions that allow us to test our model against the fast guess model and against the popular class of sequential sampling models. The first prediction--hysteresis in the transitions between guessing and stimulus-controlled behavior--was confirmed in an experiment that gradually changed the reward for speed versus accuracy. The second prediction--bimodal RT distributions--was confirmed in an experiment that required participants to respond in a way that is intermediate between guessing and accurate responding.