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.     

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.     

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.     

Task-related versus stimulus-specific practice

When people repeatedly practice the same cognitive task, their response times (RT) invariably decrease. Dutilh, Vandekerckhove, Tuerlinckx, and Wagenmakers (2009) argued that the traditional focus on how mean RT decreases with practice offers limited insight; their diffusion model analysis showed that the effect of practice is multifaceted, involving an increase in rate of information processing, a decrease in response caution, adjusted response bias, and, unexpectedly, a strong decrease in nondecision time. In this study, we aim to further disentangle these effects into stimulus-specific and task-related components. The data of a transfer experiment, in which repeatedly presented sets and new sets of stimuli were alternated, show that the practice effects on both speed of information processing and time needed for peripheral processing are partly task-related and partly stimulus-specific. The effects on response caution and response bias appear to be task-related. This diffusion model decomposition provides a perspective on practice that is more detailed and more informative than the traditional analysis of mean RT.     

Reductio ad absurdum from a dialogical perspective

It is well known that reductio ad absurdum arguments raise a number of interesting philosophical questions. What does it mean to assert something with the precise goal of then showing it to be false, i.e. because it leads to absurd conclusions? What kind of absurdity do we obtain? Moreover, in the mathematics education literature number of studies have shown that students find it difficult to truly comprehend the idea of reductio proofs, which indicates the cognitive complexity of these constructions. In this paper, I start by discussing four philosophical issues pertaining to reductio arguments. I then briefly present a dialogical conceptualization of deductive arguments, according to which such arguments (especially mathematical proofs) are best understood as a dialogue between two (fictitious) participants—Prover and Skeptic. Finally, I argue that many of the philosophical and cognitive difficulties surrounding reductio arguments are dispelled or at least further clarified once one adopts a dialogical perspective.     

Comparing perceptual and preferential decision making

Perceptual and preferential decision making have been studied largely in isolation. Perceptual decisions are considered to be at a non–deliberative cognitive level and have an outside criterion that defines the quality of decisions. Preferential decisions are considered to be at a higher cognitive level and the quality of decisions depend on the decision maker’s subjective goals. Besides these crucial differences, both types of decisions also have in common that uncertain information about the choice situation has to be processed before a decision can be made. The present work aims to acknowledge the commonalities of both types of decision making to lay bare the crucial differences. For this aim we examine perceptual and preferential decisions with a novel choice paradigm that uses the identical stimulus material for both types of decisions. This paradigm allows us to model the decisions and response times of both types of decisions with the same sequential sampling model, the drift diffusion model. The results illustrate that the different incentive structure in both types of tasks changes people’s behavior so that they process information more efficiently and respond more cautiously in the perceptual as compared to the preferential task. These findings set out a perspective for further integration of perceptual and preferential decision making in a single ramework.     

Chronic stress, but not hypercaloric diet, impairs vascular function in rats

The aim of this study was to evaluate vascular and metabolic effects of chronic mild unpredictable stress (CMS) and hypercaloric diet (HD) without carbohydrate supplementation in rats. Male Sprague-Dawley rats were randomly assigned to four groups: Control, HD, CMS, and HD plus CMS. CMS consisted of the application of different stressors for 3 weeks. The rats were killed 15 days after CMS exposure. The HD group presented higher plasma lipid concentrations, without changes in fasting glucose concentration, glucose tolerance test, and vascular function and morphology, in comparison with the control group. Stressed rats presented higher fasting blood concentration of insulin, higher homeostasis model assessment index values and area under the curve in an oral glucose tolerance test, in comparison with non-stressed rats. CMS increased the plasma concentrations of corticosterone and lipids, and the atherogenic index values, without change in high-density lipoprotein level. CMS increased intima-media thickness and induced endothelium-dependent supersensitivity to phenylephrine, and lowered the relaxation response to acetylcholine in the thoracic aorta isolated from rats fed with control or HD, in comparison with non-stressed groups. CMS effects were independent of diet. In non-stressed rats, the HD induced dyslipidemia, but did not change glucose metabolism, vascular function, or morphology. The data from this study indicate that CMS promotes a set of events which together can contribute to impair function of the thoracic aorta.