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.     

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.     

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.     

Genetic and adoptive motherhood: Stress,marital relationship,and child care support

In this paper we characterize adoptive and genetic motherhood with or without stress indicators. Participants were 86 mothers (36 adoptive, 50 genetic) with children from 0 to 12 years old. They answered questions about focal child and mother profile, marital relationship, child care support and the Lipp's Stress Symptoms Inventory for Adults. Results showed that mothers in both groups reported child care support, but there was more participation of nonrelatives in the care of adoptive children and relatives in the care of genetic children. There was greater marital stability and less conflict with the arrival of the child in the adoptive families and predominance of stress indicators in genetic mothers. We concluded that, although there are differences between adoptive and genetic motherhood, these do not imply advantages for one versus the other. Moreover, marital stability related to the adoption process and sociodemographic characteristics of adoptive mothers may have contributed to lower prevalence of stress.     

LESSONS ON SENTENTIAL MEANING FROM MEDIAEVAL SOLUTIONS TO THE LIAR PARADOX

Fourteenth-century treatises on paradoxes of the liar family, especially Bradwardine's and Buridan's, raise issues concerning the meaning of sentences, in particular about closure of sentential meaning under implication, semantic pluralism and the ontological status of 'meanings', which are still topical for current theories of meaning. I outline ways in which they tend to be overlooked, raising issues that must be addressed by any respectable theory of meaning as well as pointing in the direction of possible answers. I analyse a Bradwardinian theory of sentential meaning as it emerges from his treatment of liar sentences, exploring where it requires more thorough elaboration if it is to be a fully developed theory of sentential meaning.     

Buridan's Consequentia: Consequence and Inference Within a Token-Based Semantics

I examine the theory of consequentia of the medieval logician, John Buridan. Buridan advocates a strict commitment to what we now call proposition-tokens as the bearers of truth-value. The analysis of Buridan's theory shows that, within a token-based semantics, amendments to the usual notions of inference and consequence are made necessary, since pragmatic elements disrupt the semantic behaviour of propositions. In my reconstruction of Buridan's theory, I use some of the apparatus of modern two-dimensional semantics, such as two-dimensional matrices and the distinction between the context of formation and the context of evaluation of utterances.