Search Results (11)

With his research on Aristotle’s syllogistic, Jan Łukasiewicz initiates the branch of logic known as the calculus of names. This field deals with axiomatic systems that analyse various fragments of the logic of names, i.e., that branch of logic that studies various forms of names and functors acting on them, as well as logical relationships between sentences in which these names and functors occur. In this work, we want not only to present the genesis of the calculus of names and its first system created by Łukasiewicz, but we also want to deliver systems that extend the first. In this work, we will also show that, from the point of view of modern logic, Łukasiewicz’s approach to the syllogistic is not the only possible one. However, this does not diminish Łukasiewicz’s role in the study of syllogism. We believe that the calculus of names is undoubtedly the legacy of Łukasiewicz. Full article

The Exact Exposition of the Orthodox Faith is perhaps the most logically structured and inspired work not only in the oeuvre of the seventh-to-eighth-century theologian John Damascene, but most likely throughout the entire Greek Patristic literature. As such, the Exact Exposition definitely presents some quite intriguing features, such as the prolific use of logical distinctions, syllogisms, or full-fledged arguments, to name a few. Regarding the latter, John Damascene’s use of certain arguments in order to prove the existence of God not only hold a unique place in Byzantine theology but have also exercised a tremendous influence on Eastern Orthodox apologetics. However, what I would call his rationalization agenda comes not only with merits but with faults as well. It is to both these that the present study draws attention by evaluating them logico-philosophically and interpreting them religio-hermeneutically. What is of special interest is the fact that John Damascene’s logical faults are the most interesting parts of his theologizing. Full article

How do individuals find assurance of their personal standing before God? This article discusses the way different traditions of the Christian faith tried to answer the question—some leaving room for doubt in the process and others demanding absolute certainty from the believer. All fellowships experienced some problems with the issue due to the very nature of the question. Assurance required a reflexive act that turned the eyes of the believer away from the good things of God and the promises of the gospel toward an inspection of one’s inner man and motives that were difficult to discern. Those fellowships that emphasized a human condition in the process of salvation or assurance often struggled with their depravity before God and unworthiness to claim the promises of divine grace. This paper particularly focuses upon the struggles of the so-called Calvinists, who were more enamored with the question than the other fellowships and had difficulty developing a coherent or definitive answer, caught as they were between tensions in their theology, between the Christocentric vision of John Calvin that led toward assurance and the synergistic tendences of Theodore Beza and Heinrich Bullinger that led toward doubt. The paper provides some criticism of their theology but sympathizes with their struggle and finds faith and doubt inevitable parts of the Christian life here on earth. Full article

Anorexia nervosa is associated with impaired cognitive flexibility and central coherence, i.e., the ability to provide an overview of complex information. Therefore, the aim of the present study was to evaluate EEG features elicited from patients with anorexia nervosa and healthy controls during mental tasks (valid and invalid Aristotelian syllogisms and paradoxes). Particularly, we examined the combination of the most significant syllogisms with selected features (relative power of the time–frequency domain and wavelet-estimated EEG-specific waves, Higuchi fractal dimension (HFD), and information-oriented approximate entropy (AppEn)). We found that alpha, beta, gamma, theta waves, and AppEn are the most suitable measures, which, when combined with specific syllogisms, form a powerful tool for efficiently classifying healthy subjects and patients with AN. We assessed the performance of triadic combinations of “feature–classifier–syllogism” via machine learning techniques in correctly classifying new subjects in these two groups. The following triads attain the best classifications: (a) “AppEn-invalid-ensemble BT classifier” (accuracy 83.3%), (b) “Higuchi FD-valid-linear discriminant” (accuracy 75%), (c) “alpha amplitude-valid-SVM” (accuracy 83.3%), (d) “alpha RP-paradox-ensemble BT” (accuracy 85%), (e) “beta RP-valid-ensemble” (accuracy 85%), (f) “gamma RP-valid-SVM” (accuracy 85%), and (g) “theta RP-valid-KNN” (accuracy 80%). Our findings suggest that anorexia nervosa has a specific information-processing style across reasoning tasks in the brain as measured via EEG activity. Our findings also contribute to further supporting the view that entropy-oriented, i.e., information-based features (the AppEn measure used in this study) are promising diagnostic tools (biomarkers) in clinical applications related to medical classification problems. Furthermore, the main EEG-specific frequency waves are extremely enhanced and become powerful classification tools when combined with Aristotle’s syllogisms. Full article

While in his Science of Logic, Hegel employed neither diagrams nor formulae, his reinterpretation of Aristotle’s syllogistic logic in the “Subjective Logic” of Book III strongly suggests a diagrammatic dimension. Significantly, an early diagram depicting a “triangle of triangles” found among his papers after his death captures the organization of categories to be found in The Science of Logic. Features of this diagram help us understand Hegel’s logical project as an attempt to retrieve features of Plato’s thinking that are implicit within Aristotle’s syllogistic logic. It is argued that parallels between Hegel’s modification of Aristotle’s syllogistic figures and Peirce’s functional alignment of those syllogistic figures with his three inference forms—deduction, induction, and abduction—suggest modifications of the traditional “square of opposition” into a logical hexagon as found in recent discussions. However, Hegel had conceived of Aristotle’s syllogism as a distorted version of the “syllogism” thought by Plato to bind the parts of the cosmos into a unity as described in the dialogue Timaeus. In accord with this, it is argued that seen in the light of Hegel’s platonistic reconstruction of Aristotle’s logic, such logical hexagons should be understood as two-dimensional projections of a logical polyhedron. Full article

This publication builds on previous publications in which we constructed syntactic proofs of fuzzy Peterson’s syllogisms related to the graded square of opposition. The aim of the publication is to be formally able to find syntactic proofs of fuzzy Peterson’s logical syllogisms with forms of fuzzy intermediate quantifiers that design the graded Peterson’s cube of opposition. Full article

We aim to investigate whether EEG dynamics differ in adults with ASD (Autism Spectrum Disorders) and ADHD (attention-deficit/hyperactivity disorder) compared with healthy subjects during the performance of an innovative cognitive task, Aristotle’s valid and invalid syllogisms, and how these differences correlate with brain regions and behavioral data for each subject. We recorded EEGs from 14 scalp electrodes (channels) in 21 adults with ADHD, 21 with ASD, and 21 healthy, normal subjects. The subjects were exposed in a set of innovative cognitive tasks (inducing varying cognitive loads), Aristotle’s two types of syllogism mentioned above. A set of 39 questions were given to participants related to valid–invalid syllogisms as well as a separate set of questionnaires, in order to collect a number of demographic and behavioral data, with the aim of detecting shared information with values of a feature extracted from EEG, the multiscale entropy (MSE), in the 14 channels (‘brain regions’). MSE, a nonlinear information-theoretic measure of complexity, was computed to extract a feature that quantifies the complexity of the EEG. Behavior-Partial Least Squares Correlation, PLSC, is the method to detect the correlation between two sets of data, brain, and behavioral measures. -PLSC, a variant of PLSC, was applied to build a functional connectivity of the brain regions involved in the reasoning tasks. Graph-theoretic measures were used to quantify the complexity of the functional networks. Based on the results of the analysis described in this work, a mixed 14 × 2 × 3 ANOVA showed significant main effects of group factor and brain region* syllogism factor, as well as a significant brain region* group interaction. There are significant differences between the means of MSE (complexity) values at the 14 channels of the members of the ‘pathological’ groups of participants, i.e., between ASD and ADHD, while the difference in means of MSE between both ASD and ADHD and that of the control group is not significant. In conclusion, the valid–invalid type of syllogism generates significantly different complexity values, MSE, between ASD and ADHD. The complexity of activated brain regions of ASD participants increased significantly when switching from a valid to an invalid syllogism, indicating the need for more resources to ‘face’ the task escalating difficulty in ASD subjects. This increase is not so evident in both ADHD and control. Statistically significant differences were found also in the behavioral response of ASD and ADHD, compared with those of control subjects, based on the principal brain and behavior saliences extracted by PLSC. Specifically, two behavioral measures, the emotional state and the degree of confidence of participants in answering questions in Aristotle’s valid–invalid syllogisms, and one demographic variable, age, statistically and significantly discriminate the three groups’ ASD. The seed-PLC generated functional connectivity networks for ASD, ADHD, and control, were ‘projected’ on the regions of the Default Mode Network (DMN), the ‘reference’ connectivity, of which the structural changes were found significant in distinguishing the three groups. The contribution of this work lies in the examination of the relationship between brain activity and behavioral responses of healthy and ‘pathological’ participants in the case of cognitive reasoning of the type of Aristotle’s valid and invalid syllogisms, using PLSC, a machine learning approach combined with MSE, a nonlinear method of extracting a feature based on EEGs that captures a broad spectrum of EEGs linear and nonlinear characteristics. The results seem promising in adopting this type of reasoning, in the future, after further enhancements and experimental tests, as a supplementary instrument towards examining the differences in brain activity and behavioral responses of ASD and ADHD patients. The application of the combination of these two methods, after further elaboration and testing as new and complementary to the existing ones, may be considered as a tool of analysis in helping detecting more effectively such types of disorders. Full article

The article advocates a new approach to the Qur’an: To look at the text as a transcript of the earliest community’s intervention into major debates of its time. Rather than earlier textual traditions (“reception history”), particular burning theological questions that were en vogue in the epistemic space of Late Antiquity are identified as the essential trigger of particular Qur’anic proclamations. Thus, the new—Late Antique—perception of evil (epistemic troubles experienced in the innermost selves of individuals—which cropped up during the sectarian strife in Middle Mecca) is etiologically explained through the primordial rebellion of Diabolos/Iblīs. This figure is portrayed in the Qur’an as a daring “dissenter in heaven”—a dignity that he had proven in various Biblical contexts (Book of Job, Gospels, etc.) before. His main characteristic is his eloquence and logical reasoning, which has earned him the epithet of the “inventor of qiyās/syllogism” in later Islamic tradition. His Qur’anic development is projected against the backdrop of rabbinic, patristic, and poetic exegeses, which together attest the vitality of a most diversified “epistemic space of Late Antiquity”. Full article

We give some simple examples of applying some of the well-known elementary probability theory inequalities and properties in the field of logical argumentation. A probabilistic version of the hypothetical syllogism inference rule is as follows: if propositions A, B, C, $A\to B$, and $B\to C$ have probabilities a, b, c, r, and s, respectively, then for probability p of $A\to C$, we have $f(a,b,c,r,s)\le p\le g(a,b,c,r,s)$, for some functions f and g of given parameters. In this paper, after a short overview of known rules related to conjunction and disjunction, we proposed some probabilized forms of the hypothetical syllogism inference rule, with the best possible bounds for the probability of conclusion, covering simultaneously the probabilistic versions of both modus ponens and modus tollens rules, as already considered by Suppes, Hailperin, and Wagner. Full article

In Chan/Seon/Zen (禪, hereafter referred to as Chan) Buddhism, the gongan (公案), a word that can be literally translated as “public case”, is conceived as both the tool by which enlightenment is brought about and an expression of the enlightened mind itself. Among the diverse styles of gongan, perhaps the most puzzling is a form of its key phrase, huatou (話頭), that utilizes specific things in the world. These things are either real and empirically observable, or conversely, unreal and merely hypothetical. A typical example is the figure of the “cypress tree in the front yard”. This paper tries to demonstrate that such a huatou has a structural similarity to the dṛṣṭānta (喩), an element within the three-part syllogism of Buddhist logic, insomuch as it functions as an epistemic instrument for the disclosing of a truth. Full article

First introduced during the late 1800s, radiation therapy is fundamental to the treatment of cancer. In developed countries, approximately 60% of all patients receive radiation therapy (also known as the sixty percenters), which makes radioresistance in cancer an important and, to date, unsolved, clinical problem. Unfortunately, the therapeutic refractoriness of solid tumors is the rule not the exception, and the ubiquity of resistance also extends to standard chemotherapy, molecularly targeted therapy and immunotherapy. Based on extrapolation from recent clinical inroads with epigenetic agents to prime refractory tumors for maximum sensitivity to concurrent or subsequent therapies, the radioresistant phenotype is potentially reversible, since aberrant epigenetic mechanisms are critical contributors to the evolution of resistant subpopulations of malignant cells. Within the framework of a syllogism, this review explores the emerging link between epigenetics and the development of radioresistance and makes the case that a strategy of pre- or co-treatment with epigenetic agents has the potential to, not only derepress inappropriately silenced genes, but also increase reactive oxygen species production, resulting in the restoration of radiosensitivity. Full article