scholarly journals A cylindrical Venn diagram model for categorical syllogisms

2018 ◽  
Author(s):  
Dan Constantin Radulescu

One denotes A(M,*) by A1 and A(*,M) by A2, where * stands for either S or P, and the same for the O categorical operator. This allows to dispense with the four syllogistic figures and reduces the number of the 24 classically valid syllogisms (CVS) to only 8 (not 15) distinct CVS plus 6 (not 9) distinct existential import (ei) CVS. Out of the 36 (not 64!) distinct pairs of categorical premises (PCP or just pairs), 19 pairs entail at least one logical conclusion and thus generate valid syllogistic arguments (in short, valid syllogisms or VS) split into two subsets: the CVS and the VS\CVS. The latter ones have A(P,S), O(P,S) and I(S',P') as conclusions, not the “(S,P)-type” conclusions required of the CVS. (S',P',M' are the complementary sets of S,P,M in a universal set U.) The other results are: (i) one can also dispense with most of the rules of valid syllogisms (such as “the middle term has to be distributed in at least one premise” and “two negative premises are not allowed”), (ii) any pair of categorical premises generates at least one VS unless 1. both premises are particular, or, 2. one premise is universal and one particular and they act one on M, the middle term, and the other premise acts on M' – its complement in U, (iii) the VS set is the (disjoint) union of three equivalence classes generated respectively by (a) two universal premises acting on both M and M' , (b) two universal premises both acting on either M or M', (c) one universal premise and one particular premise both acting on either M or M', (iv) inside each equivalence class, via a relabeling transformation of the sets S,P,M, S',P',M', any of the VS can be recast (or reformulated) as any other VS from the same class. This “naming invariance” suggests that, from a set theoretical point of view, the (S,P) conclusion restriction is not meaningful. The VS\CVS subset contains 6 VS and 7 ei VS.

2018 ◽  
Author(s):  
Dan Constantin Radulescu

One denotes A(M,*) by A1 and A(*,M) by A2, where * stands for either S or P, and the same for the O categorical operator. This allows to dispense with the four syllogistic figures and reduces the number of the 24 classically valid syllogisms (CVS) to only 8 (not 15) distinct CVS plus 6 (not 9) distinct existential import (ei) CVS. Out of the 36 (not 64!) distinct pairs of categorical premises (PCP or just pairs), 19 pairs entail at least one logical conclusion and thus generate valid syllogistic arguments (in short, valid syllogisms or VS) split into two subsets: the CVS and the VS\CVS. The latter ones have A(P,S), O(P,S) and I(S',P') as conclusions, not the “(S,P)-type” conclusions required of the CVS. (S',P',M' are the complementary sets of S,P,M in a universal set U.) The other results are: (i) one can also dispense with most of the rules of valid syllogisms (such as “the middle term has to be distributed in at least one premise” and “two negative premises are not allowed”), (ii) any pair of categorical premises generates at least one VS unless 1. both premises are particular, or, 2. one premise is universal and one particular and they act one on M, the middle term, and the other premise acts on M' – its complement in U, (iii) the VS set is the (disjoint) union of three equivalence classes generated respectively by (a) two universal premises acting on both M and M' , (b) two universal premises both acting on either M or M', (c) one universal premise and one particular premise both acting on either M or M', (iv) inside each equivalence class, via a relabeling transformation of the sets S,P,M, S',P',M', any of the VS can be recast (or reformulated) as any other VS from the same class. This “naming invariance” suggests that, from a set theoretical point of view, the (S,P) conclusion restriction is not meaningful. The VS\CVS subset contains 6 VS and 7 ei VS.


2018 ◽  
Author(s):  
Dan Constantin Radulescu

One shows that a set theoretical approach to categorical syllogisms is much more natural than the“figures, moods and rules of the syllogism approach”. (The latter satisfies “Aristotle's requirementthat the middle term M should not appear in the conclusion. Striker, 2009. ) In the “set approach”one deals with the eight 3-set intersections that span a universal set U: U=MSP+MS'P+MSP'+MS'P'+M'SP+M'S'P+M'SP'+M'S'P', where S,P,M are the usual categorical terms (interpreted nowas sets) appearing in the wording of the pairs of categorical premises (PCPs) and of the logicalconclusions (LCs) which the PCPs might entail; the union of disjoints sets is denoted by a + sign;MSP:= M∩S∩P, etc.; S',P',M' are the categorical terms non-S, non-P, non-M,, now interpreted asthe complementary sets in U of the S,P,M, respectively. In this model of categorical syllogisms,when using a cylindrical Venn diagram, (Marquand 1881), (Veitch 1952), (Karnaugh 1953), it isself-evident that if a PCP entails an LC at all, (and thus generates a valid categorical argument(VCA), then the LC singles out one and only one of the 8 subsets of U, and affirms about it eitherthat it is non-empty, or, that one of the sets S,P,M,S',P',M' is empty except, possibly, the subset whichthe LC singled out. Thus the middle term M, or its complementary M', are very much part of theLC. (Of course, to satisfy Aristotle's requirement that M should not appear in the LC, an LC of thefirst type, e.g., SPM≠Ø, may be re-written, with some loss of “intuitive information”, as I(S,P), andan LC of the second type, e.g., S=SPM, may be re-written as A(S,P).) The valid syllogisms (VSs) arethose VCAs whose LCs can be re-written in the “(S,P)-format”, i.e., one of the categoricaloperators A,O,E,I is applied to the ordered pair (S,P). After the “middle term elimination”, the LCsof the VCA\VS set are of the I(S',P'), A(P,S), or O(P,S) type. It is easy to see that there are fiveclasses of PCPs – two do not entail LCs, and three do, thus generating three distinct VCA classes.Inside each VCA class, via a relabeling transformation of the sets S,P,M, S',P',M', any of the VCA(or VS) can be recast (or reformulated) as any other VCA from the same class. This “namingcovariance” suggests that, at least from a set theoretical point of view, (i) the (S,P)-format LCrestriction is not meaningful, and (ii) one may consider that there are only three distinct VCAs (andVSs), chosen as any one representative per VCA class; for example, one may choose asrepresentatives Darapti, Darii and Barbara – all the other VCAs (not only VSs) maybe written,using appropriately chosen terms, as either a Darapti, Darii or Barbara VS. There are alwaysrelabelings transforming any VCA from the VCA\VS set into a VS. The role of VCA relabelings issimilar to the role of “reduction of syllogisms” (the latter was applied only to the VSs).


Author(s):  
Roberto Luquín Guerra

Apart from his political and educational work, and from his controversial autobiography, José Vasconcelos is known for his Ibero-Americanist thought. The Cosmic Race, Indology and Bolivarism and Monroeism gather all the ideas that are attributed to his theoretical point of view. His philosophy is what we know less of and what is most criticized. Nonetheless, is there a connection between his philosophical thought and his Ibero-Americanist ideas? Abelardo Villegas says that Vasconcelos’s philosophy is the product of a racial and cultural message. Therefore, according to Villegas, his philosophy is subordinated to his Ibero-Americanist ideas. Patrick Romanell, on the other hand, states that the Ibero-Americanist ideas make up the popular and illusory side and, hence, must be separated from the philosophical thought. The aim of this paper is to elucidate this problem. In order to clarify it, we will follow Villegas viewpoint to the bitter end. His reasoning invites us to look closely at the history of Ibero-American thought as well as at Vasconcelos’s first works. Precisely by analyzing these two aspects and the point where they meet, we might be able to find an answer.


2016 ◽  
Vol 38 (6) ◽  
pp. 590-597 ◽  
Author(s):  
Philip Furley ◽  
Geoffrey Schweizer

The goal of the present paper was to investigate whether soccer referees’ nonverbal behavior (NVB) differed based on the difficulty of their decisions and whether perceivers could detect these systematic variations. On the one hand, communicating confidence via NVB is emphasized in referee training. On the other hand, it seems feasible from a theoretical point of view that particularly following relatively difficult decisions referees have problems controlling their NVB. We conducted three experiments to investigate this question. Experiment 1 (N = 40) and Experiment 2 (N = 60) provided evidence that perceivers regard referees’ NVB as less confident following ambiguous decisions as compared with following unambiguous decisions. Experiment 3 (N = 58) suggested that perceivers were more likely to debate with the referee when referees nonverbally communicated less confidence. We discuss consequences for referee training.


2016 ◽  
Vol 10 (1) ◽  
pp. 145-157
Author(s):  
KOSTA DOŠEN ◽  
ZORAN PETRIĆ

AbstractA skeleton of the category with finite coproducts${\cal D}$ freely generated by a single object has a subcategory isomorphic to a skeleton of the category with finite products ${\cal C}$ freely generated by a countable set of objects. As a consequence, we obtain that ${\cal D}$ has a subcategory equivalent with ${\cal C}$. From a proof-theoretical point of view, this means that up to some identifications of formulae the deductions of pure conjunctive logic with a countable set of propositional letters can be represented by deductions in pure disjunctive logic with just one propositional letter. By taking opposite categories, one can replace coproduct by product, i.e., disjunction by conjunction, and the other way round, to obtain the dual results.


2020 ◽  
Vol 122 (5) ◽  
pp. 1647-1669 ◽  
Author(s):  
Massimo Cane ◽  
Carmen Parra

PurposeThe reduction of food waste is still a pending issue that governments have still not resolved. In response to this problem mobile platforms are emerging that follow food ecology and the responsible consumption of food, and self-management of their access to allow the communication between people and their use of food. In this paper, the authors will analyze the main digital platforms that deal with solving this problem, especially those that fulfill a social commitment through the distribution and reduction of waste.Design/methodology/approachTo provide solutions, the authors will address the importance of new technologies in the fight against waste, using digital platforms to manage food and to eliminate the loss in surplus products. To do this, the authors will first analyze from a theoretical point of view the concepts of “loss”, “waste” and “surplus product”, incorporating data of their impact between Spain and Italy. Next, the authors will analyze the influence of new technologies in the detection and distribution of products destined to become food waste. To carry out this qualitative research, the authors will apply the research strategy of theory building from multiple case studies (particularly 16 different digital platforms against food waste were analyzed), which is a methodological approach that uses cases as the basis to develop theory inductively.FindingsThe authors must make the public aware of the importance of being responsible consumers. To this end, the authors must disclose the problems associated with food waste and surplus product, presenting alternatives and new consumption habits. For this, it is necessary to collaborate and build synergies with organizations of different origins (consumers, producers and activists) involved in sustainable agrifood models. In this sense, digital platforms are essential tools to fight against food waste, preventing certain products from being considered unfit for human consumption. In this study, the authors suggest that, based on the review of the literature and the analysis of apps and blogs, the authors look for solutions to surplus and food waste both from the environment of the entrepreneur and the consumer and all using the new technologies.Research limitations/implicationsThe research has raised different limitations. On the one hand, it is a subject that has not been analyzed from a doctrinal point of view, so it is not easy to find bibliographic references. On the other hand, digital platforms that act on food waste are not cataloged. This has made it difficult to search for elements of analysis to obtain results in the work. Finally, the sample can vary in a short period of time since the digital platforms are in a boom, which means that they constantly change.Practical implicationsThis work allows a theoretical approach to the concepts of “loss”, “wastage” and “surplus product”, incorporating data on its impact in Spain and Italy, comparing it with the rest of Europe while providing figures and data on their impact. On the other hand, it allows us to know how new technologies can help the detection and distribution of products destined to become food waste. Finally, there are examples of platforms that are offering service in different areas, incorporating a novel classification that allows us to know the differences depending on their origin and destination.Originality/valueThe originality of the work can be summarized in the following points: There are no doctrinal works that analyze in a combined way the food waste with the new technologies; The relationship with the 2030 Agenda in which responsible consumption is one of the achievements pursued by the United Nations, and the authors position the study’s research as an evidence of platforms that are currently working in the interest of reducing food waste. Furthermore, the authors provide an early classification of platforms based on their usability and objectives of reducing, reusing and recycling food.


2014 ◽  
Vol 27 (2) ◽  
pp. 93-114 ◽  
Author(s):  
Antti Silvast ◽  
Mikko J Virtanen

This article discusses the reliability of electricity supply and the management of its uncertainties from a systems theoretical point of view. We begin by outlining recent Science and Technology Studies (STS) literature about energy systems, infrastructures and practices concerning their use and argue that many current discussions hold promise in two directions: one concerns the brittleness and uncertainty of the electricity system that is seen as an ongoing achievement, the other is about broader structuring factors and contexts that should also be acknowledged when researching such systems. With an aim of developing this two-part focus, the paper advances systems theoretical considerations about the electricity infrastructure and proposes an analysis tool to study the necessary reductions of complexity of the infrastructure in two emblematic settings. The sites are infrastructure control rooms on the one hand and households on the other hand. The article concludes by discussing the different reductions of complexity by electricity users and electricity experts through using the theoretical point of view presented in the article.


Author(s):  
Natri Sutanti

Congruence is a condition in therapeutic relationship that refers to accurate matching of a person’s experience with awareness. In person-centred counselling, counsellor’s congruence is believed as one of helpful and significant aspects that facilitates clients’ growth in counselling. However, this term is quite difficult to understand as a single condition as it interrelated to the other conditions such as empathy and unconditional positive regard. Understanding congruence theoretically and practically is intriguing as well as challenging especially for a trainee counsellor that is still learning to apply theory on practice. This paper aims to critically explore congruence from person-centred counselling theory and to demonstrate some evidences of the development of congruence in practice based on the author’s counselling practice as a trainee counsellor. There are three main discussions in this paper that is to explain congruence from the theoretical point of view, to understand the relation between congruence and acceptance and to explore congruence in person-centred practice. The exploration found that trainee counsellor’s cultural background including condition of worth and language barrier is one of challenges in experiencing congruence within person-centred counselling practice.Keywords: congruence, person-centred counselling, unconditional positive regard, ontological standpoint


2011 ◽  
pp. 109-119
Author(s):  
Rajna Dragicevic

This paper explores a theoretical point of view that the collocability is determined by the meaning of a lexeme and also represents its consequence. Our main goal is to show that these two factors may contribute with different intensity, and that context may have greater or lesser effect on the meaning of a lexeme. The analysis proves that the context has a lesser effect on more frequent lexemes and does not have a permanent effect on their meaning, but on the other hand, context has a greater effect on infrequent lexemes and has a greater effect on their semantic content. This even applies in a case of a lexeme used separately. Even analysis of two unrelated languages (Serbian and German) shows that the most frequent associations on infrequent adjectives are the nouns frequently used with them, which means that frequently used collocations produce an effect on them even out of context. Furthermore, there are examples in lexicography that infrequent adjectives are defined by collocations peculiar for infrequent lexemes. On the other hand, the most frequent verbal associations of Serbian and German respondents on very frequent adjectives are not the nouns usually found in their collocations, but their antonyms, thus it is possible to conclude that the context has no any effect. The conclusion is that collocability is determined by the meaning of a lexeme and it also represents its consequence, and at the same time the collocation effect on a lexeme is greater if the lexeme is less frequent.


2017 ◽  
Vol 5 (2) ◽  
pp. 56
Author(s):  
Celestin Messanga Obama

Promotion to high office in the Cameroonian administration, appear to be one of the main topic of political communication in Cameroun. The communitarian claims of appointment put both individuals and communities in competitive situations and are often the source of social conflicts. The problem is to understand the focus of political communication on appointment in the Administration in Cameroon and the possible link that it could have with conflictuality in the country. From a theoretical point of view, each act of appointment can be understood as a message from the President of the Republic whose power of appointment is unlimited. The president’s acts of appointment; on the one hand; and the demands from communities, on the other, appear to be a kind of communication. Data analysis will be guided by the theory of "the actor and the system". From a methodological point of view, we used documentary observation in the national and international press. We also had an in-depth interview with a former minister who, however, requested anonymity. Finally, our 26-year service as an employee gives us the advantage of experience gained through participatory observation. It appeared that appointment, through the numerous and consistent advantages that it confers on the promoted, thus appears to the citizens, as the main means of access to the fortune from which the covetousness of both the individuals and their communities of origin arises. Unfortunately, the state is unable to meet all expectations. However, individual, as well as community, strategies of access to appointments expose the nation to more division than cohesion.


Sign in / Sign up

Export Citation Format

Share Document