This article is about Avicenna’s account of syllogisms comprising opposite premises. We examine the applications and the truth conditions of these syllogisms. Finally, we discuss the relation between these syllogisms and the principle of non-contradiction.

This article is about Avicenna’sAvicenna account of syllogismsSyllogism comprising opposite premises. We examine the applications and the truth conditions of these syllogismsSyllogism. Finally, we discuss the relation between these syllogismsSyllogism and the principle of non-contradiction.

We elaborate on the approach to syllogistic reasoning based on “case identification” (Stenning & Oberlander, 1995; Stenning & Yule, 1997). It is shown that this can be viewed as the formalisation of a method of proof that dates back to Aristotle, namely proof by exposition ( ecthesis ), and that there are traces of this method in the strategies described by a number of psychologists, from St rring (1908) to the present day. We hypothesised that by rendering individual cases (...) explicit in the premises, the chance that reasoners would engage in a proof by exposition would be enhanced, and thus performance improved. To do so, we used syllogisms with singular premises (e.g., this X is Y ). This resulted in a uniform increase in performance as compared to performance on the associated standard syllogisms. These results cannot be explained by the main theories of syllogistic reasoning in their current state. (shrink)

In the Organon Aristotle describes some deductive schemata in which inconsistencies do not entail the trivialization of the logical theory involved. This thesis is corroborated by three different theoretical topics by him discussed, which are presented in this paper. We analyse inference schema used by Aristotle in the Protrepticus and the method of indirect demonstration for categorical syllogisms. Both methods exemplify as Aristotle employs classical reductio ad absurdum strategies. Following, we discuss valid syllogisms from opposite premises (...) (contrary and contradictory) studied by the Stagerian in the Analytica Priora (B15). According to him, the following syllogisms are valid from opposite premises, in which small Latin letters stand for terms such as subject and predicate, and capital Latin letters stand for the categorical propositions such as in the traditional notation: (i) in the second figure, Eba,Aba ` Eaa (Cesare), Aba, Eba ` Eaa (Camestres), Eba, I ba ` Oaa (Festino), and Aba,Oba ` Oaa (Baroco); (ii) in the third one, Eab,Aab ` Oaa (Felapton), Oab,Aab ` Oaa (Bocardo) and Eab, Iab ` Oaa (Ferison). Finally, we discuss the passage from the Analytica Posteriora (A11) in which Aristotle states that the Principle of Non-Contradiction is not generally presupposed in all demonstrations (scientific syllogisms), but only in those in which the conclusion must be proved from the Principle; the Stagerian states that if a syllogism of the first figure has the major term consistent, the other terms of the demonstration can be each one separately inconsistent. These results allow us to propose an interpretation of his deductive theory as a broad sense paraconsistent theory. Firstly, we proceed to a hermeneutical analysis, evaluating its logical significance and the interplay of the results with some other points of Aristotle’s philosophy. Secondly, we point to a logical interpretation of the Aristotelian syllogisms from opposite premises in the antilogisms method proposed by Christine Ladd-Franklin in 1883, and we also present a logical treatment of the Aristotelian demonstration with inconsistent material in the paraconsistent logics Cn, 1 _ n _!, introduced by da Costa in 1963. These two issues seem having not yet been analysed in detail in the literature. (shrink)

No Órganon Aristóteles descreve alguns esquemas dedutivos nos quais a presença de inconsistências não acarreta a trivialização da teoria lógica envolvida. Esta tese é corroborada por três diferentes situações teóricas estudadas por ele, as quais são apresentadas neste trabalho. Analizamos o esquema de inferência utilizado por Aristóteles no Protrepticus e o método de demonstração indireta para os silogismos categóricos. Ambos os métodos exemplificam como Aristóteles emprega estratégias de redução ao absurdo logicamente clássicas. Na sequência, discutimos os silogismos válidos a partir (...) de premissas opostas (contrárias e contraditórias) estudadas pelo Estagirita no Analytica Priora (B15). De acordo com o autor, os seguintes silogismos são válidos a partir de premissas opostas, nos quais letras latinas minúsculas denotam termos como sujeito e predicado, enquanto que letras latinas maiúsculas denotam proposições categóricas tal como na notação tradicional: (i) na segunda figura, Eba,Aba ` Eaa (Cesare), Aba, Eba ` Eaa (Camestres), Eba, I ba ` Oaa (Festino), e Aba,Oba ` Oaa (Baroco); (ii) na terceira, Eab,Aab ` Oaa (Felapton), Oab,Aab ` Oaa (Bocardo) e Eab, Iab ` Oaa (Ferison). Por fim, discutimos a passagem do Analytica Posteriora (A11) no qual Aristóteles enuncia que o Princípio de Não-Contradição não é, em geral, pressuposto de toda demonstração (silogismo científico), mas apenas daquelas nas quais a conclusão deve ser provada a partir do Princípio; o Estagirita enuncia que se um silogismo da primeira figura tiver o termo maior consistente, os outros termos da demonstração podem ser separadamente inconsistentes. Estes resultados permitem-nos propor uma interpretação de sua teoria dedutiva como uma teoria paraconsistente lato sensu. Primeiramente, efetuamos uma análise hermenêutica, avaliando seu significado lógico e a correlação desses resultados com outros aspectos da filosofia de Aristóteles. Em segundo lugar, consignamos uma interpretação dos silogismos aristotélicos a partir de premissas opostas à luz dos antilogismos propostos por Christine Ladd-Franklin em 1883, e da demonstração aristotélica com termos inconsistentes nas lógicas paraconsistentes Cn, 1 n !, introduzidas por da Costa em 1963. Esses dois aspectos não parecem ter sido ainda detalhadamente analisados na literatura. DOI:10.5007/1808-1711.2010v14n1p71. (shrink)

n this paper, a non-classical axiomatic system was introduced to classify all moods of Aristotelian syllogisms, in addition to the axiom "Every a is an a" and the bilateral rules of obversion of E and O propositions. This system consists of only 2 definitions, 2 axioms, 1 rule of a premise, and moods of Barbara and Datisi. By adding first-degree propositional negation to this system, we prove that the square of opposition holds without using many of the other (...) rules of classical logic (including double negation elimination). We then show that the Propositional Substructural Logic SLe is the best logic to study Aristotelian Syllogisms. Also, based on the IFLe square of opposition, the rules of conversation and the rules of negation are completely proved in Muzaffar's logic. For this purpose, we used the monadic first-order logic with the same standard deductive apparatus of quantifiers in classical logic, plus the axioms of "some a is an a" and "some not-a is a not-a". Finally, to show that there is no existential commitment to general terms in categorical logic, the Strong Four-Valued Relevant-classical Logic KR4 was used. With the same existential interpretation of the quantifiers and the standard translation of the quarter quantified. (shrink)

Corcoran, John. 1974. Aristotelian Syllogisms: Valid arguments or true generalized conditionals?, Mind 83, 278–81. MR0532928 (58 #27178) This tightly-written and self-contained four-page paper must be studied and not just skimmed. It meticulously analyses quotations from Aristotle and Lukasiewicz to establish that Aristotle was using indirect deductions—as required by the natural-deduction interpretation—and not indirect proofs—as required by the axiomatic interpretation. Lukasiewicz was explicit and clear about the subtle fact that Aristotle’s practice could not be construed as correctly performed indirect (...) proof. Lukasiewicz evidence is presented fully; it is irrefutable. But, instead of considering the possibility that Aristotle’s discourses were not intended to express indirect proofs of universalized conditions presupposing axiomatic premises, Lukasiewicz came to the amazing conclusion that Aristotle did not understand indirect proof. This paper builds on the admirable Lukasiewicz scholarship to establish a conclusion diametrically opposed to the one Lukasiewicz asserted. This paper points out that if Aristotle had not been establishing an underlying logic but he was instead axiomatizing a theory of terms, Aristotelians could not claim for Aristotle the title Founder of Logic. People who take Euclid, Peano, and Zermelo to have first axiomatized geometry, arithmetic, and set theory, respectively, do not think that this qualifies them for the titles Founder of Geometry, Founder of Arithmetic, and Founder of Set Theory, respectively. Such people do think that this would qualify the three for the titles Founder of Axiomatic Geometry, Founder of Axiomatic Arithmetic, and Founder of Axiomatic Set Theory, respectively: titles that carry no honors in logic. Being the Founder of Axiomatic Term Theory would likewise carry no honors in the field of logic. CORRECTION: The paper inadvertently implied that Euclid was the first to axiomatize geometry. In order to understand Aristotle’s Analytics as a treatise on demonstration it helps to realize that axiomatized geometry was studied in Plato’s Academy when Aristotle was a student. Euclid was the author of the only ancient axiomatized geometry now available. (shrink)

A coherence-based probability semantics for categorical syllogisms of Figure I, which have transitive structures, has been proposed recently (Gilio, Pfeifer, & Sanfilippo [15]). We extend this work by studying Figure II under coherence. Camestres is an example of a Figure II syllogism: from Every P is M and No S is M infer No S is P. We interpret these sentences by suitable conditional probability assessments. Since the probabilistic inference of ~????|???? from the premise set {????|????, (...) ~????|????} is not informative, we add ????(????|(????∨????))>0 as a probabilistic constraint (i.e., an “existential import assumption”) to obtain probabilistic informativeness. We show how to propagate the assigned (precise or interval-valued) probabilities to the sequence of conditional events (????|????,~????|????,????|(????∨????)) to the conclusion ~????|???? . Thereby, we give a probabilistic meaning to the other syllogisms of Figure II. Moreover, our semantics also allows for generalizing the traditional syllogisms to new ones involving generalized quantifiers (like Most S are P) and syllogisms in terms of defaults and negated defaults. (shrink)

This paper proposes a classification of economic models into three types: historical, axiomatic and conditional. Historical or empirical models utilize the historical-deductive method, and are generalizations from the economic regularities and tendencies that we find in the real world. Axiomatic models utilize the hypothetical-deductive method; they are syllogisms whose major premise is an axiom – a self-evident truth; they are appropriate for methodological sciences such as mathematics and econometrics. Conditional economic models are likewise syllogisms, but they (...) are suitable for economics because they make for clearer and more precise economic reasoning. The criterion of truth of the substantive sciences is the conformity with reality, of the methodological science, its internal consistency. When a school of economic thought adopts mainly axiomatic models, as is the case with neoclassical economics, it implicitly falls into contradiction because their best representatives believe in the conformity with reality criterion. (shrink)

Abstract“Natural syllogisms” are arguments formally identifiable with categorical syllogisms that have an implicit universal affirmative premise retrieved from semantic memory rather than explicitly stated. Previous studies with adult participants (Politzer, 2011) have shown that the rate of success is remarkably high. Because their resolution requires only the use of a simple strategy (known as ecthesis in classic logic) and an operational use of the concept of inclusion (the recognition that an element that belongs to a subset (...) must belong to the set but not vice versa), it was hypothesized that these syllogisms would be within the grasp of non‐adult participants, provided they have acquired the notion of deductive validity. Here, 11‐year‐old children were presented with natural syllogisms embedded in short dialogs. The first experiment showed that their performance was equivalent to adults' highest level of performance in standard experiments on syllogisms. The second experiment, while confirming children's proficiency in solving natural syllogisms, showed that they outperformed children who solved non‐natural matched syllogisms in the same experimental setting. The results are also in agreement with the argumentation theory of reasoning. (shrink)

This paper continues our work on a coherence-based probability semantics for Aristotelian syllogisms (Gilio, Pfeifer, and Sanfilippo, 2016; Pfeifer and Sanfilippo, 2018) by studying Figure III under coherence. We interpret the syllogistic sentence types by suitable conditional probability assessments. Since the probabilistic inference of P|S from the premise set {.

Recent controversy over philosophical advocacy of infanticide (or the comically-styled euphemism ‘postnatal abortion’) reveals a surprisingly common premise uniting many of the opponents and supporters of the practice. This is the belief that the moral status of the early fetus or embryo with respect to a right to life is identical to that of a newly born or even very young baby. From this premise, infanticidists and strong anti-abortionists draw opposite conclusions, the former that the healthy (...) newly born have no inherent right to life and the latter that minute embryos and the very early fetus have the same right to life as young babies. (Indeed strong anti-abortionists tend to regard this right to life as identical to that possessed by adult humans.) This paper argues that these opposed conclusions are both deeply implausible and that the implausibility resides in the common premise. The argument requires some attention to the structure of the philosophical case underpinning the supposed vice of speciesism that has been given intellectual currency by many philosophers, most notably Peter Singer, and also to the reasoning behind the strong anti-abortionist adoption of the common premise. (shrink)

Discussion of the Aristotelian syllogistic over the last sixty years has arguably centered on the question whether syllogisms are inferences or implications. But the significance of this debate at times has been taken to concern whether the syllogistic is a logic or a theory, and how it ought to be represented by modern systems. Largely missing from this discussion has been a study of the few passages in the Prior Analytics where Aristotle provides explicit guidance on how to (...) individuate syllogisms. I argue that syllogisms are individuated by unordered premise pairs and so may be fruitfully thought of as multi-succedent sequents. I conclude by drawing a few consequences for the representation of the syllogistic. (shrink)

In their interesting and informative paper ‘From Szasz to Foucault: On the Role of Critical Psychiatry,’ Pat Bracken and Phil Thomas contrast, in a clear and helpful way, some central themes in the works of Thomas Szasz and Michel Foucault. They go on to endorse a form of critical psychiatry inspired by the latter. Szasz’s critique of psychiatry, they explain, is premised on binary oppositions, principally that between ‘mental’ and ‘bodily.’ Szasz begins by assuming the legitimacy of the distinction (...) and proceeds to argue that the term ‘illness’ can only be legitimately applied to what is ‘bodily.’ According to Szasz, there are medical pathologies, which are to be understood in naturalistic, biological terms, and .. (shrink)

Arguments from ignorance should be schematized: It has not been proven false that p. So it is possible that p. So, it is reasonable to believe p. Also, in opposition to standard views they should be distinguished from burden of proof and absence of evidence arguments. Much of the persuasiveness of such arguments can be located in the slippery uses of "possible." Besides equivocations on "possible" the argument is a fallacy for two reasons. First, the possibility implied by (...) the first premise does not yield the serious possibility that is needed for establishing the conclusion. Second, ignorance is never sufficient reason for belief, only adequate evidence. (shrink)

What is meant under the genuine title of Aristotle’s ta Analytika is rarely properly understood. Presumably, his analytics was inspired by the method of geometric analysis. For Aristotle, this was a regressive or heuristic procedure, departing from a proposed conclusion and asking which premises could be found in order to syllogize, demonstrate or explain it. The terms that form categorical and modal propositions play a fundamental role in analytics. Aristotle introduces letters in lieu of the triples of terms constitut­ing (...) the propositions and the three syllogistic figures that schematize them. His formulation of the three syllogistic figures refers to a syntacti­cal and predicative order and position of the triples of terms, arranged in some diagrammed schemata, which, regrettably, are missing from the extant text of the Prior Analytics. Considering planar and graphic arrangements, both vertical and horizontal orders as well as the posi­tion of the three terms involved, we propose a reconstruction, at least to some extent, of these probable lettered diagrams. In such reconstructed diagrams, we can appropriately capture the definition of syllogism as a predicative connexion of terms, and easier survey a synoptic account of all valid predicative relations and transpositions, and also reduce the imperfect syllogisms into the moods of the first figure. Aristotle’s syllogistic is an analytical calculation of terms, understood as predicates and subjects within the categorical propositions, and more precisely of three terms schematized in three figures in predicative links such that, by means of a middle, follows from necessity a conclusion of the extreme terms. The necessity of the consequence is not based on the implication or inference of the propositions, but on a predictive transi­tivity through the middle term within the syllogistic figures. Syllogism must draw its conclusion through the way its terms are predicated of one another. Aristotle in his Prior Analytics developed also a complex account of modal syllogisms within necessity and possibility of belonging. This account involves also such an analyti­cal reduction to the syllogistic figures. In this analytical perspective, we try to throw some light on his modal syllogisms, although this difficult and nowadays thoroughly discussed topic would require a much wider treatment. (shrink)

In the present study, we explore how reading habits influence the scanning and the construction of mental models in spatial reasoning. For instance, when participants are given a problem like A is to the left of B; B is to the left of C, what is the relation between A and C? They are assumed to construct the model: A B C. If reading habits influence the scanning process, then readers of French should inspect models from left to right, (...) whereas readers of Arabic should inspect them from right to left. The prediction following this analysis is that readers of French should be more inclined to produce “left” conclusions, whereas readers of Arabic should be more inclined to produce “right” conclusions. Furthermore, one may expect that readers of French show a greater ease in constructing models following a left-to-right direction than models following a right-to-left direction, whereas an opposite pattern might be expected for readers of Arabic. We tested these predictions in two experiments involving French and Yemeni participants. Experiment 1 investigated the formulation of conclusions from spatial premises, and Experiment 2, which was based on non-linguistic stimuli, examined the time required to construct mental models from left to right and from right to left. Our results show clear differences between the two groups. As expected, the French sample showed a strong left-to-right bias, but the Yemeni sample did not show the reverse bias. Results are discussed in terms of cultural influences and universal mechanisms. (shrink)

One lists the distinct pairs of categorical premises formulable via only the positive terms, S,P,M, by constructing a six by six matrix obtained by pairing the six categorical P-premises, A, O, A, O, where P* ∈ {P,P′}, with the six, similar, categorical S-premises. One shows how five rules of valid syllogism, select only 15 distinct PCPs that entail logical consequences belonging to the set L+: = {A, O, A, E, O, I}. The choice of admissible LCs can be regarded as (...) a condition separated from the conditions contained in the RofVS: the usual eight PCPs that generate valid syllogisms are obtained when the only admissible LCs belong to the set L: = {A, E, O, I} and no existential imports are addressed. A 64 PCP-matrix obtains when both PCPs and LCs may contain indefinite terms—the positive, S,P,M, terms, and their complementary sets, S′,P′, M′, in the universe of discourse, U, called the negative terms. Now one can accept eight LCs: A, I, where P* ∈ {P,P′}, S* ∈ {S,S′}, and there are 32 conclusive PCPs, entailing precise, “one partitioning subset of U” LCs. The four rules of conclusive syllogisms predict the less precise LCs, left after eliminating the middle term from the exact LCs. The RofCS also predict that the other 32 PCPs of the 64 PCP-matrix are non-conclusive. The RofVS and the RofCS are generalized, and arguments are given, for also accepting as valid syllogisms the conclusive syllogisms formulable via positive terms which entail the LCs A and O. (shrink)

When people understand a counterfactual such as “if the flowers had been roses, the trees would have been orange trees,” they think about the conjecture, “there were roses and orange trees,” and they also think about its opposite, the presupposed facts. We test whether people think about the opposite by representing alternates, for example, “poppies and apple trees,” or whether models can contain symbols, for example, “no roses and no orange trees.” We report the discovery of an inference‐to‐alternates (...) effect—a tendency to make an affirmative inference that refers to an alternate even from a negative minor premise, for example, “there were no orange trees, therefore there were poppies.” Nine experiments show the inference‐to‐alternates effect occurs in a binary context, but not a multiple context, and for direct and indirect reference; it can be induced and reduced by prior experience with similar inferences, and it also occurs for indicative conditionals. The results have implications for theories of counterfactual conditionals, and of negation. (shrink)

In this paper a set of categorical sentences called an antilogistic tetrad is presented as a perspective on Aristotle's square of opposition. An antilogistic tetrad is formed by collecting the premises of a pair of valid syllogisms the conclusions of which are contradictory categorical sentences. A set of such premises serves to bring together Aristotle's concern with debate and the syllogism, and as such may be seen as a way of “completing” Aristotle's analysis of the square of opposition.The debate (...) context is characterized by opposing views for which arguments are offered. The square of opposition captures that contending of opposing views; and is also basic to the presentation of categorical sentences, a necessary condition for the syllogism. By using C. S. Peirce's notion of abductive argument to produce the middle term, and hence to construct deductive syllogistic arguments, antilogistic tetrads may be formed on any contended subject. For that reason, the process sketched above for forming antilogistic tetrads is called “completing the square of opposition.”. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:FROM SACRIFICIAL VIOLENCE TO RESPONSIBILITY: THE EDUCATION OF MOSES IN EXODUS 2-4 Sandor Goodhart Purdue University When toward the end of his life Moses tried to stave off death, God said to him: "Did I tell you to slay the Egyptian?" (Midrash in Plaut 383) I. Education in Plato and Judaism The word "education", of course, comes from the Latin, educare, meaning "to lead out" or "to (...) bring up," and both its Latinate morphology and the semantic value it assumes in English reflect its peculiar history. To "lead out" implies in the first place leadership, which is to say a relationship between one designated as a "leader" and another (or others) designated as the "led." The notion of leadership also entails a movement through which the leader propels the led, namely from a region designated as "inside," to another designated as "outside." Within the Western context, which is to say, within the Western European historical experience which traces itselfback through the romance language speaking countries to Rome and ultimately to Greece, the primary articulator ofthe notion of education we have inherited is, of course, Plato. Although Plato's Republic is nominally about justice, and even more specifically the "just" state, commentators have long pointed out that it is really about education (see, for example, Havelock). How shall the guardians ofthe state that we shall term "just" be educated?, Plato's interlocutors ask themselves. In this regard, of course, Plato was challenging the educational system already in place at the time at the head of which was Homer and the Homeric epics, and substituting for an older oral culture founded on an elaborate system of mnemonics another founded more decisively upon writing and the alphabet. Some have argued that in place of a aural or Sandor Goodhart1 3 hearing-centered culture Plato was inaugurating a visual or video-centric cultural organization, and much work is currently being done in this area (see, for example, Ong). What was Plato's educational solution? It was an appeal, in short, to the true, to the language of reason, and to the realm of the ontological as the context in which the true could be defined. The true, as the phenomenological tradition has taught us, may be regarded as the separation of that which has being from that which does not have being, that which only appears or seems to be from that which truly is. Reason in this context is the method or modality ofthinking by which such difference or distinction between the true and the false becomes articulated. Education may then be said to be the process by which all of this occurs, by which one learns to separate appearances from reality, the true from the false, the reasonable from the unreasonable, and thereby the process by which one avoids slavery. For at bottom the enemy for Plato remains slavery and the goal remains freedom from its ravages. Plato, for one, defines his program in specific opposition to Greek tragedy, which he takes among the species ofmimesis or of mimetic poesis that he cites to be the worst threat to his program of absolute difference. The tragic poets leave us without an antidote, he tells us, to its irresistible seductions. Even the best of us—by which he would certainly include Socrates, who has been educating these young men about the processes of education—go to the theater, follow the theatrical performance with enthusiasm, beat their breasts along with the players, and finally praise as most worthy those playwrights who most enable this enthusiasm to take place. The distinction between the true and the mimetic, between the true and the imitational or representational, between that which has being and that which only shadows being, is always on the verge of collapsing in this context. And as a consequence the only safe state, Plato tells us, is the one that excludes theatrical performance from its premises. There is no place in the present context to develop any further the complicated relationship Plato has with his predecessors, and I have hinted at this relationship elsewhere (see Goodhart 261). Suffice it to say that Plato remains in this regard the master in Western circles ofall... (shrink)

The article explores a change taking place today in the fields of biology and social anthropology, signaling a shared desire to transcend the heuristic effects of the opposition between nature and culture. Acceptance of the idea that random mutations are the sole driving force behind the process of natural selection overlooks the agentive capacity of non-human living beings, revealing an anthropocentric inspiration. To critique the rhetoric surrounding the principle of natural selection, I turn to the anthropology of Tim Ingold and (...) his analysis of the metaphors that illustrate the principle. I disagree with the author, however, when he argues that these metaphors do not adequately illustrate neo-Darwinian premises. Instead, I believe that they are faithful since their apparent contradiction expresses the unease of neo-Darwinian theory itself when it combines randomness and teleology. New currents in biology, such as biosemiotics, attribute evolutionary importance to epigenetic changes. From the evolutionary perspective, they also highlight the importance of recognizing that the entire lived world possesses the capacity for agency, not just human beings. Within social anthropology, the so-called ontological turn and multispecies ethnography have been working with a new conception of the person, extendible to non-human beings, including the latter to compose a single collective with humans. Thus we can observe an attempt on the part of biologists and anthropologists alike to move beyond anthropocentrism, producer and product of the opposition between nature and culture. (shrink)

An arithmetical language, whose words are natural numbers written in hexadecimal numeration system, is defined and its applications for the representation, analysis and decision of formulae of some logical and normative systems are described and illustrated.The formulae, operations and relations of the represented system are associated as follows respectively to the numbers and the arithmetical operations and relations of the proposed language:1. Each well-formed-formula of the system is associated to a number of a set of natural numbers between zero (associated (...) to all tautologies and theses) and the binary supremum Φ of the set (Φ is associated to all contradictions and antitheses and his value is 2n-1, n depending on system’s dimensions and structure).2. Negation of a formula and disjonction and conjonction of t wo other more formulae of the system are associated respectively to the binary complement Φ-N(f) of the number associated to the first and to the binary infimun and supremum of the numbers associated to the last.3. The logical relations “f1 implies f2” (f1 -> f2), “f1 is incompat.ible with f2” (f1|f2), “f1 is the contradictory opposite of f2” (f1wf2) and “f1 is alternative to f2” (f1vf2) are true in the represented system if and only if the associated arithmetical relations, respectively “N(f1) absorbs arithmetically N(f2)”, “binary supremum of N(f1) and N(f2) is equal to Φ”, “sum of of N(f1) and N(f2) is equal to Φ” and “binary infimum of N(f1) and N(f2) is equal to 0”, are true.The applications of the proposed arithmetical language as very rapid and simplified tool of analysis and decision method are shown for the following systems: propositional logic, syllogistic, some deontic and alethic modal systems and some normative systems of statutory law:1. In the propositional logic, after fixing the maximum of variables considered, the numbers associated to these variables and to the contradictions are calculated. On this permanent basis, the evaluation of a farmula (especially in the case of many occurrences of many variables) is performed by the calculation of the associated number faster as in the traditional way.2. In the syllogistic, after the calculation of the number associated to each type of premise or conclusion, an arithmetical table of syllogisms shows that a proposed syllogism is valid if and only if the binary supremum of the numbers associated to the premises absorbs arithmetically the number associated to the conclusion. It is well-known that the search of this sort of arithmetization of syllogistic and the study of its possibilitiy has been a recurrent topic in modern logic, from Leibniz to Łukasiewicz and to-day.3. In a deontic equivalent:ial system who includes Von Wright’s deontic system of 1982 far norms of the first order, the calculation of the numbers associated to an types of permission and obligation sentences allows the im mediate arithmetical verification of an the classical relations between those sentences. The same is shown for an alethic modal system including the modlities of the first order of Lewis’s S5.4. For normative systems of statutory law, the arithmetical verification of the logical and normative relations is shown in precedent author’s papers -especially in recent “The ‘Ars Judicandi.’ Programme”-, though not yet in hexadecimal numeration system but only in binary and decimal ones.In all the represented systems, the arithmetical verification of the metalogical properties of the system -consistency and completeness- is performed in a very easy and rapid manner, after the arithmetic representation of the axiomatic basis of the latter by a system of equations. (shrink)

This paper was motivated by reflections on what makes our argument convincing and persuasive. The substantive answer in my view suggests the examination of the cognitive grounds of argumentation. In the introductory section, I consider various approaches to identifying the cognitive component in argumentation. That way, I briefly observe recent relevant publications, which I classify into two groups: those directly addressing cognitive grounds of argumentation; and papers on formal models of argumentation that take cognitive nature of persuasion as a (...) class='Hi'>premise. In the second section, I argue for phenomenologicaly inspired approach to cognitive activity as one which provides an adequate cognitive interpretation of the latter. In so doing, I touch upon key some phenomenological concepts and focuses on an analogizing apperception (appresentation). The third section accumulates all the above. I proceed from the interpretation of the argumentation as discursive activity aimed at a deliberate change in an opposite party’s position, which may not be explicitly presented in the course of arguing. It makes us turn to cognitive procedure of appresentation as it was presented by Husserl for an adequate interpretation of transfer and grasping of argumentative message’s meaning. (shrink)

This article contends that the central principle of modern philosophy is obscured by a side-debate between two opposed camps that are united in accepting a deeper flawed premise. Consider the powerful critiques of Kantian philosophy offered by Quentin Meillassoux and Bruno Latour, respectively. These two thinkers criticize Kant for opposite reasons: Meillassoux because Kant collapses thought and world into a permanent “correlate” without isolated terms, and Latour because Kant tries to purify thought and world from each other (...) rather than realizing that they are always combined in “hybrid” form. What both critiques tacitly accept is the notion that “thought” and “world” are the two major poles of the universe. I claim that this stems from the post-Cartesian assumption that thought and world are the two basic kinds of things that exist. The name “onto-taxonomy” is introduced for this view. (shrink)

Two objections are raised against Oliver and Smiley’s analysis of the collective–distributive opposition in their 2016 book: They take it as a basic premise that the collective reading of ‘baked a cake’ corresponds to a predicate different from its distributive reading, and the same applies to all predicate expressions that admit both a collective and a distributive interpretation. At the same time, however, they argue that inflectional forms of the same lexeme reveal a univocity that should be preserved (...) in a formal representation of English. These two assumptions sit uneasily. In developing their analysis, Oliver and Smiley come to the conclusion that even a singular predication such as ‘Tom baked a cake’ must be regarded as ambiguous between a collective and a distributive reading. This is so artificial that it hardly makes sense, and yet there seems to be no way out of the difficulty unless we are prepared to give up the basic premise just mentioned. (shrink)

The aim of the book is to clarify the concept of omniscience. This is done first by discussing basic questions on omniscience (chs.1-12) and secondly by offering a theory of omniscience as an axiomatic system in which also a definition of omniscience is given (ch.13). The twelve chapters deal with questions like whether everything is true what God knows, whether God's knowledge is bound to time, whether it concerns singular truths or only laws, whether it extends also to contingent future (...) events ...etc. The book is neither a book about the existence of God nor about proofs for his existence. It is a book about the possibility of a consistent concept of omniscience which can be attributed to God. And it invalidates opposite claims and shows that they are based on wrong or very doubtful premises. The pros and cons at the beginning of each chapter represent different positions and objections which are clarified and discussed in the answer to the objections. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.3 (2001) 448-449 [Access article in PDF] James Van Cleve. Problems from Kant. New York and Oxford: Oxford University Press, 1999. Pp. xii + 340. Cloth, $45.00. The author acknowledges his debt to the "great Kant books of the 1960s, Jonathan Bennett's Kant's Analytic, and P. F. Strawson's The Bounds of Sense."Their analytical spirit lives on in this book, but the analyses (...) are fresh, take surprising turns, and make unexpected connections to current concerns. In seventeen chapters Van Cleve deals with necessity and the a priori, space and geometry, incongruent counterparts, time, the ideality of matter, experience and objects, substance in the First Analogy, the Second Analogy, noumena, problems of the self, rational theology, and Kant and contemporary irrealism. To sustain the flow of argument, the discussion of certain details, often important, is postponed and taken up in fifteen appendices, and there are nearly seventy pages of careful notes.Chapter 10, "Noumena and Things in Themselves," (134 ff.) criticizes in detail the prevailing "one world" or "double aspect" view of objects, namely that Kant allows just one set of objects, but two ways of "considering" them. Things in themselves are the very same objects as appearances, but considered as they are independent of our experience of them, a view developed in Henry Allison's Kant's Transcendental Idealism. Against this Van Cleve maintains (and I concur) that "appearances are intentionalia, and that intentionalia are constructions out of states of perceivers" (150). The distinction is between two separate universes of discourse, "not between two ways of discoursing [End Page 448] about the same objects" (ibid.). There is no space to report the sharply argued detail that led him to hold the double aspect view to be unfathomable and incoherent. He takes Kant to be a phenomenalist but holding to a version far removed from the reductionist phenomenalism of Russell, Broad, Price, and others. Here the basic elements are not made out to be indubitable givens, but are, rather, sensations. The structures built on them are, according to Van Cleve, "virtual objects" in the sense in which Quine speaks about "virtual classes." To say that something is an element of a class {F:Fx} is only to say that it is F. So, likewise, to say that, e.g., a patch of red exists is short for saying that a certain representation occurs. Carnap's Kantian masterpiece, TheLogical Structure of the World (The Aufbau) could have been consulted as a comprehensive guide to the kind of virtuality here envisaged.It is Van Cleve's stated aim never to discuss Kantian arguments without making their premise and conclusion structure clear (viii). Quite a few of them he finds persuasive; in other cases the arguments are valid, but one or the other premise doubtful. Sometimes he sides with Kant against his critics, sometimes the opposite, and occasionally, as in the case of the Second Analogy, it remains unclear what Kant's argument was. He has shown in this and earlier publications that all reconstructions are flawed, so that either Kant had no good argument, or his argument has not yet been discovered.The title Problems from Kant must be taken seriously. The book rarely deals with textual problems, historical context, or translation difficulties. Rather, the focus is on perennial and still compelling problems. Themes from the First Critique are tracked to and connected with current concerns and sometimes recently ventilated issues are traced back to Kant, as in the last chapter, where the question is raised if Kant was an internal realist in the style of Putnam, or perhaps an anti-realist like Dummett. The contrast with Kant shows that like all complex positions, these are shopping baskets with several goods in them, some in Kant's inventory, others not.Logical notation is used sparingly, and only where it clarifies—no attempt here to shoehorn arguments into unneeded symbolism. Deft examples, Kant's weakness, are a strength of this book. To explain the logic of considering Van Cleve asks, "Consider me apart from my shoes, am I barefoot... (shrink)

In the Posterior Analytics Aristotle contrasts demonstrations with syllogisms through signs. In the Prior Analytics he defines a sign as a demonstrative premise. One is thus led to ask: is a sign a demonstration? This book reconstructs the history of the notion of "demonstration through signs" from roughly the third through to the thirteenth century. It examines the work of Aristotle's Greek, Arabic, and Latin commentators, both within and outside the tradition of the Posterior Analytics.

Saba Mahmood’s anthropological work studies the gain in skills, agency and capacity building by the women’s dawa movement in Egypt. These women increase their virtue toward the goal of piety by following dominant, often patriarchal norms. Mahmood argues that “teleological feminism” ignores this gain in agency because this kind of feminism only focuses on opposition or resistance to these norms. In this paper I defend Mahmood’s “anti-teleological” feminist work from criticisms that her project valorizes oppression and has no vision (...) for a nonoppressive feminist future. I argue the future envisioned by teleological feminists gets caught in “the Hegelian” trap of replicating past oppression in their feminist future. I find in Mahmood’s work the tools to escape this trap. I argue, rather than a movement of overcoming oppression, Mahmood’s work suggests an immanent and creative movement that emphasizes difference for a truly new future. I turn to a Bergsonian metaphor and argue that this movement can be seen as akin to the movement of biological evolution. I conclude using the work of Eve Sedgwick that the Egyptian women that Mahmood studies are being read in a “paranoid” fashion and demonstrate using Leila Ahmed a better “reparative” reading of these women. (shrink)

This book was undertaken before the terms 'fake news' and 'alternative facts' were coined and the further escalation of America's ideological civil war. It was prompted by deep wonderment at the way people tend to be wholly enclosed within their ideological frames and deaf to claims about reality that come from the opposite camp, no matter how valid they might be. Ideology consists of normative prescriptions regarding how society should be shaped, together with an interpretive roadmap indicating how (...) this normative vision can be implemented in reality. Ideological fixation is the result of tensions and conflicts between these two elements. The book does not focus on the normative aspect of ideology, which is largely subjective, but on its factual claims about the world, typically subordinate to, and often distorted by, the normative commitment. After theorists around 1960 proclaimed the 'death of ideology', ideological divides and clashes have reemerged with renewed intensity throughout the world, including in the liberal democracies. In the United States they have become particularly venomous. The other side is widely viewed as malicious, irrational or downright stupid, and, often, as barely legitimate. The zeal of the opposing sides is often scarcely less than that which characterized the religious ideologies of old. Indeed, historical religious ideologies have largely been replaced by 'secular religions' or 'religion substitutes'. The book is not another survey of past and present ideologies. It is an attempt to understand the cognitive, emotional and social roots of ideology and ideological fixation. It combines insights from evolutionary psychology regarding the nature of some of our deepest proclivities with a broad sweep through history. It proceeds from the Stone Age to the rise of civilization, the great religions and modernity, to a critique of fundamental factual premises that underlie some of the major debates dominating today's liberal democracies. (shrink)

The Scottish Philosophy of Common Sense originated as a protest against the philosophy of the greatest Scottish philosopher. Hume's sceptical conclusions did not excite as much opposition as might have been expected. But in Scotland especially there was a good deal of spoken criticism which was never written; and some who would have liked to denounce Hume's doctrines in print were restrained by the salutary reflection that if they were challenged to give reasons for their criticism they would find it (...) uncommonly difficult to do so. Hume's scepticism was disliked, but it was difficult to see how it could be adequately met. At this point Thomas Reid stepped into the field. He was the only man of his time who really understood the genesis of Hume's scepticism and succeeded in locating its sources. At first sight it would seem that this discovery required no peculiar perspicuity. It would seem that nobody could help seeing that Hume's sceptical conclusions were based on Locke's premises, and that Hume could never be successfully opposed by any critic who accepted Locke's assumptions. But this is precisely one of those obvious things that is noticed by nobody. And in fact Reid was the first man to see it clearly. It thus became his duty to question the assumptions on which all his own early thought had been based. The result of this reflection was the conclusion that, since the "ideal theory" of Locke and Berkeley logically led to Hume's scepticism, and since scepticism was intolerable, that theory would have to be amended, or, if necessary, abandoned. This volume contains works by Thomas Reid, Adam Ferguson, James Beattie, and Dugald Stewart. (shrink)

The presence of premises expressing comparison is a problem for the Aristotelian theory of the dialectical method, first because there is no general theory of comparison in the Organon and secondly because along with propositions on the opposition and inflexion of the terms, comparative statements seem to fall outside the explicit description which Aristotle gives of possible premises. The purpose of this paper is to offer a synthetic theory of comparisons according to Aristotle’s Topics, in an attempt both to supply (...) the aforementioned absence and to highlight the importance of the second problem. There are three main types of premises on the more, the less and the similar: some comparing the degree of possession of a predicate, others comparing the plausibility of a predication and finally, others expressing an analogy. Once expounded the very marked differences that occur between these three classes of propositions, the paper analyses the various kinds of argumentation based on comparative premises and offers a formalization of its logical laws. The complexity of this theory and the volume of topoi involved in the comparisons show the magnitude of a problem that has not been sufficiently studied. (shrink)

The presence of premises expressing comparison is a problem for the Aristotelian theory of the dialectical method, first because there is no general theory of comparison in the Organon and secondly because along with propositions on the opposition and inflexion of the terms, comparative statements seem to fall outside the explicit description which Aristotle gives of possible premises. The purpose of this paper is to offer a synthetic theory of comparisons according to Aristotle’s Topics , in an attempt both to (...) supply the aforementioned absence and to highlight the importance of the second problem. There are three main types of premises on the more, the less and the similar : some comparing the degree of possession of a predicate, others comparing the plausibility of a predication and finally, others expressing an analogy. Once expounded the very marked differences that occur between these three classes of propositions, the paper analyses the various kinds of argumentation based on comparative premises and offers a formalization of its logical laws. The complexity of this theory and the volume of topoi involved in the comparisons show the magnitude of a problem that has not been sufficiently studied. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Case against Rational Egoism in Dostoevsky’s Notes from Underground*James P. ScanlanWriting in his own voice, in letters, notebooks, and diaries, Fyodor Dostoevsky frequently attacked the philosophy of the Russian “nihilists,” as he typically called them—Nikolay Chernyshevsky, Dmitry Pisarev, and other representatives of the radical Russian intelligentsia in the third quarter of the nineteenth century. But because Dostoevsky also used fiction to argue against them, if we wish (...) to discern the full contours of his opposition, we must turn to his stories and novels; and there we face the problem of determining to what extent, if any, the statements of his narrators and characters express his own views.This problem is particularly challenging in regard to the radicals’ “Rational Egoism,” to use the label by which the Russian variant of the theory of enlightened egoism came to be known. 1 Dostoevsky’s most sustained and spirited attack on that aspect of “nihilist” philosophy is found in Part One of Notes from Underground (1864), but it is voiced by one of the darkest, least sympathetic of all his characters—the nameless narrator and protagonist known as the Underground Man. Was this repellent creature speaking for Dostoevsky? The Underground Man, moreover, can easily be viewed as a sheer irrationalist whose rejection of Rational Egoism is a tortured emotional outburst with no logical credentials. Robert L. Jackson, in his groundbreaking study of 1958, describes the Underground Man’s thinking at one point as follows: “It is impossible to argue [End Page 549] with the rationalists: reason is on their side. All that remains is irrationally to negate reason.” 2 If those words were to be taken not simply as a moment in Jackson’s rich analysis but as a comprehensive description of the Underground Man’s attitude, it would be senseless to expect philosophically nuanced arguments from him. And we would have no grounds for thinking that Dostoevsky’s own treatment of Rational Egoism went beyond emotional rejection.Critics from Vasily Rozanov to Joseph Frank have debated the Underground Man’s stance toward Rational Egoism and its relation to Dostoevsky’s, with no sign yet of a definitive resolution. Frank’s recent treatment, presented in the third volume of his monumental literary biography of Dostoevsky, offers a helpful history of the dispute as well as his own finely elaborated interpretation of the Underground Man as an irrational opponent of Rational Egoism. 3 Frank reads Notes from Underground as satire, and he contends that the Underground Man is caught in an agonizing self-contradiction: intellectually, he accepts the basic premises of the Rational Egoists’ outlook, such as the denial of free will; but he finds that, “despite the convictions of his reason,” he cannot live with the amoral and dehumanizing implications of those premises, which strip human beings of moral responsibility. 4 From a rational point of view, of course, rejection of the implications should force the Underground Man to reject the premises as well (by the hoary logical law of modus tollendo tolens), and indeed he does at times passionately condemn them. But according to Frank, these condemnations simply show the depth of his predicament: his “intellectual acceptance” of Chernyshevsky’s determinism is conjoined with “simultaneous rejection of it with the entire intuitive-emotional level of personality identified with moral conscience,” causing him to respond irrationally in a multitude of instances. 5 Frank’s Underground Man, then, is an intellectual disciple but an emotional critic of Rational Egoism; and he is triply an irrationalist: his thinking is mired in self-contradiction, he acts irrationally as a result, and his opposition to Rational Egoism has not a rational but an “intuitive-emotional” basis.But where does this leave Dostoevsky? Must we conclude that he, too, is somehow suspended between acceptance and rejection of Rational Egoism and for that reason has created in Notes from Underground a Bakhtinian equilibrium in which neither position is clearly privileged? For Frank, certainly not. It follows from Frank’s analysis that Dostoevsky himself, unlike the Underground [End Page 550] Man, is a fully consistent opponent of Rational Egoism, for that theory is the target of the inverted irony at the core of his satire; “the... (shrink)

There are good grounds for seeing a deep opposition between reason and violence. Yet some forms of argument appear to link the two; and a prominent example is the argumentum ad baculum, where the premise contains a threat. Consideration of the connection between premise and conclusion in such an argument can, it seems, yield some cases where the status of the author of the threat renders the argument not only valid but also sound. Examples of such arguments cluster (...) in the areas near Pascal's Wager and Rawls' argument for justice. However even these arguments fail to effect a reconciliation between reason and violence. (shrink)

This article studies the current US-China relationship using the dialectic ideas of I Ching. Firstly, the researcher introduces some basic theories of the topic. The dialectics of I Ching is based...

We investigate how the perceived uncertainty of a conditional affects a person's choice of conclusion. We use a novel procedure to introduce uncertainty by manipulating the conditional probability of the consequent given the antecedent. In Experiment 1, we show first that subjects reduce their choice of valid conclusions when a conditional is followed by an additional premise that makes the major premise uncertain. In this we replicate Byrne. These subjects choose, instead, a qualified conclusion expressing uncertainty. If subjects (...) are given a third statement that qualifies the likelihood of the additional premise, then the uncertainty of the conclusions they choose is systematically related to the suggested uncertainty. Experiment 2 confirms these observations in problems that omit the additional premise and qualify the first premise directly. Experiment 3 shows that the qualifying statement also affects the perceived probability of the consequent given the antecedent of the conditional. Experiment 4 investigates the effect of suggested uncertainty on the fallacies and shows that increases in uncertainty reduce the number of certain conclusions that are chosen while affirming the consequent but have no effect on denying the antecedent. We discuss our results in terms of rule theories and mental models and conclude that the latter give the most natural account of our results. (shrink)

This article deals with the relationship between philosophy and science in the writings of Karl Jaspers and with its reception in the wider scholarly literature. The problem discussed is how to characterize the relationship that exists between science—defined on pure Kantian grounds as a universally valid knowledge of phenomenal objects—and philosophy—conceived by Jaspers as the transcending mode of thinking of personal Existenz rising towards the totality and unity of Being. Two solutions to that problem arise from Jaspers’s writings. The (...) oppositionist view is based in his earlier philosophy of Existenz. It describes the discrepancy between determinateness, bestowed by science to its objects, and freedom of self-determination, which is both a synonym and a condition of possibility for Existenz. The reciprocal view is based in Jaspers’s later works, where he focuses on exploration of his concept of Being (das Umgreifende). By contrast with most of Jaspers’s commentators, the present interpretation is anchored in a developmentaland contextual understanding of Jaspers’s thought. Showing the transcendental background of this topic, the proposed interpretation allows us to abstain from viewing the two solutions as incoherent or contradictory and instead to see them as constitutive of a single philosophical course. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.3 (2001) 448-449 [Access article in PDF] James Van Cleve. Problems from Kant. New York and Oxford: Oxford University Press, 1999. Pp. xii + 340. Cloth, $45.00. The author acknowledges his debt to the "great Kant books of the 1960s, Jonathan Bennett's Kant's Analytic, and P. F. Strawson's The Bounds of Sense."Their analytical spirit lives on in this book, but the analyses (...) are fresh, take surprising turns, and make unexpected connections to current concerns. In seventeen chapters Van Cleve deals with necessity and the a priori, space and geometry, incongruent counterparts, time, the ideality of matter, experience and objects, substance in the First Analogy, the Second Analogy, noumena, problems of the self, rational theology, and Kant and contemporary irrealism. To sustain the flow of argument, the discussion of certain details, often important, is postponed and taken up in fifteen appendices, and there are nearly seventy pages of careful notes.Chapter 10, "Noumena and Things in Themselves," (134 ff.) criticizes in detail the prevailing "one world" or "double aspect" view of objects, namely that Kant allows just one set of objects, but two ways of "considering" them. Things in themselves are the very same objects as appearances, but considered as they are independent of our experience of them, a view developed in Henry Allison's Kant's Transcendental Idealism. Against this Van Cleve maintains (and I concur) that "appearances are intentionalia, and that intentionalia are constructions out of states of perceivers" (150). The distinction is between two separate universes of discourse, "not between two ways of discoursing [End Page 448] about the same objects" (ibid.). There is no space to report the sharply argued detail that led him to hold the double aspect view to be unfathomable and incoherent. He takes Kant to be a phenomenalist but holding to a version far removed from the reductionist phenomenalism of Russell, Broad, Price, and others. Here the basic elements are not made out to be indubitable givens, but are, rather, sensations. The structures built on them are, according to Van Cleve, "virtual objects" in the sense in which Quine speaks about "virtual classes." To say that something is an element of a class {F:Fx} is only to say that it is F. So, likewise, to say that, e.g., a patch of red exists is short for saying that a certain representation occurs. Carnap's Kantian masterpiece, TheLogical Structure of the World (The Aufbau) could have been consulted as a comprehensive guide to the kind of virtuality here envisaged.It is Van Cleve's stated aim never to discuss Kantian arguments without making their premise and conclusion structure clear (viii). Quite a few of them he finds persuasive; in other cases the arguments are valid, but one or the other premise doubtful. Sometimes he sides with Kant against his critics, sometimes the opposite, and occasionally, as in the case of the Second Analogy, it remains unclear what Kant's argument was. He has shown in this and earlier publications that all reconstructions are flawed, so that either Kant had no good argument, or his argument has not yet been discovered.The title Problems from Kant must be taken seriously. The book rarely deals with textual problems, historical context, or translation difficulties. Rather, the focus is on perennial and still compelling problems. Themes from the First Critique are tracked to and connected with current concerns and sometimes recently ventilated issues are traced back to Kant, as in the last chapter, where the question is raised if Kant was an internal realist in the style of Putnam, or perhaps an anti-realist like Dummett. The contrast with Kant shows that like all complex positions, these are shopping baskets with several goods in them, some in Kant's inventory, others not.Logical notation is used sparingly, and only where it clarifies—no attempt here to shoehorn arguments into unneeded symbolism. Deft examples, Kant's weakness, are a strength of this book. To explain the logic of considering Van Cleve asks, "Consider me apart from my shoes, am I barefoot... (shrink)

Four experiments investigated uncertainty about a premise in a deductive argument as a function of the expertise of the speaker and of the conversational context. The procedure mimicked everyday reasoning in that participants were not told that the premises were to be treated as certain. The results showed that the perceived likelihood of a conclusion was greater when the major or the minor premise was uttered by an expert rather than a novice (Experiment 1). The results also showed (...) that uncertainty about the conclusion was higher when the major premise was uttered by a novice and an alternative premise by an expert, compared to when the major premise was uttered by an expert and the alternative by a novice (Experiment 2). Similarly, the believability of a conclusion was considerably lower when the minor premise was uttered by a novice and denied by an expert, as opposed to when an expert uttered the minor premise and a novice denied it (Experiment 3). Experiment 4 showed that the nature of the uncertainty induced by a denial of the minor premise depended on whether or not the context was a conversation. These results pose difficult problems for current theories of reasoning, as current theories are based on the results of experiments in which the premises are treated as certain. Our discussion of the results emphasises the importance of pragmatics in reasoning, namely, the role of general knowledge about the world in assessing the probability of a premise uttered by an expert or a novice and the role of interpretations of the premise based on pragmatic inferences in revising these initial probabilities. (shrink)

One of the terminological constants in the philosophical work of Gilles Deleuze is the word 'immanence', and it has therefore become a foothold for those wishing to understand exactly what 'Deleuzian philosophy' is. Deleuze's philosophy of immanence is held to be fundamentally characterised by its opposition to all philosophies of 'transcendence'. On that basis, it is widely believed that Deleuze's project is premised on a return to a materialist metaphysics. Christian Kerslake argues that such an interpretation is fundamentally misconceived, and (...) has led to misunderstandings of Deleuze's philosophy, which is rather one of the latest heirs to the post-Kantian tradition of thought about immanence. This will be the first book to assess Deleuze's relationship to Kantian epistemology and post-Kantian philosophy, and will attempt to make Deleuze's philosophy intelligible to students working within that tradition. But it also attempts to reconstruct our image of the post-Kantian tradition, isolating a lineage that takes shape in the work of Schelling and Wronski, and which is developed in the twentieth century by Bergson, Warrain and Deleuze. (shrink)

Transitive inference (TI) plays a part in many aspects of reasoning, and is usually assessed using variants on a particular task dubbed the “IP-paradigm”. Advocates of this paradigm assume it ensures that subjects must use deduction to solve the inferential questions. The present task with 63 adults strengthened this claim by removing all possible perceptual cues and limiting as far as possible all cues from the training procedure itself. Response speed and accuracy were measured as premises were learned. Findings (...) show that when over-training and non-logical cues are avoided, adults nevertheless reach high levels of overall performance. However, key indexes of Lexical Marking, Relative-End-Anchoring, and Symbolic Distance are largely absent or in the opposite direction to the generally accepted view at the start of training, and are present only for response time (RT) at the end of training. The widely accepted strategy of retrieval from an integrated mental representation does emerge; but only after an initial associative process and a deductive process. Regarding three comparisons critical for demonstrating deductive TI, the inference was more demanding than its antecedents both in terms of accuracy and RT, and both after initial and final training. Existing theories of TI account for some of these findings, but what is required is a theory accommodating them all. (shrink)

The main object of this paper is to provide the logical machinery needed for a viable basis for talking of the ‘consequences’, the ‘content’, or of ‘equivalences’ between inconsistent sets of premisses.With reference to its maximal consistent subsets (m.c.s.), two kinds of ‘consequences’ of a propositional set S are defined. A proposition P is a weak consequence (W-consequence) of S if it is a logical consequence of at least one m.c.s. of S, and P is an inevitable consequence (I-consequence) of (...) S if it is a logical consequence of all the m.c.s. of S. The set of W-consequences of a set S it determines (up to logical equivalence) its m.c.s. (This enables us to define a normal form for every set such that any two sets having the same W-consequences have the same normal form.) The W-consequences and I-consequences will not do to define the ‘content’ of a set S. The first is too broad, may include propositions mutually inconsistent, the second is too narrow. A via media between these concepts is accordingly defined: P is a P-consequence of S, where P is some preference criterion yielding some of the m.c.s. of S as preferred to others, and P is a consequence of all of the P-preferred m.c.s. of S. The bulk of the paper is devoted to discussion of various preference criteria, and also surveys the application of this machinery in diverse contexts - for example, in connection with the processing of mutually inconsistent reports. (shrink)

This distinction has sometimes been read as purely epistemic, resting not on things, but on our knowledge of them: there is one world, not two, though it may be apprehended in two ways. But this view is patently at odds with the text. Knowledge and opinion are δυνάμεις, "faculties," to be distinguished and defined by their objects, no less than by the state of mind they produce, and Plato clearly states that the fallibility and unclearness of opinion is rooted in (...) the relative unreality of opinables. (shrink)

A number of medieval Arabic logicians discussed inferences that combine the principles of propositional and term logic, for example: Whenever H is Z then Every J is DNo D is AWhenever H is Z then S...

Previous studies have shown that 1 participants are reluctant to accept a conclusion as certainly true when it is derived from a valid conditional argument that includes a doubtful premise, and 2 participants typically link the degree of uncertainty found in a given premise set to its conclusion. Two experiments were designed to further investigate these phenomena. Ninety adult participants in Experiment 1 were first asked to judge the validity of three conditional arguments Modus Ponens, Denial of (...) the Antecedent, and Affirmation of the Consequent . They were then required to evaluate conclusion uncertainty as a function of two degrees of asserted uncertainty in the major conditional premise If p then it is very probable that q and if p then it is not very probable that q of the arguments from the first task that were otherwise unchanged. Results revealed an effect for asserted-uncertainty in two of the three argument forms. Marginal support was found for the hypothesis that perceived argument validity would be a predictor of performance. Experiment 2 investigated the way 40 adult participants combined two sources of asserted uncertainty, one in the major premise and another in the minor premise, when they had to score the uncertainty of the conclusion. The two most prominent kinds of responses were to choose the same likelihood as the weaker of the two expressed in the premises, or a lower one. However, the within-subject consistency was poor. Theoretical implications are discussed. (shrink)