Since a clear account of the fallacy of false disjunctive syllogism is missing in the literature, the fallacy is defined and its three types are differentiated after some preliminaries. Section 4 further elaborates the differentia specifica for each of the three types by analyzing relevant argument criticism of each, as well as the related profiles of dialogue. After defining false disjunctive syllogisms, it becomes possible to distinguish between a false dilemma and a false (...) disjunctive syllogism: section 5 analyzes their similarities and section 6 explains their differences. (shrink)

Disjunctive Syllogism, that is, the inference from 'not-A or B' and 'A', to 'B' can lead from true premises to a false conclusion if each of the sentences 'A' and 'not-A' is a statement of a partial truth such that affirming one of them amounts to denying the other, without each being the contradictory of the other. Such sentences inevitably occur whenever a situation which for its proper precise description needs the use of expressions such as 'most (...) probably true' and so forth, is described (less precisely) by sentences not containing such expressions. (shrink)

This paper argues that some widely used laws of implication are false, and arguments based upon them invalid. These laws are Exportation, Commutation, (as well as various restricted forms of these), Exported Syllogism and Disjunctive Syllogism. All these laws are false for the same reason – that they license the suppression or replacement in some position of some class of propositions which cannot legitimately be suppressed or replaced. These laws fail to preserve the property of (...) sufficiency of premiss set for conclusion. They are false, and can be seen to be false, independently of their respon- sibility for the paradoxes. Hence the main ‘independent’ argument for the paradoxes – that they follow from an allegedly immaculate set of laws – is undermined. Counterexamples to all these laws are produced. (shrink)

This work is a revision of the False Dilemma Fallacy (FDF). The formalized model (FM)of this fallacy has as its centerpiece a valid disjunctive syllogism, but the disjunctive premise is presumed to be false, thus making the argument unsound. Our revised model (FM2.0) focuses on the formal structure by comparing the given vs. the real argument, which is unsound because of its invalidity. This approach we believe is more pedagogically useful and a better explanation of (...) the fallacious nature of the FDF. It extends the identity of “formal fallacy” to the FDF. The abstract is formatted in two columns. The English abstract goes on this side. (shrink)

The relation between ex falso and disjunctive syllogism, or even the justification of ex falso based on disjunctive syllogism, is an old topic in the history of logic. This old topic reappears in contemporary logic since the introduction of minimal logic by Johansson. The disjunctive syllogism seems to be part of our general non-problematic inferential practices and superficially it does not seem to be related to or to depend on our acceptance of the frequently (...) disputable ex falso rule. We know that the acceptance of the ex falso is a sufficient condition for the acceptance of the disjunctive syllogism, but the interesting question is: is the ex falso a necessary condition for the acceptance of the disjunctive syllogism? The aim of the present paper is to discuss some possible ways to define systems that combines the preservation of the disjunctive syllogism with the rejection of the ex falso. (shrink)

The validity of argument by disjunctive syllogism has been denied by proponents of relevant and paraconsistent logic. DS is stigmatised for its role in inferences — most notably C.I. Lewis's derivation of that fallacy of irrelevance ex falso quodlibet — that involve both it and other rules of inference governing disjunction, or, to speak more precisely, other rules of inference taken to apply to the very same disjunction that obeys DS. In avoiding these inferences the road less travelled (...) is to deny the identity rather than to deny DS: what follows is, then, an exercise in disjoining disjunctions. (shrink)

In the present paper, we prove the normalization theorem and the consistency of the first-order classical logic with disjunctive syllogism. First, we propose the natural deduction system SCD for classical propositional logic having rules for conjunction, implication, negation, and disjunction. The rules for disjunctive syllogism are regarded as the rules for disjunction. After we prove the normalization theorem and the consistency of SCD, we extend SCD to the system SPCD for the first-order classical logic with (...) class='Hi'>disjunctive syllogism. It can be shown that SPCD is conservative extension to SCD. Then, the normalization theorem and the consistency of SPCD are given. (shrink)

Routley-Meyer type ternary relational semantics are defined for relevant logics including Routley and Meyer’s basic logic B plus the reductio rule and the disjunctive syllogism. Standard relevant logics such as E and R (plus γ ) and Ackermann’s logics of ‘strenge Implikation’ Π and Π ′ are among the logics considered.

We provide Routley-Meyer type semantics for relevant logics including Contractionless Ticket Entailment TW (without the truth constant t and o) plus reductio R and Ackermann’s rule γ (i.e., disjunctive syllogism). These logics have the following properties. (i) All have the variable sharing property; some of them have, in addition, the Ackermann Property. (ii) They are stable. (iii) Inconsistent theories built upon these logics are not necessarily trivial.

Relevantism, as a matter of definition, rejects classical logic as incorrect and adopts instead a relevant logic as encapsulating correct inference. It rejects classical logic on the grounds that the rule of Material Detachment, from A and not A or B to infer B,, sometimes leads from truth to falsity. Relevantism — although promoted by some relevant logicians, and an integral part of ultralogic — has recently encountered heavy, but interesting, criticism from relevance logicians themselves.

This paper offers general support for what Valerie Plumwood’s paper is trying to achieve by supporting the rejection of each of her four “false laws of logic”: exportation, illegitimate replacement, commutation (aka. permutation) and disjunctive syllogism. We start by considering her general characterizations of entailment, beginning with her stated definition of entailment as the converse of deducibility. However, this applies to a wide range of relevant logics and so is not able to be used as a criterion (...) for deciding what laws to include in a logic. In this context, we examine the two key differences between deduction from premises to conclusion and entailment from antecedent to consequent. We also consider her use of sufficiency as a general characterizing feature. We then discuss Plumwood’s syntactic criteria used to reject the first three of her false laws of logic and add the Relevance Condition in this context. We next consider semantic characterizing criteria for a logic. After making a case against using truth, we introduce Brady’s logic MC of meaning containment. We then examine the content semantics for MC and use it to reject all of Plumwood’s false laws of logic together with some others. We follow with the related Depth Relevance Condition, which is a syntactic cri- terion satisfied by MC. This clearly rejects the first three of these laws and many others, but not the fourth law. We conclude by giving our overall support for her general enterprise. (shrink)

Valerie Plumwood introduced in "Some false laws of logic" a series of arguments on how the rules Exported Syllogism, Disjunctive Syllogism, Commutation, and Exportation are not acceptable. Based on this we define the class of Plumwood algebras - logical matrices that do not verify any of these theses. Afterwards we provide conditional variants of the characteristic matrix of the logic RM3 that are also Plumwood algebras. These matrices are given an axiomatization based on First Degree Entailment (...) and are endowed with Belnap-Dunn Semantics. Finally we provide results of Soundness and Completeness in the strong sense for each of the defined variants. (shrink)

This chapter discusses the relation between Kant’s views on the foundations of syllogistic inference in ‘The False Subtlety of the Four Syllogistic Figures’, the views of eighteenth-century German authors who wrote on syllogism, and the conception of metaphysics that Kant developed in 1762-1764. Kant’s positions are, on the whole, rather original, even though they are not as independent from the intellectual context as Kant’s later, Critical philosophy. Despite Kant’s polemical tone, his views on syllogism are not primarily (...) motivated by polemical purposes. They are strongly influenced by his views on the method of metaphysics. (shrink)

Kant’s early work The False Subtlety of the Four Syllogistic Figures is typically considered a narrow, technical work still embedded in the tradition of Wolffian logic. I argue instead that it needs to be considered in light of Kant’s developing theory of cognition and his corresponding criticism of the Wolffian single faculty theory. Whereas the mature Kant criticizes the rationalists for misrepresenting the nature of sensibility, the urgent task facing him at this stage seems to have been a proper (...) determination of the nature of the understanding. On the Wolffian framework, the latter is defined in a merely nominal manner, in terms of a generic cognitive task: the distinct representation of the possible. On Kant’s view, however, distinctness entails a capacity to relate representations, which only happens in the act of judgment. Thus, the stated aim of the False Subtlety notwithstanding, the work attempts to reorganize the logical operations around the capacity to judge. In turn, by defining the higher faculty of cognition in terms of an act of relating representations, Kant wants to show that this faculty cannot stem from a power of representation that we share with non-rational animals and must instead rest on a different fundamental power, which at the time he alternatively calls “inner sense” or “consciousness”. (shrink)

This chapter focuses on one of the common fallacies in Western philosophy called 'affirming a disjunct' (AAD). It presents a few examples of fallacies in arguments caused by an ambiguity in the English word or. Because context makes the meaning clear in everyday usage, we might never have thought about this ambiguity before, but we actually use the word or in two very distinct ways. One type of or is known as “inclusive”, and the other type is known as “exclusive”. (...) AAD occurs when someone mistakenly believes that an inclusive or is an exclusive or. Importantly, not every or statement can fall prey to AAD. The argument known as a disjunctive syllogism sets out two possibilities that are mutually exclusive. When someone is dead, she/he is not alive, and when someone is alive, she/he is not dead. (shrink)

Is there some general reason to expect organisms that have beliefs to have false beliefs? And after you observe that an organism occasionally occupies a given neural state that you think encodes a perceptual belief, how do you evaluate hypotheses about the semantic content that that state has, where some of those hypotheses attribute beliefs that are sometimes false while others attribute beliefs that are always true? To address the first of these questions, we discuss evolution by natural (...) selection and show how organisms that are risk-prone in the beliefs they form can be fitter than organisms that are risk-free. To address the second question, we discuss a problem that is widely recognized in statistics – the problem of over-fitting – and one influential device for addressing that problem, the Akaike Information Criterion (AIC). We then use AIC to solve epistemological versions of the disjunction and distality problems, which are two key problems concerning what it is for a belief state to have one semantic content rather than another. (shrink)

Islamic law has an advanced legal theory, apart from the four basic decision-making methods, many judgment-gaining theories based on interpretation and reasoning have been derived which have been developed by Islamic jurists in the process. Islamic jurists have used some of their knowledge and techniques to correct the problematic results that arise from both the incorrect use of methods of obtaining judgments and the expansion of the scope of these methods. With these interdisciplinary studies, it was aimed to interpret the (...) criticisms directed against the analogy process and the causes accurately. One of the methods used at the point of revealing whether these criticisms and objections are based on a justified reason and evidence is the debating method. The method of debating, which has become an independent discipline along with fiqh and kalām in the Islamic scientific tradition, began to form during the periods when sects were formed (II century Hijri). The discipline of debate, which has found a practical field in the methodology of Islamic jurisprudence (fiqh), has been particularly effective in interpreting analogy (qiyas), which constitutes an important part of fiqh, and is even assumed to be among the methods of inference (istidlāl). Many Fasād al-waḍʻ (invalidity of an argument of syllogism) is one of the methods of debating has been used in uṣūl al-fiqh. Fasād al-waḍ‘ has been described as the binding of a provision to a cause (ʻillat) that is the opposite of what that cause requires. This is a situation that completely invalidates the cause. In Fasād al-wad‘, the objector proves that the analogy is erroneous by directing objections to the person who brings the evidence. Since Fasād al-wad‘ is a type of objection directed to the basis of the fiction of analogy, it has been accepted by Islamic jurists as one of the strong objections directed to the cause/analogy. However, the issue of which cause this type of objection can be directed against has been discussed among Islamic jurists. Hanafīs accept Fasād al-wad‘ as a sound objection method, but they think that it is not possible to object to the effective causes (al-ʻillat al-muaththirah) with it. Because, according to Hanafīs, the correctness of the effective quality has been revealed by the Qur’ān, the Sunnah and the consensus (ijmā’). Because these proofs do not produce false qualifications. According to Shafeis, all causes and provision can be objected with Fasād al-wad’. In fact, some Shāfi'ī jurists consider this method as a general type of objection, not aunique one to the analogy. Due to these different interpretations that Islāmic law schools attribute to the conditions of analogy and the nature of Fasād al-wad‘, different results may arise in furû issues. In this study, Fasād al-wad‘as a type of objection to the analogy process in Islamic legal procedure has been examined and the nature of Fasād al-wad‘ has been tried to be revealed by determining the comparative furû. Thus, it is aimed to identify and analyse the diversity of legal reasoning methods, which have an important place in the logic of law in Islam and can be gathered under the name of analogy. (shrink)

False dilemma is a specific form of reasoning : despite the fact that it is based on a deductively valid argument form, it is rightly depicted as fallacy. A systematic exposition of false dilemma is missing in theoretical approaches to fallacies. This article formulates six criteria for a well-grounded exposition of a fallacy, suggesting also a systematic exposition of false dilemma. These criteria can be used to both explain, and categorise, the various false dilemma fallacies. The (...) article introduces distinction between four types of false dilemma : False quandary, Defeasible sound quandary, False obstruction and Defeasible sound obstruction. The types of criticism appropriate for each variant of false dilemma are suggested. Being able to discover false dilemma in situations when it is important to make good and free choices is a significant dimension of critical thinking. It may liberate us from accepting the consequences that necessarily follow from prearranged alternatives, when these are not the only alternatives possible. It may also liberate us from refraining from actions on the basis of obstructive disjunctive statements. In that respect, the faculty of critical thinking directed at uncovering reasoning based on false dilemma may also initiate the discovery of new alternatives, or discover the ways of unifying seemingly opposing alternatives. Thus, a well-developed ability to understand the tricky argumentative moves of false dilemma may be a good step towards initiating some features of creative thinking. (shrink)

Consider the reasonable axioms of subjunctive conditionals if p → q1 and p → q2 at some world, then p → at that world, and if p1 → q and p2 → q at some world, then → q at that world, where p → q is the subjunctive conditional. I show that a Lewis-style semantics for subjunctive conditionals satisfies these axioms if and only if one makes a certain technical assumption about the closeness relation, an assumption that is probably (...) false. I will then show how Lewisian semantics can be modified so as to assure and even when the technical assumption fails, and in fact in one sense the semantics actually becomes simpler then. (shrink)

Aristotle's modal syllogistic has been an object of study ever since the time of Theophrastus; but these studies have been somewhat desultory. Remarkably, in the 1990s several new lines of research have appeared, with series of original publications by Fred Johnson, Richard Patterson and Ulrich Nortmann. Johnson presented for the first time a formal semantics adequate to a de re reading of the apodeictic syllogistic; this was based on a simple intuition linking the modal syllogistic to Aristotelian metaphysics. Nortmann developed (...) an ingenious de dicto analysis. Patterson articulated the links between the modal syllogistic and the metaphysics, using an analysis which strictly speaking is neither de re nor de dicto. My own studies in this field date from 1976, when my colleague Peter Roeper and I jointly wrote a paper "Aristotle's apodeictic syllogisms" for the XXIInd History of Logic Conference in Krakow. This paper contained the disjunctive reading of particular affirmative apodeictic propositions, which I still favour. Nonetheless, I did not consider that paper's results decisive or comprehensive enough to publish, and my 1981 book The Syllogism contained no treatment of the modal syllogism. The paper's ideas lay dormant till 1989, when I read Johnson's and Patterson's initial articles. I began publishing on the topic in 1991. Gradually my thoughts acquired a certain comprehensiveness and systematicity, till in 1993 I was able to take a semester's sabbatical to write up a draft of this book. (shrink)

We present evidence that preschool children oftentimes understand disjunctive sentences as if they were conjunctive. The result holds for matrix disjunctions as well as disjunctions embedded under every. At the same time, there is evidence in the literature that children understand or as inclusive disjunction in downward-entailing contexts. We propose to explain this seemingly conflicting pattern of results by assuming that the child knows the inclusive disjunction semantics of or, and that the conjunctive inference is a scalar implicature. We (...) make two assumptions about implicature computation in the child: that children access only a proper subset of the adult alternatives, and that children possess the adult capacity to strengthen sentences with implicatures. As a consequence, children are expected to sometimes not compute any implicatures at all, but in other cases they are expected to compute an implicature that is different from the adult implicature. We argue that the child’s conjunctive strengthening of disjunctive sentences realizes the latter possibility: the adult infers that the conjunction is false but the child infers that the conjunction is true. This behaviour is predicted when our assumptions about child development are coupled with the assumption that a covert exhaustive operator is responsible for strengthening in both the child and the adult. Specifically, children’s conjunctive strengthening is predicted to follow from the same mechanism used by adults to compute conjunctive free choice implicatures in response to disjunctive permission sentences. We furthermore argue that this parallel between the child and the adult extends to disambiguation preferences. In particular, we present evidence that children prefer to strengthen disjunctions to conjunctions, in matrix and embedded positions ; this result mirrors previous findings that adults prefer to compute free choice, at the root and under every. We propose a disambiguation strategy that explains the preference for conjunctive strengthening – by both the child and the adult – even though there is no general preference for exhaustification. Specifically, we propose that the preference for a conjunctive strengthening follows from a pragmatic preference for a complete answer to the Question Under Discussion. (shrink)

In this paper, I offer reasons to conclude that either belief impermissivism or credal impermissivism is false. That is to say, I argue against the conjunction of belief impermissivism and credal impermissivism. I defend this conclusion in three ways. First, I show what I take to be an implausible consequence of holding that for any rational credence in p, there is only one correlating rational belief-attitude toward p, given a body of evidence. Second, I provide thought experiments designed to (...) support the intuition that there are at least a few credences in some cases for which more than one belief-attitude is rationally permissible. Third, I provide one possible theoretical grounding for my position by appeal to Jamesian values. (shrink)

Logic is a central and highly useful part of philosophy. Its value is particularly evident when it comes to keeping our thinking about disjunctive probabilities clear. Because of the two meanings of “or”, logic can show how the likelihood of a disjunction being true can be determined quite easily. To gauge the chance that one of two or more exclusive alternatives is true, one need only sum up their respective likelihoods. And to know the chance that at least one (...) of two or more compatible alternatives is true, one simply has to figure the chance that it is false that all of them are false! (shrink)

Although inference to the best explanation is ubiquitous in science and our everyday lives, there are numerous objections to the viability of IBE. Many of these objections have been thoroughly discussed, however, at least one objection to IBE has not received adequate treatment. We term this objection the “Disjunction Objection”. This objection challenges IBE on the grounds that it seems that even if H is the best explanation, it could be that the disjunction of its rivals is more likely to (...) be true. As a result, IBE appears to license accepting a hypothesis that is more likely than not to be false. Despite these initial appearances, we argue that the Disjunction Objection fails to impugn IBE. (shrink)

In this paper I examine Avicenna’s conception of the consequence relation. I will consider in particular his categorical and hypothetical logics. I will first analyse his definition of the implication and will show that this relation is not a consequence relation in his frame. Unlike the medieval logicians, he does not distinguish explicitly between material and formal consequences. The arguments discussed in al-Qiyās, where the conclusion is true only in some matters, and would seem close to a material consequence for (...) that reason, are rejected explicitly as not syllogistic. He also rejects the ‘enthymemes’ unless they are complemented by their missing premise and the superfluous premises which, according to him, should promptly be ruled out. It seems then that the consequence relation in his theory is formal. It can be characterized as being ‘productivity in all matters’ or ‘necessary truth preserving’. It is illustrated by some single premise arguments, and above all by all kinds of syllogisms which, in his theory, are more numerous and various than in Aristotle’s one. The syllogism may contain two or more premises, including disjunctive ones. When it is hypothetical, it may lead to several conclusions. The premises may be in conflict, but then, the conclusion is false. He thus rejects the principle according to which ‘anything follows from a contradiction’. But, unlike what some scholars say, he does not admit any connexive principle. In the compound syllogisms, the conclusion follows by steps, each step taking two premises at once. (shrink)

Mody and Carey (2016) investigated children's capacity to reason by the disjunctive syllogism by hiding stickers within two pairs of cups (i.e., there is one sticker in cup A or B, and one in cup C or D) and then showing one cup to be empty. They found that children as young as 3 years of age chose the most likely cup (i.e., not A, therefore choose B; and disregard C and D) and suggested that these children were (...) representing the dependent relationship between A and B by applying the logical operator “or”. However, it is possible that children succeeded using simpler strategies, such as avoiding the empty cup and choosing within the manipulated pair. We devised a new version of the task in which a sticker was visibly removed from one of the four cups so that 2.5- to 5-year-old children (N = 100) would fail if they relied on such strategies. We also included a conceptual replication of Mody and Carey's (2016) original condition. Our results replicated their findings and showed that even younger children, 2.5 years of age, could pass above chance levels. Yet, 2.5-, 3- and 4-year-olds failed the new condition. Only 5-year-old children performed above chance in both conditions and so provided compelling evidence of deductive reasoning from the premise “A or B", where “or” is exclusive. We propose that younger children may instead conceive of the relationship between A and B as inclusive “or” across both versions of the task. (shrink)

Dâwûd al-Qarisî (Dâvûd al-Karsî) was a versatile and prolific 18th century Ottoman scholar who studied in İstanbul and Egypt and then taught for long years in various centers of learning like Egypt, Cyprus, Karaman, and İstanbul. He held high esteem for Mehmed Efendi of Birgi (Imâm Birgivî/Birgili, d.1573), out of respect for whom, towards the end of his life, Karsî, like Birgivî, occupied himself with teaching in the town of Birgi, where he died in 1756 and was buried next to (...) Birgivî. Better known for his following works on Arabic language and rhetoric and on the prophetic traditions (hadith): Sharḥu uṣûli’l-ḥadîth li’l-Birgivî; Sharḥu’l-Ḳaṣîdati’n-nûniyya (two commentaries, in Arabic and Turkish); Şarḥu’l-Emsileti’l-mukhtalifa fi’ṣ-ṣarf (two commentaries, in Arabic and Turkish); Sharḥu’l-Binâʾ; Sharḥu’l-ʿAvâmil; and Sharḥu İzhâri’l-asrâr, Karsî has actually composed textbooks in quite different fields. Hence the hundreds of manuscript copies of his works in world libraries. Many of his works were also recurrently printed in the Ottoman period. One of the neglected aspects of Karsî is his identity as a logician. Although he authored ambitious and potent works in the field of logic, this aspect of him has not been subject to modern studies. Even his bibliography has not been established so far (with scattered manuscript copies of his works and incomplete catalogue entries). This article primarily and in a long research based on manuscript copies and bibliographic sources, identifies twelve works on logic that Karsî has authored. We have clarified the works that are frequently mistaken for each other, and, especially, have definitively established his authorship of a voluminous commentary on al-Kâtibî’s al-Shamsiyya, of which commentary a second manuscript copy has been identified and described together with the other copy. Next is handled his most famous work of logic, the Sharhu Îsâghûcî, which constitutes an important and assertive ring in the tradition of commentaries on Îsâghûcî. We describe in detail the nine manuscript copies of this work that have been identified in various libraries. The critical text of Karsî’s Sharhu Îsâghûcî, whose composition was finished on 5 March 1745, has been prepared based on the following four manuscripts: (1) MS Kayseri Raşid Efendi Kütüphanesi, No. 857, ff.1v-3v, dated 1746, that is, only one year after the composition of the work; (2) MS Bursa İnebey Yazma Eser Kütüphanesi, Genel, No.794B, ff.96v-114v, dated 1755; (3) MS Millet Kütüphanesi, Ali Emiri Efendi Arapça, No. 1752, ff.48v-58r, dated 1760; (4) MS Beyazıt Yazma Eser Kütüphanesi, Beyazıt, No. 3129, ff.41v-55v, dated 8 March 1772. While preparing the critical text, we have applied the Center for Islamic Studies (İslam Araştırmaları Merkezi, İSAM)’s method of optional text choice. The critical text is preceded by a content analysis. Karsî is well aware of the preceding tradition of commentary on Îsâghûcî, and has composed his own commentary as a ‘simile’ or alternative to the commentary by Mollâ Fanârî which was famous and current in his own day. Karsî’s statement “the commentary in one day and one night” is a reference to Mollâ Fanârî who had stated that he started writing his commentary in the morning and finished it by the evening. Karsî, who spent long years in the Egyptian scholarly and cultural basin, adopted the religious-sciences-centered ‘instrumentalist’ understanding of logic that was dominant in the Egypt-Maghrib region. Therefore, no matter how famous they were, he criticized those theoretical, long, and detailed works of logic which mingled with philosophy; and defended and favored authoring functional and cogent logic texts that were beneficial, in terms of religious sciences, to the seekers of knowledge and the scholars. Therefore, in a manner not frequently encountered in other texts of its kind, he refers to the writings and views of Muhammad b. Yûsuf al-Sanûsî (d.1490), the great representative of this logical school in the Egyptian-Maghrib region. Where there is divergence between the views of the ‘earlier scholars’ (mutaqaddimûn) like Ibn Sînâ and his followers and the ‘later scholars’ (muta’akhkhirûn), i.e., post-Fakhr al-dîn al-Râzî logicians, Karsî is careful to distance himself from partisanship, preferring sometimes the views of the earliers, other times those of the laters. For instance, on the eight conditions proposed for the realization of contradiction, he finds truth to be with al-Fârâbî, who proposed “unity in the predicative attribution” as the single condition for the realization of contradiction. Similarly, on the subject matter of Logic, he tried to reconcile the mutaqaddimûn’s notion of ‘second intelligibles’ with the muta’akhkhirûn’s notion of ‘apprehensional and declarational knowledge,’ suggesting that not much difference exists between the two, on the grounds that both notions are limited to the aspect of ‘known things that lead to the knowledge of unknown things.’ Karsî asserts that established and commonly used metaphors have, according to the verifying scholars, signification by correspondence (dalâlat al-mutâbaqah), adding also that it should not be ignored that such metaphors may change from society to society and from time to time. Karsî also endorses the earlier scholars’ position concerning the impossibility of quiddity (mâhiyya) being composed of two co-extensive parts, and emphasizes that credit should not be given to later scholars’ position who see it possible. According to the verifying scholars (muhaqqîqûn), it is possible to make definition (hadd) by mentioning only difference (fasl), in which case it becomes an imperfect definition (hadd nâqis). He is of the opinion that the definition of the proposition (qadiyya) in al-Taftâzânî’s Tahdhîb is clearer and more complete: “a proposition is an expression that bears the possibility of being true or false”. He states that in the division of proposition according to quantity what is taken into consideration is the subject (mawdû‘) in categorical propositions, and the temporal aspect of the antecedent (muqaddam) in hypothetical propositions. As for the unquantified, indefinite proposition (qadiyya muhmalah), Karsî assumes that if it is not about the problems of the sciences, then it is virtually/potentially a particular proposition (qadiyya juz’iyyah); but if it is about the problems of the sciences, then it is virtually/potentially a universal proposition (qadiyya kulliyyah). This being the general rule about the ambiguous (muhmal) propositions, he nevertheless contends that, because its subject (mawdû‘) is negated, it is preferable to consider a negative ambiguous (sâliba muhmalah) proposition like “human (insân) is not standing” to be a virtually/potentially universal negative (sâliba kulliyyâh) proposition. He states that a disjunctive hypothetical proposition (shartiyya al-munfasila) that is composed of more than two parts/units is only seemingly so, and that in reality it cannot be composed of more than two units. Syllogism (qiyâs), according to Karsî, is the ultimate purpose (al-maqsad al-aqsâ) and the most valuable subject-matter of the science of Logic. For him, the entire range of topics that are handled before this one are only prolegomena to it. This approach of Karsî clearly reveals how much the ‘demonstration (burhân)-centered’ approach of the founding figures of the Muslim tradition of logic like al-Fârâbî and Ibn Sînâ has changed. al-Abharî, in his Îsâghûjî makes no mention of ‘conversion by contradiction’ (‘aks al-naqîd). Therefore, Karsî, too, in his commentary, does not touch upon the issue. However, in his Îsâghûjî al-jadîd Karsî does handle the conversion by contradiction and its rules. Following the method of Îsâghûjî, in his commentary Karsî shortly touches on the four figures (shakl) of conjuctive syllogism (qiyâs iqtirânî) and their conditions, after which he passes to the first figure (shakl), which is considered ‘the balance of the sciences’ (mi‘yâr al-‘ulûm), explaining the four moods (darb) of it. In his Îsâghûjî al-jadîd, however, Karsî handles all the four figures (shakl) with all their related moods (darb), where he speaks of fife moods (darb) of the fourth figure (shakl). The topic of ‘modal propositions’ (al-muwajjahât) and of ‘modal syllogism’ (al-mukhtalitât), both of which do not take place in the Îsâghûjî, are not mentioned by Karsî as well, either in his commentary on Îsâghûjî or in his Îsâghûjî al-jadîd. Karsî proposes that the certainties (yaqîniyyât), of which demonstration (burhân) is made, have seven, not six, divisions. After mentioning (1) axioms/first principles (awwaliyyât), (2) observata/sensuals (mushâhadât), (3) experta/empiricals (mujarrabât), (4) acumenalia (hadthiyyât), (5) testata (mutawâtirât), and (6) instictives (fitriyyât), that is, all the ‘propositions accompanied by their demonstrations,’ Karsî states that these six divisions, which do not need research and reflection (nazar), are called badîhiyyât (self-evidents), and constitute the foundations (usûl) of certainties (yaqîniyyât). As the seventh division he mentions (7) the nazariyyât (theoreticals), which are known via the badîhiyyât, end up in them, and therefore convey certainty (yaqîn). For Karsî, the nazariyyât/theoreticals, which constitute the seventh division of yaqîniyyât/certainties, are too numerous, and constitute the branches (far‘) of yaqîniyyât. Every time the concept of ‘Mughâlata’ (sophistry) comes forth in the traditional sections on the five arts usually appended to logic works, Karsî often gives examples from what he sees as extreme sûfî sayings, lamenting that these expressions are so widespread and held in esteem. He sometimes criticizes these expressions. However, it is observed that he does not reject tasawwuf in toto, but excludes from his criticism the mystical views and approaches of the truth-abiding (ahl al-haqq), shârî‘â-observant (mutasharri‘) leading sufis who have reached to the highest level of karâmah. (shrink)

The form of the conditional syllogism resembles that of the categorical syllogism, while its subject matter is at least a conditional premise, but its conclusion is always conditional conjunctive or disjunctive. This mixed structure to which we apply the rules of the categorical syllogism, is a structure of which Aristotle did not have an idea, and which the Stoics did not conceive, and which the non-Arabian logicians did not know until in modern times. But what we (...) have to notice here is the putting of a conditional matter in the form of the categorical syllogism, and it is this kind of hybridization, if we dare to say, which generated this mixed structure which appeared for the first time in the history of logic in the treatise on the logic of Ibn Sina and which can be considered a discovery by this author until proof to the contrary, and that the ancient Arabian logicians have taken the habit of exhibiting in their treatises. (shrink)

In this paper, we make a case for the disjunctive view of phenomenal consciousness: consciousness is essentially disjunctive in being either physical or non-physical in the sense that it has both physical and non-physical possible instances. We motivate this view by showing that it undermines two well-known conceivability arguments in philosophy of mind: the zombie argument for anti-physicalism, and the anti-zombie argument for physicalism. By appealing to the disjunctive view, we argue that two hitherto unquestioned premises of (...) these arguments are false. Furthermore, making use of the resources of this view, we formulate distinct forms of both physicalism and anti-physicalism. On these formulations, it is easy to see how physicalists and anti-physicalists can accommodate the modal intuitions of their opponents regarding zombies and anti-zombies. We conclude that these formulations of physicalism and anti-physicalism are superior to their more traditional counterparts. (shrink)

We show that the name “Lucas-Penrose thesis” encompasses several different theses. All these theses refer to extremely vague concepts, and so are either practically meaningless, or obviously false. The arguments for the various theses, in turn, are based on confusions with regard to the meaning of these vague notions, and on unjustified hidden assumptions concerning them. All these observations are true also for all interesting versions of the much weaker thesis known as “Gö- del disjunction”. Our main conclusions are (...) that pure mathematical theorems cannot decide alone any question which is not purely mathematical, and that an argument that cannot be fully formalized cannot be taken as a mathematical proof. (shrink)

Generalized Quantifier Theory defines superlative quantifiers at most n and at least n as truth-conditionally equivalent to comparative quantifiers fewer than n+1 and more than n \1. It has been demonstrated, however, that this standard theory cannot account for various linguistic differences between these two types of quantifiers. In this paper I discuss how the distinction between assertibility and truth-conditions can be applied to explain this phenomenon. I draw a parallel between the assertibility of disjunctions and superlative quantifiers, and argue (...) that those assertibility conditions are essentially modal. I use epistemic logic to formalize the assertibility conditions and revisit some of the linguistic puzzles related to superlative quantification. (shrink)

Boethius' treatise De Hypotheticis Syllogismis provided twelfth-century philosophers with an introduction to the logic of conditional and disjunctive sentences but this work is the only part of the logica vetus which is no longer studied in the twelfth century. In this paper I investigate why interest in Boethius acount of hypothetical syllogisms fell off so quickly. I argue that Boethius' account of compound sentences is not an account of propositions and once a proper notion of propositionality is available the (...) argument forms accepted by Boethius are seen to be incoherent. It was Peter Abaelard who first understood the nature of propositionality and propositional connectives and used this to criticise Boethius' claims in De Hypothetics Syllogismis. In place Boethius' confusion Abaelard offered a simple and correct account of the hypothetical syllogism. (shrink)

Ikhwan-i Safa is known as a group of thinkers who wrote treatises in the style of the first scientific encyclopedia in the history of Islamic thought. Ikhwan-i Safa, which emerged in the vicinity of Basra at a time when religious and political conflicts were intense, aims to clean the religion, which they believe has moved away from its essence with false information and false thoughts, with philosophy. For this purpose, the Ikhwan's views on science and wisdom, who use (...) all kinds of religious, philosophical and scientific knowledge with an eclectic approach, are important in understanding the scientific understanding of the classical age of Islamic thought. Ikhwan-i Safa, who states that they are the heirs of every thought they find true, regardless of its source, advises its members not to be hostile to any of the sciences, not to turn their backs on any of the books, and not to be attached to any of the sects with bigotry. In this study, the approaches of İhvân-ı Safâ to the science of logic will be discussed within their understanding of science based on this broad acquis. According to Ikhwan-i Safa, who defines logic as the measure of philosophy and the instrument of the philosopher, since philosophy is the highest of human endeavours after Prophethood, logic, which is the measure of philosophy, must also be the highest of measures and instruments. In the study, it will be emphasized how the Ikhwan approached the science of logic in his treatises in the context of concept, proposition and syllogism, which are the main subjects of classical logic, and whether they made a unique contribution to this science. (shrink)

In this paper is constructed an analogue of the square of opposition for propositions about relations between two non-empty sets. Unlike the classical square of opposition, the proposed scheme uses all logically possible syllogistic constants, formulated in V.I. Markin’s universal language for traditional positive syllogistic theories. This scheme can be called “Logical lantern”. The basic constants of this language are representing the five basic relations between two non-empty sets: equity, strict inclusion, reversed strict inclusion, intersection and exclusion (considered are only (...) the relations between sets, but not the relations of the sets to the universe). The other relations between sets are combinations (disjunctions) of the basic ones. There are 32 constants and 32 respective propositions, and the proposed diagram expresses and/or allows to deduce the logical relations among those propositions. The constructed scheme, making it possible to visually see the logical relations among propositions about relations between two non-empty sets, allows us to suggest considering logical relations not discussed previously: many-place Aristotelian-like logical relations among propositions: exhaustive _n_-place contrariety and exhaustive _n_-place subcontrariety (_n_ is a natural number, \(n>2\) ). (shrink)

Semantic Holism is the claim that any semantic path from inferential semantics (the indeterminate semantics forced by the classical inference rules of PC) reaches all the way to classical semantics if it is even one step long. In our joint paper Semantic Holism, Belnap and I showed that some such semantic paths are two steps long, but we left open a number of questions about the lengths of semantic paths. Here I answer the most important of these questions by showing (...) that there are infinitely long semantic paths that begin at inferential semantics but that do not even reach classical semantics. I do this by showing how to construct such an infinite semantic path from the members of the family of (n–1)-out-of-n-disjunction connectives. (shrink)

Principles of communication allow the listener to infer (upon hearing (1) that unless the speaker believed that (1alt) were false, the speaker would have uttered (1alt).

Malink’s interpretation is designed to validate Aristotle’s claims of validity and invalidity of syllogistic-style arguments, as well as his conversion claims. The remaining sorts of claims in Aristotle's text are allowed to fall out as they may. Thus, not all of Aristotle’s examples turn out correct: on some occasions, Aristotle claims that a given pair of terms yields a true (false) sentence of a given type although, under Malink’s interpretation, the sentence in question is false (true). Similarly, some (...) of Aristotle’s claims of invalidity of nonsyllogistic-style arguments come out false. For example, under Malink’s interpretation, ‘A applies to all B’ and ‘B necessarily applies to all C’ entail ‘A necessarily applies to some B’, contrary to what Aristotle says. (shrink)