This paper focuses on Aristotle’s discussion of PNC in Metaphysics Gamma and argues that the argument operates at three different levels: ontological, doxastic, and semantic through the invocation of three philosophical personae: the first one can only state what is otherwise unprovable, the second one can only confirm that we should trust PNC, the third one denies PNC and must be silenced. Aristotle cannot prove what is beyond proof. This situation results in a fundamental ambiguity in the figure of the (...) philosopher. The Metaphysics is written from the standpoint of an investigative thinker who admits her puzzlement before a question that will forever remain open and imagines another philosopher who has achieved a god-like insight into the first principles of all things. The path from the first figure to the second one, however, remains an enigmatic leap. (shrink)

Scholars often assert that Plato and Aristotle share the view that discursive thought is internal speech. However, there has been little work to clarify or substantiate this reading. In this paper I show Plato and Aristotle share some core commitments about the relationship of thought and speech, but cash out TIS in different ways. Plato and Aristotle both hold that discursive thinking is a process that moves from a set of doxastic states to a final doxastic state. The resulting judgments (...) can be true or false. Norms govern these final judgments and, in virtue of that, they govern the process that arrives at those judgments. The principal norm is consistency. However, the philosophers differ on the source of this norm. For Plato, persuasiveness and accuracy ground non-contradiction because internal speech is dialogical. For Aristotle, the Principle of Non-Contradiction grounds a Doxastic Thesis that no judgment can contradict itself. For Aristotle, metaphysics grounds non-contradiction because internal speech is monological. (shrink)

Aristotle gave seven arguments for the law of non-contradiction. The first one is against a special case of dialetheism, the view that only some contradictions are true, and other six arguments are mostly against trivialism, the view that everything and consequently every contraction is true. Aristotle never argued that dialetheism entails trivialism. Unlike Aristotle, Avicenna, in his defense of LNC, not only considers trivialism and argues against it, but also argues that dialetheism entails trivialism. The argument that dialetheism entails trivialism (...) is called explosion. It is usually known that the first argument for explosion is given by the twelfth century logician William of Soissons. In this paper, we will meet Avicenna’s different argument for explosion and then I will demonstrate that this argument is a non-sequitur. (shrink)

Why is there something rather than nothing? This paper explores one particular argument in favor of the answer that 'the existence of nothing' would amount to a logical contradiction. This argument consists of positing the existence of a novel entity, called a bion, of which all contingent things can be composed yet itself is non-contingent. First an overview of historical attempts to compile a systematic and exhaustive list of answers to the question is presented as context. Then follows an analysis (...) of how the antropic principle would manifest itself in a world that consists of information and at the same time conforms to modal realism. Next, a thought experiment introduces bions as the foundation of such a world, showing how under these circumstances the ultimate origin of all existing things would be explained. The non-contingent nature of bions themselves is subsequently argued via a discussion of the principle of non-contradiction. Finally, this theory centered on the existence of bions is integrated into the worldview of Popperian metaphysics. According to the latter's criteria, I conclude that bion theory provides an integral answer to why there is something rather than nothing. (shrink)

Hume’s Treatise, with its celebrated bundle theory of the self, is a significant contribution to the embryonic Newtonian experimental philosophy of the enlightenment. But the theory is inadequate as it stands, as the appendix to the Treatise makes clear. For this account of the self, apparently, rests on contradictory principles — propositions, fortunately, that can be reconciled, according to Hume. My paper is a critical exploration of Hume’s argument for this intriguing suggestion.

The aim of this paper is to present and analyze arguments provided for the Psychological Principle of Non-Contradiction which states that one cannot have, or cannot be described as having, contradictory beliefs. By differentiating two possible interpretations of PNC, descriptive and normative, and examining arguments provided for each of them separately I point out the flaws in reasoning in these arguments and difficulties with aligning PNC with the empirical data provided by research done in cognitive and clinical psychology. I claim (...) that PNC cannot be derived from any metaphysical stance regarding the mental phenomena and that having contradictory beliefs should be regarded as possible. Furthermore, I argue that interpreting a subject as having contradictory beliefs, and therefore abandoning PNC, can be more effective in explaining the phenomena of contradictory beliefs and irrational behaviour than solutions consistent with the PNC. (shrink)

The fundamental problem of Christology is the apparent contradiction of Christ as recorded at Chalcedon. Christ is human and Christ is divine. Being divine entails being immutable. Being human entails being mutable. Were Christ two different persons there’d be no apparent contradiction. But Chalcedon rules as much out. Were Christ only partly human or only partly divine there’d be no apparent contradiction. But Chalcedon rules as much out. Were the very meaning of ‘mutable’ and/or ‘immutable’ other than what they are, (...) there’d be no apparent contradiction. But the meaning is what it is, and changing the meaning of our terms to avoid the apparent contradiction of Christ is an apparent flight from reality. What, in the end, is the explanation of the apparent contradiction of Christ? Theologians and philosophers have long advanced many consistency-seeking answers, all of which increase the metaphysical or semantical complexity of the otherwise strikingly simple but radical core of Christianity’s GodMan. In this paper, I put the simplest explanation on the theological table: namely, Christ appears to be contradictory because Christ is contradictory. This explanation may sound complicated to the many who are steeped in the mainstream account of logic according to which logic precludes the possibility of true contradictions. But the mainstream account of logic can and should be rejected. Ridding theology of the dogma of mainstream logic illuminates the simple though striking explanation of the apparent contradiction of Christ — namely, that Christ is a contradictory being. Just as the simplest explanation to the apparent roundness of the earth has earned due acceptance, so too should the simplest explanation of the apparent contradiction of Christ. (shrink)

Ethics is of vital importance to the Swedish educational system, as in many other educational systems around the world.Yet, it is unclear how ethics should be dealt with in school, and prior research and evaluations have found serious problems regarding ethics in education.The field of moral education lacks clear and widely accepted definitions of key concepts, and these ambiguities negatively impact both research and educational practice. This thesis draws a distinction between three approaches to ethics in school – the descriptive (...) ethics approach, the value transmission approach, and the inquiry ethics approach – and studies in what way (if at all) they are prescribed by the national curriculum for the Swedish compulsory school, how they relate to students’ moral reasoning about technology choices and online behaviour, and what pedagogical merits and disadvantages they have. Hopefully, this both contributes to reducing the ambiguities of the field, and to answering the question of how ethics should be dealt with in education. The descriptive ethics approach asserts that school should teach students empirical facts about ethics, such as what views and opinions people have. The value transmission approach holds that school should mediate some set of predefined values to the students and make sure the students come to accept these values.The inquiry ethics approach is the view that school should teach students to reason and think critically about ethics and to engage in ethical inquiry. The role of ethics in the curriculum has not been studied in light of the above distinction, in prior research,and such an investigation is undertaken here.The results suggest that ethics has a prominent, but complicated, role in the Swedish national curriculum. Although no explicit distinction is drawn or acknowledged in the curriculum, all three approaches are prescribed throughout the curriculum, albeit to different degrees. In the general section of the curriculum, the value transmission and inquiry ethics approaches are more extensively prescribed than the descriptive ethics approach. It was found that most of the syllabi contained explicit references to ethics, while some only contained implicit references to ethics, and two syllabi lacked references to ethics altogether. In the syllabi, the inquiry ethics approach is the most dominant, both in the sense of being present in the most syllabi, and in the sense of being more strongly prescribed in many of the syllabi where several approaches occur.The value transmission approach has the weakest role in the syllabi. In total, the inquiry ethics approach is the approach most strongly prescribed by the curriculum. But prior research has shown that inquiry ethics is very rarely implemented in the classroom. In this thesis, it is found that the inquiry ethics and the value transmission approaches are incompatible, given certain reasonable interpretations, which makes the finding that inquiry ethics is rarely implemented less surprising, since value transmission is practiced in schools. Some possible causes, and some consequences, of this is discussed. The students, in their moral reasoning about technology choices, reasoned in accordance with several classical normative theories – including consequentialism, deontological ethics and virtue ethics – and in doing so, they expressed reasoning that in the discussion is found to be in conflict with the values of the value foundation in the curriculum. These findings complement earlier findings, for example that students in their actions contradict the value foundation, by adding that such conflicts also exist in their reasoning. The existence of these conflicts is found to be problematic for a value transmission approach. Many of the students defended very restrictive views on disclosing personal information online, and prior research as well as the present data has shown that adults typically hold views that are very similar to these, concerning how they think that young people ought to act online. On the other hand, youths’ actual online behaviour, as reported in earlier studies, differs considerably from this. In line with this, the students also seemed to endorse a form of private morals view, according to which moral choices are simply up to one’s own taste, which would yield an escape exit from the restrictive views mentioned above, and permit any behaviour. In the discussion, it is argued that this is the result of an attempt at value transmission from the grown-up community, probably including teachers, which might seem to work, since the students claim to hold certain views, but which likely instead constitutes a false security, since these values are not actually accepted, but only paid lip service to, and the adults are therefore wrong in their belief that the students are protected by a certain set of values (that they think the students are upholding), since the students in fact do not uphold, and therefore do not act based upon, these values. This situation risks making the students more vulnerable than had no value transmission attempt been taken in the first place. Hence, the attempted value transmission runs the risk of counteracting its purpose of helping the students acquire a safe online behaviour. Throughout the moral reasoning mentioned above, extensive variations in the students’ reasoning were found, both interpersonally and intrapersonally, both in the decision method and in the rightness criterion dimensions, as well as in between the dimensions.The existence of such variations is a novel finding, and while possible applications in future research are discussed, it is also noted that this existence constitutes a reason to question the successfulness of both the value transmission and the inquiry ethics endeavours of the educational system. The results and discussions described above highlight the importance of investigating the merits of the different approaches. Several arguments that arise from the material of this thesis are presented, evaluated and discussed. The ability of each approach to fulfil some alleged key aims of ethics education is scrutinised; their abilities to educate for good citizenship, to educate for quality of life of the individual, and to facilitate better educational results in other subjects are all investigated, as well as the ability of each approach to help counteract the influence from online extremist propaganda aimed at young people and to promote safe online behaviour in general. It is concluded that the inquiry ethics approach has the strongest support from the material of this thesis. Some consequences for school practice are discussed, and it is concluded that changing the role of ethics in the curriculum would be beneficial, downplaying the role of value transmission and further increasing, and making more explicit and clear, the role of inquiry ethics. It is also shown that there are strong reasons for the inclusion of a new subject in the Swedish compulsory education with special focus on ethics. 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It has long been recognized that negation in Aristotle’s term logic differs syntactically from negation in classical logic: modern external negation attaches to propositions fully formed, whereas Aristotelian internal negation forms propositions from sentential constituents. Still, modern external negation is used to render Aristotelian internal negation, as may be seen in formalizations of Aristotle’s semantic principles of non-contradiction and of excluded middle. These principles govern the distribution of truth values among pairs of contradictory propositions, and Aristotelian contradictories always consist of (...) an affirmation and a denial. So how should we formalize a false denial? In the literature, we find that a false denial is formalized by means of two negation signs attached to a one-place predicate. However, it can be shown that this rendering leads to an incorrect picture of Aristotle’s principles. In this paper, I propose a solution to this technical problem by devising a formal notation especially for Aristotelian propositions in which internal negation is differentiated from external negation. I will also analyze both principles, each of which has two logically equivalent forms, a positive and a negative one. The fact that Aristotle’s principles are distinct and complementary is reflected in my new formalizations. (shrink)

Celem tego tekstu jest rekonstrukcja i analiza argumentów przedstawianych za Psychologiczną Zasadą Niesprzeczności, stwierdzającą, że żaden podmiot nie może mieć sprzecznych przekonań lub być opisany jako posiadający sprzeczne przekonania. Poprzez rozróżnienie dwóch możliwych interpretacji PZN, deskryptywnej i normatywnej, oraz dokładne zbadanie argumentacji przedstawionej dla każdej z nich z osobna, wskazuję zawarte w nich błędy oraz problemy związane z uzgodnieniem ich z wynikami badań prowadzonych w psychologii poznawczej i klinicznej. Uzasadniam, dlaczego PZN nie może być wyprowadzona z żadnego ze stanowisk metafizycznych (...) dotyczących nastawień sądzeniowych i że posiadanie sprzecznych przekonań powinno być uznane za możliwe. Następnie piszę, dlaczego zinterpretowanie niektórych podmiotów jako posiadających sprzeczne przekonania może być bardziej efektywne w wyjaśnianiu przypadków nieracjonalnego zachowania niż rozwiązania zgodne z PZN. (shrink)

We here attempt to address certain criticisms of the philosophical import of the so-called Brazilian approach to paraconsistency by providing some epistemic elucidations of the whole enterprise of the logics of formal inconsistency. In the course of this discussion, we substantiate the view that difficulties in reasoning under contradictions in both the Buddhist and the Aristotelian traditions can be accommodated within the precepts of the Brazilian school of paraconsistency.

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.

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)