This mainly historical paper provides a comprehensive discussion of the (heretoforth neglected) evidence of Peripatetic syllogistic in Sextus Empiricus. The paper sets out to show that it is likely that in Sextus (and Apuleius) there is valuable evidence of a transitional period in later ancient logic that is marked out as such by a number of characteristics, which include the following: (i) A Peripatetic term ‘categorical syllogism’ is newly in use, but no term ‘hypothetical syllogism’ has been (...) established yet. (ii) Stoic and Peripatetic logic are treated as complementing each other. (iii) The reversion of quantified propositions from predicate-subject to subject-predicate formulation is still fairly new. (iv) The so-called crocodile example is used to show that induction lacks the feature of concluding by necessity that is a defining mark of Aristotelian syllogisms. (v) The use of the expression katholikê protasis for categorical universal premise-propositions is distinctive of the period. (vi) The argument forms displayed by Sextus’ three examples appear to be indirectly related to the soon-to-appear Platonist hypothetical syllogistic. (vii) There are parallels that suggest that Sextus’ source belongs to the same historical period of logic as Apuleius’ source and as some probably recent source of Alexander of Aphrodisias’ Prior Analytics commentary (that is presented along with some later views and arguments, which may include Alexander’s own). Small differences between the three authors show that Sextus did not draw from the Greek handbook that was Apuleius’ source. (shrink)

ABSTRACT: Galen’s Institutio Logica is the only introduction to logic in Greek that has survived from antiquity. In it we find a theory that bears some resemblance to propositional logic. The theory is commonly understood as being essentially Stoic. However, this understanding of the text leaves us with a large number of inconsistencies and oddities. In this paper I offer an comprehensive alternative interpretation of the theory. I suggest that it is Peripatetic at base, and has drawn (...) on Stoic elements, but adapted them to an overall decidedly non-Stoic conception of logic and language, a conception indebted to Aristotelian logic in many respects. This interpretation makes it possible to reduce the seeming inconsistencies dramatically. The Peripatetic theory on which Galen draws was possibly developed in the first century BCE. Importantly, it differs from Stoic logic in that it shuns the latter’s syntactic approach, and considers certain linguistic assumptions and language conventions as part of the logical theory itself. My reconstruction of the theory results in a logic of propositions which differs wildly both from Stoic logic and from the ‘classical’ propositional logic of the 20th century. Interestingly, though, the theory in Galen shows that the ancients grappled with a number of logico-linguistic problems that over the last two decades have again become a matter of debate among contemporary logicians and linguists. (shrink)

The essay is an attempt to map the philosophical and soteriological horizons of the thought-world of Raimon Panikkar who is quintessentially and uniquely a Hindu peripatetic philosopher. In trying to locate the ‘Hindu’ character of Panikkar’s philosophical thinking, the focus is on the civilizational matrix called ‘Hinduism’ which is at once meta- physical and mythico-logical, existential and ethical, ecological and ecumenical. In a significant sense this is what prompted Panikkar to develop a hermeneutic of dialogue between the Abrahamic and (...) the Indic, more specifically, the worldviews of the Christian, Buddhist, and the Hindu. A phenomenological analysis of the ‘life-world ’of Christians in South India will attest to this. In this philosophical and soteriological journey, Panikkar identifies various problems encountered in comparative philosophy and religion. He argues for the case of what he calls imparative philosophy which employs diatopical hermeneutics in etching the contours for a meaningful dialogue among the various civilisations, religions and philosophies of the world. Keywords; Panikkar, Hindu, Christian, Buddhist, imperative philosophy, diatopical hermeneutics. (shrink)

ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i.e. modus ponens (or Law of Detachment). ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call (...) any arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)

ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for both Stoic and early Peripatetic logic, and have often been used as such – in particular for early Peripatetic hypothetical syllogistic and Stoic propositional logic. By contrast, this paper explores the role Alexander himself played in the development and transmission of those theories. There are three areas in particular where he seems to have made a difference: First, he drew a connection between certain passages (...) from Aristotle’s Topics and Prior Analytics and the Stoic indemonstrable arguments, and, based on this connection, appropriated at least four kinds of Stoic indemonstrables as Aristotelian. Second, he developed and made use of a specifically Peripatetic terminology in which to describe and discuss those arguments – which facilitated the integration of the indemonstrables into Peripatetic logic. Third, he made some progress towards a solution to the problem of what place and interpretation the Stoic third indemonstrables should be given in a Peripatetic and Platonist setting. Overall, the picture emerges that Alexander persistently (if not always consistently) presented passages from Aristotle’s logical œuvre in a light that makes it appear as if Aristotle was in the possession of a Peripatetic correlate to the Stoic theory of indemonstrables. (shrink)

ABSTRACT: A very brief summary presentation of western ancient logic for the non-specialized reader, from the beginnings to Boethius. For a much more detailed presentation see my "Ancient Logic" in the Stanford Encyclopedia of Philosopy (also on PhilPapers).

ABSTRACT: The 3rd BCE Stoic logician "Chrysippus says that the number of conjunctions constructible from ten propositions exceeds one million. Hipparchus refuted this, demonstrating that the affirmative encompasses 103,049 conjunctions and the negative 310,952." After laying dormant for over 2000 years, the numbers in this Plutarch passage were recently identified as the 10th (and a derivative of the 11th) Schröder number, and F. Acerbi showed how the 2nd BCE astronomer Hipparchus could have calculated them. What remained unexplained is why Hipparchus’ (...) logic differed from Stoic logic, and consequently, whether Hipparchus actually refuted Chrysippus. This paper closes these explanatory gaps. (1) I reconstruct Hipparchus’ notions of conjunction and negation, and show how they differ from Stoic logic. (2) Based on evidence from Stoic logic, I reconstruct Chrysippus’ calculations, thereby (a) showing that Chrysippus’ claim of over a million conjunctions was correct; and (b) shedding new light on Stoic logic and – possibly – on 3rd century BCE combinatorics. (3) Using evidence about the developments in logic from the 3rd to the 2nd centuries, including the amalgamation of Peripatetic and Stoic theories, I explain why Hipparchus, in his calculations, used the logical notions he did, and why he may have thought they were Stoic. OPEN ACCESS LINK. (shrink)

This paper examines Ibn Taymiyya’s (1263–1328) critique of the Aristotelian logical tradition, with a particular focus on his theory of definition (ḥadd). Ibn Taymiyya argues that Aristotelian logic, premised upon fixed metaphysical categories, fails to serve as a practical instrument for epistemic inquiry and knowledge production, as it claims. Ibn Taymiyya’s critique can be divided into two main classes: general and metaphysical. His general criticisms undermine the validity of Aristotelian definitions through multiple dialectical arguments such as regress, disagreement, and (...) redundancy, showing that definitions are not epistemically useful. His metaphysical criticisms, on the other hand, strike at the foundations of Peripatetic metaphysics by rejecting the distinctions between a) quiddity and its existence, and between b) essential and concomitant predicates. I have also argued that Ibn Taymiyya’s position cannot be reduced to nominalism, empiricism, or conventionalism. Rather, his theory of meaning aligns more closely with modern pragmatics, wherein speech acts derive their meaning from their communicative, intentional, and contextual functions. (shrink)

Abu Nasr Muhammad Al-Farabi (870–950 AD), the second outstanding representative of the Muslim peripatetic after al Kindi (801–873 AD), was born in Turkestan about 870 AD. Al-Farabi’s studies commenced in Farab, then he travelled to Baghdad, where he studied logic with a Christian scholar named Yuhanna b. Hailan. Al-Farabi wrote numerous works dealing with almost every branch of science in the medieval world. In addition to a large number of books on logic and other sciences, he came (...) to be known as the “Second Teacher” (al-Mou’allim al-Thani), Aristotle being the first. One of Al-Farabi’s most important contributions was clarifying the func- tions of logic as follows: 1. He defined logic and compared it with grammar, and discussed the clas- sification and fundamental principles of science in a unique and useful manner. 2. He made the study of logic easier by dividing it into two categories: Takhayyul (idea) and Thubut (proof). 3. He believed that the objective of logic is to correct faults we may find in ourselves and in others, and faults that others find in us. 4. He said that if we do not comprehend logic, we must either have faith in all people, or mistrust all people, or differentiate between them. Such actions would be undertaken without a basis of evidence or experimen- tation. In this paper, I will analyse the functions of logic in Al-Farabi’s works, Enumeration of the Sciences, Book on the Syllogism, Book on Dialectic, Book on Demonstration and Ring Stones of Wisdom, in order to present his contributions in the field of logic. (shrink)

Shihab al-Din al-Suhrawardi was born around 1154, probably in northwestern Iran. Spurred by a dream in which Aristotle appeared to him, he rejected the Avicennan Peripatetic philosophy of his youth and undertook the task of reviving the philosophical tradition of the "Ancients." Suhruwardi's philosophy grants an epistemological role to immediate and atemporal intuition. It is explicitly anti-Peripatetic and is identified with the pre-Aristotelian sages, particularly Plato. The subject of his hikmat al-Ishraq --now available for the first time in (...) English--is the "science of lights," a science that Suhrawardi first learned through mystical exercises reinforced later by logical proofs and confirmed by what he saw as the parallel experiences of the Ancients. It was completed on 15 September 1186 and at sunset that evening, in the western sky, the sun, the moon, and the five visible planets came together in a magnificent conjunction in the constellation of Libra. The stars soon turned against Suhrawardi, however, who was reluctantly put to death by the son of Saladin, the sultan of Egypt, in 1191. (shrink)

This academic paper provides a historical reflection on the problem of the origin of science in order to determine the reasons for differences in determining the date and content of the first scientific achievements. The application of historical-genetic research methods in the disciplinary aspect contributes to the distinction of particular scientific programs in the science body frame with a different relationship between the object and subject of cognition, the internal logic of ideas and worldviews. As a result, the existing (...) research concerned with the conditions of knowledge function in different types of society or with the relations between the structure of knowledge and its purpose, was supplemented by an explication of forms of the continuity of program components – ontological, epistemological and axiological basis of specific scientific cognition/knowledge. In particular, it is established that the ancient world atomistic and peripatetic programs follow the structural pattern of the scientific explanation of the Pythagorean one (scientific and philosophical at the same time), contributing a new subject content in it. (shrink)

In this article I argue for the thesis that Alexander's main argument, in Ethical Problems I, is an attempt to block the implication drawn by the Stoics and other ancient philosophers from the double potential of use exhibited by human life, a life that can be either well or badly lived. Alexander wants to resist the thought that this double potential of use allows the Stoics to infer that human life, in itself, or by its own nature, is neither good (...) nor bad. Furthermore, I shall argue that Alexander's main argument establishes that human life, despite exhibiting a double potential of use, is by its own nature or intrinsically good. Finally, given that this is not a conclusion that the Stoics are likely to accept, I shall also contend that the argument should be regarded as conducted for the most part in foro interno, as a way of persuading the Peripatetics themselves of the falsity of the Indifference Implication, precisely because of the risk that such an implication be derived from their own theoretical framework. (shrink)

The idea that there is a coherent and morally relevant concept of sexual perversions has been increasingly called into question. In what follows, I will be concerned with two recent attacks on the notion of sexual perversion: those of Graham Priest and Igor Primoratz. Priest’s paper is the deeper of the two. Primoratz goes methodically through various accounts of sexual perversion and finds difficulties in them. This is no small task, of course, but unlike Priest he does not attempt to (...) provide any diagnosis of why any attempt to analyse the concept of sexual perversion must fail. Priest argues that sexual perversion is an “inapplicable concept”: the presuppositions that would allow us to make sense of the notion have been rightly rejected. Without the theoretical backdrop of an Aristotelian moral teleology, we cannot provide a satisfactory account of sexual perversion, for only such a teleological world-view allows us to give some sense to the idea that a sexual practice might be morally wrong because it is unnatural. Priest surveys accounts of perversion that don’t appeal to any idea of unnaturalness and rejects them—rightly I believe. But, Priest argues, Aristotle’s own moral teleology is part and parcel of his wider views about purpose in nature. This natural teleology has been shown to be explanatorily superfluous. Though some sciences still talk of functions, this can be understood in terms of contributions to evolutionary survival. Though there is considerable disagreement about the details of the right account of function, all versions of this scientifically respectable teleology are morally neutral: it would not follow from the fact that homosexual intercourse does nothing to propagate the agents’ genetic material to future generations that it is therefore morally wrong. Here too I think Priest is right. He also considers what he calls “Aristotelian revivalism” in Roger Scruton’s account of sexual perversion. I think Priest sells Aristotelianism short. I have no interest in defending Scruton’s own understanding of the Aristotelian moral framework nor his particular account of sexual perversion. I shall, however, argue that Aristotelian moral philosophy provides a more useful framework for thinking about these issues than Priest implies, and attempt to defend an account of sexual perversion within the context of this framework. (shrink)

In philosophy, especially in the rich Eastern philosophical heritage, the issue of revelation, which occupies an important place, was approached as a problem by the Eastern peripatetics and explained it as a special form of knowledge belonging to the highest level of reason. Al-Kindi, Farabi, Ibn Sina, Ibn Rushd, Ibn Khaldun and other Eastern philosophers, taking revelation beyond the religious framework, comprehensively examined it as a phenomenon presented to society as an independent and pure thought, guiding the development of separate (...) cultures and civilizations, uniting different peoples and nations around a single idea, and approached it from various aspects. As we have noted, despite the great importance that philosophers attach to this issue, since the issue of revelation in their worldview has not been studied at the appropriate level in Azerbaijan, this topic can be considered quite relevant. As a result of the rapid and intensive nature of information exchange, the human brain, overloaded with information, increases its knowledge and information base with every passing second; on the other hand, it shortens its life. Today, millions of "web" sites that embrace the world and are called "spider webs" have become a material force to a greater extent than at the beginning of the last century, and have succeeded in changing the balance of forces striving for leadership in the world in their favor. Religious feelings and our way of life, which is considered the spiritual treasure of people and has become national customs and traditions that have filtered through the memory of centuries, are losing their vitality and are giving way to the material interests of an increasingly globalized world. However, it is also a fact that the sense of holiness, which no ideology can destroy, and which is born with us from nature, cannot be subordinated to these interests. In this sense, we consider it more important to bring to the fore the saving function of revelation, its universal essence that can benefit and help global problems, not as a controversial problem. For this reason, the fact that the monograph resonates with the demands of the modern era also emphasizes its relevance. (shrink)

We can find a common point between the Islamic peripatetic (of Al-Farabi, Ibn Sina (Avicenna), and Ibn Rushd (Averroes) (1126-98)) and Enlightenment philosophies based on their use of rationality. The overall objective of this paper is to present some of the different aspects of rationality in these two philosophies. We can find a kind of congruence between these philosophies. They commonly defend universality, unity, and permanence of reason. They do not accept a priori truths, and emphasize the limits of (...) rationality. On their respective views, rationality corrects its mistakes gradually. This suggests that we can have a dialogue between Western Enlightenment and Islamic cultures through rationality. This paper aims to reconstruct Islamic peripatetic and Enlightenment philosophies on the basis of their notion of the rationality. It tries to show this by referring to the major Muslim peripatetic philosophers and to Enlightenment philosophy as described by Ernst Cassirer (1874-1945). (shrink)

As we have noted, in the philosophy of Eastern Peripateticism the problem of revelation has not yet been studied in a philosophical aspect. According to the Eastern Peripatetic, revelation, inspiration and dreams, as esoteric knowledge, have an intuitive character. Imagination plays a major role in their acquisition. It is directly related to the evolutionary stage of mental cognition. However, philosophers considered the divine to be the source of all three knowledge‟s of mental cognition. In these matters, they persistently emphasized, (...) that the origin of personality, the divine will are decisive factors. From this it becomes clear that the Eastern Peripatetics, commenting on their philosophical views, tried to reconcile religion with philosophy. (shrink)

The Paris Convention on Climate Change is a convention under the United Nations Framework Convention on Climate Change that deals with greenhouse gas emission reduction, coordination and financing issues. The Convention shall enter into force from 2020. The Paris Climate Convention is an international environmental law with stronger social norms than other international law areas. Furthermore, the national characteristics of the norm have been doubled as a result of adopting the nationally determined contribution as the most important mechanism. In this (...) context, this paper examines the issues of the Paris Climate Convention at the international legal level. We examine the issue of enhancing normative efficiency through international trials of the Paris Convention and the International Court of Justice. Second, we examine possible conflicts between the Paris Climate Convention and the WTO law. This is to look at the bilateral issues between the WTO and the Parisian climate treaty, which represents the interests of developmentalists in the basic framework of the confrontation between developmentalists and environmentalists. Of course, when the two norms are in harmony, the normative effectiveness of the Paris Climate Convention is increased. Third, we briefly discuss the role of the domestic courts in raising the Paris Climate Convention, human rights issues, and normative effectiveness. In the end, the Paris Climate Convention enhances the normative effectiveness and suggests ways for lawyers and key actors to move forward. (shrink)

In this article, the authors showed the wandering, the East consider revelations, inspirations and dreams from irrational knowledge, and they have an intuitive function as esoteric knowledge. On getting his image plays a big role. This is due to the improvement of the stage of mental cognition. But philosophers believe that divine knowledge, consisting of three sources of esoteric knowledge. Thus the philosophers of the East tried to match each other's philosophy and religion when they comment on their philosophical thought. (...) In this article, the authors found wandering, East believe the revelation, inspiration and dream of irrational knowledge, and they have the intuitive function, as esoteric knowledge. For its image plays an important role. It is associated with improved mental stage of knowledge. But philosophers believe that the divine knowledge, which consists of three sources of esoteric knowledge. Thus, philosophers tried to meet the East of philosophy and religion to each other when they comment on their philosophy. (shrink)

This is material I have used for teaching introductory level formal logic at Pomona College. The coverage is fairly standard--propositional calculus and basic first-order logic--but includes a little bit of more advanced material that are often omitted, in particular proof of soundness and completeness of propositional calculus. The proof system is a natural deduction style sequent calculus that Gerhard Gentzen presents in his "Die Wiederspruchsfreiheit der reinen Zahlentheorie" (1936). Exercise material and a proof checker are available online.

Trivalent theories of indicative conditionals are thought to be at odds with trivalent theories of presupposition, and in particular, with an adequate analysis of the presuppositions of conditionals. We address this challenge based on (i) a semantics for conditionals and modals that combines trivalence with context updates, and (ii) a principle for felicitous assertion that we call Avoid Void: do not assert a sentence that takes the value void everywhere in the context. This account highlights the semantic differences between conditionals (...) and other presupposition carriers, and yields the intuitively correct presuppositions of conditionals. Finally, we develop a trivalent logic C# ("C-sharp"), which implements Avoid Void at the level of reasoning. This yields a Strawsonian notion of entailment, on which false antecedents as well as contradictory premises do not allow one to infer arbitrary information. (shrink)

This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for Cut—elimination, but (...) the other does not.). (shrink)

This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, it is then shown how we can use pure higher-order (...) class='Hi'>logic to ask, and begin to answer, metaphysical questions with non-trivial implications. In particular, while we must reject the popular idea that structural differences between sentences correspond to parallel distinctions in the logical structure of extra-linguistic reality, it may still be possible to give a purely logical characterization of objectual aboutness and related notions. (shrink)

This essay reconsiders the concept of karma not as a mere moral law of retribution but as the ontological and phenomenological structure of dependent origination (pratītyasamutpāda). By integrating early Nikāya sources, Abhidharma analyses, and Mahāyāna elaborations, karma is explored as the logic that underlies existence itself. Rather than reducing karma to linear causation across lifetimes, this essay situates it in the framework of aśūnyatā—the emptiness of both self and phenomena (ātma-śūnyatā and dharma-śūnyatā). Karma, understood as conditional arising, becomes the (...) foundation upon which Buddhist philosophy, ethics, and soteriology unfold. The essay concludes that the recognition of karma as dependent arising provides the ground for liberation: by seeing karma as empty yet conditionally real, one realizes that freedom from the binding chain of action is possible. (shrink)

We explore some possibilities for developing epistemic logic using truthmaker semantics. We identify three possible targets of analysis for the epistemic logician. We then list some candidate epistemic principles and review the arguments that render some controversial. We then present the classic Hintikkan approach to epistemic logic and note—as per the ‘problem of logical omniscience’—that it validates all of the aforementioned principles, controversial or otherwise. We then lay out a truthmaker framework in the style of Kit Fine and (...) present six different ways of extending this semantics with a conditional knowledge operator, drawing on notions of implication and content that are prominent in Fine’s work. We demonstrate that different logics are thereby generated, bearing on the aforementioned epistemic principles. Finally, we offer preliminary observations about the prospects for each logic. (shrink)

Modal Interpretations of quantum mechanics distinguish between the realm of possibility, where the dynamical state determines what may be the case, and the realm of actuality, where the value state represents what actually is the case. In particular, the Modal-Hamiltonian Interpretation proposes an ontology in which there are no individual objects: quantum systems are characterized as non-individual bundles of properties. The aim of the present paper is to propose some first steps towards the development of a new modal logic (...) adapted to describe a possibilist modality in an ontology of properties. The main idea consists in conceiving possibility as fundamental and introducing actuality as an operator acting on possible facts. On this basis, propositions referring to possible facts and propositions referring to actual facts are distinguished, and some relations between the realm of possibility and the realm of actuality are introduced. (shrink)

At least since Aristotle’s famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to the doctrine of the open future--the doctrine that future contingent statements are not true. But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking back) it was the case that it would happen. How can it be that, looking forwards, it isn’t true that there will be a sea battle, while also being true (...) that, looking backwards, it was the case that there would be a sea battle? This tension forms, in large part, what might be called the problem of future contingents. A dominant trend in temporal logic and semantic theorizing about future contingents seeks to validate both intuitions. Theorists in this tradition--including some interpretations of Aristotle, but paradigmatically, Thomason (1970), as well as more recent developments in Belnap, et. al (2001) and MacFarlane (2003, 2014)--have argued that the apparent tension between the intuitions is in fact merely apparent. In short, such theorists seek to maintain both of the following two theses: (i) the open future: Future contingents are not true, and (ii) retro-closure: From the fact that something is true, it follows that it was the case that it would be true. It is well-known that reflection on the problem of future contingents has in many ways been inspired by importantly parallel issues regarding divine foreknowledge and indeterminism. In this paper, we take up this perspective, and ask what accepting both the open future and retro-closure predicts about omniscience. When we theorize about a perfect knower, we are theorizing about what an ideal agent ought to believe. Our contention is that there isn’t an acceptable view of ideally rational belief given the assumptions of the open future and retro-closure, and thus this casts doubt on the conjunction of those assumptions. (shrink)

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of (...) the original pure system with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). (shrink)

The paper tries to spell out a connection between deductive logic and rationality, against Harman's arguments that there is no such connection, and also against the thought that any such connection would preclude rational change in logic. One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form); but the paper points out a serious (...) obstacle to any such view. (shrink)

This article discusses various dangers that accompany the supposedly benign methods in behavioral evoltutionary biology and evolutionary psychology that fall under the framework of "methodological adaptationism." A "Logic of Research Questions" is proposed that aids in clarifying the reasoning problems that arise due to the framework under critique. The live, and widely practiced, " evolutionary factors" framework is offered as the key comparison and alternative. The article goes beyond the traditional critique of Stephen Jay Gould and Richard C. Lewontin, (...) to present problems such as the disappearance of evidence, the mishandling of the null hypothesis, and failures in scientific reasoning, exemplified by a case from human behavioral ecology. In conclusion the paper shows that "methodological adaptationism" does not deserve its benign reputation. (shrink)

This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the verdicts, hypotheses, or conjectures of any science. In work currently in progress, we argue for the unique suitability of LF for the formalization of logic, mathematics, syntax, and semantics. The present document specifies the language and (...) rules of LF, lays out some notational conventions, and states some basic technical facts about the system. (shrink)

Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much (...) more, I argue. "If you love me, kiss me", a conditional imperative, mixes a declarative antecedent ("you love me") with an imperative consequent ("kiss me"); it is satisfied if you love and kiss me, violated if you love but don't kiss me, and avoided if you don't love me. So we need a logic of three -valued imperatives which mixes declaratives with imperatives. I develop such a logic. (shrink)

The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in (...) particular, Löwenheim and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth. (shrink)

In the philosophy of logic, the Adoption Problem is a challenge to the claim that reasoners can, in certain ways, rationally change which logic they use. The (alleged) problem is that if someone does not already infer in accordance with some fundamental logical principles (such as Universal Instantiation or Modus Ponens), then they cannot rationally begin to do so: the “adoption” of these principles is either unnecessary or impossible. In the literature, three issues have emerged as especially contentious: (...) (1) How should we understand the argument for the Adoption Problem? What exactly is the argument’s conclusion, and how is it established, if at all? (2) How could someone who thinks that the rational adoption of logic is possible respond to the Adoption Problem? (3) What are the consequences of the Adoption Problem for related issues in the philosophy of logic? In this paper, we address each question in turn. We suggest that the Adoption Problem is best understood in the form of an inconsistent quartet of theses regarding logical inference. We classify positions on logical adoption in terms of which of these theses is abandoned, and we show that such a taxonomy of positions is useful for delineating the scope and consequences of the Adoption Problem. (shrink)

The present volume is a sequel to Deontic Logic: Introductory and Systematic Readings : its purpose is to offer a view of some of the main directions of research in contemporary deontic logic. Most of the articles included in Introductory and Systematic Readings represent what may be called the standard modal approach to deontic logic, in which de on tic logic is treated as a branch of modal logic, and the normative concepts of obligation, permission (...) and prohibition are regarded as analogous to the "alethic" modalities necessity, possibility and impossibility. As Simo Knuuttila shows in his contribution to the present volume, this approach goes back to late medieval philosophy. Several 14th century philosophers observed the analogies between deontic and alethic modalities and discussed the deontic interpretations of various laws of modal logic. In contemporary deontic logic the modal approach was revived by G. H. von Wright's classic paper 'Deontic Logic'. Certain analogies between deontic and alethic modalities are obvious and uncontroversial, but the standard approach has often been criticized on the ground that it exaggerates the analogies and tends to ignore those features of normative concepts which distinguish them from other modalities. (shrink)

In this paper, the authors show that there is a reading of St. Anselm's ontological argument in Proslogium II that is logically valid (the premises entail the conclusion). This reading takes Anselm's use of the definite description "that than which nothing greater can be conceived" seriously. Consider a first-order language and logic in which definite descriptions are genuine terms, and in which the quantified sentence "there is an x such that..." does not imply "x exists". Then, using an ordinary (...) logic of descriptions and a connected greater-than relation, God's existence logically follows from the claims: (a) there is a conceivable thing than which nothing greater is conceivable, and (b) if <em>x</em> doesn't exist, something greater than x can be conceived. To deny the conclusion, one must deny one of the premises. However, the argument involves no modal inferences and, interestingly, Descartes' ontological argument can be derived from it. (shrink)

As George Boole saw it, the laws of logic are the laws of thought, and by this he meant, not that human thought is actually governed by the laws of logic, but, rather, that it should be. Boole’s view that the laws of logic have normative implications for how we ought to think is anything but an outlier. The idea that violating the laws of logic involves epistemic impropriety has seemed to many to be just obvious. (...) It has seemed especially obvious to those who see propositional justification as more fundamental than doxastic justification. Whatever other principles are required for defining propositional justification, the laws of logic seem indispensable. The idea that violation of the laws of logic involves some sort of epistemic impropriety—whatever the peculiarities of our psychology may be—has served as a fixed point around which defenders of the fundamentality of propositional justification are united, whatever their other differences. This paper challenges that common thread in defenses of the fundamentality of propositional justification. It is argued that the laws of logic have no bearing whatever on epistemic justification. Once we see why this should be so, the way is paved for seeing why it is that doxastic justification is more fundamental than propositional justification. (shrink)

Multiple generality has long been known to cause confusion. For example, “Everyone has a donkey that is running” has two readings: either (i) there is a donkey, owned by everyone, and it is running; or (ii) everyone owns some donkey or other, and all such donkeys run. Medieval logicians were acutely aware of such ambiguities, and the logical problems they pose, and sought to sort them out. One of the most ambitious undertakings in this regard is a pair of massive (...) logical diagrams (magnae figurae) which map out the logical interrelations of two sets of doubly-general forms. These appear in a fourteenth-century MS of John Buridan’s Summulae de Propositionibus. In this paper, I present these diagrams, and determine the truth conditions of their different forms. To that end, I have developed a bespoke system of diagrams to display their truth conditions. As we will see, such forms present significant difficulties for an all-encompassing account of the role form plays in logic. Accordingly, they can tell us important things about the role logical form plays in Buridan’s account of logical foundations. (shrink)

In this paper I discuss a prevailing view by which logical terms determine forms of sentences and arguments and therefore the logical validity of arguments. This view is common to those who hold that there is a principled distinction between logical and nonlogical terms and those holding relativistic accounts. I adopt the Tarskian tradition by which logical validity is determined by form, but reject the centrality of logical terms. I propose an alternative framework for logic where logical terms no (...) longer play a distinctive role. This account employs a new notion of semantic. (shrink)

Burgess (1997), building on Quine (1953), convincingly argued that claims in quantified modal logic cannot be understood as synonymous with or logically equivalent to claims about the analyticity of certain sentences. According to modal normativism, metaphysically necessary claims instead express or convey our actual semantic rules. In this paper, I show how the normativist can use Sidelle’s (1992a, 1995) neglected work on rigidity to account for two important phenomena in quantified modal logic: the necessity of identity and the (...) substitutivity of identicals into modal contexts. (shrink)

Graham Priest distinguishes between two kinds of Sorites paradoxes: standard Sorites, such as the paradox of the Heap, and non-standard Sorites, such as the Ship of Theseus. The former concerns properties of objects, whereas the latter concerns their identity conditions. Priest notes that the standard Sorites has been solved in fuzzy logic and proposes a logic of fuzzy identity to solve the non-standard Sorites in a similar way. Ideally, a definition of fuzzy identity would satisfy the fuzzy equivalents (...) of the classical principles of identity: it should (i) be a fuzzy equivalence relation and (ii) validate a fuzzy version of the substitutivity of identicals. However, Priest’s definition fails to meet the latter requirement and only applies to a special case of the non-standard Sorites. I suggest an improvement on his logic that overcomes these shortcomings, provides the two Sorites with a unified solution, and also applies to reasoning about vague objects in general. (shrink)

The tableau-like system KE is generalized to intuitionistic propositional logic by means of labeled signed formulas and constraints between labels, mimicking the relational semantics. To improve on proof-search and exploiting the meaning of negation, we further endow the system with free-variables. The resulting system enjoys the subformula property and terminates, either with a proof or a finite countermodel, without any extra mechanism. Proof and countermodel search is guided by generalizations of traditional reasoning patterns.

If modus ponens is valid, then you should take up smoking.

One innovation in this paper is its identification, analysis, and description of a troubling ambiguity in the word ‘argument’. In one sense ‘argument’ denotes a premise-conclusion argument: a two-part system composed of a set of sentences—the premises—and a single sentence—the conclusion. In another sense it denotes a premise-conclusion-mediation argument—later called an argumentation: a three-part system composed of a set of sentences—the premises—a single sentence—the conclusion—and complex of sentences—the mediation. The latter is often intended to show that the conclusion follows from (...) the premises. The complementarity and interrelation of premise-conclusion arguments and premise-conclusion-mediation arguments resonate throughout the rest of the paper which articulates the conceptual structure found in logic from Aristotle to Tarski. This 1972 paper can be seen as anticipating Corcoran’s signature work: the more widely read 1989 paper, Argumentations and Logic, Argumentation 3, 17–43. MR91b:03006. The 1972 paper was translated into Portuguese. The 1989 paper was translated into Spanish, Portuguese, and Persian. (shrink)

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic thatnorms beliefas classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterizedegrees of determinacy. It applies the methodology above to focus ondegree (...) logic. This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allowdegreesof consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail. (shrink)

Gila Sher approaches knowledge from the perspective of the basic human epistemic situation—the situation of limited yet resourceful beings, living in a complex world and aspiring to know it in its full complexity. What principles should guide them? Two fundamental principles of knowledge are epistemic friction and freedom. Knowledge must be substantially constrained by the world (friction), but without active participation of the knower in accessing the world (freedom) theoretical knowledge is impossible. This requires a grounding of all knowledge, empirical (...) and abstract, in both mind and world, but the fall of traditional foundationalism has led many to doubt the viability of this ‘classical’ project. Sher challenges this skepticism, charting a new foundational methodology, foundational holism, that differs from others in being holistic, world-oriented, and universal (i.e., applicable to all fields of knowledge). Using this methodology, Epistemic Friction develops an integrated theory of knowledge, truth, and logic. This includes (i) a dynamic model of knowledge, incorporating some of Quine’s revolutionary ideas while rejecting his narrow empiricism, (ii) a substantivist, non-traditional correspondence theory of truth, and (iii) an outline of a joint grounding of logic in mind and world. The model of knowledge subjects all disciplines to demanding norms of both veridicality and conceptualization. The correspondence theory is robust and universal yet not simplistic or naive, admitting diverse forms of correspondence. Logic’s grounding in the world brings it in line with other disciplines while preserving, and explaining, its strong formality, necessity, generality, and normativity. (shrink)

Philosophical action theory seems to be in pretty good shape. The same may not be true for the study of human action in economics. Famous is the rant that the study of human action in economics gives reason to tremble for the reputation of the subject. But how does this come about? Since economic action is about action, the broader study must surely have a strong impact on the more specific field. The paper sets out, from the ground up, how (...) an essential concept in economic theory–the concept of competition–can fundamentally benefit from insights derived exclusively from analytical action theory broadly conceived. In doing so, the paper delivers on an old Austrian promise: it is sometimes claimed that Austrian economists understand competition better than most economists. This may be a bold claim, since Austrian economists have neither traced the understanding of subjectivity to its very origin (the theory of intentionality), nor have they traced their sympathy for methodological individualism in relation to market processes to its very ground (the theory of (human) action). This paper aims to fill this gap. Moreover, by grounding an Austrian view of competition in analytic action theory, it succeeds in avoiding the serious problems of the dominant equilibrium approach. By explaining competition as rivalry, the paper draws on the philosophy and logic of human action to bring the (economic) agent back into play. In this way, a case is made for an integrated view of Austrian theory as an amalgam of Austrian economics and analytic action theory. (shrink)