We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply (...) general propositions. We consider and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle’s with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality. (shrink)

ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; (...) Stoic basic principles of propositional logic; 4. Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments. (shrink)

reasons for the disappreciation as well as for the rehabilitation of Stoic logic; it is found in I. M. Bochenski's Ancient Formal Logic (Amsterdam, 1951), and it clearly portrays the difference in attitude of the logicians of the twentieth century towards the Stoic logical system.

This chapter contains sections titled: Introduction The Stoic Logical System Conclusion Bibliography.

In this paper I would like to argue that Stoic logic is a kind ofrelevant logic rather than the classical logic. To realize this purpose I willtry to keep as close as possible to Stoic calculus as expressed with the helpof their arguments.

This paper is a discussion of Gabriel, Hülser and Schlotter’s 2009 article on a possible causal relation between Stoic logic and Frege. The paper provides detailed argument for why Rudolf Hirzel should not be taken as the qualified middleman in philosophical discussion with whom Frege learned what he ‘borrowed’ without acknowledgement from Stoic logic. Additionally, this paper offers some modest findings about some aspects of Frege's and Hirzel's lives and work habits, which may help us understand (...) a little better Frege's connection to Hirzel and to Stoic logic as well as Frege’s failure to acknowledge the Stoics. This paper is a purely historical offshoot of my essay ‘Frege plagiarized the Stoics’. Zero direct insights into either Frege’s or Stoic philosophy are offered. OPEN ACCESS. Choose 'without proxy' below. (shrink)

This book uncovers and examines the confusion in antiquity between Aristotle's hypothetical syllogistic and Stoic logic, and offers a fresh perspective on the ...

This paper shows that, for the Hertz–Gentzen Systems of 1933, extended by a classical rule T1 and using certain axioms, all derivations are analytic: every cut formula occurs as a subformula in the cut’s conclusion. Since the Stoic cut rules are instances of Gentzen’s Cut rule of 1933, from this we infer the decidability of the propositional logic of the Stoics. We infer the correctness for this logic of a “relevance criterion” and of two “balance criteria”, and (...) hence that a particular derivable sequent has no derivation that is “normal” in the sense that the first premiss of each cut is cut-free. We also infer that Cut is not admissible in the Stoic system, based on the standard Stoic axioms, the T1 rule and the instances of Cut with just two antecedent formulae in the first premiss. OPEN ACCESS. (shrink)

I argue that the Stoic logic is explosive. The claim applies to the Stoics' syllogistic in the strictest sense, because there is a provable syllogism which qualifies as a principle of explosion. It applies also to the general consequence operation, in the sense that every sentence is derivable from any pair containing both a sentence and the negation of the sentence. Finally, it applies to the connective of implication (conditional), in the sense that any conditional is derivable, providing (...) its antecedent is a conjunction of a sentence and the negation of the sentence. All three claims allow weakening, i.e., additions of extra premises to an inference or extra conjuncts to the antecedent of an implication, respectively. Consequently, no concept of relevance, let alone paraconsistency or connexivity is applicable to the Stoic logic; in particular, the Stoics' connective of implication is either material (Boolean) or formal (strict). (shrink)

This very brief paperli provides plausible answers to the two residual questions that Jamie Tappenden states, but leaves unanswered, in his 2024 paper ‘Following Bobzien: Some notes on Frege’s development and engagement with his environment’, namely, why Frege read Sigwart’s Logik and what caused Frege to read Prantl. (This paperli is merely historical and offers no special philosophical insights of any sort.) ---------- OPEN ACCESS. Choose 'without proxy' below.

In this paper we give a detailed comparison of the key elements of Frege’s formal language of thought and apparently similar views in Stoic formal logic. That is, we compare their views on the following topics: connectives, negation, simple sentences, propositional content, predicates and their incompleteness, and quantifications. We show that in most of these cases the similarities between Frege’s views and the Stoic views are only superficial. Frege’s views are far more systematic, better developed and can (...) in no case directly or fully be traced back to Stoic ideas. Furthermore, we show that Prantl, pace Bobzien 2021, is in most of these cases not a reliable source with respect to Stoic logic and that it is very unlikely that Frege’s views on logic were influenced by Prantl’s interpretation of Stoic formal logic. (shrink)

This paper deals with Aristotelian and Stoic logic. In the first part the author writes about the history of logic and shows, why Stoic logic had not been studied properly from the Middle Ages up to the beginning of the 20th century, when an increasing interest in the study of Stoic logic is visible. The paper describes the character of Aristotelian and Stoic logic respectively. Stoic logic is first introduced (...) as a system of propositional logic. On this basis a complementarity between the two logical systems of Antiquity is stated. The ways to support the thesis that Stoic logic involved some features of predicative logic are shown at the end of the first part. The ways in which the two rival logical systems were perceived by the authors of the first centuries A. D., namely Galen and Boethius, is described in the second part. Galen is seen as the first to develop an objective synthesis of the two systems. In his Eisagogé dialektiké he tries to show the goals of both rival logical systems. Boethius, in his De hypotheticis syllogismis, is also combining the Aristotelian and the Stoic logic. However, his synthesis is different from Galen's because Boethius probably forms the synthesis unknowingly and indirectly through compiling his confused sources. (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich (...) contemporary discussion. Much of Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

ABSTRACT: A detailed presentation of Stoic theory of arguments, including truth-value changes of arguments, Stoic syllogistic, Stoic indemonstrable arguments, Stoic inference rules (themata), including cut rules and antilogism, argumental deduction, elements of relevance logic in Stoic syllogistic, the question of completeness of Stoic logic, Stoic arguments valid in the specific sense, e.g. "Dio says it is day. But Dio speaks truly. Therefore it is day." A more formal and more detailed account (...) of the Stoic theory of deduction can be found in S. Bobzien, Stoic Syllogistic, OSAP 1996. (shrink)

The majority of formal accounts attribute to Stoic logicians the classical truth-functional understanding of the material conditional and exclusive disjunction.These interpretations were disputed,...

Women have played a prominent role in environmental preservation in all societies, including societies facing serious environmental problems. Women in places like Nigeria’s Niger Delta carry out tasks such as farming, fetching of firewood for domestic use, fetching of water, and the like. These activities involve the use of natural resources and thus make women more vulnerable when there are problems such as oil pollution, gas flaring, and other related activities that endanger the environment. In the Niger Delta women have (...) protested against oil related activities that damage their environment. They have also participated in other events to conserve their environment. The paper adopts an ecofeminist perspective in critiquing environmental mismanagement in the Niger Delta. It highlights the fact that women are prominent in campaigning for a sustainable Niger Delta. There is need for writers from academic and social circles writing on the Niger Delta not to ignore the women’s voices. (shrink)

ABSTRACT: A detailed presentation of Stoic logic, part one, including their theories of propositions (or assertibles, Greek: axiomata), demonstratives, temporal truth, simple propositions, non-simple propositions(conjunction, disjunction, conditional), quantified propositions, logical truths, modal logic, and general theory of arguments (including definition, validity, soundness, classification of invalid arguments).

The first monograph on Stoic modal logic. Part 1 discusses the Stoic notion of propositions (assertibles, axiomata): their definition; their truth-criteria; the relation between sentence and proposition; propositions that perish; propositions that change their truth-value; the temporal dependency of propositions; the temporal dependency of the Stoic notion of truth; pseudo-dates in propositions. Part 2 discusses Stoic modal logic: the Stoic definitions of their modal notions (possibility, impossibility, necessity, non-necessity); the logical relations between the (...) modalities; modalities as properties of propositions; contingent propositions; the relation between the Stoic modal notions and those of Diodorus Cronus and Philo of Megara; the role of ‘external hindrances’ for the modalities; the temporal dependency of the modalities; propositions that change their modalities; the principle that something possible can follow from something impossible; the interpretations of the Stoic modal system by B. Mates, M. Kneale, M. Frede, J. Vuillemin and M. Mignucci are evaluated. -/- For a shorter, updated, English version of Part 1 of the book see S. Bobzien, ‘Stoic Logic’, in K. Algra et al. (eds), The Cambridge History of Hellenistic Philosophy, Cambridge 1999, 92-157. For a shorter, updated, English version of Part 2 of the book see S. Bobzien 'Chrysippus' Modal Logic and its Relation to Philo and Diodorus', in K. Doering / Th. Ebert (eds) Dialektiker und Stoiker (Stuttgart 1993) 63-84. (shrink)

This paper is an attempt to reject the classical interpretation of Stoic ethics as virtue ethics. The typical assumptions of this interpretation, that virtue is the supreme good and that happiness can be reduced to virtue, are questioned. We first lay out the conceptual framework of Stoic philosophy and present an outline of their reduction of happiness to virtue. The main part of the paper provides an argument for reinterpretation of virtue as rationality. In the last part of (...) the paper – more speculative – we argue against the possibility of reduction of happiness to virtue. The main point of the argument is the conceptual incompatibility of the two notions. (shrink)

The wider topic to which the content of this paper belongs is that of the relationship between formal logic and real argumentation. Of particular potential interest in this connection are held to be substantive arguments constructed by philosophers reputed equally as authorities in logical theory. A number of characteristics are tentatively indicated by the author as likely to be encountered in such arguments. The discussion centers afterwards, by way of specification, on a remarkable piece of argument quoted in Cicero’s (...) dialog On Divination and ascribed to Stoic thinkers. The Stoics’ formal theory of inference is summarily referred to in this context, with special emphasis on their basic deductive schemata (‘indemonstrables’), some of them recognizable as links in the overall structure of the quoted argument. The main lines of Cicero’s criticism of the Stoic argument are next commented upon, with emphasis on his implied view as to the requirements of a good argument. Towards the end of the paper, a few considerations are added on the changes in the prevailing style of argumentation conspicuous in the three famous Roman Stoics. (shrink)

Literature on the Stoa usually concentrates on historical accounts of the development of the school and on Stoicism as a social movement. In this 1977 text, Professor Rist's approach is to examine in detail a series of philosophical problems discussed by leading members of the Stoic school. He is not concerned with social history or with the influence of Stoicism on popular beliefs in the Ancient world, but with such questions as the relation between Stoicism and the thought of (...) Aristotle, the meaning and purpose of such Stoic paradoxes as 'all sins are equal', and the philosophical interrelation of Stoic physics and ethics. There are chapters on aspects of Stoic logic and on the thought of particular thinkers such as Panaetius and Posidonius, but ethical problems occupy the centre of the stage. (shrink)

The theory of mental models is a current cognitive approach trying to describe the way people make inferences. According to this theory, people reason from possibilities or models linked to sentences. Sometimes, such possibilities or models are transformed by the action of a semantic modulation. The point this paper is intended to make is that Stoic logic also has the machinery to explain semantic processes such as that of modulation. This is shown by means of the criterion Chrysippus (...) of Soli provided for conditional sentences and the theory of sign related to that criterion. (shrink)

After Plato's Forms, and Aristotle's substances, the Stoics posited the fundamental reality of lekta - the meanings of sentences, distinct from the sentences themselves. This volume analyses the resulting unique, complex, and consistent cosmic view in which lekta are the keystones of the structure of reality: they are all there is to say.

ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental (...) rules which establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out. (shrink)