The main objective o f this descriptive paper is to present the general notion of translation between logical systems as studied by the GTAL research group, as well as its main results, questions, problems and indagations. Logical systems here are defined in the most general sense, as sets endowed with consequence relations; translations between logical systems are characterized as maps which preserve consequence relations (that is, as continuous functions between those sets). In this sense, logics together (...) with translations form a bicomplete category of which topological spaces with topological continuous functions constitute a full subcategory. We also describe other uses of translations in providing new semantics for non-classical logics and in investigating duality between them. An important subclass of translations, the conservative translations, which strongly preserve consequence relations, is introduced and studied. Some specific new examples of translations involving modal logics, many-valued logics, para- consistent logics, intuitionistic and classical logics are also described. (shrink)

Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation into conditional connectives (...) may show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory. (shrink)

. In order to define universal logic in the most general way, I start by observing some essential dualisms within Logic. First, I illustrate philosophical dualisms: the two meanings of the word “Truth”, the two argumentative faculties of the human mind, the two ways of conceiving Logic as a whole (calculus/language), the two reasoning faculties of human mind, the two kinds of the metaphysics of logic (ontology/henology). Then I observe the formal dualisms between classical logic and intuitionist logic: the (...) two logical versions of a true proposition, the two kinds of a proof, the two kinds of a theoretical organization, the two kinds of square of opposition, the two main, mutual translations: the double negation translation KGG and its inverse translation PSR° (i.e. the application of the principle of sufficient reason suitably restricted). Incidentally, Béziau’s paradox is resolved as a consequence of this limitation in the application of PSR. As a comprehensive system of all previous dualisms but especially relying on the two kinds of theoretical organizations Universal Logic is defined as the following triadic structure: classical logic, intuitionist logic and their translations KGG and PSR°. In the light of this definition Béziau’s five questions about Universal Logic are successfully answered. In particular, the answer to the second question is obtained by taking into account that modal logic and Vasiliev’s original paraconsistent logic may be reduced to intuitionist logic; this result suggests an open question: whether only two main families of logics exist, i.e. the family of those reducible to classical logic and the family of those reducible to intuitionist logic. In order to answer Beziau’s first question the validity of Universal Logic for also Eastern thought is illustrated. (shrink)

Building on the notational principles of C. S. Peirce’s graphical logic, Pietarinen has tried to develop a propositional logic unfolding in the medium of sound. Apart from its intrinsic interest, this project serves as a concrete test of logic’s range. However, I argue that Pietarinen’s inaugural proposal, while promising, has an important shortcoming, since it cannot portray double-negation without thereby portraying a contradiction.

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is (...) translatable to a derivation in the associated display calculus. A key insight in this converse translation is a canonical representation of display sequents as labeled polytrees. Labeled polytrees, which represent equivalence classes of display sequents modulo display postulates, also shed light on related correspondence results for tense logics. (shrink)

We present epistemic multilateral logic, a general logical framework for reasoning involving epistemic modality. Standard bilateral systems use propositional formulae marked with signs for assertion and rejection. Epistemic multilateral logic extends standard bilateral systems with a sign for the speech act of weak assertion (Incurvati and Schlöder 2019) and an operator for epistemic modality. We prove that epistemic multilateral logic is sound and complete with respect to the modal logic S5 modulo an appropriate translation. The logical framework developed provides the (...) basis for a novel, proof-theoretic approach to the study of epistemic modality. To demonstrate the fruitfulness of the approach, we show how the framework allows us to reconcile classical logic with the contradictoriness of so-called Yalcin sentences and to distinguish between various inference patterns on the basis of the epistemic properties they preserve. (shrink)

A analysis of some concepts of logic is proposed, around the work of Edelcio de Souza. Two of his related issues will be emphasized, namely: opposition, and quasi-truth. After a review of opposition between logical systems [2], its extension to many-valuedness is considered following a special semantics including partial operators [13]. Following this semantic framework, the concepts of antilogic and counterlogic are translated into opposition-forming operators [15] and specified as special cases of contradictoriness and contrariety. Then quasi-truth [5] is (...) introduced and equally translated as a product of two partial operators. Finally, the reflections proposed around opposition and quasi-truth lead to a third new logical concept: quasi-opposition, borrowing the central feature of partiality and opening the way to a potential field of new investigations into philosophical logic. (shrink)

This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, (...) such as completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics. (shrink)

Interpretations are generally regarded as the formal representation of the concept of translation.We do not subscribe to this view. A translation method must indeed establish relative consistency or have some uniformity. These are requirements of a translation. Yet, one can both be more strict or more flexible than interpretations are. In this article, we will define a general scheme translation. It should incorporate interpretations but also be compatible with more flexible methods. By doing so, we want to account for methods (...) that seem to imply a sense of translation but are not reducible to interpretations. The main example will be the relative consistent proof between ZF and NBG given by Novak (1950). Further, we will explore a way of combining interpretations. This should account for truth conditions discarded by interpretations in translated theories. (shrink)

This paper aims to strengthen some algebraic results of subin- tuitionistic logic, giving a more strict characterization of some subintu- itionistic logics in the Abstract Algebraic hierarchy than was given in previous literature. We focus on subintuitionistic logics that are ob- tained by weakening the intuitionistic restrictions on Kripke frames, which are persistence, reflexivity, and transitivity. We prove that the subintuitionistic logics with persistence are algebraizable, while those without persistence are not. We also aim to get a more fine-grained understanding (...) of subintuitionistic logics and their modal companions, specifically with regards to subintuitionistic logics which require an om- niscient base world. As a result of this work, some of the gap can be closed between subintuitionistic logics which require there to be a base world that can access every other world and those that do not. (shrink)

Sentences containing definite descriptions, expressions of the form ‘The F’, can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ιx[F, G] is read as ‘The F is G’. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INFι of intuitionist negative free logic extended by such a quantifier, which was presented in (...) (Kürbis 2019), INFι is first compared to a system of Tennant’s and an axiomatic treatment of a term forming ι operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INFι in which the G of ιx[F, G] is restricted to identity. INFι is then compared to an intuitionist version of a system of Lambert’s which in addition to the term forming operator has an operator for predicate abstraction for indicating scope distinctions. The two systems will be shown to be equivalent through a translation between their respective languages. Advantages of the present approach over the alternatives are indicated in the discussion. (shrink)

I argue for the thesis (UL) that there are certain logical abilities that any rational creature must have. Opposition to UL comes from naturalized epistemologists who hold that it is a purely empirical question which logical abilities a rational creature has. I provide arguments that any creatures meeting certain conditions—plausible necessary conditions on rationality—must have certain specific logical concepts and be able to use them in certain specific ways. For example, I argue that any creature able to grasp theories must (...) have a concept of conjunction subject to the usual introduction and elimination rules. I also deal with disjunction, conditionality and negation. Finally, I put UL to work in showing how it could be used to define a notion of logical obviousness that would be well suited to certain contexts—e.g. radical translation and epistemic logic—in which a concept of obviousness is often invoked. (shrink)

Dynamic epistemic logic (DEL) extends purely modal epistemic logic (S5) by adding dynamic operators that change the model structure. Propositional dynamic logic (PDL) extends basic modal logic with programs that allow the de nition of complex modalities. We provide a common generalisation: a logic that is dynamic in both senses, and one that is not limited to S5 as its modal base. It also incorporates, and signi cantly generalises, all the features of existing extensions of DEL such as BMS [3] (...) and LCC [21]. Our dynamic operators work in two steps. First, they provide a multiplicity of transformations of the original model, one for each action in a purely syntactic action structure (in the style of BMS). Second, they specify how to combine these multiple copies to produce a new model. In each step, we use the generality of PDL to specify the transformations. The main technical contribution of the paper is to provide an axiomatisation of this general dynamic dynamic logic (GDDL). This is done by providing a computable translation of GDDL formulas to equivalent PDL formulas, thus reducing the logic to PDL, which is decidable. The proof involves switching between representing programs as terms and as automata. We also show that both BMS and LCC are special cases of GDDL, and that there are interesting applications that require the additional generality of GDDL, namely the modelling of private belief update. More recent extensions and variations of BMS and LCC are also discussed. (shrink)

Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical (...) forms of ordinary language sentences consequently may be taken to be much less misleading than logicians in the first half of the 20th century often thought them to be. This was realized by Richard Montague, who used the theory of types to translate fragments of ordinary language into a logical language. Semantics is commonly divided into lexical semantics, which studies the meaning of words, and compositional semantics, which studies the way in which complex phrases obtain a meaning from their constituents. The strength of type-logical semantics lies with the latter, but type-logical theories can be combined with many competing hypotheses about lexical meaning, provided these hypotheses are expressed using the language of type theory. (shrink)

The program put forward in von Wright's last works defines deontic logic as ``a study of conditions which must be satisfied in rational norm-giving activity'' and thus introduces the perspective of logical pragmatics. In this paper a formal explication for von Wright's program is proposed within the framework of set-theoretic approach and extended to a two-sets model which allows for the separate treatment of obligation-norms and permission norms. The three translation functions connecting the language of deontic logic with the language (...) of the extended set-theoretical approach are introduced, and used in proving the correspondence between the deontic theorems, on one side, and the perfection properties of the norm-set and the ``counter-set'', on the other side. In this way the possibility of reinterpretation of standard deontic logic as the theory of perfection properties that ought to be achieved in norm-giving activity has been formally proved. The extended set-theoretic approach is applied to the problem of rationality of principles of completion of normative systems. The paper concludes with a plaidoyer for logical pragmatics turn envisaged in the late phase of Von Wright's work in deontic logic. (shrink)

We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justi cations and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a logic of assertions and conjectures: looking at the (...) S4 modal translation, we give a de nition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is de ned and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, de ned as a hypothesis that in some situation the truth of p is epistemically necessary. (shrink)

The identity theory’s rise to prominence in analytic philosophy of mind during the late 1950s and early 1960s is widely seen as a watershed in the development of physicalism, in the sense that whereas logical behaviourism proposed analytic and a priori ascertainable identities between the meanings of mental and physical-behavioural concepts, the identity theory proposed synthetic and a posteriori knowable identities between mental and physical properties. While this watershed does exist, the standard account of it is misleading, as (...) it is founded in erroneous intensional misreadings of the logical positivists’—especially Carnap’s—extensional notions of translation and meaning, as well as misinterpretations of the positivists’ shift from the strong thesis of translation-physicalism to the weaker and more liberal notion of reduction-physicalism that occurred in the Unity of Science programme. After setting the historical record straight, the essay traces the first truly modern identity theory to Schlick’s pre-positivist views circa 1920 and goes on to explore its further development in Feigl, arguing that the fundamental difference between the Schlick-Feigl identity theory and the more familiar and influential Place-Smart-Armstrong identity theory has resurfaced in the deep and seemingly unbridgeable gulf in contemporary philosophy of consciousness between inflationary mentalism and deflationary physicalism. (shrink)

We consider a basic logic with two primitive uni-modal operators: one for certainty and the other for plausibility. The former is assumed to be a normal operator, while the latter is merely a classical operator. We then define belief, interpreted as “maximally plausible possibility”, in terms of these two notions: the agent believes \ if she cannot rule out \ ), she judges \ to be plausible and she does not judge \ to be plausible. We consider four interaction properties (...) between certainty and plausibility and study how these properties translate into properties of belief. We then prove that all the logics considered are minimal logics for the highlighted theorems. We also consider a number of possible interpretations of plausibility, identify the corresponding logics and show that some notions considered in the literature are special cases of our framework. (shrink)

The received view in the history of the philosophy of psychology is that the logical positivists—Carnap and Hempel in particular—endorsed the position commonly known as “logical” or “analytical” behaviourism, according to which the relations between psychological statements and the physical-behavioural statements intended to give their meaning are analytic and knowable a priori. This chapter argues that this is sheer legend: most, if not all, such relations were viewed by the logical positivists as synthetic and knowable only a posteriori. It (...) then traces the origins of the legend to the logical positivists’ idiosyncratic extensional or at best weakly intensional use of what are now considered crucially strongly intensional semantic notions, such as “translation,” “meaning” and their cognates, focussing on a particular instance of this latter phenomenon, arguing that a conflation of explicit definition and analyticity may be the chief source of the legend. (shrink)

This review places this translation and commentary on Book A of Prior Analytics in historical, logical, and philosophical perspective. In particular, it details the author’s positions on current controversies. The author of this translation and commentary is a prolific and respected scholar, a leading figure in a large and still rapidly growing area of scholarship: Prior Analytics studies PAS. PAS treats many aspects of Aristotle’s Prior Analytics: historical context, previous writings that influenced it, preservation and transmission of its manuscripts, editions (...) of its manuscripts, interpretations, commentaries, translations, and its influence on subsequent logic, philosophy, and mathematics. All this attention is warranted because Prior Analytics marks the origin of logic: the field that, among other things, asks of a given proposition whether it follows from a given set of propositions; and, if it follows, how we determine that it follows; and, if it does not follow, how we determine that it does not follow. This translation and commentary is not suitable for use in an undergraduate course. It has too many quirks that the teacher would want to warn against. A copy editor should have dealt with these things and with other matters such as incorrect punctuation and improper end-of-line divisions. The prose is heavily laden with glaring clichés. The one-page preface contains “longer than I care to remember”, “more than I can possibly list here”, “first and foremost”, and “last and by no means least”—a sentence later is devoted to thanking the “incredibly meticulous and helpful copy-editor”. A few pages later the translator reveals the need “to find a path between the Scylla … and the Charybdis …”. Moreover, the index is far from meeting the needs of undergraduate students. The attention to scholarly detail is not what one hoped for from Oxford University Press. At 26b10-15, this translation reads “let swan and white be chosen as white things” for what Smith correctly translates “let swan and snow be selected from among those white things”. At 41b16, “angles AB and CD” should read “angles AC and BD”. Despite this book’s flaws, it will be found useful if not indispensable for those currently engaged in Prior Analytics studies. The alternatives suggested to Robin Smith’s translation choices are often worth consideration. It is to be emphasized, however, that this book is unsuitable for those entering Prior Analytics studies. (shrink)

SALOQUM-1, the first treatise in The Cohesive Tetrad Treatise Series, develops the Logic of Sabda and examines its implications for human dignity and law in the age of data. Within the hierarchy of the Cohesive Tetrad corpus, the canonical book The Cohesive Tetrad: Jalan Menuju Kebenaran establishes the overall architecture of truth governance, the SALOQUM-1 Treatise occupies the intermediate doctrinal level, and a downstream corpus of journal articles translates its arguments into journal ready studies in law, ethics, public reason, and (...) artificial intelligence governance. SALOQUM names the ordered relation between Sabda, Logic, Qualia, and Mistika as four interlocking languages of truth, and this first treatise develops the language of the Logic of Sabda within that corpus. Building on the canonical book, the treatise reconstructs Sabda as Revelatory Word, the authoritative source of norm and telos, and contrasts this grounding with modern attempts to base dignity solely on capacity, evolutionary fitness, or social contract. It argues that these secular foundations are too fragile to withstand the pressures of large scale data, algorithmic governance, and market incentives that gradually erode the moral standing of persons. Within the four pillar architecture of Sabda, Logic, Qualia, and Mistika, the intentional spiritual dimension of journeying toward direct encounter with the transcendent, it proposes an epistemic and ethical framework for truth governance in which legal norms, institutional procedures, and AI systems are answerable to minimal axioms of human dignity. The Logic of Sabda is then used to reorient central domains such as the rule of law, rights discourse, public reason, and the regulation of digital technologies, with akhlak, moral character and conduct, presented as the observable surface where claims about truth, justice, and fairness must finally be tested. The treatise offers a set of disciplined conceptual tools for jurists, policymakers, and designers of data intensive systems who wish to protect human dignity while preserving the genuine achievements of modern law, science, and democratic deliberation. (shrink)

Schleiermacher’s Icoses is the first book-length study of the 1813 Academy address “Ueber die verschiedenen Methodes des Uebersetzens”; in addition to celebrating its 200 years of influence, the book undertakes a comprehensive examination of the whole argument, from its theory of hermeneutics to its foreignizing theory of translation and all the passing “poetic” elements on which Schleiermacher’s rhetoric always so heavily relied. The “icoses” in the title are specifically an articulation of the Gefühle/feelings that lie at the heart of Schleiermacher’s (...) hermeneutics—specifically, his insistence that feelings are shaped by society, and so seem “objective” or “universal,” but are experienced inwardly by each individual, so that they seem “subjective” and “private.” Research-based “feeling one’s way into an author” is guided by culture, and is therefore not, pace certain twentieth-century hermeneutical philosophers, mystical but “icotic.” -/- TESTIMONIA -/- Robinson's intriguing study of Schleiermacher's 1813 Academy address "On the Different Methods of Translating," which grew out of an article commemorating its bicentennial, is the first book-length commentary on the address. Robinson works meticulously through the entire text, both the German original and his own English translation, exposing its logical and other argumentative flaws mercilessly, but in order not to attack or dismiss it, rather to show that logic is not the right interpretive lens through which to view Schleiermacher's project. The right lens, Robinson suggests, is what he calls "icoses": social ecologies that shape our thought and convictions as members of a social group. The result is a fresh look at Schleiermacher's address and the hermeneutics that inform it, and one that generates surprising new insights into foreignization, feeling-based hermeneutics, and the Romantic ethos of estrangement. (Radegundis Stolze, Technische Universität Darmstadt) -/- Robinson's reading of Schleiermacher deals in detail with the whole address, and more, bringing out numerous problems that have remained hidden, dormant, and should be discussed. It provocatively picks up what any close reader feels: Schleiermacher's is not a highly coherent account of translation -­ it got some things right but left many gaps and contradictions. Robinson's inquiry suggests how the unresolved problems might be approached in an unexpected way: by a hermeneutic blurring of distinctions between the subjective and the objective, the psychological and the linguistic, the individual and the social. (Anthony Pym, Professor of Translation and Intercultural Studies Rovira i Virgili University, Visiting Professor Monterey Institute of International Studies). (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

This paper proposes a novel symbolic formalization of dialectical logic, synthesizing Hegelian ontological structures with insights from Buddhist philosophy to construct a rigorous "Dialectical Logic Symbol System" (DLSS). The system introduces a unique set of operators including Being ὄ, Nothing ⌀, Negation ¬, the Affirmation/Copula ≡, and the Self ἐ situated within a topological framework of four specific logical positions. These positions map the phenomenological movement of consciousness as it alternates between "entering" (nominalization) and "leaving" (adjectivization) conceptual terms. The (...) study systematically derives the logical categories of the Doctrine of Being, Essence, and Actuality (AC), demonstrating how determinate being and standard definitions are generated through the dialectical interplay of negation and position-shifting operators (such as Identity). Crucially, the system culminates in the Category of Substantial Relationships by introducing the operator of the "Self" ἐ. The "Self" ἐ functions as a transient catalytic agent that intervenes in the logical calculus to generate irreducible subjective determinations (represented as new terms a, b), thereby integrating the subjective construction of meaning into the formal derivation of objective reality. Furthermore, this paper utilizes DLSS to reconstruct the Three Laws of Thought of traditional formal logic. By translating dialectical formulas into propositional forms, the study proves that within a closed logical "Loop," the "Specific Law of Identity" (P=P) and "Specific Contradiction" (P∧¬P) can hold simultaneously without leading to inferential explosion. This paper argues against the "direct" validity of the Three Laws of Thought, positing that they are not absolute axioms but "specific" laws that hold only under specific loop paths. Thereby, the study demonstrates that contradiction is not the rendering of definition into meaninglessness, but the deepening of meaning, thus integrating traditional formal logic as a special state within dialectical movement. (shrink)

This essay aims to provide a modal logic and hyperintensional semantics for Charles Parsons (1980)'s treatment of rational intuition as a mathematical modality. Similarly to treatments of the property of knowledge in epistemic logic, I argue that rational intuition can be codified by a modal operator governed by the modal $\mu$-calculus. Via correspondence results between fixed point modal propositional logic and the bisimulation-invariant fragment of monadic second-order logic, a precise translation can then be provided between the notion of (...) `intuition-of', i.e., the cognitive phenomenal properties of thoughts, and the modal operators regimenting the notion of `intuition-that'. I argue that intuition-that can further be shown to entrain conceptual elucidation, by way of figuring as a dynamic-interpretational modality which induces the reinterpretation of both domains of quantification and the intensions and hyperintensions of mathematical concepts that are formalizable in monadic first- and second-order formal languages. Hyperintensionality is countenanced via a topic-sensitive epistemic two-dimensional truthmaker semantics. I relate the modal logic and hyperintensional semantics for the modality to self-knowledge, because of Gödel's footnotes and fragment in which (I) Gödel relates rational intuition to (i) the realistic aspect of idealism, and to (ii) self-knowledge, and (II) I countenance fixed points in automata for the epistemic modal mu-calculus (iii) to characterize the iteration of epistemic states, and (iv) to specify how Gödel's claim to Wang that intuition might be computational might be characterized. (shrink)

Can God’s foreknowledge change? There are two ways to interpret this question. First, is God capable of knowing future things that God, at present, does not know? Call this addition to divine foreknowledge. Second, is God capable of not knowing the things that God, at present, does know? Call this subtraction from divine foreknowledge. Peter Abelard rejected both possibilities. His rivals, Alberic of Paris and his school (the Albricani), held not only that both were possible, but even that both were (...) true: God comes to know new things, and even comes not to know things formerly known. Accordingly, the Albricani argued that these such alterations in divine knowledge do not entail that there is any alteration in God. Here, I show how they developed their arguments along these lines, anticipating a later debate between Ockham and Robert Holcot, and much later thinking about infinity in David Hilbert. -/- This paper also includes, by way of an appendix, the first ever Latin edition and English translation of key passages from two important 12th-century logical texts associated with Alberic's school: -/- H10 (Bibliothèque de l’Arsenal, 910, fols 163ra–186vb) and H17 (Staatsbibliothek zu Berlin – Stiftung Preußischer Kulturbesitz, lat. fol. 624, fols 87vb–96vb). (shrink)

Nāgārjuna's arguments in the Mūlamadhyamakakārikā rely extensively on modus tollens, yet this inference is invalid in the paraconsistent frameworks typically used to formalize the catuṣkoṭi. We develop a modal extension of Belnap-Dunn semantics to address this, expressed as: ¬□(v(P) = t) ∧ ¬□(v(P) = f) ∧ ¬□(v(P) = b) ∧ ¬□(v(P) = n). This formula applies self-reflexively, resolves longstanding interpretive debates regarding verses within Nāgārjuna’s Mūlamadhyamakakārikā and Vigrahavyāvartanī such as his “no thesis” defense, and bridges interpretive gaps between traditionally-designated (...) Eastern and Western logical traditions, providing a Western analytical translation of Indian dialectic into symbolic modal logic that is system-agnostic across K, T, S4, S5, non-normal logics, and neighborhood semantics. The modal operators function classically while the four-valued structure is modalized, preserving modus tollens at the level of modal reasoning while accommodating paraconsistent valuation at the object level. Self-application produces a non-terminating regress that is virtuous rather than vicious: each application is self-contained, demonstrating the unavailability of stable ground rather than constituting a failure to find it. (shrink)

The text "Artificial Intelligence and Analytic Pragmatism" was translated from the book by Robert B. Brand: Between Saying and Doing: Towards an Analytical Pragmatism. Chapter 3. Oxford University Press. pp. 69 - 92.

Husserl introduces a phenomenological concept called “motivation” early in the First Investigation of his magnum opus, the Logical Investigations. The importance of this concept has been overlooked since Husserl passes over it rather quickly on his way to an analysis of the meaningful nature of expression. I argue, however, that motivation is essential to Husserl’s overall project, even if it is not essen- tial for defining expression in the First Investigation. For Husserl, motivation is a relation between mental acts (...) whereby the content of one act make some fur- ther meaningful content probable. I explicate the nature of this relation in terms of “evidentiary weight” and differentiate it from Husserl’s notion of Evidenz, often translated as “self-evidence”. I elucidate the importance of motivation in Husserl’s overall phenomenological project by focusing on his analyses of thing-perception and empathy. Through these examples, we can better understand the continuity between the Logical Investigations and Husserl’s later work. (shrink)

A presente dissertação tem como objetivo uma apresentação da proposta de Charles Kielkopf, de tradução da lógica deôntica standard em uma lógica normal alética e de seusresultados quanto à construção de um sistema de lógica deôntica que capture conceitos eprincípios kantianos como necessidade causal e as formulações do Imperativo Categórico acerca do Reino da Natureza e do Reino dos Fins. Uma vez que este processo resulta em uma interpretação de aspectos da filosofia kantiana, optou-se inicialmente por uma apresentação em linhas (...) gerais destas concepções e, tendo em vista as dificuldades referentes a aplicabilidade de um processo de tradução entre princípios deônticos e ônticos,fez-se necessária também uma exposição acerca do problema das barreiras inferenciais, bem como de sua conseqüência mais imediata, a saber, o Dilema de Jörgensen. Num segundo momento, também foi feita uma caracterização dos sistemas modais normais, tanto deônticos quanto aléticos, bem como da noção de tradução entre lógicas e dos modelos de Dawson. O capítulo final consiste justamente num exame crítico da proposta de Kielkopf, o qual faz uso dos modelos de Dawson para desenvolver uma lógica deôntica a partir do sistema lógico K1. Tais modelos de Dawson permitem a definição de uma lógica deôntica em termos de modalidades aléticas iteradas, com o que este modelo constitui-se em uma maneira de evitar os problemas referentes às barreiras inferenciais. O desenvolvimento de uma alternativa para a atribuição de um status lógico a concepções deônticas não constitui,contudo, o aspecto inovador desta proposta, tal aspecto encontra-se justamente na utilização por Kielkopf, de seu modelo formal como uma ferramenta para a investigação de concepções filosóficas, no caso, as concepções kantianas já citadas. -/- The current dissertation has as its main objective an exposition and critical analysis of Charles Kielkopf's translation of the Standard Deontic Logic (SDL) into a normal alethic logic, and the resulting construction of a system of deontic logic that captures Kantian fundamental concepts and principles such as the concept of causal necessity and the formulations of the Categorical Imperative concerning Kingdom of Nature and Kingdom of Ends. Since this process results in an interpretation of aspects of the Kantian philosophy, it has been chosen,initially, a presentation in general lines of these concepts and, considering the difficulties regarding the applicability of a translation process between deontic and ontic principles, it was done necessary also an exhibition concerning the problem of the inferential barriers, as well as of his more immediate consequence, i. e., Jörgensen's Dilemma. In a secon dmoment, it was also made a characterization of normal modal systems, deontic ones andalethic ones, as well as of the notions of translation between logics and of Dawson modelling. The final chapter consists of a critical examination of Kielkopf's proposal, which uses Dawson modelling to develop a deontic logic based on the alethic system K1. Such Dawson modelling allows the definition of a deontic modalities in terms of iterated alethic modalities,therefore this model constitutes a way of avoiding the problems regarding inferential barriers. The development of an alternative for attribution of logical status to deontic concepts doesn't constitute, however, in an innovative aspect of this proposal, such aspect can be founded inthe use made by Kielkopf of his formal model as a tool for the investigation of philosophical concepts, such as the Kantian concepts already mentioned. (shrink)

Purpose – To review and discuss Luciano Floridi’s 2019 book The Logic of Information: A Theory of Philosophy as Conceptual Design, the latest instalment in his philosophy of information (PI) tetralogy, particularly with respect to its implications for library and information studies (LIS). Design/methodology/approach – Nine scholars with research interests in philosophy and LIS read and responded to the book, raising critical and heuristic questions in the spirit of scholarly dialogue. Floridi responded to these questions. Findings – Floridi’s PI, including (...) this latest publication, is of interest to LIS scholars, and much insight can be gained by exploring this connection. It seems also that LIS has the potential to contribute to PI’s further development in some respects. Research implications – Floridi’s PI work is technical philosophy for which many LIS scholars do not have the training or patience to engage with, yet doing so is rewarding. This suggests a role for translational work between philosophy and LIS. Originality/value – The book symposium format, not yet seen in LIS, provides forum for sustained, multifaceted and generative dialogue around ideas. (shrink)

Since the publication of the Remarks on the Foundations of Mathematics, Wittgenstein’s interpreters have endeavored to reconcile his general constructivist/anti-realist attitude towards mathematics with his confessed anti-revisionary philosophy. In this article, the author revisits the issue and presents a solution. The basic idea consists in exploring the fact that the so-called “non-constructive results” could be interpreted so that they do not appear non-constructive at all. The author substantiates this solution by showing how the translation of mathematical results, given by the (...) possibility of translation between logics, can be seen as a tool for partially implementing the solution Wittgenstein had in mind. (shrink)

In their recent paper Bi-facial truth: a case for generalized truth values Zaitsev and Shramko [7] distinguish between an ontological and an epistemic interpretation of classical truth values. By taking the Cartesian product of the two disjoint sets of values thus obtained, they arrive at four generalized truth values and consider two “semi-classical negations” on them. The resulting semantics is used to define three novel logics which are closely related to Belnap’s well-known four valued logic. A syntactic characterization of (...) these logics is left for further work. In this paper, based on our previous work on a functionally complete extension of Belnap’s logic, we present a sound and complete tableau calculus for these logics. It crucially exploits the Cartesian nature of the four values, which is reflected in the fact that each proof consists of two tableaux. The bi-facial notion of truth of Z&S is thus augmented with a bi-facial notion of proof. We also provide translations between the logics for semi-classical negation and classical logic and show that an argument is valid in a logic for semi-classical negation just in case its translation is valid in classical logic. (shrink)

In this paper, I investigate the relationship between preference and judgment aggregation, using the notion of ranking judgment introduced in List and Pettit. Ranking judgments were introduced in order to state the logical connections between the impossibility theorem of aggregating sets of judgments and Arrow’s theorem. I present a proof of the theorem concerning ranking judgments as a corollary of Arrow’s theorem, extending the translation between preferences and judgments defined in List and Pettit to the conditions on (...) the aggregation procedure. (shrink)

We present a formal account of subjectivity without external foundations. Over an extended LP/FDE truth alphabet, we axiomatize a self-ascriptive relation R(x,x) and a Subject Unicity (SU) scheme. We separate the linguistic lag operator X from the intra-perspectival successor σ, redefine same-place equivalence (≈), and license the identity sign (=) only via explicit upgrade anchors at the fix layer (Augenblick). Under a no-third-channel guard that blocks explosion while preserving the contradiction value B, we prove that within each connected cover the (...) set of subject candidates A/≈ collapses to a single class. This distinction between coordinate identity and event identity prevents premature global identification while yielding a constructive criterion of identity at stabilization. Conceptually, the system couples Hegelian dialectics with Lacanian failure of subsumption: contradiction is treated not as error but as structural motor. Aligning Tarskian/Gödelian limits with a Lacanian “delegated deficit,” we accordingly read R(x,x). The σ-translation captures how contradiction (B) is conserved and truth (T) emerges post hoc, offering a logic-driven reconstruction of dialectical temporality and the singular emergence of the subject. 본 논문은 외부 준거 없이 닫히는 형식 체계 위에서 주체의 자기귀속 R(x,x)과 주체 단일성(SU)을 공리화한다. 언어적 시차 연산자 X와 관점 내부 후속자 σ를 분리하고, 동일장소 동치 ‘≈’와 등호 승격(앵커) 규칙을 도입해 동일성의 작동 조건을 제시한다. 확장 LP/FDE 값층에서 모순값 B를 보존하고 제3채널 금지(No3) 가드를 둘 때, 연결 성분/커버 내부에서 주체-후보 집합 A/≈가 단일 동치류로 붕괴함을 증명한다. 이는 좌표 동일화와 사건 동일화를 구분하여 과도한 전역 동일시를 차단하고, Augenblick(고정층)에서만 ‘=’이 면허됨을 보인다. 결과적으로 주체는 속성의 총합이 아니라 사후적 표지에 의해 고정되는 규칙적 자기지시로 나타난다. 본문은 헤겔적 변증법(모순의 내재적 운동)과 라캉적 포섭 실패를 접합해 모순을 결함이 아니라 구조적 동력으로 제시하고, 타르스키/괴델류 한계를 라캉의 ‘대리-결손’과 접속해 R(x,x)를 해석한다. σ-번역은 모순(B)의 보존과 진리(T)의 사후적 출현을 기술하며, 이를 통해 변증법적 시간성과 주체의 단독성이 파라일관 논리 장치로 재구성될 수 있음을 보인다. (shrink)

The Marburg neo-Kantians argue that Hermann von Helmholtz's empiricist account of the a priori does not account for certain knowledge, since it is based on a psychological phenomenon, trust in the regularities of nature. They argue that Helmholtz's account raises the 'problem of validity' (Gueltigkeitsproblem): how to establish a warranted claim that observed regularities are based on actual relations. I reconstruct Heinrich Hertz's and Ludwig Wittgenstein's Bild theoretic answer to the problem of validity: that scientists and philosophers can depict the (...) necessary a priori constraints on states of affairs in a given system, and can establish whether these relations are actual relations in nature. The analysis of necessity within a system is a lasting contribution of the Bild theory. However, Hertz and Wittgenstein argue that the logical and mathematical sentences of a Bild are rules, tools for constructing relations, and the rules themselves are meaningless outside the theory. Carnap revises the argument for validity by attempting to give semantic rules for translation between frameworks. Russell and Quine object that pragmatics better accounts for the role of a priori reasoning in translating between frameworks. The conclusion of the tale, then, is a partial vindication of Helmholtz's original account. (shrink)

These remarks take up the reflexive problematics of Being and Nothingness and related texts from a metalogical perspective. A mutually illuminating translation is posited between, on the one hand, Sartre’s theory of pure reflection, the linchpin of the works of Sartre’s early period and the site of their greatest difficulties, and, on the other hand, the quasi-formalism of diagonalization, the engine of the classical theorems of Cantor, Gödel, Tarski, Turing, etc. Surprisingly, the dialectic of mathematical logic from its inception (...) through the discovery of the diagonal theorems can be recognized as a particularly clear instance of the drama of reflection according to Sartre, especially in the positing and overcoming of its proper value-ideal, viz. the synthesis of consistency and completeness. Conversely, this translation solves a number of systematic problems about pure reflection’s relations to accessory reflection, phenomenological reflection, pre-reflective self-consciousness, conversion, and value. Negative foundations, the metaphysical position emerging from this translation between existential philosophy and metalogic, concurs by different paths with Badiou’s Being and Event in rejecting both ontotheological foundationalisms and constructivist antifoundationalisms. (shrink)

This essay by Nishida Kitarō from 1927, translated into English here for the first time, is from the initial period of what has come to be called “Nishida philosophy” (Nishida tetsugaku), when Nishida was first developing his conception of “place” (basho). Nishida here inquires into the relationship between logic and consciousness in terms of place and implacement in order to overcome the shortcomings of previous philosophical attempts—from the ancient Greeks to the moderns—to dualistically conceive the relationship between being (...) and knowing in terms of subject-object or form-matter. During the course of articulating his novel approach to consciousness and cognition, Nishida discusses what he takes to be the weaknesses of Greek hylomorphism, Kantian (and neo-Kantian) dualism, and Husserlian phenomenology. Dissatisfied with the attribution of mere passivity to placiality, and turning away from consciousness objectified as a subject of statement, Nishida imparts to consciousness qua place a certain logical independence as an active yet un-objectifiable “predicate.” This investigation of consciousness as the unobjectifiable place for objectification leads Nishida to the notion of what precedes consciousness itself, a “place of nothing” (mu no basho) that envelops the dichotomized structures of subject-predicate, being-nothing, subject-object, universal-particular, et cetera. (shrink)

IMAGO TEXT 2020 ABSTRACTS -/- (German abstract below) The text presents a structural analysis and a logical theory of creativity. It argues that creativity emerges from the translation between two forms of precision, thus from the ubiquitous transformation between incompatible forms of thought and articulation. This transformation allows for unexpected surpluses and innovations, in conjunction with fallacies, waste and noise. Common myths and misconceptions – i.e. about creativity as a force in dire supply - are debunked, as are (...) mistaken strategies for creativity-enhancement. Instead, suggestions are offered as to how educational institutions can channel and enable ubiquitous energies – instead of investing much resources and effort into their suppression. -/- Der Text präsentiert eine strukturelle Analyse und eine logische Theorie der Kreativität. Er argumentiert, dass Kreativität aus der Übersetzung zwischen zwei Formen der Präzision hervorgeht, aus der allgegenwärtigen Transformation zwischen unvereinbaren Formen des Denkens und der Artikulation, was zu Überschuß und produktiven Abweichungen wie auch Abfall und Fehlschlüssen führt. Verbreitete Mythen und Missverständnisse – etwa zu Kreativität als Mangelware – werden diskutiert sowie Strategien zur Kreativitätsförderung. Es geht um Vorschläge, wie pädagogische Institutionen die stets vorhandenen kreativen Energien kanalisieren und ermöglichen können, anstatt sie mit viel Aufwand zu unterdrücken. (shrink)

This article advances a disciplined reconciliation between phenomenology and critical theory through a weak ontology of agency. Rather than ultimate foundations, it offers an operational framework of four strata – the pre-reflective (body and schema), the social (forms and fields), the pulsional-symbolic (logics of return and the signifier), and the projective (the temporal organization of action) – coordinated by two operators: epoché (descriptive opening) and negativity (the non-identical’s veto). A triadic method (description → negative test → re-description) governs inter-strata (...) shifts via escalation criteria (explanatory residue, strong circularity, semantic immunization, opaque overdetermination, temporal decoupling, indexing failure) and a downward rule whenever higher-level hypotheses prove merely nominal. Three rights of veto – primacy of the object, historicity of forms, and the ban on totalization – prevent local sovereignties. Canonical lexicons (Adorno, Heidegger, Sartre, Merleau-Ponty, Habermas) are translated as operators, not essences, under public conditions of critique (justifiability, contestability, reversibility). The upshot is a non-foundational realism: decisions are defeasible and auditable by a second reader with a transparent record of reasons. The paper closes with anticipated objections and methodological safeguards, and outlines application paths (aesthetics, social theory, law, conceptual history) without displacing the ontological focus. (shrink)

This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These (...) acts are not propositions; they do not have truth-values. Our formalization is related to the input/ output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL3 as a formalization of Kant’s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant’s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL3. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant’s theoretical philosophy. (shrink)

The phrase _secundum quid et simpliciter_ is the Latin expression translating and labelling the sophism described by Aristotle as connected with the use of some particular expression “absolutely or in a certain respect and not in its proper sense.” This paper presents an overview of the analysis of this fallacy in the history of dialectics, reconstructing the different explanations provided in the Aristotelian texts, the Latin and medieval dialectical tradition, and the modern logical approaches. The _secundum quid_ emerges as a (...) strategy that is based on the pragmatic dimension of arguments, and in particular the complex passage from an utterance (what is said) to its logical form (a proposition in an argument). The medieval and modern logical theories attempted to explain from different philosophical perspectives how the pragmatically enriched semantic representation can be achieved, justified, and most importantly manipulated. The different analyses of this fallacy bring to light various dimensions of the pragmatics of arguments, and the complex interdependence between context, meaning, and inferences. (shrink)

The Javanese philosophical concept of “Gemah Ripah Loh Jinawi” paints a vivid picture of a dreamed utopia, often translated as a land of abundant natural wealth, fertility, and profound peace and prosperity. While this vision frequently appears to remain an elusive ideal in contemporary reality, this article argues for a re-evaluation of its essence, moving beyond a purely materialist interpretation. We draw parallels between “Gemah Ripah Loh Jinawi” and concepts such as the Judaic notion of “Shalom” and the “pursuit (...) of happiness” embedded in Thomas Jefferson’s Declaration of Independence, demonstrating a shared yearning for a holistic well-being that transcends mere economic prosperity. Furthermore, by employing Neutrosophic Logic, we aim to analyze “Gemah Ripah Loh Jinawi” as a complex, multi-dimensional aspiration, acknowledging its degrees of truth, falsity, and inherent indeterminacy. This framework allows for a nuanced understanding of how this Javanese ideal seeks a complete abundance, blending material wealth with profound spiritual growth, offering a potent vision for human flourishing beyond the confines of modern materialism. (shrink)

This programmatic paper introduces a novel ontological and epistemological framework rooted in the concept of Phase Ontology, fundamentally re-envisioning the nature of knowledge, reality and consciousness. Departing from traditional representational, probabilistic and inferential models, we propose that meaning and order emerge not from static correspondence, but from asymptotic phase coherence-a dynamic process of resonant alignment between observer and observed. Drawing upon insights from quantum theory, the philosophy of mind and advanced systems theory, the paper synthesizes key concepts from previous (...) works, including the epistemic vector, phase-operated curvature, cyclical cognition and modularity as a topological principle. We argue that cognition is a recursive, four-phase process (recursion, iteration, asymptotic stabilization, reinitiation) where time is understood as a dynamic field of resonance rather than a linear progression. Central to this framework is the re-evaluation of modularity. We introduce the anthropic modularity function M(x) and the concept of a modular golden mean (M(x)≈σ/2), proposing that optimal system stability and intelligibility reside within a "quasi-crystalline" state of unstructured integration. This state, characterized by long-range order without translational symmetry, represents a critical "overload limit" for conventional, binary modes of understanding, yet it constitutes a highly coherent and adaptive form of organization, empirically suggested by the intricate structure of neural networks. Ultimately, this paper posits that any finite, perceived meaning is an inherently asymptotic and "binary" projection onto an underlying reality that exists "beyond any limits." It calls for a fundamental shift in scientific and philosophical inquiry, advocating for a new logic and mathematics capable of grasping phase relations and non-periodic orders. This approach fosters an epistemology of humility, acknowledging that knowledge is not a descriptive endpoint but a continuous, dynamic alignment within the resonant tapestry of existence. (shrink)

The purpose of this introduction is to give a rough overview of the discussion of the formalization of arguments, focusing on deductive arguments. The discussion is structured around four important junctions: i) the notion of support, which captures the relation between the conclusion and premises of an argument, ii) the choice of a formal language into which the argument is translated in order to make it amenable to evaluation via formal methods, iii) the question of quality criteria for such (...) formalizations, and finally iv) the choice of the underlying logic. This introductory discussion is supplemented by a brief description of the genesis of the special issue, acknowledgements, and summaries of each article. (shrink)

Translated from: W.V.O.Quine, W. H. O. (1986): Philosophy of Logic. Second Edition. Harvard University Press. Cambridge, Massachusetts and London, England, 47-61.

Universal Logic is the study of the formal properties of logical systems in terms of the ways in which these formal features are found across systems of various kinds. A crucial example of this problematic is found at the heart of cognitive science. Brains are computers or computer-like things. But the digital logic of computers and the logic of computer programs do not correspond in any direct way with the processes of brains, either at the neural level, or at the (...) level of psychological descriptions of reasoning and inference processes. There have been many approaches to this problem, typically involving the idea of some sort of brain-based universal semantics or syntactics that is realized in different forms in different languages. These accounts do not extend very successfully to other supposed forms of common tacit mental life, such as culture, climates of opinion, habitus, practices, norms, scripts, schemas, worldviews, and so forth. Nor do any of these concepts fit very well with known neural processes. The alternative approaches appeal to versions of the notion of individual habit, most recently summarized in a major book recently published by Cambridge University Press (Caruana in Habits: Pragmatist Approaches from Cognitive Science, Neuroscience, and Social Theory. Cambridge University Press, Cambridge, 2020). My approach is to see the language capabilities of each person as an assemblage of language patterns that have patterned relations to one another, and that are unique to each person. The evidence that this is how the brain actually works comes from bilinguals, who do not have two parallel downloaded language systems, but who have a mixed system with no neural separation between linguistic capacities. This is a better model for the heterogeneous tacit capacities that make up the logic of practices: an assemblage of patterns that allow for mutual interaction. What makes up the “system” are patterned forms of behavior that are recognized by others as “signals.” Language and linguistic expressions serve, among other things, as props to inferences: as substitutes for elements of inferences, and as surrogates for inferences, which enable extensions of inferences beyond experience. It is a “system” not in the sense that it corresponds to some neural structure, but in the sense that the patterns which are learned in the course of language learning have causal relations with one another in the brain, and in the behavioral responses of others, form the “signal system.”. (shrink)

I will begin this comparative analysis with Quine, focusing on the front matter and first chapter of Word and Object (alongside From a Logical Point of View and two other short pieces), attempting to illuminate there a (1) basis of excessive, yet familiar, chaos, (2) method of improvised, dramatic distortion, and (3) consequent neo-Pragmatist metaphysics. Having elaborated this Quinian basis, method and metaphysics, I will then show that they can be productively translated into James Mercer’s poetic lyrics for The Shins, (...) with an emphasis on the first song, entitled “Caring is Creepy,” from their debut studio album, Oh, Inverted World! Finally, I will explain why Quine and Mercer are particularly suited to this translation (in contrast to other philosophically-rich pop lyricists such as Bob Dylan, and other pragmatist philosophers like Robert Brandom), in the course of which important implications will emerge for our globalized world today. (shrink)

Title: The Interconnection between Logic and Usul al-Fiqh in the Philosophy of Taha Abderrahmane Abstract: This article examines the profound relationship between Logic (Mantiq) and the Principles of Islamic Jurisprudence (Usul al-Fiqh) within the philosophical project of the Moroccan thinker Taha Abderrahmane. Unlike the traditional subordination of Usul to Aristotelian formal logic, Abderrahmane proposes a "Natural Logic" deeply rooted in the Arabic linguistic and ethical tradition. He argues for a transition from abstract demonstration (Burhan) to a communicative, dialogical (...) argumentation (Hujaj) that serves human conduct (Taklif). The study explores his concept of "Integral Reason," where logical validity is inseparable from ethical value. By "Usul-izing" logic rather than "Logicizing" Usul, Abderrahmane seeks to revive the creative potential of Islamic legal theory as a performative and ethical system of reasoning. This research highlights how his approach challenges Western logocentrism, offering a localized yet universal alternative for understanding the foundational structures of Islamic thought. (shrink)