The focus of this paper is the analysis of the epistemological and practical role played bypathe/affections in Epicurus’ philosophy. Epicurus firstly considered the affections not as emotional/passional conditions, but as firm criteria of truth and more specifically as the third criterion of the canonic (i.e. the epistemological part of his philosophical system). In this article the critical reactions (in particular by the Peripatetic side: Aristocles of Messene) against the Epicurean position about the function of the affections will be investigated too. (...) Finally, two parts of this paper are devoted to the Cyrenaic tripartition ofpathe(in all likelihood, a subject criticized by Epicurus) and to the probable doctrinal relationship between Epicurus’patheand Aristotle’sNicomachean EthicsBook 2. (shrink)

The aim of the present book is to give a comprehensive account of the ‘state of the art’ of substructural logics, focusing both on their proof theory and on their semantics (both algebraic and relational. It is for graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics as well as specialists and researchers.

"Questo volume esamina la dottrina epicurea dei minimi che rappresenta un nodo cruciale della filosofia di Epicuro e un autentico punto di svolta rispetto all'atomismo di Leucippo e Democrito. Il libro è organizzato in tre capitoli dedicati rispettivamente: all'analisi filologica e teorica delle fonti primarie, alla ricostruzione del contesto storico-filosofico a cui la dottrina dei minimi verosimilmente fa riferimento, e, infine, all'approfondimento dello sviluppo della teoria dei minimi in ambito prevalentemente geometrico all'interno della scuola di Epicuro. L'esame critico delle fonti (...) antiche, anche attraverso l'attenta analisi della letteratura secondaria, conferma il ruolo decisivo giocato dai minimi nella scienza della natura epicurea. Si tratta della prima monografia interamente consacrata allo studio di questa significativa dottrina in tutta la sua ampiezza storica e teorica."--Provided by publisher. (shrink)

This book deals with some Peripatetic philosophers of the Hellenistic age who were direct and indirect pupils of Aristotle. The main focus of the book is Aristotle's school in the Hellenistic period, a subject not particularly explored by the scholars. Three main issues are addressed in the chapters of the book: the problem of knowledge, the question of time, and the doctrine of the soul. More specifically the topics addressed are: the problem of sense-perception and the method of multiple explanations (...) in the field of meteorology in Aristotle, Theophrastus and Epicurus, the epistemology of Strato, the notion of time in Eudemus and Strato, the conception of sleep in Clearchus, the doctrine of divination in Cratippus. Finally, the Appendix examines the probable influence of the physics of Strato on the medicine of Asclepiades of Bithynia. These themes are investigated by comparing the positions of the Peripatetics with Aristotle's philosophy, but above all by contextualising the doctrines of the Peripatetics within the broader framework of Hellenistic philosophies. (shrink)

Starting from the ‘Dewey Lectures’, Rawls presents his conception of justice within a contextualist framework, as an elaboration of the basic ideas embedded in the political culture of liberal-democratic societies. But how are these basic ideas to be justified? In this article, I reconstruct and criticize Rawls’s strategy to answer this question. I explore an alternative strategy, consisting of a genealogical argument of a pragmatic kind – the kind of argument provided by authors like Bernard Williams, Edward Craig and Miranda (...) Fricker. I outline this genealogical argument drawing on Rawls’s reconstruction of the origins of liberalism. Then, I clarify the conditions under which this kind of argument maintains vindicatory power. I claim that the argument satisfies these conditions and that pragmatic genealogy can thus partially vindicate the basic ideas of liberal-democratic societies. (shrink)

Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...) to a logical calculus is not as straightforward as it may seem. We show that these facts are problematic for the proof-theoretic project but the problems can be solved. Our thesis is that the consequence relation relevant for proof-theoretic semantics is the one given by the sequent-to-sequent derivability relation in Gentzen systems. (shrink)

In this paper, I argue that one approach to normative political theory, namely contextualism, can benefit from a specific kind of historical inquiry, namely genealogy, because the latter provides a solution to a deep-seated problem for the former. This problem consists in a lack of critical distance and originates from the justificatory role that contextualist approaches attribute to contextual facts. I compare two approaches to genealogical reconstruction, namely the historiographical method pioneered by Foucault and the hybrid method of pragmatic genealogy (...) as practiced by Bernard Williams, arguing that they both ensure an increase in critical distance while preserving contextualism’s distinctiveness. I also show, however, that only the latter provides normative action-guidance and can thus assist the contextualist theorist in the crucial task of discerning how far certain contextual facts deserve their justificatory role. I prove this point by showing how a pragmatic genealogy of the practice of punishment can inform the contextualist’s reflection about the role this practice should play in a transitional scenario, i.e. in the set of circumstances societies go through in the aftermath of large-scale violence and human rights violations. (shrink)

The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Classical Logic in (...) terms of appropriate matrix bundles and as semilattice-based logics, showing that the notion of consequence in these logics can be interpreted in terms of truth (or non-falsity) and meaningfulness (or meaninglessness) preservation. Finally, we use Płonka sums of matrices to investigate the pure variable inclusion companions of an arbitrary finitary logic. -/- . (shrink)

I discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. I argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads me to select as a plausible candidate LL, a fragment of linear logic that differs from R in that it rejects both contraction and distribution.

In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant *c* in a given logic: its operational meaning, given by the operational rules for *c* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing *c* which can be proved in the same calculus. Subsequently, we use the (...) same strategy to counter Quine's meaning variance argument against deviant logics. In a nutshell, we claim that genuine rivalry between (similar) logics *L* and *L'* is possible whenever each constant in *L* has the same operational meaning as its counterpart in *L'* although differences in global meaning arise in at least one case. (shrink)

Pragmatic vindicatory genealogies provide both a cause and a rationale and can thus affect the space of reasons. But how far is the space of reasons affected by this kind of genealogical argument? What normative and evaluative implications do these arguments have? In this paper, I unpack this issue into three different sub-questions and explain what kinds of reasons they provide, for whom are these reasons, and for what. In relation to this final sub-question I argue, most importantly, that these (...) arguments are ambiguous about what they give us reasons for, meaning that they can be interpreted both as justifications for recognizing the normative standing of certain norms, values, and practices - and thus for living by them - and as excuses for those that do so. I illustrate this point by reference to the genealogical vindication of honour cultures, showing how the vindicatory argument can illuminate such case as one of excusing moral ignorance. Drawing on legal theory and moral philosophy, I show that different evaluative and normative implications hang on the result of the interpretation as either justification or excuse, and show that this ambiguity is a virtue rather than a limitation. (shrink)

This short note deals with an epigram preserved by the Anthologia Palatina Book IX (360) attributed to a Metrodorus whom, especially for chronological reasons, one tends to identify with the Epicurean Metrodorus of Lampsacus, at least from the Phoinix von Kolophon by Gustav Adolph Gerhard (1909). This epigram looks like a “symmetrical” polemical reply to the immediately preceding one (AP IX 359), which can be attributed (but not without difficulty) to the Hellenistic poet Posidippus. The careful historical-philosophical examination of the (...) contents of this alleged Epicurean epigram (360) leads to believe that it is basically impossible that the author is an Epicurean philosopher such as Metrodorus. (shrink)

In this short note I would like to reflect again upon paragraphs 39–40 of Epicurus’ Letter to Herodotus and, more specifically, on the text printed in the last critical edition by Tiziano Dorandi, which I quote below together with the critical apparatus :495 ἀλλὰ μὴν καὶ τὸ πᾶν ἐστι · σώματα μὲν γὰρ ὡς ἔστιν, αὐτὴ ἡ αἴσθησις ἐπὶπάντων μαρτυρεῖ, καθ’ ἣν ἀναγκαῖον τὸ ἄδηλον τῷλογισμῷ τεκμαίρεσθαι, ὥσπερ προεῖπον. [40] τόπος δὲ εἰ500 μὴ ἦν ὃ κενὸν καὶ χώραν καὶ ἀναφῆ (...) φύσιν ὀνομάζομεν, οὐκἂν εἶχε τὰ σώματα ὅπου ἦν οὐδὲ δι’ οὗ ἐκινεῖτο, καθάπερφαίνεται κινούμενα.495–496 de scholiis glossematibusque in tribus Epicuri epistulis et in RS i, vid. Dorandi, Epicuro 277–8 496–497 σώματα καὶ κενόν duce Gass. suppl. V. d. Muehll: σώματα καὶ τόπος Us. Traditam lectionem defendere conatur Arndt 26. Vid. K. Algra, Elenchos 15 100 et D. Obbink, Philodemus On Piety. Part 1 338–9 497 σώματα ΦFP4: σώμα· τὰ BP1498 πάντων om. Φ 499 τόπος δὲ Us.: τὸ πρόσθε B1: τὸ πρόσθεν B2PΦ: πρόσθεν F Cf. Lucr. 1.426–7 et vid. Sedley, Phronesis 183–4 εἰ δὲ Φ 500 ὃ Φ: ὃ* B2: ὃν B1, ut vid.: ὂν PF ὃ post κενὸν traiecit Φ προεῖπον τὸ πρόσθεν· εἰ δὲ μὴ ἦν ὃ κενὸν Brieger, Seele 5 Vid. Dorandi, Epicuro 282–4 501 ἦν B: εἴη ΦFP4: ἔνι P1 502 οὐδ’ Us.: οὔτε B2PF: ὅτε B1503 περιληπτικῶς rec. (shrink)

Journal Name: Apeiron Issue: Ahead of print.

Two Worlds represents an attempt to overcome the boundaries between science fiction and fantasy. The story is set in a remote future, on an Earth very different from today: the Chimeric development has taken human evolution on strange paths, paths that have led to the advent of other races; hybrid species that possess in their modified DNA genes coming from birds and fishes. The presence of a mysterious Tower of Seeds—a long forgotten place—will rekindle in some people new hopes and (...) the desire, perhaps utopian, to restore the ancient environmental balance with planet Earth. (shrink)

La Jetée is a Chris Marker movie composed by still images, photographs, with the exception of a very short sequence. The paper aims to account for the experience of temporality induced by photography, framing the structural analysis of the movie in a phenomenological horizon, in particular with regard to the Husserlian’s notion of “Living Present”.

We consider the class of pointed varieties of algebras having a lattice term reduct and we show that each such variety gives rise in a natural way, and according to a regular pattern, to at least three interesting logics. Although the mentioned class includes several logically and algebraically significant examples (e.g. Boolean algebras, MV algebras, Boolean algebras with operators, residuated lattices and their subvarieties, algebras from quantum logic or from depth relevant logic), we consider here in greater detail Abelian ℓ-groups, (...) where such logics respectively correspond to: i) Meyer and Slaney’s Abelian logic [31]; ii) Galli et al.’s logic of equilibrium [21]; iii) a new logic of “preservation of truth degrees”. (shrink)

Paraconsistent weak Kleene logic is the $3$-valued logic based on the weak Kleene matrices and with two designated values. In this paper, we investigate the poset of prevarieties of generalized involutive bisemilattices, focussing in particular on the order ideal generated by Α$\textrm{lg} $. Applying to this poset a general result by Alexej Pynko, we prove that, exactly like Priest’s logic of paradox, $\textrm{PWK}$ has only one proper nontrivial extension apart from classical logic: $\textrm{PWK}_{\textrm{E}}\textrm{,}$ PWK logic plus explosion. This $6$-valued logic, (...) unlike $\textrm{PWK} $, fails to be paraconsistent. We describe its consequence relation via a variable inclusion criterion and identify its Suszko-reduced models. (shrink)

Kant’s view of human beings is, as much of his philosophy, notoriously based on the dichotomy between the phenomenal and the noumenal world. This dichotomy digs a rift across human nature by separating the animal and the rational parts of it, their heteronomous and autonomous components, their sense of duty and their self-love. Human beings, for Kant, inhabit both worlds. On the one hand, even if we agree with Kant that the fundamental moral norms are constitutive of our rational and (...) autonomous agency and therefore inescapable, it remains unclear whether and how far these norms can motivate finite and heteronomous human beings, normally concerned with their own ends, interests and inclinations. On the other hand, although moral actions may express who we really are as rational beings, they may nonetheless leave us with an unfulfilled but legitimate need to reconcile morality with our own ends as finite, animal beings, inevitably concerned with living our own lives. Sasha Mudd described these phenomena as two forms of alienation: moral alienation (the estrangement of the heteronomous agent, motivated by happiness and inclinations, from a morality perceived as alien, foreign, and hardly motivating) and practical alienation (the estrangement of the autonomous moral agent from her empirical and heteronomous dimension – her projects, desires, aspirations, inclinations, and so on). On Mudd’s account, Kant successfully escape the first kind of alienation through his doctrine of respect. Here I argue, contra Mudd, that there are at least two ways in which Kant leaves moral agents alienated from morality itself. (shrink)

Negli ultimi due anni sono stati pubblicati due importanti libri sul progresso morale: 'Moral Progress' di Philp Kitcher e 'A Better Ape' di Victor Kumar e Richmond Campbell. In questa nota critica, recensisco entrambi i libri e problematizzo il modo in cui cercano rispettivamente di legare tra loro il tema del progresso morale con la teoria dell'evoluzione.

Se la tradizione continentale, da Nietzsche a Foucault, ha sottolineato le implicazioni critiche e destabilizzanti del metodo genealogico, gli approcci analitici hanno dimostrato che esso può anche offrire sostegno ai propri oggetti di indagine: norme comportamentali, pratiche, concetti e così via. Un resoconto genealogico, per esempio, può avere un carattere giustificativo quando individua una relazione funzionale necessaria tra il concetto o la pratica in esame e bisogni umani abbastanza fondamentali. La questione che voglio affrontare riguarda le presunte capacità giustificative di (...) questo tipo di spiegazioni genealogiche. In che misura modificano davvero lo spazio delle ragioni? Sostengo che la loro portata normativa e valutativa è variabile e che l'esame di alcuni casi limite aiuta a dimostrarlo. Più specificamente, ritengo che in alcuni casi le ragioni offerte attraverso queste spiegazioni siano ragioni non tanto per giustificare l'uso di certi concetti o pratiche, quanto per giustificare coloro che li vivono. (shrink)

In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.

Towards biodeconstruction -- Between life and death: différance -- The absolute programme -- The text and the living -- Between life and death: the bond -- Beyond life death: autoimmunity -- Living on: the arche-performative.

This paper discusses Habermas’s argument that justice requires solidarity as its ‘reverse side’, whereby the former provides the necessary global framework for establishing intersubjective solidarity whilst the latter constitutes an important precondition for igniting social and political change in the direction of social justice. In this paper I argue that such a paradigm of reciprocity might be fruitfully complemented by a less apparent yet substantial nexus: that between solidarity and perceived injustice, which I contend also triggers the emergence of solidarity. (...) Drawing from Arendt’s thematisation of solidarity as a principle that stems from human suffering and recent scholarship on transitional post-conflict justice, I analyse the negative and reactive aspect of solidarity and the role of negative emotions in its emergence. (shrink)

Authors have paid considerable attention to how to define the meaningful work construct. This has led to providing comprehensive definitions in the light of different theoretical frameworks that reflect a degree of contestation within the field. Several of them have proposed definitions linked to the individuals’ pervasive sense of the value of their work. Others have offered descriptions centred on their temporal, episodic nature and emphasising the individual’s occasional work experience. These definitions reflected a potential temporal condition as well as (...) the variety of time perspectives underpinning the authors’ conceptualizations of the construct. This paper conducted a broad literature review to analyse works which have adopted a temporal framework or supported a time-based definition of the construct. The analysis indicates two different conceptualizations of the construct: as a permanent/steady mindset and as a changeable/episodic experience. As a reflective paper, the present contribution develops an overall framework for views and theories on meaningful work. It reports a critical review on the matter to elevate understanding of meaningful work for further research and applied implications in work and organizational studies. (shrink)

This paper intends to verify the extent and effectiveness of the transforming appropriation of the Derridean concept of ‘differance’ by Stiegler with respect to the problems that, according to Stiegler, make this creative critical operation necessary; in particular with respect to the most recent question concerning the possibility of thinking about and putting into practice a ‘neganthropological différance’ capable of facing the ecological crisis that today seems to threaten the very existence of life on earth. The paper goes back to (...) Technics and Time 1. to analyze the distinction between ‘vital difference’ and ‘noetic difference’ that constitutes the condition of possibility of the ‘neganthropological différance.’ In this perspective, the distinction proposed by Stiegler seems to re-propose the hierarchically oriented oppositional structure that characterizes metaphysical thought and in particular the opposition between man and animal, attributing to the human being the ability to free himself from the constraints of his biological-natural condition. Finally, the paper attempts to account for the repercussions of this approach on the very possibility of an effective response to the ecological crisis, concluding with a provocation regarding the role that theory can and must play with regard to such an urgent and far-reaching problem. (shrink)

Jan Patočka, perhaps more so than any other philosopher in the twentieth century, managed to combine intense philosophical insight with a farsighted analysis of the idea and challenges facing Europe as a historical, cultural and political signifier. As a political dissident in communist Czechoslovakia he also became a moral and political inspiration to a generation of Czechs, including Václav Havel. He accomplished this in a time of intense political repression when not even the hint of a unified Europe seemed visible (...) by showing in exemplary fashion how concrete thought can be without renouncing in any way its depth. Europe as an idea and a political project is a central issue in contemporary political theory. Patočka’s political thought offers many original insights into questions surrounding the European project. Here, for the first time, a group of leading scholars from different disciplines gathers together to discuss the specific political impact of Patočka’s philosophy and its lasting significance. (shrink)

We investigate some properties of two varieties of algebras arising from quantum computation - quasi-MV algebras and $\sqrt{^{\prime }}$ quasi-MV algebras - first introduced in \cite{Ledda et al. 2006}, \cite{Giuntini et al. 200+} and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of $\sqrt{^{\prime }}$ quasi-MV algebras; we give a representation of semisimple $\sqrt{^{\prime }}$ quasi-MV algebras in terms of algebras of functions; (...) finally, we describe the structure of free algebras with one generator in both varieties. (shrink)

The aim of this article is to show how both Jan Patočka and Jürgen Habermas, starting from a reinterpretation of the idea of «lifeworld», engaged a critique of modern civilisation, aiming (with different outcomes) at a redefinition of the concept of political community. In order to achieve this goal, I firstly focus on Patočka’s understanding of modern rational civilisation and its attempt to fix the fracture between «life» and «world». At this stage, I take also advantage of Hans Blumenberg’s distinction (...) between these two terms, in order to better clarify Patočka’s stance on this problem. Secondly, I analyse Habermas’ ideas of lifeworld and system, and their uncoupling in modern societies, as well as the reemergence of this issue in Habermas’ recent works on the European economic and political crisis. Finally, I focus on the very different ways in which Patočka and Habermas tackled the ideas of conflict and crisis in contemporary world, also in view of a possible path out of this crisis through a re-constitution of Europe. (shrink)

In questo saggio traccio un profilo del pensiero di Bernard Williams, concentrandomi su temi relativi alla filosofia morale e, più nello specifico, ricostruendo la sua disamina dell’idea di oggettività in questa disciplina. Dopo aver esaminato le sue critiche all’idea di teoria etica normativa, offro un inquadramento metaetico della sua posizione e concludo mostrando le sue affinità con la riflessione etica degli antichi Greci e, in particolar modo, di Aristotele.

El artículo versa sobre el concepto de símbolo en el pensamiento de Giambattista Vico. El símbolo en Vico no se encuentra indagando una presunta “naturaleza de las cosas” detrás de la mente, ni puede ser entendido como un producto que surge en la mente humana como si esta última existiese ya en su pureza prescindiendo de la dinámica simbólica. Más bien, el símbolo hace a la mente y la mente hace al símbolo: la mente se desvela en Vico como facultad (...) originariamente simbólica, capaz de conectar, de unir los muchos, contando fábulas, como se muestra en el caso de Homero. Desde este punto de vista, se puede instaurar un paralelismo entre la dinámica del símbolo en Vico y la determinación de extensión que caracteriza la noción de símbolo en Warburg. (shrink)

L’anno appena trascorso è stato dimenticabile (per ovvie ragioni) e i filosofi politici hanno una ragione in più per dimenticarlo data la prematura scomparsa di Gerald Gaus. Tuttavia, essi potrebbero forse trovare una qualche consolazione nel fatto che il 2020 ha visto la pubblicazione di due notevoli opere dedicate alla loro disciplina: 'Utopohobia', di David Estlund e 'What is Political Philosophy?', di Charles Larmore. In questo saggio, dopo aver offerto una sintesi criminalmente breve del nucleo argomentativo dei due volumi, li (...) metterò in dialogo, usando le risorse dell'uno per interrogare e problematizzare alcune tesi dell'altro (e viceversa). (shrink)

Evidence has emerged that the civic engagement movement in US higher education may not be fulfilling its transformative potential, having lost sight of its core democratic purposes. Civic engagement conceptualised only in terms of activity and place - programmes in communities - may be easily accommodated to prevailing technocratic practices. For the civic engagement movement to challenge and change higher education, it must promote democratic processes and purposes - and pursue institutional change strategies aimed at realigning the work of the (...) academy to serving democracy. (shrink)

In this paper, I would like to show how the movements of never stable meanings that link biography and religion are figured and interwoven throughout a kind of ineffable literary and philosophical notion of religion. Religion is a notion that can be understood through a cluster of topics such as origin, promise, dissociation, the unconditional, forgiveness, the undeconstructable and the possibility of the impossible—terms and expressions that Derrida suggests describe God.

While working on the Italian translation of Life Death, I became aware of some inaccuracies on Derrida’s part that might weaken the effectiveness of his deconstruction of the notion of ‘reproduction’. Not only, such inaccuracies seem to lead Derrida’s interpretation of reproduction toward a conception of ‘life’ that might even hint at an undeconstructed metaphysical background. I have already dealt with such inaccuracies in detail in two articles published in French, here I will recall their outcomes in order to try (...) to test the most problematic hypothesis they have led me to formulate: the Derridean conception of ‘life’ implies a metaphysical background. (shrink)

This study draws a comparative framework between deconstructive reading of texts and jazz standards. It will be argued that both are defined by the constant play of tradition and innovation. On the one hand, the repetition of a set of rules and dominant understanding of texts/tunes that generates tradition. On the other hand, invention and improvisation that take on that tradition and generate innovation. The act of reading/playing becomes also an act of invention/improvisation that manifests a constant tension between the (...) old that is handed down through writing/recording and the new that is generated by the reader/musician. (shrink)

Cet article se concentre principalement sur Boéthos, philosophe épicurien qui a été souvent négligé : aucune source ancienne, excepté Plutarque, ne le mentionne. L’étude tente d’examiner la perspective philosophique de Boéthos et, plus particulièrement, son attitude envers la géométrie.

Varieties like groups, rings, or Boolean algebras have the property that, in any of their members, the lattice of congruences is isomorphic to a lattice of more manageable objects, for example normal subgroups of groups, two-sided ideals of rings, filters (or ideals) of Boolean algebras.algebraic logic can explain these phenomena at a rather satisfactory level of generality: in every member A of a τ-regular variety ������ the lattice of congruences of A is isomorphic to the lattice of deductive filters on (...) A of the τ-assertional logic of ������. Moreover, if ������ has a constant 1 in its type and is 1-subtractive, the deductive filters on A ∈ ������ of the 1-assertional logic of ������ coincide with the ������-ideals of A in the sense of Gumm and Ursini, for which we have a manageable concept of ideal generation. However, there are isomorphism theorems, for example, in the theories of residuated lattices, pseudointerior algebras and quasi-MV algebras that cannot be subsumed by these general results. The aim of the present paper is to appropriately generalise the concepts of subtractivity and τ-regularity in such a way as to shed some light on the deep reason behind such theorems. The tools and concepts we develop hereby provide a common umbrella for the algebraic investigation of several families of logics, including substructural logics, modal logics, quantum logics, and logics of constructive mathematics. (shrink)