A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as Kant (...) conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (shrink)

We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan’s Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular (...) we examine the Fréchet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction Cn+1 of n + 1 conditional events to the family {Cn,En+1|Hn+1}. We consider the relation with the notion of quasi-conjunction and we examine in detail the coherence of the prevision assessments related with the conjunction of three conditional events. Based on conjunction, we also give a characterization of p-consistency and of p-entailment, with applications to several inference rules in probabilistic nonmonotonic reasoning. Finally, we examine some non p-valid inference rules; then, we illustrate by an example two methods which allow to suitably modify non p-valid inference rules in order to get inferences which are p-valid. (shrink)

This article focuses on the interpretation of the metaphysical deductions of the higher cognitive faculties in Gabriele Gava’s Kant’s Critique of Pure Reason and the Method of Metaphysics. The aim is to assess the role that Kant’s general logic plays in these metaphysical deductions, the consequences for the analysis of the faculties, and the place of general logic in Gava’s overall theoretical analysis of Kant’s first Critique.

. In this paper, the significance of using general logic-systems and finite consequence operators defined on non-organized languages is discussed. Results are established that show how properties of finite consequence operators are independent from language organization and that, in some cases, they depend only upon one simple language characteristic. For example, it is shown that there are infinitely many finite consequence operators defined on any non-organized infinite language L that cannot be generated from any finite logic-system. On (...) the other hand, it is shown that for any nonempty language L, a set map is a finite consequence operator if and only if it is defined by a general logic-system. Simple logic-system examples that determine specific consequence operator properties are given. (shrink)

In this paper I consider whether there is a measure of coherence that could be rightly claimed to generalize the notion of logical equivalence. I show that Fitelson’s (2003) proposal to that effect encounters some serious difficulties. Furthermore, there is reason to believe that no mutual-support measure could ever be suitable for the formalization of coherence as generalized logical equivalence. Instead, it appears that the only plausible candidate for such a measure is one of relative overlap. The measure I propose (...) in this paper is quite similar to Olsson’s (2002) proposal but differs from it by not being susceptible to the type of counterexample that Bovens and Hartmann (2003) have devised against it. (shrink)

The question motivating my investigation is: Are the basic philosophical principles underlying the "core" system of contemporary logic exhausted by the standard version? In particular, is the accepted narrow construal of the notion "logical term" justified? ;As a point of comparison I refer to systems of 1st-order logic with generalized quantifiers developed by mathematicians and linguists . Based on an analysis of the Tarskian conception of the role of logic I show that the standard division of terms (...) into logical and extra-logical is partly arbitrary. I argue that the semantic principles of Tarskian logic allow any higher order mathematical predicate or relation to function as a logical term in a 1st-order system, provided it is introduced in the right way into the syntactic-semantic apparatus. ;Formally, I propose a new, "constructive", semantic characterization of logical terms. A logical term is defined by a function which, given a model, "shows" how to construct relations, sets, or n-tuples of individuals which satisfy it. I discuss the linguistic applicability of the extended logic and bring numerous examples. ;One chapter is devoted to branching quantification--a non-standard logico-linguistic construction obtained by affixing a non-linear, partially-ordered quantifier-prefix to a well-formed formula. Although standard branching quantifiers were given a complete account by Henkin and Walkoe, it is not altogether clear what the meaning of branching generalized quantifiers is. I propose a new analysis of the generalized branching prefix which extends the existent, partial, definitions due to Barwise, and I develop a generalization leading to a "family" of branching structures. ;In conclusion I discuss the philosophical impact of the generalized conception of logic on such issues as the logicist thesis, the interaction between mathematics and logic, ontological commitment via logic, metaphysics and logical semantics. (shrink)

We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class of structures (...) in contrast to the permissibility of classical first-order logic. We make a distinction between deductive and inductive inference via the notions of compactness and weak compactness. Connections with the arithmetical hierarchy and formal learning theory are explored. For the latter, we argue against the identification of inductive inference with the notion of learnable in the limit. Several results highlighting desirable properties of these hierarchies of generalized logical consequence are also presented. (shrink)

There are two ways interpreters have tended to understand the nature of the laws of Kant’s pure general logic. On the first, these laws are unconditional norms for how we ought to think, and will govern anything that counts as thinking. On the second, these laws are formal criteria for being a thought, and violating them makes a putative thought not a thought. These traditions are in tension, in so far as the first depends on the possibility of (...) thoughts that violate these laws, and the second makes violation impossible. In this essay I develop an interpretation of Kant’s pure general logic that overcomes this tension. It accounts for the possibility of logical mistakes, as the first tradition does, while still establishing the absolute impossibility of logical aliens, as the second tradition does. I then argue that the formalist insight that illogical exercises of the understanding are not alternative ways coherent thoughts could have been, but are mere confusions, is fundamental for achieving a proper understanding of the absolute normativity of the laws of pure general logic. (shrink)

In the Critique of Pure Reason, Kant uses the term “logic” in a bewildering variety of ways, at times making it close to impossible to determine whether he is referring to (among others) general logic, transcendental logic, transcendental analytic, a "special" logic relative to a specific science, a "natural" logic, a logic intended for the "learned" (Gelehrter), some hybrid of these logics, or even some still-more abstract notion that ranges over all of these (...) uses. This paper seeks to come to grips with Kant's complex use of "logic." Kant is standardly regarded as saying that since Aristotle, there need be no more concern about logic as a discipline or a field of study, and that Aristotle (with some minor embellishments, in terms of presentation) is the last word in logic. I argue here that, in spite of Hegel, Peirce, Strawson, and others, one must take into consideration Kant’s sophisticated critique of Aristotle’s logic in order to see Kant’s own conception of logic in contrast to that of Aristotle’s. In this way, Kant's strategy in the First Critique—grounded as it is in logic—becomes more plausible, defensible, and, consequently, more attractive. (shrink)

In the paper, I have presented a portrait of Jerzy Pelc as a teacher. He followed in the footsteps of Kazimierz Twardowski and his direct disciples and tried to develop his students’ skills of critical thinking and clear speaking—the basics of good work in philosophy. These skills are connected with methodological postulates of criticism and precision which were shared by all the members of the Lvov-Warsaw School. Jerzy Pelc treated these postulates also as didactic postulates arising out of the conceptions (...) of logical culture and general logic. In my article, I have sketched a general picture of the relation between logic and didactics, I have presented the aforementioned postulates, the concepts of logical culture and general logic and its curriculum. (shrink)

In this paper we make an attempt to study classes of models by using general logics. We do not believe that Lww is always the best logic for analyzing a class of models. Let K be a class of models and L a logic. The main assumptions we make about K and C are that K has the L-amalgamation property and, later in the paper, that K does not omit L-types. We show that, if modified suitably, most (...) of the results of stability theory hold in this context. The main difference is that existentially closed models of K play the role that arbitrary models play in traditional stability theory. We prove e. g. a structure theorem for the class of existentially closed models of K assuming that K is a trivial superstable class with ndop. (shrink)

This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book (...) is the authors' uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation"--Publisher. (shrink)

In this paper we define and study a generalized notion of a logical system that covers on an equal formal basis sentential, equational and sequential systems. We develop a general theory of equivalence between generalized logics that provides, first, a conception of algebraizable logic , second, a formal concept of equivalence between sequential systems and, third, a notion of equivalence between sentential and sequential systems. We also use our theory of equivalence for developing a general algebraic approach (...) to conjunctive non-pseudo-axiomatic self-extensional sentential logics. Finally, we consider within the framework of the mentioned approach various sequential formulations for some well-known sentential logics. (shrink)

Rolando Chuaqui y yo, nos encontramos una ´ unica vez, en Bah´ıa Blanca en agosto 1992, en el Simposio Latino- Americano de L´ ogica Matem´ atica. Lamentablemente, Chuaqui muri´ o antes de mi pr´ oxima visita a Am´ erica del Sur, igual que otro gran l´ ogico latinoamericano, Carlos Alchourr´ on. Chuaqui estuvo en Bah´ıa Blanca juntos con varios alumnos que hablaron sobre aspectos de la l´.

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and (...) most notably, a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi. (shrink)

In this paper, I consider the basis for Kant's praise of Wolff's general logic as "the best we have." I argue that Wolff's logic was highly esteemed by Kant on account of its novel analysis of the three operations of the mind (tres operationes mentis), in the course of which Wolff formulates an argument for the priority of the understanding's activity of judging.

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

In Kant’s Critique of Pure Reason and the Method of Metaphysics (CUP 2023), I argue that the first Critique is not only a ‘propaedeutic’ to metaphysics, but actually already establishes parts of metaphysics. These parts belong to what Kant calls transcendental philosophy. Additionally, I also provide an account of Kant’s critique of dogmatism and Wolff as its main defender. In this paper, I take up Luigi Filieri’s and Davide Dalla Rosa’s invitation to further develop my characterization of transcendental philosophy and (...) I respond to Michael Walschots’s objections against my interpretation of Kant’s critique of Wolff’s dogmatism. (shrink)

In this paper I lay the foundations for an understanding of one of Fichte's most neglected and least understood texts: the late lecture course on Transcendental Logic. I situate this work in the context of Fichte's lifelong struggle with the problem of understanding the relation between logic and philosophy – a problem that I show to figure centrally both in Fichte's own revolutionary thinking and in his response to Kant's notorious denunciation of the Wissenschaftslehre. By attending to this (...) context we can understand Fichte's philosophical ambitions in the late lectures: a critique of particular doctrines of general logic; a critique of the conception of thought presupposed both by the traditional logic and by Kant himself; and a new conception of the relation between logic and the philosophical theory of experience. (shrink)

Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. _Generalized Galois Logics_ develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.

In the Critique of Pure Reason, Kant conceives of general logic as a set of universal and necessary rules for the possibility of thought, or as a set of minimal necessary conditions for ascribing rationality to an agent . Such a conception, of course, contrasts with contemporary notions of formal, mathematical or symbolic logic. Yet, in so far as Kant seeks to identify those conditions that must hold for the possibility of thought in general, such conditions (...) must hold a fortiori for any specific model of thought, including axiomatic treatments of logic and standard natural deduction models of first-order predicate logic. Kant's general logic seeks to isolate those conditions by thinking through – or better, reflecting on – those conditions that themselves make thought possible. (shrink)