Leibniz: Philosophy of Language

The theses in this book are: 1) the tension between the Leibnizian theory of the tropes and their use is resolved in a "pragmatic of discourse" that gives the metaphor a richer dimension than the theorized one, that is, that of "a mechanism capable of combining elements coming from different conceptual spaces into a new metaphorical conceptual space, 'shapeless' to which the metaphor itself provides an adequate language to describe and structure it"; 2) the role of metaphors is placed for (...) Leibniz in the context of a 'multi-method' idea that combines the inventive and the formalizing moment and allows for a multiplicity of directions; 3) the Leibniz system is organized according to a 'logic' that is not deductive but analogical; 4) the valid relations in the system are not only connections of a logical nature; on the contrary, the organization is 'reticular', and the primacy of a relation depends from time to time on the prevalence assigned to a metaphor according to the problem being faced; 5) Leibniz's central metaphors are "emerging parts of a wider submerged translation", i.e. they are both expression and conceptualizing vehicle of a cognitive strategy that wants to govern the complexity of knowledge by organizing it around themes; this strategy is alternative to the Cartesian formulation of "Method" based on the disjunction of objects and notions and instead gives philosophical expression to the Baroque sense of the constant mutability that rules the world. (shrink)

Leibniz's conceptual containment theory says that singular propositions of the form a is F are true when the complete concept of being a contains the concept of being F. In this paper, I provide a new semantics for first-order logic built around this idea. The semantics resolves longstanding problems for Leibniz's theory and can represent, without possible worlds, both hyperintensional distinctions among properties and a certain kind of presumably impossible situation that standard approaches cannot represent. The semantics also captures the (...) strong soundness and completeness of classical first-order logic. (shrink)

Mates’ book has already been widely read and justly praised. It is full of clear, interesting arguments on most of the topics which engage contemporary readers of Leibniz, expertly and extensively marshalls texts, and includes a short but unusually good biography and outline of Leibniz’s system. Since I write here for an unusually well-informed and well-motivate audience, I allow myself compressed formulations of controversial arguments, antecedently acknowledging need for elaboration. I focus on a cluster of interconnected, central concerns: the nature (...) and role of nominalism, individual concepts, contingency, rational explanation, bestness and perception. (shrink)

This essay argues that, with his much-maligned “infinite analysis” theory of contingency, Leibniz is onto something deep and important – a tangle of issues that wouldn’t be sorted out properly for centuries to come, and then only by some of the greatest minds of the twentieth century. The first two sections place Leibniz’s theory in its proper historical context and draw a distinction between Leibniz’s logical and meta-logical discoveries. The third section argues that Leibniz’s logical insights initially make his “infinite (...) analysis” theory of contingency more rather than less perplexing. The last two sections argue that Leibniz’s meta-logical insights, however, point the way towards a better appreciation of (what we should regard as) his formal theory of contingency, and its correlative, his formal theory of necessity. (shrink)

Conceptual atomism is a doctrine deeply rooted in the tradition of western thought. It originated with Aristotle, was present in the entire Aristotelian tradition and came to its most pure expression in the work of Leibniz. However, ab initio this doctrine suffered from certain difficulty labelled traditionally “aporia generis”, namely the problem of how it is possible to reconcile the absolute simplicity of the primitive concepts with the existence of transcendental concepts, that is, concepts necessarily included in every concept. In (...) this paper the entire problem is subject to an analysis and a solution is suggested, based on a distinction between two different kinds of conceptual containment: the primitive concepts do not contain the transcendentals formally, that is, as constituents thatcan be revealed by means of definitional analysis, but they nevertheless do contain them virtually, that is, they strictly imply them. It is noted that the germ of this solution is already present in Aristotle. (shrink)

We first present an edition of the manuscript LH VII, B 2, 39 in which Leibniz develops a new formalism in order to give rigorous definitions of positive, of privative, and of primitive terms.This formalism involves a symbolic treatment of conceptual quantification which differs quite considerably from Leibniz’s “standard” theory of “indefinite concepts” as developed, e.g., in the “General Inquirles” In the subsequent commentary we give an interpretation and a critical evaluation of Leibniz’s symbolic apparatus. It turns out that the (...) definition of privative terms and primitive terms lead to certain inconsistencies which, however, can be avoided by slight modifications. (shrink)

The dream of Leibniz and that of Frege, to create a lingua characteristica in order to demonstrate conceptual thought, incorporates in a wider process, the division and tension between the distinct Spheres which the human sub-species have been creating. Spheres which remain hidden by natural language, essentially spoken language. For the creation and demonstration of the Conceptual Sphere the establishing of a language of characteres has become indispensable, essentially written language. Is a consequence a tension is established between Natural language-Formal (...) language with their corresponding reductionist tendences. (shrink)

In this paper, an interpretation of "necessity", inspired by a Leibnizian idea and based on the method of dialogical logic, is introduced. The semantic rules corresponding to such an account of necessity are developed, and then some peculiarities, and some potential advantages, of the introduced dialogical explanation, in comparison with the customary explanation offered by the possible worlds semantics, are briefly discussed.

The article deals with the issue of public items (objects, processes, events) in the philosophy of Leibniz. Starting from the famous passage of the Monadology which illustrates his conception of the substance by the image of a city perceived from different perspectives, the author shows how Leibniz conceives the public character of certain items, i.e. the reality of the phenomena that express them, not only in disagreement with the causal model, according to which public items would be the causal source (...) of shared perceptions, but in disagreement even with the correspondence model, according to which shared perceptions would correspond to external objects. The key to understand the position of Leibniz is rather to look at his concept of the compossible, which makes it possible to explain the congruence between shared perceptions without having to resort to the concept of correspondence. (shrink)

The account of vagueness Bertrand Russell provided in his 1923 paper, entitled simply “Vagueness” (see Russell [1923]1997), has been thought by some to be inconsistent. One main objection, raised by Timothy Williamson (1994), is that Russell’s attempt early in the paper to distinguish vagueness from generality is at odds with the definition of vagueness he presents later in the same paper. It is as if, as Williamson puts it, Russell “backslides” from his previous distinction (1994, 60), resulting in a conflation (...) of generality and vagueness that is at best problematic for a rigorous account of the phenomenon of vagueness. In this paper, I will defend Russell from this particular objection. While his 1923 paper may not be as clear at various points as one might hope, I do believe it is possible to construct a single theory of vagueness that can be applied equally well to his earlier and later discussions. Thus, Russell’s view is not ultimately inconsistent. In this paper, I will first present the interpretation of Russell’s concept of vagueness that falls prey to the charge of conflating vagueness and generality. Once the problem is clear, I will present an alternative interpretation, one that arises from certain reflections on G. W. Leibniz’s theory of perception. This Leibnizian interpretation of Russell, I will argue, resolves the apparent contradiction in Russell’s account of vagueness. (shrink)

The Dissertatio praeliminaris is one of the early works of Leibniz in which he proposes an elaborate critique, while presenting his own principles. In accepting several points of Nizolius's philosophy, the young Leibniz tries moreover to defend theses which have constituted the basis of many of his later theories. Three major topics will be examined in this article. First, the question of definition, which is taken from a grammar point of view, where clarity is, in fact, the only criterion to (...) establish the signification of words in usage. Second, perhaps the most important, concerns the problem of nominalism that puts Nizolius in opposition with Leibniz: they do not agree on the determination of signification, meaning whether it stands on conventions or on mental concepts. Third, the link between demonstration and induction as a consequence of a nominalistic approach is also discussed in Leibniz's preface. We are thus better able to understand the origins of Leibniz's philosophical reflection. (shrink)

In this paper, the author develops a theory of concepts and shows that it captures many of the ideas about concepts that Leibniz expressed in his work. Concepts are first analyzed in terms of a precise background theory of abstract objects, and once concept summation and concept containment are defined, the axioms and theorems of Leibniz's calculus of concepts (in his logical papers) are derived. This analysis of concepts is then seamlessly connected with Leibniz's modal metaphysics of complete individual concepts. (...) The fundamental theorem of Leibniz's modal metaphysics of concepts is proved, namely, whenever an object x has F contingently, then (i) the individual concept of x contains the concept F and (ii) there is a (counterpart) complete individual concept y which doesn't contain the concept F and which `appears' at some other possible world. Finally, the author shows how the concept containment theory of truth can be made precise and made consistent with a modern conception of truth. (shrink)

There are two accounts of the relation between subject and predicate in Leibniz's writings. The former, which appears in De arte combinatoria, is based on an interpretation of this relation in terms of sum and parts and can be viewed as an anticipation of mereology. The latter, which operates after 1686, is based on an interpretation of this relation in terms of inherence. Metaphysical reasons, linked with the discovery of infinitesimal calculus, explain this shift.

I claim that a genealogy of the philological racism known as ‘orientalism’ should include Leibniz as a founding figure. This argument is framed and motivated by recent publications that seek to exclude Leibniz from the history of race and racism by arguing that he insists on a linguistic, rather than ‘racial,’ schematic of human diversity. A survey of nineteenth-century race theory reveals that this distinction is not only specious, but these recent defenses only further implicate Leibniz in the linguistic tradition (...) that is orientalist racism. (shrink)

The main aim of our paper is to implement Leibniz's analysis of the conditional right in the framework of a dialogical approach to Public Announcement Logic. According to our view, on one hand: PAL furnishes a dynamic epistemic operator which models communication exchange between different agents that seems to be very close to Leibniz understanding of the dynamics between the truth of a proposition and the knowledge of the truth of that proposition (Leibniz calls the latter certification of its truth); (...) on the other hand, the dialogical approach provides a semantics for the dynamic epistemic operator in the context of conditional right by means of which: (i) the exchange between agents leading to a public announcement amounts to the (contractual) interaction of commitments of both the benefactor and the beneficiary of a conditional right (ii) the notion of certification is understood as an action, namely as a move where the beneficiary asks the benefactor to stand to his commitments, (iii) some restrictions specific to the logical nature of the head and the tail of the conditional right can be implemented by combining PAL with some features of linear logic within the same theory of meaning. (shrink)

In Part 1 of this short book, Rescher provides an overview of the nature and source of Leibniz’s interest in the theory and practice of cryptanalysis, including his unsuccessful bid to secure an apprentice for John Wallis (1616-1703) with a view to perpetuating the Englishman’s remarkable deciphering abilities. In Part 2, perhaps the most interesting part of the book, Rescher offers his account of the inner workings of Leibniz’s cipher machine. Part 3 provides a brief pictorial history of such machines (...) and related technologies. Finally, in Part 4 Rescher analyzes some of Leibniz’s own relatively scant attempts at decryption. Though there is little of direct philosophical interest in this work, its account of Leibniz’s forays into the field of encryption and in particular its reconstruction of his remarkable machine are fascinating and should hold considerable appeal for those interested in Leibniz’s pursuits more broadly and in the histories of cryptography and machine design. (shrink)

Despite holding that all concepts are strictly speaking innate, Leibniz attempts to accommodate the common belief that at least some concepts are adventitious by appealing to his theory of ideal action. The essential idea is that an innate concept can be considered adventitious, in a sense, just in case its ideal cause is to be found outside the mind of the one who possesses the concept. I explore this attempt at accommodation and argue that it fails. [See external link for (...) English draft.]. (shrink)

On its face, Leibniz's argument for primitive concepts seems to imply that unless we can analyze non-primitive concepts into their primitive constituents, we cannot grasp them. This implication, together with Leibniz's belief that we do conceive of some non-primitive concepts, entails that we can analyze some non-primitive concepts into their primitive components. However, Leibniz claims elsewhere that we are incapable of doing this. To resolve this inconsistency, I argue that, for Leibniz, grasping a concept is not an all-or-nothing affair; instead (...) we possess concepts in degrees. When reinterpreted in line with this, Leibniz's argument can avoid the inconsistency. (shrink)

In seiner Dissertano de arte combinatoria entwickelt G. W. Leibniz eine Methode, um Prädikate von einem Subjekt und Subjekte zu einem Prädikat zu finden, und er stellt eine Formel auf, um deren Anzahl zu berechnen. Ich möchte im Folgenden erläutern, wie diese Methode funktioniert und warum sie sowohl einen Teil der, wie Leibniz es nennt, logica inventiva als auch eine direkte Folge seiner Variationslehre bildet, die den zentralen Teil seiner Dissertano ausmacht. Im letzten Abschnitt dieses Beitrages werde ich auf einige (...) theoretische und historische Zusammenhänge zwischen der logica inventiva und der aristotelischen Logik eingehen. Insbesondere werde ich erläutern, in welcher Weise Leibniz' Methode mit einigen traditionellen Versuchen in Verbindung steht, die tota minora eines gegebenen Terms zu bestimmen, und ob die aristotelische Theorie der kategorischen Propositionen in der Lage war, Leibniz' Methode zum Auffinden von Subjekten und Prädikaten innerhalb der logica inventiva zu begründen. (shrink)

What I intend to show is that the Leibnizian language studies—the formal ones as well as those on natural languages—from his early plans for academies and language societies on up to his studies of etymology and to his interest in foreign languages and in logical, geometrical, arithmetical, and other formal calculi, has to be seen as an important contribution to the idea of enlightenment. Their importance was such that Christian Wolff was able to transform the Leibnizian ideas into the mighty (...) movement of Leibniz-Wolffian metaphysics, a movement paralleled to the tradition of Thomasius. Both tradiions later found their unification in Kant’s critical philosophy. (shrink)

This paper is concerned with the problem of the validity of Leibniz's principle of the identity of indiscernibles in physics. After briefly surveying how the question is currently discussed in recent literature and which is the actual meaning of the principle for what concerns physics, we address the question of the physical validity of Leibniz's principle in terms of the existence of a sufficient number of naming predicates in the formal language of physics. This approach allows us to obtain in (...) a formal way the result that a principle of the identity of indiscernibles can be justified in the domain of classical physics, while this is not the case in the domain of quantum physics. (shrink)

This is the first, and indeed the definitive systematic account of the wide-ranging philosophical ideas of Leibniz. The author, a highly respected analytical philosopher, has brought his own formidable abilities to bear on the unwieldy and inaccessible corpus of Leibniz's work.