The topic of our analysis is the argument for the existence of substances given by Bernard Bolzano in Athanasia, where he essentially employs two ontological categories: substance and adherence. Bolzano considers the real and conditioned Inbegriff of all adherences, which are wirklich and nicht selbst bestehen. He claims that the formed collection is dependent on something external and non-adherential, which therefore is a substance. Bolzano’s argumentation turns out to be structurally similar to his argument for the existence of God from (...) Lehrbuch der Religionswissenschaft, but in each of these reasonings, we find different plausible interpretations of the key concept “Inbegriff”. The latter argumentation refers to the mereological totality of existentially conditioned objects. We propose the explication of the Bolzanian Inbegriff of all adherences using two types of predication: we consider its extension as composed of certain intensional counterparts of adherences. In our approach, we use a fragment of the theory of abstract objects formulated by E. Zalta, describing two different relations between individuals and properties: extensional exemplification and intensional encoding. We put our reconstruction in a wider context of Bolzano’s ontology, formulating the needed axioms with two primitive predicates of second order... is an adherence,... is conditioned by something real as well as the conditionally introduced first order predicate constant \ for Inbegriff of all adherential ideas. Finally, we sketch a model for our theory. (shrink)

RÉSUMÉ: Dans cet article, j’entreprends de clarifier le projet (frégéen) d’une logique de l’arithmétique -- tel qu’il a été discuté par Natorp et Rickert -- en distinguant trois questions directrices. Le nombre est-il un objet logique? L’arithmétique est-elle réductible à la logique? Est-il possible de déduire les opérations arithmétiques de lois purement logiques? Ma thèse est que la distinction rigoureuse de ces trois questions permet de lever une grande partie des obscurités qui affectent en généralle programme d’une logique de l’arithmétique. (...) La contribution néo-kantienne à ce programme se trouve du même coup éclairée d’une lumière nouvelle.ABSTRACT: In this article, I try to shed light on the (Fregean) project of a logic of arithmelic-as discussed by Natorp and Rickert-by outlining three main questions. Is the number a logical object? Is arithmetic reducible to logic? Is it possible to deduce the arithmetical operations from purely logical laws? I argue that rigorous distinction between these three questions makes it possible to elucidate many problems affecting the program of a logic of arithmetic. The Neo-Kantian contribution to this program is at the same time considered in a new light. (shrink)

open journal of Philosophical Investigations (PI) is an international journal dedicated to the latest advancements in philosophy. The goal of this journal is to provide a platform for academicians all over the world to promote, share, and discuss various new issues and developments in different areas of philosophy. -/- All manuscripts to be prepared in English or Persian and are subject to a rigorous and fair peer-review process. Generally, accepted papers will appear online. The journal publishes papers including the following (...) fields: -/- · Analytic Philosophy · Ancient Greek and Roman Philosophy · Art Aesthetics · Comparative Philosophy West and Chinese · Eastern Philosophy . Islamic philosophy · Epistemology · Ethics · Hermeneutics · History of Religious Thought · History of Western Philosophy · Language Logic . (shrink)

The argument for modal collapse is partly responsible for the widespread rejection of the so-called Principle of Sufficient Reason in recent times. This paper discusses the PSR against the background of the recent debate about grounding and develops principled reasons for rejecting the argument from modal collapse.

G. F. Stout is famous as an early twentieth century proselyte for abstract particulars, or tropes as they are now often called. He advanced his version of trope theory to avoid the excesses of nominalism on the one hand and realism on the other. But his arguments for tropes have been widely misconceived as metaphysical, e.g. by Armstrong. In this paper, I argue that Stout’s fundamental arguments for tropes were ideological and epistemological rather than metaphysical. He moulded his scheme to (...) fit what is actually given to us in perception, arguing that our epistemic practices would break down in an environment where only universals were given to us. (shrink)

This paper defends a realist account of the composition of Newtonian forces, dubbed ‘residualism’. According to residualism, the resultant force acting on a body is identical to the component forces acting on it that do not prevent each other from bringing about its acceleration. Several reasons to favor residualism over alternative accounts of the composition of forces are advanced. (i) Residualism reconciles realism about component forces with realism about resultant forces while avoiding any threat of causal overdetermination. (ii) Residualism provides (...) a systematic semantics for the term ‘force’ within Newtonian mechanics. (iii) Residualism allows us to precisely apportion the causal responsibility of each component force in the ensuing acceleration. (iv) Residualism handles special cases such as null forces, single forces, and antagonistic forces in a natural way. (v) Residualism provides a neat picture of the causal powers of forces: each force essentially has two causal powers⎯the power to bring about accelerations (sometimes together with other co-directionnal forces) and the power to prevent other forces from doing so⎯exactly one of which is manifested at a time. (vi) Residualism avoids commitment to unobservable effects of forces: forces cause either stresses (tensile or compressive) or accelerations. (shrink)

This paper is aimed at understanding one central aspect of Bolzano's views on deductive knowledge: what it means for a proposition and for a term to be known a priori. I argue that, for Bolzano, a priori knowledge is knowledge by virtue of meaning and that Bolzano has substantial views about meaning and what it is to know the latter. In particular, Bolzano believes that meaning is determined by implicit definition, i.e. the fundamental propositions in a deductive system. I go (...) into some detail in presenting and discussing Bolzano's views on grounding, a priori knowledge and implicit definition. I explain why other aspects of Bolzano's theory and, in particular, his peculiar understanding of analyticity and the related notion of Ableitbarkeit might, as it has invariably in the past, mislead one to believe that Bolzano lacks a significant account oï a priori knowledge. Throughout the paper, I point out to the ways in which, in this respect, Bolzano's antagonistic relationship to Kant directly shaped his own views. (shrink)

This essay focuses on a recently prominent notion of ground which is distinctive for how it links metaphysics to explanation. Ground is supposed to serve both as the common factor in diverse in virtue of questions as well as the structuring relation in the project of explaining how some phenomena are “built” from more fundamental phenomena. My aim is to provide an opinionated synopsis of this notion of ground without engaging with others. Ground, so understood, generally resists illumination by appeal (...) to more familiar models of explanation. Nevertheless, its distinctive explanatory and metaphysical aspects guide us on characterizing its explanatory logic and its metaphysical features. Some issues concerning the meta-question of what grounds ground are explored, as well as some recent skeptical challenges to ground. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

In spite of its significance for everyday and philosophical discourse, the explanatory connective has not received much treatment in the philosophy of logic. The present paper develops a logic for based on systematic connections between and the truth-functional connectives.

Both through his own work and that of his students, Franz Clemens Brentano had an often underappreciated influence on the course of 20 th - and 21 st -century philosophy. _The Routledge Handbook of Franz Brentano and the Brentano School_ offers full coverage of Brentano’s philosophy and his influence. It contains 38 brand-new essays from an international team of experts that offer a comprehensive view of Brentano’s central research areas—philosophy of mind, metaphysics, and value theory—as well as of the principal (...) figures shaped by Brentano’s school of thought. A General Introduction serves as an overview of Brentano and the contents of the volume and three separate bibliographies point students and researchers on to further avenues of inquiry. Systematic and detailed, _The Routledge Handbook of Franz Brentano and the Brentano School_ provides readers with a valuable reference to Brentano’s work, and to his lasting importance in the history of philosophy and in contemporary debates. (shrink)

This presentation aims to clarify the historical and theoretical background of the studies included in this issue of Philosophiques, which focus on the work of Husserl during the period of Halle . After a brief description of Husserl’s early years of apprenticeship in philosophy between 1876 and his studies with Brentano in Vienna, I identify several steps that marked the development of his philosophy from his arrival in Halle to the publication of the Logical Investigations : his studies under the (...) direction of C. Stumpf, the publication of the first volume of Philosophy of Arithmetic, the researches belonging to the project of the second volume of this work, the abandonment of this project and the development of the phenomenology of the Logical Investigations. The last part of this paper is an examination of the philosophical issues underlying the disputatio on D. W. Smith’s recent book on Husserl’s philosophy. (shrink)

Ce numéro de Philosophiques rend hommage au philosophe d’origine autrichienne Edmund Husserl (1859-1938) à l’occasion de son 150e anniversaire de naissance. Il est consacré à l’oeuvre du jeune Husserl durant la période de Halle (1886-1901) et réunit plusieurs spécialistes des études husserliennes qui jettent un regard neuf sur cette période méconnue dans la philosophie du père de la phénoménologie. Avec un souci de situer Husserl dans le contexte historique auquel appartiennent ses principaux interlocuteurs durant cette période, ces études portent sur (...) des thèmes tels l’intentionnalité dans son rapport à Bernard Bolzano, Franz Brentano et Kazimierz Twardowski ; sa théorie du jugement et des assomptions ; sa philosophie des mathématiques et de la logique ; sa contribution au débat sur la Gestalt ; ses échanges avec le néokantisme de Marbourg, et notamment avec Paul Natorp, etc. Ces études sont suivies d’une disputatio autour d’un ouvrage récent portant sur le projet philosophique de Husserl et le sens de sa phénoménologie aujourd’hui. (shrink)

Amongst the entities making up social reality, are there necessary relations whose necessity is not a mere reflection of the logical connections between corresponding concepts? We distinguish three main groups of answers to this question, associated with Hume and Adolf Reinach at opposite extremes, and with Searle who occupies a position somewhere in the middle. We first set forth Reinach’s views on what he calls ‘material necessities’ in the realm of social entities. We then attempt to show that Searle has (...) not identified a sustainable position somewhere between the Humean and the Reinachian extremes. This is because Searle’s position is threatened by circularity, and to steer clear of that danger it must incorporate at least some elements of Reinach’s essentialism. (shrink)

Intentionality (‘directedness’, ‘aboutness’) is both a central topic in contemporary philosophy of mind, phenomenology and the cognitive sciences, and one of the themes with which both analytic and Continental philosophers have separately engaged starting from Brentano and Edmund Husserl’s ground-breaking Logical Investigations (1901) through Roderick M. Chisholm, Daniel C. Dennett’s The Intentional Stance, John Searle’s Intentionality, to the recent work of Tim Crane, Robert Brandom, Shaun Gallagher and Dan Zahavi, among many others. In this paper, I shall review recent discussions (...) of intentionality, including some recent explorations of the history of the concept (paying particular attention to Anselm), and suggest some ways the phenomenological approach of Husserl and Heidegger can still offer insights for contemporary philosophy of mind and consciousness. (shrink)

To talk about simple concepts presupposes that the notion of concept has been aptly explicated. I argue that a most adequate explication should abandon the set-theoretical paradigm and use a procedural approach. Such a procedural approach is offered by Tichý´s Transparent Intensional Logic (TIL). Some main notions and principles of TIL are briefly presented, and as a result, concepts are explicated as a kind of abstract procedure. Then it can be shown that simplicity, as applied to concepts, is well definable (...) as a property relative to conceptual systems, each of which is determined by a finite set of simple (‘primitive’) concepts. Refinement as a method of replacing simple concepts by compound concepts is defined. (shrink)

In this paper I discuss Künne’s Modest Theory of truth, and develop a variation on a worry that Field expresses with respect to Horwich’s related view. The worry is not that deflationary accounts are false, but rather that, because they take propositions as truth-bearers, they are not philosophically interesting. Compatibly with the intuitions of ordinary speakers, we can understand proposition so that the proposals do account for a property that such truth-bearers have. Nevertheless, we saliently apply the truth-concept also to (...) entities such as utterances or assertions , and the de flationary accounts do not provide a similarly deflationary account for those applications. In fact, there are good reasons to suspect that no such account would be forthcoming; we need something more substantive or in flationary there. (shrink)

The possibility of error is related to the existence a norm. Connections are spelled out to the notion of infallibility and to that of a modifying predicate, to traditional truth theories in connection with “truth of things”, as well as the primacy of the negative cases, for instance “ false friend”.

That uses of language not only can, but even normally do, have the character of actions was a fact largely unrealised by those engaged in the study of language before the present century, at least in the sense that there was lacking any attempt to come to terms systematically with the action-theoretic peculiarities of language use. Where the action-character of linguistic phenomena was acknowledged, it was normally regarded as a peripheral matter, relating to derivative or nonstandard aspects of language which (...) could afford to be ignored. (shrink)

The essay is a partial investigation into the semantics of the explanatory connective ‘because’. After three independently plausible assumptions about ‘because’ are presented in some detail, it is shown how their interaction generates a puzzle about ‘because’, once they are combined with a common view on conceptual analysis. Four possible solutions to the puzzle are considered.

I present an argument for an interpretation of Kant's views on the nature of the ‘content [Inhalt]’ of ‘cognition [Erkenntnis]’. In contrast to one of the longest standing interpretations of Kant's views on cognitive content, which ascribes to Kant a straightforwardly psychologistic understanding of content, and in contrast as well to the more recently influential reading of Kant put forward by McDowell and others, according to which Kant embraces a version of Russellianism, I argue that Kant's views on this topic (...) are of a much more Fregean bent than has traditionally been admitted or appreciated. I conclude by providing a sketch of how a better grasp of Kant's views on cognitive content in general can help bring into sharper relief what is, and what is not, at stake in the recent debates over whether Kant accepts a particular kind of cognitive content—namely, non-conceptual content. (shrink)

Leibniz frequently argued that reasons are to be weighed against each other as in a pair of scales, as Professor Marcelo Dascal has shown in his article "The Balance of Reason." In this kind of weighing it is not necessary to reach demonstrative certainty – one need only judge whether the reasons weigh more on behalf of one or the other option However, a different kind of account about rational decision-making can be found in some of Leibniz's writings. In his (...) article "Was Leibniz's Deity an Akrates?" Professor Jaakko Hintikka has argued that Leibniz developed a new vectorial model for rational decisions which is better suited to complicated decisions, where values are complementary to each other. This model, related closely to his work in metaphysics and the philosophy of mind, is a heuristic device which helps in finding rational combinations - and in an ideal case an optimum - between plural inclinations to the good. I shall argue that Leibniz applies more or less implicitly both of these models in his practical rationality. In simple situations he applied the pair of scales model and in more complicated situations he applied the vectorial model. (shrink)

Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora . These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science . In this paper we will do two things. First of all, we will (...) propose a general and systematized account of the Classical Model of Science. Secondly, we will offer an analysis of the philosophical significance of this model at different historical junctures by giving an overview of the connections it has had with a number of important topics. The latter include the analytic-synthetic distinction, the axiomatic method, the hierarchical order of sciences and the status of logic as a science. Our claim is that particularly fruitful insights are gained by seeing themes such as these against the background of the Classical Model of Science. In an appendix we deal with the historiographical background of this model by considering the systematizations of Aristotle’s theory of science offered by Heinrich Scholz, and in his footsteps by Evert W. Beth. (shrink)

This paper concentrates on some aspects of the history of the analytic-synthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...) that is, within the Classical Model of Science: scientific knowledge as cognitio ex principiis . But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

Narrowly speaking, the correspondence theory of truth is the view that truth is correspondence to a fact -- a view that was advocated by Russell and Moore early in the 20 th century. But the label is usually applied much more broadly to any view explicitly embracing the idea that truth consists in a relation to reality, i.e., that truth is a relational property involving a characteristic relation (to be specified) to some portion of reality (to be specified). During the (...) last 2300 years this basic idea has been expressed in many ways, resulting in a rather extended family of views, theories, and theory sketches. The members of the family employ various concepts for the relevant relation (correspondence, conformity, congruence, agreement, accordance, copying, picturing, signification, representation, reference, satisfaction) and/or various concepts for the relevant portion of reality (facts, states of affairs, situations, events, objects, sequences of objects, sets, properties, tropes). The resulting multiplicity of versions and reformulations of the theory is due to a blend of substantive and terminological differences. (shrink)

Let me start with a well-known story. Kant held that logic and conceptual analysis alone cannot account for our knowledge of arithmetic: “however we might turn and twist our concepts, we could never, by the mere analysis of them, and without the aid of intuition, discover what is the sum [7+5]” (KrV, B16). Frege took himself to have shown that Kant was wrong about this. According to Frege’s logicist thesis, every arithmetical concept can be defined in purely logical terms, and (...) every theorem of arithmetic can be proved using only the basic laws of logic. Hence, Kant was wrong to think that our grasp of arithmetical concepts and our knowledge of arithmetical truth depend on an extralogical source—the pure intuition of time (Frege 1884, §89, §109). Arithmetic, properly understood, is just a part of logic. (shrink)

In philosophical logic and proof theory, we often find multiple-conclusion systems that induce a conjunctive reading of premises and a disjunctive reading of conclusions. In mathematical logic, in contrast, we often find multiple-conclusion systems that induce a conjunctive reading of both premises and conclusions. This paper studies some technical and philosophical aspects of this latter approach to multiple-conclusion consequence. The takeaway is that, while the importance of disjunctive multiple conclusions is beyond doubt, conjunctive multiple conclusions also have philosophical interest. First, (...) because there is some evidence that there are arguments with conjunctive multiple conclusions in natural language. Second, because conjunctive multiple conclusions are compatible with the reflexivity and transitivity of logical consequence, and this allows them to cohere better with some of our best accounts of what logical consequence is. (shrink)

A running commentary is offered on the first half of Frege’s Grundlagen der Arithmetik, §17, and suggests that Frege anticipated the method of demonstration used by Paul Bernays for the Deduction Theorem.

This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. -/- The chapters of which this book is composed discuss the (...) subject from a rich variety of angles, including the history of logic, the proper interpretation of logical validity, natural deduction rules, the notions of harmony and of synonymy, the structure of proofs, the logical status of equality, intentional phenomena, and the proof theory of second-order arithmetic. All chapters relate directly to questions that have driven Schroeder-Heister's own research agenda and to which he has made seminal contributions. The extensive autobiographical chapter not only provides a fascinating overview of Schroeder-Heister's career and the evolution of his academic interests but also constitutes a contribution to the recent history of logic in its own right, painting an intriguing picture of the philosophical, logical, and mathematical institutional landscape in Germany and elsewhere since the early 1970s. The papers collected in this book are illuminatingly put into a unified perspective by Schroeder-Heister's comments at the end of the book. Both graduate students and established researchers in the field will find this book an excellent resource for future work in proof-theoretic semantics and related areas. (shrink)

In this paper I investigate the idea that in conceptual analysis we are in a substantial way concerned with revealing metaphysical grounds. I argue that a recent proposal fails, according to which we aim to reveal what complex concepts are grounded in. The notion ofcomposition, rather than that ofgrounding, is the best way to understand the intuitive hierarchy of concepts. In an analysis we reveal thecomponentsorpartsof complex concepts and their structure. Finally, I propose an alternative role for grounding in our (...) accounts of analysis: in analyses we reveal truths about the composition of concepts that serve as grounds for truths about theirfunctions, which are what we want to understand. (shrink)

As it is presently employed, grounding permits grounding many things from one ground. In this paper, I show why this is a mistake by pushing for a uniqueness principle on grounding. After arguing in favor of this principle, I say something about it and kinds of grounding, discuss a similar principle, and consider its import on a formal feature of grounding, ontology, and ontological simplicity.

Logicism is the view that mathematical truths are logical truths. But a logical truth is commonly thought to be one with a universally valid form. The form of “7 > 5” would appear to be the same as “4 > 6”. Yet one is a mathematical truth, and the other not a truth at all. To preserve logicism, we must maintain that the two either are different subforms of the same generic form, or that their forms are not at all (...) what they appear. The historical record shows that Russell pursued both these options, but that the struggle with the logical paradoxes pushed him away from the first kind of response and toward the second. An object cannot itself have a kind of inner logical complexity that makes a proposition have a different logical form merely in virtue of being about it, nor can their representatives in logical forms be single things different for different forms, at least not without postulating too many such objects and thereby creating Cantorian diagonal paradoxes. There are only apparent objects which are actually fragments of logical forms, different in different cases. (shrink)

Philosophers have long tried to articulate the specific epistemic status of judgements that neither need nor admit of justification by drawing on the metaphor of ‘the light of truth’. In contrast, in Brentano's account of intuitive judgement correctness is central: intuitive or immediately evident judgements are ‘characterized as correct (right)’. The aim of my paper is to introduce and explore Brentano’s correctness-based view. I will conclude by relating it to the work of his students Meinong, Stumpf, and Husserl, who gradually (...) eroded Brentano’s insights. (shrink)

This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is (...) a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their place in early modern philosophy; the notion of judgement and logical theory in Wolff, Kant and Neo-Kantians like Windelband; their development in the Husserlian phenomenological paradigm; and the work of Bolzano, Russell and Frege. The papers, whose authors include Per Martin-Löf, Göran Sundholm, Michael Della Rocca and Robin Rollinger, represent a finely judged editorial selection highlighting work on philosophers exercised by the question of whether or not an epistemic notion of judgement has a role to play in logic. The volume will be of profound interest to students and academicians for its application of historical developments in philosophy to the solution of vexatious contemporary issues in the foundation of logic. ​. (shrink)

In this study two strands of inferentialism are brought together: the philosophical doctrine of Brandom, according to which meanings are generally inferential roles, and the logical doctrine prioritizing proof-theory over model theory and approaching meaning in logical, especially proof-theoretical terms.

This paper explores a novel notion of self-explanation that combines ideas from two sources: the tripartite account of explanation, according to which a proposition can help explain another either in the capacity of a reason why the latter obtains or in the capacity of an explanatory link, and the notion of an empty-base explanation, which generalizes the ideas of explanation by zero-grounding and explanation by status. After having introduced these ideas and the novel notion of self-explanation, I argue that the (...) latter has the potential to resist extant arguments against the possibility of self-explanation. In the remainder of the paper, I discuss candidates for such self-explanatory propositions and suggest possible applications for Humeanism about laws of nature, the debate on the grounds of ground, the rationalist tradition, and philosophical theology. (shrink)

What does it mean that some proposition follows from others? The standard way of spelling out the notion proceeds in modal terms: x follows from y iff necessarily, if y is true, so is x. But although this yields a useful and manageable account of consequence, it fails to capture certain aspects of our pre-theoretical understanding of consequence. In this paper, an alternative notion of logical consequence, based on the idea of grounding, is developed.

The paper’s central theme is the link between phenomenology and the notion of the mathesis universalis, a link articulated by Husserl in the third volume of the Ideas: “My way to phenomenology was essentially determined by the mathesis universalis.” The paper suggests three interpretations of the phenomenology—mathesis universalis nexus: the first is related to the development of Husserl’s conception of the foundations of arithmetic; the second is based on the role of the theory of manifolds in Husserl’s Logical Investigations; and (...) the third reflects the importance of the distinction between “generalization” and “formalization” for phenomenology. After examining these interpretations, the paper explores which is most helpful for understanding why Husserl distanced himself from Bolzano, arguing that the third interpretation provides the most edifying answer. (shrink)

Bernard Bolzano (1781–1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part–whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano’s mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano’s infinite sums can be equipped (...) with the rich and original structure of a non-commutative ordered ring, and that Bolzano’s views on the mathematical infinite are, after all, consistent. (shrink)

I argue for a new delimitation of what Kant means by ‘cognition [Erkenntnis]’, on the basis of the intermediate, transitional place that Kant gives to cognition in the ‘progression [Stufenleiter]’ of our representations and our consciousness of them. I show how cognition differs from mental acts lying earlier on this progression—such as sensing, intuiting, and perceiving—and also how cognition differs from acts lying later on this progression—such as explaining, having insight, and comprehending. I also argue that cognition should not be (...) confused with ‘knowledge [Wissen]’, insofar as knowledge represents the culmination of a separate orthogonal progression of acts of ‘holding-true’. Along the way, I show how having in focus the specific progression from representation, to consciousness, to cognition allows us to better appreciate the architectonic significance of the progression of Kant’s analysis in the first Critique, and also helps to illuminate the unity of Kant’s account of cognition itself across its variety of forms. (shrink)

In Modal Logic as Metaphysics, Timothy Williamson claims that the possibilism-actualism (P-A) distinction is badly muddled. In its place, he introduces a necessitism-contingentism (N-C) distinction that he claims is free of the confusions that purportedly plague the P-A distinction. In this paper I argue first that the P-A distinction, properly understood, is historically well-grounded and entirely coherent. I then look at the two arguments Williamson levels at the P-A distinction and find them wanting and show, moreover, that, when the N-C (...) distinction is broadened (as per Williamson himself) so as to enable necessitists to fend off contingentist objections, the P-A distinction can be faithfully reconstructed in terms of the N-C distinction. However, Williamson’s critique does point to a genuine shortcoming in the common formulation of the P-A distinction. I propose a new definition of the distinction in terms of essential properties that avoids this shortcoming. (shrink)

Frege’s account, according to which the problem of how thoughts are apprehended should be a part of psychology, has led scholars to the idea that every consideration regarding subjectivity is absent in this author. From the latter follows a certain way of conceiving the relation between Frege and Husserl which establishes an absolute chasm between both authors regarding the topic mentioned. In the present contribution an extremely different view is defended, namely, that Frege plays an intermediate role between 19th century (...) Platonism and husserlian phenomenology. The main focus of the argument is the commitment between naturalism and idealism which characterizes Platonism before Frege and the beginning of its overcoming carried out by him. (shrink)

In standard model-theoretic semantics, the meaning of logical terms is said to be fixed in the system while that of nonlogical terms remains variable. Much effort has been devoted to characterizing logical terms, those terms that should be fixed, but little has been said on their role in logical systems: on what fixing their meaning precisely amounts to. My proposal is that when a term is considered logical in model theory, what gets fixed is its intension rather than its extension. (...) I provide a rigorous way of spelling out this idea, and show that it leads to a graded account of logicality: the less structure a term requires in order for its intension to be fixed, the more logical it is. Finally, I focus on the class of terms that are invariant under isomorphisms, as they render themselves more easily to mathematical treatment. I propose a mathematical measure for the logicality of such terms based on their associated Löwenheim numbers. (shrink)