A common view relating compositional semantics and the objects of assertion holds the following: Sentences φ and ψ expresses the same proposition iff φ and ψ have the same modal profile. Following Dummett, Evans, and Lewis, Stanley argues that this view is fundamentally mistaken. According to Dummett, we must distinguish the semantic contribution a sentence makes to more complex expressions in which it occurs from its assertoric content. Stojnić insists that views which distinguish the roles of content and semantic value (...) must nevertheless ensure a tight connection between the two. But, she contends, there is a crucial disanalogy between the views that follow Lewis and the views that follow Dummett. Stanley’s Dummettian view is argued to contain a fatal flaw: On such views, there is no way to secure an appropriate connection between semantic value and a theoretically motivated notion of assertoric content. I will review the background issues from Dummett, Evans, Lewis, and Stanley, and provide a principled way of bridging the gap between semantic value and a theoretically motivated notion of assertoric content. (shrink)

If natural kinds were defined on the basis of fixed and immutable essences, then – with the end of essentialism in life sciences – their end, at least for those kinds confined to the living realm, would ensue as well (1-2). If appropriately revised and adapted, however, natural kinds may still play an important theoretical role, not only for the sake of philosophical speculation, but also in accomodating scientific practices and in providing an adequate rendering of human reasoning. The proposal (...) outlined in this paper moves from the historical and disjunctive solutions of Millikan and Boyd, but it departs from them in that it offers a conventionalist interpretation of natural kinds. The bulk of the theory is presented through the case study of the distinction between sexes and genders (3). A few remarks on how to further the proposal are offered in the final section (4). (shrink)

Husserl’s Logical Grammar is intended to explain how complex expressions can be constructed out of simple ones so that their meaning turns out to be determined by the meanings of their constituent parts and the way they are put together. Meanings are thus understood as structured contents and classified into formal categories to the effect that the logical properties of expressions reflect their grammatical properties. As long as linguistic meaning reduces to the intentional content of pre-linguistic representations, however, it is (...) not trivial to account for how semantics relates to syntax in this context. In this paper, I analyze Husserl’s Logical Grammar as a system of recursive rules operating on representations and suggest that the syntactic form of representations contributes to their semantics because it carries information about semantic role. I further discuss Husserl’s syntactic account of the unity of propositions and argue that, on this account, logical form supervenes on syntactic form. In the last section I draw some implications for the phenomenology of thought and conjecture that the structural features it displays are likely to convey the syntactic structures of an underlying language-like representational system. (shrink)

Meta-ontology (in van Inwagen's sense) concerns the methodology of ontology, and a controversial meta-ontological issue is to what extent ontology can rely on linguistic analysis while establishing the furniture of the world. This paper discusses an argument advanced by some ontologists (I call them unifiers) against supporters of or coincident entities (I call them multipliers) and its meta-ontological import. Multipliers resort to Leibniz's Law to establish that spatiotemporally coincident entities a and b are distinct, by pointing at a predicate F (...) () made true by a and false by b . Unifiers try to put multipliers in front of a dilemma: in attempting to introduce metaphysical differences on the basis of semantic distinctions, multipliers either (a) rest on a fallacy of verbalism, entailed by a trade-off between a de dicto and a de re reading of modal claims, or (b) beg the question against unifiers by having to assume the distinction between a and b beforehand. I shall rise a tu quoque, showing that unifiers couldn't even distinguish material objects (or events) from the spatiotemporal regions they occupy unless they also resorted to linguistic distinctions. Their methodological aim to emancipate themselves from linguistic analysis in ontological businesses is therefore problematic. (shrink)

Expressively equivalent logical languages can enunciate logical notions in notationally diversified ways. Frege’s Begriffsschrift, Peirce’s Existential Graphs, and the notations presented by Wittgenstein in the Tractatus all express the sentential fragment of classical logic, each in its own way. In what sense do expressively equivalent notations differ? According to recent interpretations, Begriffsschrift and Existential Graphs differ from other logical notations because they are capable of “multiple readings.” We refute this interpretation by showing that there are at least three different kinds (...) of such multiple readings. While readings of the first kind do not capture any essential difference among notations but only among vocabularies, corresponding to readings of the second and the third kind two general parameters according to which notations may differ are defined: linearity vs. non-linearity, and tabularity vs. non-tabularity. This answers the question of how there can be substantially different but expressively equivalent logical notations. (shrink)

Peirce and Frege both distinguished between the propositional content of an assertion and the assertion of a propositional content, but with different notational means. We present a modification of Peirce’s graphical method of logic that can be used to reason about assertions in a manner similar to Peirce’s original method. We propose a new system of Assertive Graphs, which unlike the tradition that follows Frege involves no ad hoc sign of assertion. We show that axioms of intuitionistic logic can be (...) derived from AGs, and argue that AGs analyse and represent assertions and illocutionary content in a way which is motivated both by its logical properties and its historical connection with the ideas that led to the development of the graphical method. (shrink)

This paper provides an analysis of the notational difference between Beta Existential Graphs, the graphical notation for quantificational logic invented by Charles S. Peirce at the end of the 19th century, and the ordinary notation of first-order logic. Peirce thought his graphs to be “more diagrammatic” than equivalently expressive languages for quantificational logic. The reason of this, he claimed, is that less room is afforded in Existential Graphs than in equivalently expressive languages for different ways of representing the same fact. (...) The reason of this, in turn, is that Existential Graphs are a non-linear, occurrence-referential notation. As a non-linear notation, each graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic that are obtained by permuting those elements that in the graphs lie in the same area. As an occurrence-referential notation, each Beta graph corresponds to a class of logically equivalent but syntactically distinct sentences of the ordinary notation of first-order logic in which the identity of reference of two or more variables is asserted. In brief, Peirce’s graphs are more diagrammatic than the linear, type-referential notation of first-order logic because the function that translates the latter to the graphs does not define isomorphism between the two notations. (shrink)

In ‘Swimming Happily in Chinese Logic’ (2021) I suggested that the root conception of knowing for the ancient Chinese Mohists was knowing-as, a conception that fits well with perspectivism in the Zhuangzi, a key Daoist text. Drawing on Wittgenstein’s discussion of both seeing-as and samples, and developing the analogy between seeing-as and knowing-as, I explore various forms of knowing with particular reference to the Mozi, in attempting to make sense of ancient Chinese epistemology and thereby shed light on the whole (...) phenomenon of knowing. (shrink)

In this paper I examine a series of criticisms that have been levelled against Quine's naturalized epistemology, regarding its response to the problem of scepticism. Barry Stroud and Michael Williams, assuming that Quine wishes to refute scepticism, argue that Quine not only fails to undertake this refutation, but is also committed to theses (such as the inscrutability of reference and the underdetermination of theory by evidence) which imply versions of scepticism of their own. In Quine's defence, Roger Gibson argues that (...) Quine can succeed in showing sceptical doubts to be incoherent. But I contend that both parties of this dispute wrongly assume that Quine wishes to defeat the sceptic in a traditional way. Instead, Quine is happy to 'acquiesce' in scepticism about a certain kind of justification. No logical justification of our scientific beliefs is possible on his view. But Quine thinks that pragmatic justification is possible, and acknowledging that this is his view leads to the resolution of a number of interpretive quandaries. (shrink)

Some naturalistic conceptions of philosophical methodologies interpret the doctrine that philosophy is continuous with science to mean that philosophical investigations must implement empirical methods and must not depart from the experimental results that the scientific application of those methods reveal. In this paper, I argue that while our answers to philosophical questions are certainly constrained by empirical considerations, this does not imply that the methods by which these questions are correctly settled are wholly captured by empirical methods. Many historical cases (...) of successful answers to philosophical questions involve strategies and methods that allow the divergence from empirically established results. I develop this idea and then illustrate it with Frege's methodology in his Foundations of Arithmetic. (shrink)

My aim in this paper is to critically evaluate John Campbell's (2002) characterization of the sense of demonstrative terms and his account of why an object's location matters in our understanding of perceptually-based demonstrative terms. Campbell thinks that the senses of a demonstrative term are the different ways of consciously attending to an object. I will evaluate Campbell's account of sense by exploring and comparing two scenarios in which the actual location of a seen object is different from its perceived (...) location. I do this in order to motivate the following point: Campbell's characterization of the sense of a demonstrative term turns sense into a psychologistic notion. As a consequence of this, it is difficult to see how sense could underwrite reference. In short, I shall be arguing that Campbell's account of the ways of perceiving an object is simply inadequate as an account of the Fregean notion of sense, according to which the senses of a demonstrative term are the different ways of thinking about an object. (shrink)

The science of physics has been extremely successful over the last four centuries, mainly for one reason: It does everything it can to disregard anything that has to do with non-physical parts of reality. Although the human body is a physical body, large parts of what distinguishes human beings, sometimes briefly called the human condition, does not belong to the physical domain. This implies that physics (and other sciences of the material universe) offers nothing more than self-imposed helplessness when it (...) comes to questions as to what it means to be human. Yet it is possible to scrutinize the way in which physics (and other sciences) is delineated from the rest of reality: to reconsider its boundaries as they were set about four centuries ago. In other words, it is possible to look for features within the physical that are related to something outside the physical which physics itself ignores. The key concept to do so is proposed to be meaning, in its two variants of reference and sense. Meaning provides a viable perspective to illuminate the deep structure of reality as it extends beyond physics and across its boundaries. (shrink)

In every introductory course on logic, students learn that expressions like ‘somebody’, ‘nothing’ or ‘every woman’ are not names or referring expressions, but quantifiers, and that, owing to this,...

The present paper is a continuation of a previous one by the same title, the content of which faced the issue concerning the relations of coreference and qualification in compliance with the Navya-Nyāya theoretical framework, although prompted by the Advaita-Vedānta enquiry regarding non-difference. In a complementary manner, by means of a formal analysis of equivalence, equality, and identity, this section closes the loop by assessing the extent to which non-difference, the main issue here, cannot be reduced to any of the (...) former. The following sections of this study will focus on the assessment of the eventual possibility of causation and transformation in non-difference. (shrink)

Say that an audience understands a given utterance perfectly only if she correctly identifies which proposition (or propositions) that utterance expresses. In ideal circumstances, the participants in a conversation will understand each other’s utterances perfectly; however, even if they do not, they may still understand each other’s utterances at least in part. Although it is plausible to think that the phenomenon of partial understanding is very common, there is currently no philosophical account of it. This paper offers such an account. (...) Along the way, I argue against two seemingly plausible accounts which use Stalnaker’s notion of common ground and Lewisian subject matters, respectively. (shrink)

ABSTRACT In ‘The philosophical basis of intuitionistic logic’, Michael Dummett discusses two routes towards accepting intuitionistic rather than classical logic in number theory, one meaning-theoretical and the other ontological. He concludes that the former route is open, but the latter is closed. I reconstruct Dummett's argument against the ontological route and argue that it fails. Call a procedure ‘investigative’ if that in virtue of which a true proposition stating its outcome is true exists prior to the execution of that procedure; (...) and ‘generative’ if the existence of that in virtue of which a true proposition stating its outcome is true is brought about by the execution of that procedure. The problem with Dummett's argument then is that a particular step in it, while correct for investigative procedures, is not correct for generative ones. But it is the latter that the ontological route is concerned with. (shrink)

I. An argument is presented for the conclusion that the hypothesis that no one will ever decide a given proposition is intuitionistically inconsistent. II. A distinction between sentences and statements blocks a similar argument for the stronger conclusion that the hypothesis that I have not yet decided a given proposition is intuitionistically inconsistent, but does not block the original argument. III. A distinction between empirical and mathematical negation might block the original argument, and empirical negation might be modelled on Nelson''s (...) strong negation, but only on intuitionistically unacceptable assumptions. IV. Intuitionists may have to accept the original argument, and therefore be committed to a dubious view of time on which there cannot be merely inductive evidence for statements about the infinite future. (shrink)

Without directly addressing the Demarcation Problem for logic—the problem of distinguishing logical vocabulary from others—we focus on distinctive aspects of logical vocabulary in pursuit of a second goal in the philosophy of logic, namely, proposing criteria for the justification of logical rules. Our preferred approach has three components. Two of these are effectively Belnap’s, but with a twist. We agree with Belnap’s response to Prior’s challenge to inferentialist characterisations of the meanings of logical constants. Belnap argued that for a logical (...) constant to exist, its rules must be conservative over a previously given consequence relation and guarantee the uniqueness of the constant. The twist is that we require logical vocabulary to be provably conservative, not over a previously given formal consequence relation, but over a previously given meaningful vocabulary of a language. Uniqueness is also a feature defined in terms of provability: if two syntactically distinguished expressions are governed by the same rules, then formulas with them as main operators are interderivable. Belnap’s criteria are not only those for the existence of a logical constant, but more: they are what distinguishes logical vocabulary from all other expressions. It is the defining mark of a logical constant that it is provably conservative over the fragment of the language which excludes it and that its rules guarantee its uniqueness. The third component is the topic neutrality of logic. The provable conservativeness of logic over a previously given vocabulary of a language is motivated, in part, by appeal to molecularism in the theory of meaning. Molecularity is a feature endorsed by the theory of meaning as a whole, so it does not distinguish logical constants from other expressions. The same is true for conservativeness. We argue that molecularity, and hence conservativeness, are implicit presuppositions of speakers’ use of language: the addition of new vocabulary to a language is presupposed to be conservative. But this presupposition is one that we should be able reflectively to endorse (such as when attempting a rational reconstruction of the use of the vocabulary). Thus, where conservativeness is found to fail, this defect should be remedied and the use of the vocabulary corrected (as in classical negation) or excised altogether (as in pejoratives). We go on to characterise a notion of topic neutrality, which we argue applies to logical vocabulary. We then note that reflective endorsement of the conservativeness of a topic neutral vocabulary requires a proof that the vocabulary is conservative relative to any base vocabulary. Thus we require that logical vocabulary be demonstrably conservative. Allying this requirement, distinctive of logic, to a general consideration about the commitments of assertion yields a mode of justification for logical constants akin to some conceptions of Harmony, i.e., to the idea that the consequences of assertion of a logical complex need to be warranted by the grounds and ought to be the strongest consequences warranted by the grounds. Intuitionistic logic acquires a somewhat familiar justification but emanating from a new motivation. (shrink)

El presente texto es una guía para una primera lectura de los Los fundamentos de la aritmética de Gottlob Frege para estudiantes del grado de Filosofía. -/- No pretende hacer ninguna aportación a la investigación sobre Frege sino ofrecer los instrumentos para hacer una primera lectura mediante la recopilación y la ordenación de los textos relevantes de los estudiosos de Frege, especialmente de la literatura en inglés. En la mayor parte de los casos, las referencias a otros autores (Autorfecha) preceden (...) a una traducción de los escritos referidos así como una unificación de la terminología, el recorte de lo no relevante y el añadido de las explicaciones pertinentes para hacer el texto accesible a un estudiante del grado de Filosofía. En el caso de que la cita justifique una afirmación que no se desarrolla, se verá precedida por la palabra "ver" dentro del paréntesis de la referencia. El texto usado para las citas de Los fundamentos de la aritmética es la traducción de Ulises Moulines dado que el que esto escribe no sabe alemán. La guía no supone más matemáticas que las que se estudian en los cursos anteriores a la universidad. Sin embargo, es recomendable haber hecho un curso elemental de lógica matemática y teoría de conjuntos. La razón fundamental es que la formalización de ciertas proposiciones permite aclarar extremos que se hacen muy enojosos sin esos instrumentos. (shrink)

This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

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)

Explores the stable core of Wittgenstein's philosophy as developed from the Tractatus to the Philosophical Investigations.

EbertPhilip A and RossbergMarcus, eds.* * _ Essays on Frege’s Basic Laws of Arithmetic_. Oxford: Oxford University Press, 2019. Pp. xii + 673. ISBN: 978-0-19-871208-4 ; 978-0-19-102005-6, 978-0-19-178024-0. doi: 10.1093/oso/9780198712084.001.0001.

This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...) volume includes 35 contributions. It is divided into nine parts: 1. Who Created the Concept of God; 2. Omniscience, Omnipotence, Timelessness and Spacelessness of God; 3. God and Perfect Goodness, Perfect Beauty, Perfect Freedom; 4. God, Fundamentality and Creation of All Else; 5. Simplicity and Ineffability of God; 6. God, Necessity and Abstract Objects; 7. God, Infinity, and Pascal's Wager; 8. God and (Meta-)Mathematics; and 9. God and Mind. (shrink)

Nominalizations are expressions that are particularly challenging philosophically in that they help form singular terms that seem to refer to abstract or derived objects often considered controversial. The three standard views about the semantics of nominalizations are [1] that they map mere meanings onto objects, [2] that they refer to implicit arguments, and [3] that they introduce new objects, in virtue of their compositional semantics. In the second case, nominalizations do not add anything new but pick up objects that would (...) be present anyway in the semantic structure of a corresponding sentence without a nominalization. In the first and third case, nominalizations in a sense ‘create’ new objects’, enriching the ontology on the basis of the meaning of expressions. I will argue that there is a fourth kind of nominalization which requires a quite different treatment. These are nominalizations that introduce ‘new’ objects, but only partially characterize them. Such nominalizations generally refer to events or tropes. I will explore an account according on which such nominalizations refer to truth makers. (shrink)

In the section “Validity and Existence in Logik, Book III,” I explain Lotze’s famous distinction between existence and validity in Book III of Logik. In the following section, “Lotze’s Platonism,” I put this famous distinction in the context of Lotze’s attempt to distinguish his own position from hypostatic Platonism and consider one way of drawing the distinction: the hypostatic Platonist accepts that there are propositions, whereas Lotze rejects this. In the section “Two Perspectives on Frege’s Platonism,” I argue that this (...) is an unsatisfactory way of reading Lotze’s Platonism and that the Ricketts-Reck reading of Frege is in fact the correct way of thinking about Lotze’s Platonism. (shrink)

Kiinnostukseni kohteena seuraavassa on tietty suosittu ”intellektualistinen” käsitys kielen ja käsitteiden oppimisesta ja ymmärtämisestä. Käsitys on sinällään hyvin periteinen, ja voidaan väittää, että se on ollut ainakin piilevästi sisäänrakennettuna useiden uuden ajan filosofien teorioissa. Jätän tämän väitteen tarkemman erittelyn kuitenkin filosofian historioitsijoiden selvitettäväksi, ja keskityn seuraavassa käsityksen enemmän tai vähemmän julkilausuttuihin ilmentymiin nykyajan filosofiassa. Se on vaikuttanut monissa vaikutusvaltaisissa lähestymistavoissa kieleen, merkitykseen ja mieleen.

In this paper, I distinguish between two possible versions of Amie Thomasson’s easy ontology project that differ in virtue of positing atomic or holistic application conditions, and evaluate the strengths of a holistic version over a non-holistic version. In particular, I argue that neither of the recently identified regress or circularity problems are troublesome for the supporter of easy ontology if they adopt a holistic account of application conditions. This is not intended to be a defence of easy ontology from (...) all possible objections, but rather to compare holistic and non-holistic versions of the view. This discussion is also significant in that it serves to highlight two distinct forms of easy ontology, which, I argue, need to be distinguished when assessing the merits of the easy approach in future work. (shrink)

Aktivnost integracije i distribucije prožima cjelokupni čovjekov jezik, mišljenje i djelovanje; njegov praktični i teorijski um, uz pomoć malog broja operacija (konjunkcija, negacija, kvantifikacija) koje čine logičke konstante, sabire i razdjeljuje varijabilne elemente jezika, svijeta i mišljenja u beskonačne konačnosti (skupovi, klase, relacije, atributi) u kojima se koreliraju realne stimulacije i virtualne simulacije, čijom se konstrukcijom, rekonstrukcijom i dekonstrukcijom formiraju i transformiraju "dobro uređene formule" jezičko-gramatičkih i mentalno-psiholoških struktura koje se u svijetu saznanja imenuju pojmom svijeta, pojmom jezika, pojmom duha. (...) Svijet pojmova, koji se uzima u kvantificiranoj formi govora / "(x) (Fx) / kao realni ili egzistentni, a u substitutivnoj formi / " { x : Fx}" / kao virtualni ili subzistentni zbog apstraktnosti klasa i relacija, konstruira mrežu multipliciranih logičkih općenitosti, njihovih relacija ili zakonitih sukcesija koje se mogu izraziti, parafrazirati i prevesti iz jedne notacije u drugu salva veritate ed salva congruentia. (shrink)

A comprehensive survey of Martin-Löf's constructive type theory, considerable parts of which have only been presented by Martin-Löf in lecture form or as part of conference talks. Sommaruga surveys the prehistory of type theory and its highly complex development through eight different stages from 1970 to 1995. He also provides a systematic presentation of the latest version of the theory, as offered by Martin-Löf at Leiden University in Fall 1993. This presentation gives a fuller and updated account of the system. (...) Earlier, brief presentations took no account of the issues related to the type-theoretical approach to logic and the foundations of mathematics, while here they are accorded an entire part of the book. Readership: Comprehensive accounts of the history and philosophy of constructive type theory and a considerable amount of related material. Readers need a solid background in standard logic and a first, basic acquaintance with type theory. (shrink)

In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics, meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.

This book has two objectives: to be a contribution to the understanding of Frege's theory of truth – especially a defence of his notorious critique of the correspondence theory - and to be an introduction to the practice of interpreting philosophical texts.