Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s (...) type-restrictions are unjustifiable, the type-restrictions imposed by STT are justified by a Fregean semantics. What is more, this Fregean semantics provides us with a principled way to resist Linnebo and Rayo’s Semantic Argument for CTT. We end by examining an alternative approach to cumulative types due to Florio and Jones; we argue that their theory is best seen as a misleadingly formulated version of STT. (shrink)

This paper investigates the connection between two recent trends in philosophy: higher-orderism and conceptual engineering. Higher-orderists use higher-order quantifiers (in particular quantifiers binding variables that occupy the syntactic positions of predicates) to express certain key metaphysical doctrines, such as the claim that there are properties. I argue that, on a natural construal, the higher-orderist approach involves an engineering project concerning, among others, the concept of existence. I distinguish between a modest construal of this project, on which it aims at engineering (...) higher-order analogues of the familiar notion of first-order existence, and an ambitious construal, on which it additionally aims at engineering a broadened notion of existence that subsumes first-order and higher-order existence. After identifying a substantial problem for the ambitious project, I investigate a possible response which is based on adopting a cumulative type theory as the background higher-order logic. While effective against the problem at hand, this strategy turns out to undermine a major reason to embrace higher-orderism in the first place, namely the idea that higher-orderism dissolves a range of otherwise intractable debates in metaphysics. Higher-orderists are therefore best advised to pursue their engineering project on the modest variant and against the background of standard type theory. (shrink)

Recent debates in metaphysics have highlighted the significance of type theories, such as Simple Type Theory (STT), for our philosophical analysis. In this chapter, I present the salient features of a constructive type theory in the style of Martin-Löf, termed CTT. My principal aim is to convey the flavour of this rich, flexible and sophisticated theory and compare it with STT. I especially focus on the forms of quantification which are available in CTT. A (...) further aim is to argue that a comparison between a plurality of theories is beneficial to the philosophical analysis. We may, for example, discover helpful features of one theory that we may want to import into another context, thus enriching our repertoire of formal tools. Or, through comparison with a less well-known theory, we may gain a better understanding of the characteristics of the theories we are familiar with. As argued in this chapter, CTT has much to offer in all of these respects. (shrink)

Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist (...) reading). While STT, understood as a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

I here discuss two problems facing Russellian act-type theories of propositions, and argue that Fregean act-type theories are better equipped to deal with them. The first relates to complex singular terms like '2+2', which turn out not to pose any special problem for Fregeans at all, whereas Soames' theory currently has no satisfactory way of dealing with them (particularly, with such "mixed" propositions as the proposition that 2+2 is greater than 3). Admittedly, one possibility stands out as (...) the most promising one, but it requires that the Russellian treat complex properties as constituents of propositions. This leads to the second major problem for Russellians: that of proliferating propositions. I show how the most direct solution to this problem, that of rejecting complex predicative propositional constituents is available to Fregeans but very implausible for Russellians, since this virtually means rejecting complex properties. (shrink)

I explore the possibility of a structuralist interpretation of homotopy type theory (HoTT) as a foundation for mathematics. There are two main aspects to HoTT's structuralist credentials. First, it builds on categorical set theory (CST), of which the best-known variant is Lawvere's ETCS. I argue that CST has merit as a structuralist foundation, in that it ascribes only structural properties to typical mathematical objects. However, I also argue that this success depends on the adoption of a strict (...) typing system which undermines the metaphysical seriousness of this structuralism. Homotopy type theory adds to CST a distinctive theory of identity between sets, which arguably allows its objects to be seen as ante rem structures. I examine the prospects for such a view, and address many other interpretive problems as they arise. (shrink)

This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the homotopy type theory book for dependent type theory augmented with axioms for univalence and higher inductive types. We adopt a cartesian cubical type theory proposed by Angiuli, Brunerie, Coquand, Favonia, (...) Harper, and Licata as the implicit foundation, confining our presentation to elementary results such as function extensionality, the derivation of weak connections and path induction, the groupoid structure of types, and the Eckmman–Hilton duality. (shrink)

Minimal Type Theory (MTT) is based on type theory in that it is agnostic about Predicate Logic level and expressly disallows the evaluation of incompatible types. It is called Minimal because it has the fewest possible number of fundamental types, and has all of its syntax expressed entirely as the connections in a directed acyclic graph.

This paper applies homotopy type theory to formal semantics of natural languages and proposes a new model for the linguistic phenomenon of copredication. Copredication refers to sentences where two predicates which assume different requirements for their arguments are asserted for one single entity, e.g., "the lunch was delicious but took forever". This paper is particularly concerned with copredication sentences with quantification, i.e., cases where the two predicates impose distinct criteria of quantification and individuation, e.g., "Fred picked up and (...) mastered three books." In our solution developed in homotopy type theory and using the rule of existential closure following Heim analysis of indefinites, common nouns are modeled as identifications of their aspects using HoTT identity types, e.g., the common noun book is modeled as identifications of its physical and informational aspects. The previous treatments of copredication in systems of semantics which are based on simple type theory and dependent type theories make the correct predictions but at the expense of ad hoc extensions (e.g., partial functions, dot types and coercive subtyping). The model proposed here, also predicts the correct results but using a conceptually simpler foundation and no ad hoc extensions. (shrink)

This is the formal YACC BNF specification for Minimal Type Theory (MTT). MTT was created by augmenting the syntax of First Order Logic (FOL) to specify Higher Order Logic (HOL) expressions using FOL syntax. Syntax is provided to enable quantifiers to specify type. FOL is a subset of MTT. The ASSIGN_ALIAS operator := enables FOL expressions to be chained together to form HOL expressions.

What is absolutely unrestricted quantification? We distinguish two theoretical roles and identify two conceptions of absolute generality: maximally strong generality and maximally inclusive generality. We also distinguish two corresponding kinds of absolute domain. A maximally strong domain contains every potential counterexample to a generalisation. A maximally inclusive domain is such that no domain extends it. We argue that both conceptions of absolute generality are legitimate and investigate the relations between them. Although these conceptions coincide in standard settings, we show how (...) they diverge under more complex assumptions about the structure of meaningful predication, such as cumulative type theory. We conclude by arguing that maximally strong generality is the more theoretically valuable conception. (shrink)

Rather than an emphasis on style as unique to an author, this study argues for the notion of group styles. Three are proposed: tight, loose, and balanced. Examples of each type are illustrated.

Minimal Type Theory (MTT) shows exactly how all of the constituent parts of an expression relate to each other (in 2D space) when this expression is formalized using a directed acyclic graph (DAG). This provides substantially greater expressiveness than the 1D space of FOPL syntax. -/- The increase in expressiveness over other formal systems of logic shows the Pathological Self-Reference Error of expressions previously considered to be sentences of formal systems. MTT shows that these expressions were never truth (...) bearers, thus never sentences of any formal logic system. (shrink)

There is some intuitive plausibility to the idea that composers create musical works by indicating sonic types in a historical context. But the idea is technically indefensible as it stands, requiring a thorough representational reform that also eliminates the type-theoretic commitments of current versions. On the reformed account, musical 'indication' is an operation of high level representational interpretation of concrete sounds, that can both explain the creativity of composers, and the often successful interpretations of their listeners. This approach also (...) bypasses contentious issues regarding the status of both indicated and 'initiated' types, as extensively discussed in the BJA. (shrink)

It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the same conclusion would have to be identified. In this paper it will be shown that the question, which reductions we accept in our system, is not only important if we see them as generating a theory of proof identity but is (...) also decisive for the more general question whether a proof has meaningful content. There are certain reductions which would not only force us to identify proofs of different arbitrary formulas but which would render derivations in a system allowing them meaningless. To exclude such cases, a minimal criterion is proposed which reductions have to fulfill to be acceptable. (shrink)

Plays, symphonies and other works in the performing arts are generally regarded, ontologically speaking, as being types, with individual performances of those works being regarded as tokens of those types. But I show that there is a logical feature of type theory which makes it impossible for such a theory to satisfactorily explain a 'double performance' case that I present: one in which a single play performance is actually a performance of two different plays. Hence type (...) theories fail, both for plays and for the related performing art of music as well. (shrink)

The following bare-bones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. Every set is found at some stage. At any stage S: for any sets found before S, we find a set whose members are exactly those sets. We find nothing else at S.' Surprisingly, this story already guarantees that the sets are arranged in well-ordered levels, and suffices for quasi-categoricity. I show this by presenting Level Theory, a simplification of (...) set theories due to Scott, Montague, Derrick, and Potter. (shrink)

As emphasized by Alonzo Church and David Kaplan (Church 1974, Kaplan 1975), the philosophies of language of Frege and Russell incorporate quite different methods of semantic analysis with different basic concepts and different ontologies. Accordingly we distinguish between a Fregean and a Russellian tradition in intensional semantics. The purpose of this paper is to pursue the Russellian alternative and to provide a language of intensional logic with a model-theoretic semantics. We also discuss the so-called Russell-Myhill paradox that threatens simple Russellian (...) type theory if propositions satisfies very strict principles of individuation. One way of avoiding the paradox is to adopt a ramified rather than a simple theory of types. (shrink)

Types are fundamental for conceptual modeling and knowledge representation, being an essential construct in all major modeling languages in these fields. Despite that, from an ontological and cognitive point of view, there has been a lack of theoretical support for precisely defining a consensual view on types. As a consequence, there has been a lack of precise methodological support for users when choosing the best way to model general terms representing types that appear in a domain, and for building sound (...) taxonomic structures involving them. For over a decade now, a community of researchers has contributed to the development of the Unified Foundational Ontology (UFO) - aimed at providing foundations for all major conceptual modeling constructs. At the core of this enterprise, there has been a theory of types specially designed to address these issues. This theory is ontologically well- founded, psychologically informed, and formally characterized. These results have led to the development of a Conceptual Modelling language dubbed OntoUML, reflecting the ontological micro-theories comprising UFO. Over the years, UFO and OntoUML have been successfully employed on conceptual model design in a variety of domains including academic, industrial, and governmental settings. These experiences exposed improvement opportunities for both the OntoUML language and its underlying theory, UFO. In this paper, we revise the theory of types in UFO in response to empirical evidence. The new version of this theory shows that many of OntoUML’s meta-types (e.g. kind, role, phase, mixin) should be considered not as restricted to substantial types but instead should be applied to model endurant types in general, including relator types, quality types, and mode types. We also contribute with a formal characterization of this fragment of the theory, which is then used to advance a new metamodel for OntoUML (termed OntoUML 2). To demonstrate that the benefits of this approach are extended beyond OntoUML, the proposed formal theory is then employed to support the definition of UFO-based lightweight Semantic Web ontologies with ontological constraint checking in OWL. Additionally, we report on empirical evidence from the literature, mainly from cognitive psychology but also from linguistics, supporting some of the key claims made by this theory. Finally, we propose a computational support for this updated metamodel. (shrink)

It is often claimed that the theory of function levels proposed by Frege in Grundgesetze der Arithmetik anticipates the hierarchy of types that underlies Church’s simple theory of types. This claim roughly states that Frege presupposes a type of functions in the sense of simple type theory in the expository language of Grundgesetze. However, this view makes it hard to accommodate function names of two arguments and view functions as incomplete entities. I propose and defend (...) an alternative interpretation of first-level function names in Grundgesetze into simple type-theoretic open terms rather than into closed terms of a function type. This interpretation offers a still unhistorical but more faithful type-theoretic approximation of Frege’s theory of levels and can be naturally extended to accommodate second-level functions. It is made possible by two key observations that Frege’s Roman markers behave essentially like open terms and that Frege lacks a clear criterion for distinguishing between Roman markers and function names. (shrink)

In a lengthy review article, C. Anthony Anderson criticizes the approach to property theory developed in Quality and Concept (1982). That approach is first-order, type-free, and broadly Russellian. Anderson favors Alonzo Church’s higher-order, type-theoretic, broadly Fregean approach. His worries concern the way in which the theory of intensional entities is developed. It is shown that the worries can be handled within the approach developed in the book but they remain serious obstacles for the Church approach. The (...) discussion focuses on: (1) the fine-grained/coarse-grained distinction, (2) proper names and definite descriptions, (3) the paradox of analysis and Mates’ puzzle, and (4) the logical, semantical, and intentional paradoxes. (shrink)

This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our (...) theory is a proof-theoretically conservative extension of the ramified theory of positive truth up to. (shrink)

CORCORAN RECOMMENDS COCCHIARELLA ON TYPE THEORY. The 1983 review in Mathematical Reviews 83e:03005 of: Cocchiarella, Nino “The development of the theory of logical types and the notion of a logical subject in Russell's early philosophy: Bertrand Russell's early philosophy, Part I”. Synthese 45 (1980), no. 1, 71-115 .

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the (...) mathematical theory of categories, dating from the mid-twentieth century, includes a theory of always-self-predicative universals--which can be seen as forming the "other bookend" to the never-self-predicative universals of set theory. The self-predicative universals of category theory show that the problem in the antinomies was not self-predication per se, but negated self-predication. They also provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought. (shrink)

In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention (...) to applications. Firstly, it is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. (shrink)

Type identity theory was dismissed in 1967 by many philosophers due to Hilary Putnam’s multiple realisability objection seeming fatal. This paper delves into a critique of type identity theory, thereby paving the way for introducing an alternative theory of mind: emergentism. The longstanding philosophical discourse around the mind has been dominated by the binary opposition of classical physicalist and dualist theories. However, the impact of scientific discovery on contemporary thought has sparked an increasing inclination towards (...) reductive physicalist frameworks, with the aim of aligning with the scientific method. Thus, contemporary thinkers have branched out to explore new physicalistic ideas. This paper examines the inherent challenges in all reductive physicalist theories, shedding light on their limitations and proposing potential solutions to overcome the obstacles. This analysis demonstrates that type identity theory, akin to its reductive counterparts, fails to accommodate for the irreducibility of consciousness. This is consciousness as characterised by Thomas Nagel’s “what is it likeness” of experience, which is inherently subjective. Instead, this paper contends that emergentism offers a compelling alternative despite being a physicalist theory. It posits consciousness as a higher-order phenomenon, one that transcends reduction to its constituent components. I argue that this attribute of emergentism makes it a promising theory in the ongoing quest for an understanding of the mind and consciousness. (shrink)

This paper distinguishes two types of qualia theory, which I call Galilean and non-Galilean qualia theories. It also offers considerations against each type of theory. To my mind the considerations are powerful. In any case, they bring out the importance of distinguishing the two types of theory. For they show that different considerations come into play—or considerations come into play in quite different ways—in assessing the two types of theory.

In a series of papers Ladyman and Presnell raise an interesting challenge of providing a pre-mathematical justification for homotopy type theory. In response, they propose what they claim to be an informal semantics for homotopy type theory where types and terms are regarded as mathematical concepts. The aim of this paper is to raise some issues which need to be resolved for the successful development of their types-as-concepts interpretation.

The article contains a critical analysis of Wittgenstein’s theory of logical symbolism. According to an influential interpretation, Wittgenstein presented in the Tractatus a new method of solving paradoxes. This method seems a simple and effective alternative to Russell’s type theory. Wittgenstein’s theory of logical symbolism is based on the requirement of clear notation and the context principle: the type of a symbol only “shows” itself in the way we use the signs of our language. The (...) function sign φ(φx) does not express any paradox, because the syntactic rules for its use, written in clear notation, should “show” us that φ(φx) = ψ(φx). Many researchers (Davant, Ishiguro, Mounce, Ruffino, Friedlander, Jolley, Livingston, Ladov, et al.) follow this interpretation. However, the difficulty of such a view on Wittgenstein’s theory of logical symbolism is that there hides the fallacy of petitio principii. Indeed, in examples of a functional sign of the form φ(φx), we are interested not only in the question of whether the functions φ are different symbols, but also in how this functional sign φ(φx) itself excludes the symbolization of the same object by different ways. This interpretation is contrasted with the idea that Wittgenstein’s theory of logical symbolism is in fact a modified analogue of Russell’s simple theory of types. The reciprocality principle becomes the core of Wittgenstein’s theory: the combinatorial potential of the “prototype” of a functional sign is identical to the combinatorial potential of the “prototype” of an argument. According to Wittgenstein, only describing the combinatorial potential of linguistic expressions (symbols) can vanish the illusion of paradoxes. The function cannot be its argument, because the function sign φ(φx) already contains the “prototype” of its argument, “showing” us that φ(φx) = φx. The correctness of this interpretation does not exclude the possibility that the differences between Russell and Wittgenstein are in fact nothing more than façon de parler. (shrink)

Recent investigations surprisingly indicate that single RNA "stem-loops" operate solely by chemical laws that act without selective forces, and in contrast, self-ligated consortia of RNA stem-loops operate by biological selection. To understand consortial RNA selection, the concept of single quasi-species and its mutant spectra as drivers of RNA variation and evolution is rethought here. Instead, we evaluate the current RNA world scenario in which consortia of cooperating RNA stem-loops are the basic players. We thus redefine quasispecies as RNA quasispecies consortia (...) and argue that it has essential behavioral motifs that are relevant to the inherent variation, evolution and diversity in biology. We propose that qs-c is an especially innovative force. We apply qs-c thinking to RNA stem-loops and evaluate how it yields altered bulges and loops in the stem-loop regions, not as errors, but as a natural capability to generate diversity. This basic competence-not error-opens a variety of combinatorial possibilities which may alter and create new biological interactions, identities and newly emerged self identity functions. Thus RNA stem-loops typically operate as cooperative modules, like members of social groups. From such qs-c of stem-loop groups we can trace a variety of RNA secondary structures such as ribozymes, viroids, viruses, mobile genetic elements as abundant infection derived agents that provide the stem-loop societies of small and long non-coding RNAs. (shrink)

In the domain of ontology design as well as in Knowledge Representation, modeling universals is a challenging problem.Most approaches that have addressed this problem rely on Description Logics (DLs) but many difficulties remain, due to under-constrained representation which reduces the inferences that can be drawn and further causes problems in expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but, so far they have not been applied in the formalization of ontologies. To bridge this (...) gap, we present in this paper a theory for representing ontologies in a dependently typed framework which relies on strong formal foundations including both a constructive logic and a functional type system. The language of this theory defines in a precise way what ontological primitives such as classes, relations, properties, etc., and thereof roles, are. The first part of the paper details how these primitives are defined and used within the theory. In a second part, we focus on the formalization of the role primitive. A review of significant role properties leads to the specification of a role profile and most of the remaining work details through numerous examples, how the proposed theory is able to fully satisfy this profile. It is demonstrated that dependent types can model several non-trivial aspects of roles including a formal solution for generalization hierarchies, identity criteria for roles and other contributions. A discussion is given on how the theory is able to cope with many of the constraints inherent in a good role representation. (shrink)

We present an overview of typed and untyped disquotational truth theories with the emphasis on their (non)conservativity over the base theory of syntax. Two types of conservativity are discussed: syntactic and semantic. We observe in particular that TB—one of the most basic disquotational theories—is not semantically conservative over its base; we show also that an untyped disquotational theory PTB is a syntactically conservative extension of Peano Arithmetic.

Commonplace syntactic constructions in natural language seem to generate ontological commitments to a dazzling array of metaphysical categories - aggregations, sets, ordered n-tuples, possible worlds, intensional entities, ideal objects, species, intensive and extensive quantities, stuffs, situations, states, courses of events, nonexistent objects, intentional and discourse objects, general objects, plural objects, variable objects, arbitrary objects, vague kinds and concepts, fuzzy sets, and so forth. But just because a syntactic construction in some natural language appears to invoke a new category of entity, (...) are we theoreticians epistemically justified in holding that there are such entities? This would hardly seem sufficient. To be epistemically justified, the ontology to which we theoreticians are committed must pass strict standards: the entities must be of the sort required by our best comprehensive theory of the world. The thesis of this paper is that fine-grained type-free intensional entities are like this. If the thesis is right, these entities have a special objective status perhaps not possessed by some of the other ontological categories associated with special syntactic constructions in natural language. In fact, it is plausible to hold that fine-grained type-free intensional entities provide the proper minimal framework for constructing logical and linguistic theories. In this paper my strategy will be to survey the competing conceptions of fine-grained type-free intensionality and to present arguments in support of one of them. Following this narrowing down process, I will go on to the indicated epistemological considerations. (shrink)

Research on the status and experience of women in academia in the last 30 years has challenged conventional explanations of persistent gender inequality, bringing into sharp focus the cumulative impact of small scale, often unintentional differences in recognition and response: the patterns of 'post-civil rights era' dis­crimination made famous by the 1999 report on the status of women in the MIT School of Science. I argue that feminist standpoint theory is a useful resource for understanding how this sea (...) change in understanding gender inequity was realized. At the same time, close attention to activist research on workplace environment issues suggests ways in which our understanding of standpoint theory can fruitfully be refined. I focus on the implications of two sets of distinctions: between types of epistemic injustice (and correlative advantage) that may affect marginalized knowers; and between the resources of situated knowledge and those of a critical standpoint on knowledge production. (shrink)

Manzotti (2021) surveys recent variants of identity theories, defending his own preferred version, mind-object identity theory (MOI). According to this view, experiences are identical with the external objects, and the mind is thus literally “spread” in the world. Manzotti supports this view with considerations about indiscernibility of properties and other theoretical considerations. He claims that brain-mind accounts of identity commit the “fallacy of the center,” locating conscious mind inside the skull. Amongst other recent works, he comments on our (Polák (...) and Marvan, 2018) article, in which we defended a standard, neurocentrist version of type identity theory, and supplemented it with a sketch of neuro-phenomenal typing. Manzotti holds that although we appeal to neuro-phenomenal types in our account of mind-brain identity, we nevertheless “lack a convincing explanation as to why the type of neural processes should be identical to the type of one's experience.” This is a fair point. We didn't do much in our 2018 article to support our views on the principles of neuro-phenomenal typing, either by detailed theoretical considerations or by empirical evidence. In this short rejoinder, we offer the missing argument. By doing so, we also respond both to Manzotti's cited objection and to the charge of the “fallacy of the center.” -/- . (shrink)

I investigate why Frege rejected the theory of types, as Russell presented it to him in their correspondence. Frege claims that it commits one to violations of the law of excluded middle, but this complaint seems to rest on a dogmatic refusal to take Russell’s proposal seriously on its own terms. What is at stake is not so much the truth of a law of logic, but the structure of the hierarchy of the logical categories, something Frege seems to (...) neglect. To come to a better understanding of Frege’s response, I proceed to investigate his conception of the nature of the logical categories, and how it differs from Russell’s. I argue that, for Frege, our grasp of the logical categories cannot be severed from our grasp of the Begriffsschrift notation itself. Russell, on the other hand, attaches no such importance to notation. From Frege’s point of view, Russell has not succeeded in presenting an alternative conception of the logical hierarchy, since such a conception must go in tandem with the development of a notation. Moreover, Frege has good reasons to think that Russell’s proposal does not admit of a suitable notation. (shrink)

In Languages of Art, Nelson Goodman presents a general theory of symbolic notation. However, I show that his theory could not adequately explain possible cases of natural language notational uses, and argue that this outcome undermines, not only Goodman's own theory, but any broadly type versus token based account of notational structure.Given this failure, an alternative representational theory is proposed, in which different visual or perceptual aspects of a given physical inscription each represent a different (...) letter, word, or other notational item. Such a view is strongly supported by the completely conventional relation between inscriptions and notation, as shown by encryption techniques etc. (shrink)

The general concept of a trope – that of a non-shareable character-grounder – admits of a distinction between modifier tropes and module tropes. Roughly, a module trope is self-exemplifying whereas a modifier trope is not. This distinction has wide-ranging implications. Modifier tropes are uniquely eligible to be powers and fundamental determinables, whereas module tropes are uniquely eligible to play a direct role in perception and causation. Moreover, each type of trope theory faces unique challenges concerning character- grounding. Modifier (...) trope theory faces challenges concerning the inscrutability of predication and the incompatibility with bundle theory, whereas module trope theory faces challenges concerning character overdetermination and a collapse into austere nominalism. These differences indicate that the modifier/module distinction divides the advantages of general trope theory and thus presents the trope theorist with a pivotal choice. (shrink)

Talk of different types of cells is commonplace in the biological sciences. We know a great deal, for example, about human muscle cells by studying the same type of cells in mice. Information about cell type is apparently largely projectible across species boundaries. But what defines cell type? Do cells come pre-packaged into different natural kinds? Philosophical attention to these questions has been extremely limited [see e.g., Wilson (Species: New Interdisciplinary Essays, pp 187–207, 1999; Genes and the (...) Agents of Life, 2005; Wilson et al. Philos Top 35(1/2):189–215, 2007)]. On the face of it, the problems we face in individuating cellular kinds resemble those biologists and philosophers of biology encountered in thinking about species: there are apparently many different (and interconnected) bases on which we might legitimately classify cells. We could, for example, focus on their developmental history (a sort of analogue to a species’ evolutionary history); or we might divide on the basis of certain structural features, functional role, location within larger systems, and so on. In this paper, I sketch an approach to cellular kinds inspired by Boyd’s Homeostatic Property Cluster Theory, applying some lessons from this application back to general questions about the nature of natural kinds. (shrink)

In this paper, I present a two-pronged argument devoted to defending the type-identity theory of mind against the argument presented by Kripke in _Naming and Necessity_. In the first part, the interpersonal case, I show that since it is not possible to establish the metaphysical conditions for phenomenal identity, it is not possible to argue that there can be physical differences between two subjects despite their phenomenal identity. In the second part, the intrapersonal case, I consider the possibility (...) of imagining one and the same individual having the same phenomenal state while counterfactually being in very different physical states. I argue that this case should respect Kripke’s implicit theory of personal identity—but this proves to be a very difficult task to accomplish, thus preventing the argument from getting off the ground. Therefore, I maintain, that the type-identity theory is still the better option to solve the mind–body problem. (shrink)

Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and validity in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; one given proposition is a consequence of a second if the latter contains all of the information contained by the former; an argument is valid if the conclusion contains no information beyond that of the premise-set. This (...) paper locates information-theoretic approaches historically, philosophically, and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyze validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity. (shrink)

This paper attempts to reconcile critics and defenders of inclusive fitness by constructing a synthesis that does justice to the insights of both. I argue that criticisms of the regression-based version of Hamilton’s rule, although they undermine its use for predictive purposes, do not undermine its use as an organizing framework for social evolution research. I argue that the assumptions underlying the concept of inclusive fitness, conceived as a causal property of an individual organism, are unlikely to be exactly true (...) in real populations, but they are approximately true given a specific type of weak selection that Hamilton took, on independent grounds, to be responsible for the cumulative assembly of complex adaptation. Finally, I reflect on the uses and limitations of “design thinking” in social evolution research. The debate about the foundations of inclusive fitness theory that has followed in the wake of Nowak, Tarnita and Wilson’s (1) critique has been remarkably polarizing. After several rounds of rebuttals and replies, there is still little evidence of any serious reconciliation between the theory’s critics (2-10) and its defenders (11-24). It doesn’t have to be this way. I believe that, on the main points of disagreement, it is possible to find a way forward that does justice to the insights of both camps. My aim in this paper is to find that way forward. (shrink)

Information-theoretic approaches to formal logic analyse the "common intuitive" concept of propositional implication (or argumental validity) in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; an argument is valid if the conclusion contains no information beyond that of the premise-set. This paper locates information-theoretic approaches historically, philosophically and pragmatically. Advantages and disadvantages are identified by examining such approaches in themselves and (...) by contrasting them with standard transformation-theoretic approaches. Transformation-theoretic approaches analyse validity (and thus implication) in terms of transformations that map one argument onto another: a given argument is valid if no transformation carries it onto an argument with all true premises and false conclusion. Model-theoretic, set-theoretic, and substitution-theoretic approaches, which dominate current literature, can be construed as transformation-theoretic, as can the so-called possible-worlds approaches. Ontic and epistemic presuppositions of both types of approaches are considered. Attention is given to the question of whether our historically cumulative experience applying logic is better explained from a purely information-theoretic perspective or from a purely transformation-theoretic perspective or whether apparent conflicts between the two types of approaches need to be reconciled in order to forge a new type of approach that recognizes their basic complementarity. (shrink)

Neutrosophic theory has many applications in graph theory, bipolar single valued neutrosophic graphs (BSVNGs) is the generalization of fuzzy graphs and intuitionistic fuzzy graphs, SVNGs. In this paper we introduce some types of BSVNGs, such as subdivision BSVNGs, middle BSVNGs, total BSVNGs and bipolar single valued neutrosophic line graphs (BSVNLGs), also investigate the isomorphism, co weak isomorphism and weak isomorphism properties of subdivision BSVNGs, middle BSVNGs, total BSVNGs and BSVNLGs.

Quine maintained that philosophical and scientific theorizing should be conducted in an untyped language, which has just one style of variables and quantifiers. By contrast, typed languages, such as those advocated by Frege and Russell, include multiple styles of variables and matching kinds of quantification. Which form should our theories take? In this article, I argue that expressivity does not favour typed languages over untyped ones.

Montague (1970) interprets a small fragment of English through the use of two basic types of objects: individuals and propositions. My dissertation develops an alternative semantics that only uses one basic type (hence, *single-type semantics*). Such a semantics has been conjectured by Partee (2006) as a ‘minimality test’ for the Montagovian type system, which captures the lowest ontological requirements on any successful semantics for Montague’s fragment. The development of this semantics answers a number of important open questions (...) about the salience of the Montagovian type system, the robustness of semantic theories w.r.t. their basic-type choice, and the classification of these theories according to their objects’ informational strength. (shrink)

Corcoran, John. 2005. Meanings of word: type-occurrence-token. Bulletin of Symbolic Logic 11(2005) 117. -/- Once we are aware of the various senses of ‘word’, we realize that self-referential statements use ambiguous sentences. If a statement is made using the sentence ‘this is a pronoun’, is the speaker referring to an interpreted string, a string-type, a string-occurrence, a string-token, or what? The listeners can wonder “this what?”. -/- John Corcoran, Meanings of word: type-occurrence-token Philosophy, University at Buffalo, Buffalo, (...) NY 14260-4150 E-mail: [email protected] The four-letter written-English expression ‘word’, which plays important roles in applications and expositions of logic and philosophy of logic, is ambiguous (multisense, or polysemic) in that it has multiple normal meanings (senses, or definitions). Several of its meanings are vague (imprecise, or indefinite) in that they admit of borderline (marginal, or fringe) cases. This paper juxtaposes, distinguishes, and analyses several senses of ‘word’ focusing on a constellation of senses analogous to constellations of senses of other expression words such as ‘expression’, ‘symbol’, ‘character’, ‘letter’, ‘term’, ‘phrase’, ‘formula’, ‘sentence’, ‘derivation’, ‘paragraph’, and ‘discourse’. Consider, e.g., the word ‘letter’. In one sense there are exactly twenty-six letters (letter-types or ideal letters) in the English alphabet and there are exactly four letters in the word ‘letter’. In another sense, there are exactly six letters (letter-repetitions or letter-occurrences) in the word-type ‘letter’. In yet another sense, every new inscription (act of writing or printing) of ‘letter’ brings into existence six new letters (letter-tokens or ink-letters) and one new word that had not previously existed. The number of letter-occurrences (occurrences of a letter-type) in a given word-type is the same as the number of letter-tokens (tokens of a letter-type) in a single token of the given word. Many logicians fail to distinguish “token” from “occurrence” and a few actually confuse the two concepts. Epistemological and ontological problems concerning word-types, word-occurrences, and word-tokens are described in philosophically neutral terms. This paper presents a theoretical framework of concepts and principles concerning logicography, including use of English in logic. The framework is applied to analytical exposition and critical evaluation of classic passages in the works of philosophers and logicians including Boole, Peirce, Frege, Russell, Tarski, Church and Quine. This paper is intended as a philosophical sequel to Corcoran et al. “String Theory”, Journal of Symbolic Logic 39(1974) 625-637. https://www.academia.edu/s/cdfa6c854e?source=link -/- . (shrink)

Using tools like argument diagrams and profiles of dialogue, this paper studies a number of examples of everyday conversational argumentation where determination of relevance and irrelevance can be assisted by means of adopting a new dialectical approach. According to the new dialectical theory, dialogue types are normative frameworks with specific goals and rules that can be applied to conversational argumentation. In this paper is shown how such dialectical models of reasonable argumentation can be applied to a determination of whether (...) an argument in a specific case is relevant are not in these examples. The approach is based on a linguistic account of dialogue and text from congruity theory, and on the notion of a dialectical shift. Such a shift occurs where an argument starts out as fitting into one type of dialogue, but then it only continues to makes sense as a coherent argument if it is taken to be a part of a different type of dialogue. (shrink)

Abstract: Without directly taking sides in the design/anti-design debate, this paper defends the following position: the assertion that biological evolution “is” design-free presupposes the possibility to model biological evolution in a design-free way. Certainly, there are design-free models of evolution based on cumulative selection. But “to model” is a verb denoting “modeling” as the process leading to a model. So any modeling – trivially – needs “previous human design.” Nevertheless, contrary to other scientific activities which legitimately consider models while (...) ignoring the process leading to them, evolution theory must take into account the human activity of modeling required by its corresponding models. (shrink)

I distinguish two roles for a fitness concept in the context of explaining cumulative adaptive evolution: fitness as a predictor of gene frequency change, and fitness as a criterion for phenotypic improvement. Critics of inclusive fitness argue, correctly, that it is not an ideal fitness concept for the purpose of predicting gene-frequency change, since it relies on assumptions about the causal structure of social interaction that are unlikely to be exactly true in real populations, and that hold as approximations (...) only given a specific type of weak selection. However, Hamilton took this type of weak selection, on independent grounds, to be responsible for cumulative assembly of complex adaptations. In this special context, I argue that inclusive fitness is distinctively valuable as a criterion for improvement and a standard for optimality. Yet to call inclusive fitness a criterion for improvement and a standard for optimality is not to make any claim about the frequency with which inclusive fitness optimization actually occurs in nature. This is an empirical question that cannot be settled by theory alone. I close with some reflections on the place of inclusive fitness in the long running clash between ‘causalist’ and ‘statisticalist’ conceptions of fitness. (shrink)