I discuss Frege's argument - later called the slingshot - that if a construction is extensional and preserves logical equivalence then it is truth-functional. I consider some simple apparent counterexamples and conclude that they are not sentence-embedding in the required way.

Quine argues that if sentences that are set theoretically equivalent are interchangeable salva veritate, then all transparent operators are truth-functional. Criticisms of this argument fail to take into account the conditional character of the conclusion. Quine also argues that, for any person P with minimal logical acuity, if ‘belief’ has a sense in which it is a transparent operator, then, in that sense of the word, P believes everything if P believes anything. The suggestion is made that he intends that (...) result to show us that ‘believes’ has no transparent sense. Criticisms of this argument are either based on unwarranted assertions or on definitions of key terms that depart from Quine’s usage of those terms. (shrink)

This paper presents a new reconstruction of Wittgenstein’s famous (and controversial) rule-following arguments. Two are the novel features offered by our reconstruction. In the first place, we propose a shift of the central focus of the discussion, from the general semantics and the philosophy of mind to the philosophy of mathematics and the rejection of the notion of a function. The second new feature is positive: we argue that Wittgenstein offers us a new alternative notion of a rule (to replace (...) the rejected functions), a notion reminiscent of Category Theory’s notion of a morphism. (shrink)

Hylomorphically complex objects are things that change their parts or matter or that might have, or have had, different parts or matter. Often ontologists analyze such objects in terms of sets (or functions, understood set-theoretically) or other extensional entities such as mereological fusions or quantities of matter. I urge two reasons for being wary of any such analyses. First, being extensional, such things as sets are ill-suited to capture the characteristic modal and temporal flexibility of hylomorphically complex (...) objects. Secondly, sets are often appealed to because they seem to contain their members. But the idea that sets do contain their members, in the ordinary sense of containment, is a substantive metaphysical position that makes analyses that rely on that idea for their plausibility much more metaphysically committing than is generally thought. (shrink)

I present and discuss three previously unpublished manuscripts written by Bertrand Russell in 1903, not included with similar manuscripts in Volume 4 of his Collected Papers. One is a one-page list of basic principles for his “functional theory” of May 1903, in which Russell partly anticipated the later Lambda Calculus. The next, catalogued under the title “Proof That No Function Takes All Values”, largely explores the status of Cantor’s proof that there is no greatest cardinal number in the variation of (...) the functional theory holding that only some but not all complexes can be analyzed into function and argument. The final manuscript, “Meaning and Denotation”, examines how his pre-1905 dis­tinction between meaning and denotation is to be understood with respect to functions and their arguments. In them, Russell seems to endorse an extensional view of functions not endorsed in other works prior to the 1920s. All three manuscripts illustrate the close connection between his work on the logical paradoxes and his work on the theory of meaning. (shrink)

Arguments are given against the thesis that properties and propositional functions are identical. The first shows that the familiar extensional treatment of propositional functions -- that, for all x, if f(x) = g(x), then f = g -- must be abandoned. Second, given the usual assumptions of propositional-function semantics, various propositional functions (e.g., constant functions) are shown not to be properties. Third, novel examples are given to show that, if properties were identified with propositional (...) class='Hi'>functions, crucial fine-grained intensional distinctions would be lost. (shrink)

The purpose of this paper is to assess the general viability of Donald Davidson's paratactic theory of indirect discourse, as well as the specific plausibility of a reincarnated form of the Davidsonian paratactic theory, Gary Kemp's propositional paratactic theory. To this end I will provide an introduction to the Davidsonian paratactic theory and the theory's putative strengths, thereafter noting that an argument from ambiguity seems to effectively undermine Davidson's proposal. Subsequently, I will argue that Kemp's modification of Davidson's theory – (...) that is, Kemp's attempt to respond to the ambiguity objection – adequately handles the classic argument from ambiguity but fails in the face of a new problem of ambiguity that I will introduce. Finally, I will argue that there are more devastating and basic problems for the paratactic theory generally, and that even if Kemp's modifications had succeeded, they would not have given adequate plausibility to the paratactic proposal. (shrink)

Recent work in philosophy of language has raised significant problems for the traditional theory of propositions, engendering serious skepticism about its general workability. These problems are, I believe, tied to fundamental misconceptions about how the theory should be developed. The goal of this paper is to show how to develop the traditional theory in a way which solves the problems and puts this skepticism to rest. The problems fall into two groups. The first has to do with reductionism, specifically attempts (...) to reduce propositions to extensional entities-either extensional functions or sets. The second group concerns problems of fine grained content-both traditional 'Cicero'/'Tully' puzzles and recent variations on them which confront scientific essentialism. After characterizing the problems, I outline a non-reductionist approach-the algebraic approach-which avoids the problems associated with reductionism. I then go on to show how the theory can incorporate non-Platonic (as well as Platonic) modes of presentation. When these are implemented nondescriptively, they yield the sort of fine-grained distinctions which have been eluding us. The paper closes by applying the theory to a cluster of remaining puzzles, including a pair of new puzzles facing scientific essentialism. (shrink)

Tichý’s Transparent Intensional Logic (TIL) is an overarching logical framework apt for the analysis of all sorts of discourse, whether colloquial, scientific, mathematical or logical. The theory is a procedural (as opposed to denotational) one, according to which the meaning of an expression is an abstract, extra-linguistic procedure detailing what operations to apply to what procedural constituents to arrive at the product (if any) of the procedure that is the object denoted by the expression. Such procedures are rigorously defined as (...) TIL constructions. Though TIL analytical potential is very large, deduction in TIL has been rather neglected. Tichý defined a sequent calculus for pre-1988 TIL, that is TIL based on the simple theory of types. Since then no other attempt to define a proof calculus for TIL has been presented. The goal of this paper is to propose a generalization and adjustment of Tichý’s calculus to TIL 2010. First, I briefly recapitulate the rules of simple-typed calculus as presented by Tichý. Then, I propose the adjustments of the calculus so that it be applicable to hyperintensions within the ramified hierarchy of types. TIL operates with a single procedural semantics for all kinds of logical-semantic context, be it extensional, intensional or hyperintensional. I show that operating in a hyperintensional context is far from being technically trivial. Yet, it is feasible. To this end, we introduce a substitution method that operates on hyperintensions. It makes use of a four-place substitution function (called Sub) defined over hyperintensions. (shrink)

Standard approaches to proper names, based on Kripke's views, hold that the semantic values of expressions are (set-theoretic) functions from possible worlds to extensions and that names are rigid designators, i.e.\ that their values are \emph{constant} functions from worlds to entities. The difficulties with these approaches are well-known and in this paper we develop an alternative. Based on earlier work on a higher order logic that is \emph{truly intensional} in the sense that it does not validate the axiom (...) scheme of Extensionality, we develop a simple theory of names in which Kripke's intuitions concerning rigidity are accounted for, but the more unpalatable consequences of standard implementations of his theory are avoided. The logic uses Frege's distinction between sense and reference and while it accepts the rigidity of names it rejects the view that names have direct reference. Names have constant denotations across possible worlds, but the semantic value of a name is not determined by its denotation. (shrink)

The theory of variable embodiments has been primarily formulated to model ordinary objects as things that change their parts over time. A variable embodiment /f/ is a sui generis whole constructed from a principle f, the principle of a variable embodiment, and it is manifested at different times by different things picked out by such a principle f. This principle is usually clarified as a function that picks out, at any given time the variable embodiment exists, its corresponding manifestation at (...) that time, and it fails to pick out anything at any other time. The first purpose of this article is to examine and refute three natural understandings of such a principle. Specifically, first, we argue against the view that it should be understood extensionally as either a partial function or total function. Next, we provide some motivations to reject the understanding of the principle as a function in intensional terms, where the notion of intension is analyzed in terms of a specific version of a possible world semantics. The second goal of the article is to make it plausible that the principle has an intensional character and, on the basis of the results achieved, to formulate some constraints that an account of such a principle should meet. (shrink)

In this paper I argue that a truth functional account of conditional statements ‘if A then B’ not only is inadequate, but that it eliminates the very conditionality expressed by ‘if’. Focusing only on the truth-values of the statements ‘A’ and ‘B’ and different combinations of these, one is bound to miss out on the conditional relation expressed between them. But this is not a flaw only of truth functionality and the material conditional. All approaches that try to treat conditionals (...) as mere functions of their antecedents and consequents will end up in some sort of logical atomism where causal matters simply are reduced to the joint occurrence of A and B. What we need is a non-extensional approach to conditionals that can account for hypotheticality, potentiality, and dependency, none of which can be understood by looking to the antecedent or consequent per se. (shrink)

In this paper, first the term 'prioritarianism' is defined, with some mathematical precision, on the basis of intuitive conceptions of prioritarianism, especially the idea that "benefiting people matters more the worse off these people are". (The prioritarian weighting function is monotonously ascending and concave, while its first derivation is smoothly descending and convex but positive throughout.) Furthermore, (moderate welfare) egalitarianism is characterized. In particular a new symmetry condition is defended, i.e. that egalitarianism evaluates upper and lower deviations from the social (...) middle symmetrically and equally negatively (as do e.g. variance and Gini). Finally, it is shown that this feature distinguishes egalitarianism also extensionally from prioritarianism. (shrink)

Lexical semantics has a problem. As Allesandro Lenci put it, the problem is that it cannot distinguish semantic from non-semantic relationships within its data. (2008, 2014). The data it relies on are patterns of co-occurrence of lexemes within linguistic corpora. But patterns of co-occurrence can reflect either our knowledge of what the world is like or our knowledge of what words mean -- matters of fact or matters of meaning. -/- In this essay, I develop a semantic theory which draws (...) this distinction in a way which makes it discernible in lexical semantics and cognitive science research. In doing so, this theory unifies truth-functional and structuralist approaches to semantics, and provides an integrated explanation of meaning and reference. -/- I base this semantic theory on linguistic dispositions to pair words with words, and to pair words with things, both based on learned patterns of association. These dispositions manifest themselves in verbal behavior, and (in Part 2) I propose a new neurophysical model to account for these dispositions which underlie both the intensional and extensional patterns in that behavior. (shrink)

It is generally assumed that humans are the only animals who can possess a concept of death. However, the ubiquity of death in nature and the evolutionary advantages that would come with an understanding of death provide two prima facie reasons for doubting this assumption. In this paper, my intention is not to defend that animals of this or that nonhuman species possess a concept of death, but rather to examine how we could go about empirically determining whether animals can (...) have a concept of death. In order to answer this question, I begin by sketching an account of concept possession that favours intensional classification rather than mere extensional discrimination. Further, I argue that the concept of death should be construed as neither binary nor universal. I then present a proposal for a set of minimal conditions that must be met to have a concept of death. I argue that having a minimal understanding of death entails first expecting a dead individual to be alive, and then grasping its non-functionality and irreversibility. Lastly, I lay out the sort of observational and experimental evidence that we should look for to determine whether animals have the capacity for a minimal comprehension of death. (shrink)

The cognitive experience view of thought holds that the content of thought is determined by its cognitive-phenomenal character. Adam Pautz argues that the cognitive experience view is extensionally inadequate: it entails the possibility of mix-and-match cases, where the cognitive-phenomenal properties that determine thought content are combined with different sensory-phenomenal and functional properties. Because mix-and-match cases are metaphysically impossible, Pautz argues, the cognitive experience view should be rejected. This paper defends the cognitive experience view from Pautz’s argument. I build on resources (...) in the philosophy of mind literature to show that cognitive-phenomenal properties are modally independent from sensory-phenomenal and functional properties. The result is that mix-and-match cases, though modally remote, are metaphysically possible. The possibility of mix-and-match cases allows us to move from defensive posture to a critical one: it poses problems for any theory of content that imposes rationality constraints, including Pautz’s positive view, phenomenal functionalism. (shrink)

According to psychological constructivism, emotions result from projecting folk emotion concepts onto felt affective episodes (e.g., Barrett 2017, LeDoux 2015). Moreover, while constructivists acknowledge there’s a biological dimension to emotion, they deny that emotions are (or involve) affect programs. So they also deny that emotions are natural kinds. However, the essential role constructivism gives to felt experience and folk concepts leads to an account that’s extensionally inadequate and functionally inaccurate. Moreover, biologically-oriented proposals that reject these commitments are not similarly encumbered. (...) Recognizing this has two implications: biological mechanisms are more central to emotion than constructivism allows, and the conclusion that emotions aren’t natural kinds is premature. (shrink)

This chapter argues that while quotation marks are polysemous, the thread that runs through all uses of quotation marks that involve reference to expressions is pure quotation, in which an expression formed by enclosing another expression in quotation marks refers to that enclosed expression. We defend a version of the so-called disquotational theory of pure quotation and show how this device is used in direct discourse and attitude attributions, in exposition in scholarly contexts, and in so-called mixed quotation in indirect (...) discourse and attitude attributions. We argue that uses of quotation marks that extend beyond pure quotation have two features in common. First, the expressions appearing in quotation marks are intended to be understood, and that they are intended to be understood is essential to the function that such quotations play in communication, though this does not always involve the expressions contributing their extensional properties to fixing truth conditions for the sentences in which they appear. Second, they appeal to a relation to the expression appearing in quotation marks that plays a role in determining the truth conditions of the sentences in which they appear. (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)

The common account of the analog vs digital distinction is based on features of physical systems, being related to the usage of continuous vs discrete supports respectively. It is proposed here to alternatively characterize the concepts of analog and digital as related to coding systems, of which a formal definition is given, by suggesting that the distinction refers to the strategy adopted to define the coding function: extensional in digital systems, isomorphic intensional in analog systems. This thesis is supported (...) by examples, in particular of analog systems exploiting discrete supports, and is discussed to explain why digital coding is currently so widespread in technological and social practice. (shrink)

We have a rough idea of what artifacts are: artifacts are objects made to serve a certain purpose. However, there is no consensus on how to specify this definition. Essentialists argue that objects are grouped into artifact kinds by sharing non-trivial artifact essences, while anti-essentialists argue that there is no such essence to be found. However, the prominent essentialist and anti-essentialist accounts suffer from extensional and definitional problems. I argue that the problems current essentialist and anti-essentialist accounts face mainly (...) stem from the assumption of artifact concept monism. According to artifact concept monism, there is only a single way to group objects into artifact kinds. To remedy the problems that stem from artifact concept monism, this paper offers an alternative framework by drawing parallels from the debates on species concept pluralism and art concept pluralism. (shrink)

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the Problem of (...) Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

A novel theory of comparative risk is developed and defended. Extant theories are criticized for failing the tests of extensional and formal adequacy. A unified diagnosis is proposed: extant theories consider risk to be a univariable function, but risk is a multivariate function. According to the theory proposed, which we call the unified theory of risk, the riskiness of a proposition is a function of both the proportion and the modal closeness of the possible worlds at which the proposition (...) holds. It is argued the theory passes the tests of extensional and formal adequacy. (shrink)

The conventional wisdom has it that between 1905 and 1919 Russell was critical to pragmatism. In particular, in two essays written in 1908–9, he sharply attacked the pragmatist theory of truth, emphasizing that truth is not relative to human practice. In fact, however, Russell was much more indebted to the pragmatists, in particular to William James, as usually believed. For example, he borrowed from James two key concepts of his new epistemology: sense-data, and the distinction between knowledge by acquaintance and (...) knowledge by description. Reasonable explanation of this is that, historically, Russell’s logical realism and James’s pragmatism have the same roots—the German philosopher Rudolph Hermann Lotze (1817–1881). In this paper we are going to explore the fact that in 1905, under Lotze’s influence, Russell married propositions with beliefs. A few years later this step also made Russell prone to embrace the theory of truth-making that has its roots in James. In contrast to the concept of sense-data and to the distinction between knowledge by acquaintance and knowledge by description, however, the understanding that we believe propositions—and not, for example, simply grasp them—was in tension with Russell’s Principle of Extensionality, according to which propositions can be logically connected with other propositions only as truth-functions. The point is that when we judge a mind-relation (for example, a relation of belief) to a proposition, the latter cannot be determined as true or false. The two most talented pupils of Russell, Wittgenstein and Ramsey, severely criticized the central place propositional attitudes play in Russell’s logic. Wittgenstein analyzed “A believes that p” to “ ‘p’ says p” (5.542). Ramsey criticized Russell’s beliefs in propositions the other way round: He stressed that belief is an ambiguous term that can be interpreted for the better in the sense of pragmatism. Prima facie surprisingly, he maintained that his “pragmatism is derived from Mr Russell.” (1927: 51). (shrink)

This is what I hope is an illuminating, and to a certain degree, novel exposition of Montague Grammar. It is against many standard interpretations, and perhaps even against things Montague himself says at times. However, it makes more sense of how his various commitments fit together in a systematic way. Why, for instance, is it called "Montague Grammar" rather than "Montague Semantics," and what role does his commitment to Fregeanism plays in his conception of language? It is clear that he (...) is committed to the idea that function application is the fundamental mode of semantic composition, and that he is committed to an intensional framework. However, intensions have, since Carnap, been understood as nearly conceptually equivalent to functions from possible worlds to sets of individuals. But, in truth, possible worlds semantics is just dressed up extensional semantics. There are just more objects to go around to serve as inputs for functions, whatever we think of their ontological status. That is, possible worlds semantics is really a semantic reduction of intensional semantics achieved by expanding our ontological commitments. It would be difficult to make sense of Montague's strong commitment to Fregean semantics, if his notion of intension was that of Carnap's. According to my interpretation, Montague's notion of intension must be distinct from the version adopted by possible world semantics. Montague took seriously the idea that intensional semantics was something quite different from extensionalist semantics. The first was not reducible to the second semantically speaking. Just as Frege believed that meaning consisted of both sense and reference, so too did Montague. However, just as Frege also believed, Montague thought that sense and reference were systematically related. As I illustrate, interpreting Montague as adopting a different notion of intension can also resolve the apparent problem of distinguishing the difference in meaning between intensional equivalents. It might also enable us to draw a distinction in epistemic logic between an agent having contradictory beliefs and believing contradictions. (shrink)

Simple partial logic (=SPL) is, broadly speaking, an extensional logic which allows for the truth-value gap. First I give a system of propositional SPL by partializing classical logic, as well as extending it with several non-classical truth-functional operators. Second I show a way based on SPL to construct a system of tensed ontology, by representing tensed statements as two kinds of necessary statements in a linear model that consists of the present and future worlds. Finally I compare that way (...) with other two ways based on Łukasiewicz’s three-valued logic and branching temporal logic. (shrink)

Comic is one of the paradigmatic forms of hybrid media, and coming up with a satisfactory definition for it has been difficult. Sam Cowling and Ley Cray (2022) take a functional approach and offer an Intentional Picture-Reading View which defines comics as something that is “aptly intended to be picture-read.” I show that the view is extensionally inadequate as is because formally ambitious prose and concrete poetry, too, are aptly intended to be picture-read. The way forward, I argue, is to (...) look at more medium-specific non-depictive images (such as speech balloons and panels) to set comics apart from other hybrid media. (shrink)

The conditional interpretation of general categorical statements like ‘All men are animals’ as universally quantified material conditionals ‘For all x, if x is F, then x is G’ suggests that the logical structure of law statements is conditional rather than categorical. Disregarding the problem that the universally quantified material conditional is trivially true whenever there are no xs that are F, there are some reasons to be sceptical of Frege’s equivalence between categorical and conditional expressions. -/- Now many philosophers will (...) claim that the material conditional interpretation of laws statements, dispositions ascriptions, or any causal claim is generally accepted as wrong and outdated. Still, there seem to be some basic logical assumptions that are shared by most of the participants in the debate on causal matters which at least stems from the traditional truth functional interpretation of conditionals. This is indicated by the vocabulary in the philosophical debate on causation, where one often speaks of ‘counterfactuals’, ‘possible worlds’ and ‘necessity’ without being explicit on whether or to what extent one accepts the logical-technical definition of these notions. To guarantee a non-Humean and non-extensional approach to causal relations, it is therefore important to be aware of the logical and metaphysical implications of the technical vocabulary. -/- In this paper we want to show why extensional logic cannot deal with causal relations. Via a logical analysis of law-like statements ‘All Fs are Gs’ we hope to throw some new light on interrelated notions like causation, laws, induction, hypotheticality and modality. If successful, our analysis should be of relevance for a deeper understanding of any type of causal relations, whether we understand them to be laws, dispositions, singulars or categoricals. (shrink)

African jurisprudence, like African philosophy, continues to be hotly debated. This article contends that the debate straddles the uniqueness claim which either emphasises the existence or possibility of a peculiar legal framework on the continent, and a historical co-extensional position reiterating that African jurisprudence is a continuum of other legal traditions. The article argues that there is no uniquely African jurisprudence, and that what obtains within the structures of jurisprudence on the continent also exists within various legal traditions elsewhere, (...) and as such can at best be described as ‘jurisprudence in Africa’ rather than ‘African jurisprudence’. It defends this thesis through analytic and comparative explications of the content of natural law theory and legal positivism as experienced on the continent. It concedes that relics of the colonial legal experience create contestations that inform scholars’ calls for a return to traditional legal systems. It concludes that a reconstructive jurisprudence in Africa must take cognisance of the continent’s historical and evolutionary legal experiences, but that a unified or monolithic theory may not be sufficient to address the choice of functional jurisprudence. Keywords African jurisprudence, jurisprudence in Africa, African legal evolution, diffused legal theories. (shrink)

This paper is the twin of (Duží and Jespersen, in submission), which provides a logical rule for transparent quantification into hyperprop- ositional contexts de dicto, as in: Mary believes that the Evening Star is a planet; therefore, there is a concept c such that Mary be- lieves that what c conceptualizes is a planet. Here we provide two logical rules for transparent quantification into hyperpropositional contexts de re. (As a by-product, we also offer rules for possible- world propositional contexts.) One (...) rule validates this inference: Mary believes of the Evening Star that it is a planet; therefore, there is an x such that Mary believes of x that it is a planet. The other rule validates this inference: the Evening Star is such that it is believed by Mary to be a planet; therefore, there is an x such that x is believed by Mary to be a planet. Issues unique to the de re variant include partiality and existential presupposition, sub- stitutivity of co-referential (as opposed to co-denoting or synony- mous) terms, anaphora, and active vs. passive voice. The validity of quantifying-in presupposes an extensional logic of hyperinten- sions preserving transparency and compositionality in hyperinten- sional contexts. This requires raising the bar for what qualifies as co-denotation or equivalence in extensional contexts. Our logic is Tichý’s Transparent Intensional Logic. The syntax of TIL is the typed lambda calculus; its highly expressive semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The two non-standard features we need are a hyper- intension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hy- perintensions. (shrink)

This thesis starts with three challenges to the structuralist accounts of applied mathematics. Structuralism views applied mathematics as a matter of building mapping functions between mathematical and target-ended structures. The first challenge concerns how it is possible for a non-mathematical target to be represented mathematically when the mapping functions per se are mathematical objects. The second challenge arises out of inconsistent early calculus, which suggests that mathematical representation does not require rigorous mathematical structures. The third challenge comes from (...) renormalisation group (RG) explanations of universality. It is argued that the structural mapping between the world and a highly abstract minimal model adds little value to our understanding of how RG obtains its explanatory force. I will address the first and second challenges from the similarity perspective. The similarity account captures representations as similarity relations, providing a more flexible and broader conception of representation than structuralism. It is the specification of the respect and degree of similarity that forges mathematics into a context of representation and directs it to represent a specific system in reality. Structuralism is treatable as a tool for explicating similarity rela-tions set-theoretically. The similarity account, combined with other approaches (e.g., Nguyen and Frigg’s extensional abstraction account and van Fraassen’s pragmatic equivalence), can dissolve the first challenge. Additionally, I will make a structuralist response to the second challenge, and suggestions regarding the role of infinitesimals from the similarity perspective. In light of the similarity account, I will propose the “hotchpotch picture” as a method-ological reflection of our study of representation and explanation. Its central insight is to dissect a representation or an explanation into several aspects and use different theories (that are usually thought of competing) to appropriate each of them. Based on the hotchpotch picture, RG explanations can be dissected to the “indexing” and “inferential” conceptions of explanation, which are captured or characterised by structural mappings. Therefore, structuralism accommodates RG explanations, and the third challenge is resolved. (shrink)

This dissertation is about the relationship between Epistemology and other domains. In it I want to show that in an important sense, Epistemology is an autonomous domain. That is, epistemic vocabulary (e.g., “knowledge”, “justification”, “rationality”, “epistemic reason”, etc.) cannot be analyzed without remainder into non-epistemic vocabulary. Epistemic phenomena must be explained in terms of epistemic reasons and the form of assessment proprietary to them. Although epistemic vocabulary cannot be reduced to the vocabulary of other domains, Epistemology is nonetheless connected with (...) other domains in an important way. In this dissertation I focus on the connection between Epistemology and the Philosophy of Mind. I distinguish different forms cognitive self-monitoring can take and corresponding forms of cognitive autonomy. The kind of self-monitoring that receives the most attention involves simulating interpersonal argumentation. I argue that the capacity to self-monitor in this way grounds familiar epistemic standards (e.g., knowledge and justification) and explains how reasons get their grip on us. On the picture that emerges, Epistemology and Philosophy of Mind need to be done in tandem. Epistemology gives us the normative framework that is modeled by the self-monitoring system. The self-monitoring system, conversely, explains the kind of activity we engage in that makes that normative framework applicable to us. Epistemic reasons themselves are just episodes of this kind of activity. In Chapter 1 I argue that epistemic luck cannot be analyzed in non-epistemic terms. Here I generalize Jennifer Lackey’s criticism of Duncan Pritchard’s safety-based account of epistemic luck to all reductive theories. I argue that they will either be extensionally inadequate, or they will illicitly presuppose the vocabulary they are trying to reduce. The upshot is that epistemic luck can only be understood in terms of the epistemic assessment of reasons. By extension, we can’t give a reductive analysis of knowledge. This is not to say we cannot analyze knowledge, just that we can’t analyze away the epistemic vocabulary without remainder. In chapter 2 I explain the relation between epistemic luck, epistemic justification, and knowledge. I argue that previous work in the defeasible reasoning tradition, despite being on the right track, fell short of realizing its full potential. This is because the account of how these three things relate given by its proponents was insufficiently unified, which encouraged many epistemologists to abandon the defeasible reasoning tradition entirely. I argue that a unified and principled account of their relation is possible, and it allows for an elegant analysis of knowledge. In slogan form: good reasons are apparent to the knowing subject. In chapter 3 I extend the defeasible reasoning tradition to explain how knowledge is gradable. I show that this enables us to bring the debates about fake barns and knowledge from falsehoods to ecumenical resolutions, while also shedding light on a new kind of case. Furthermore, I explain how background assumptions are themselves defeasible and some of the epistemic significance of this fact. In chapter 4 I make the connection between Epistemology and Philosophy of Mind. I argue that the self-monitoring system of cognitively mature humans uses a model of the normative framework described in the previous chapters to regulate its own cognition. Here I build on that claim to develop an account of the role played by knowledge and justification in doxastic social coordination. I build on the claim that background assumptions are themselves defeasible to develop an account of the foundations of knowledge according to which they are social but not brutely sociological. In chapter 5 I discuss the relation between the epistemic states of cognitively mature humans, children, and non-human animals. I do this in a way meant to integrate an insight from virtue epistemology into the reasons-first picture developed here: positive epistemic standing is a state attributable to the subject. In chapter 6 I discuss the metaphysics of epistemic reasons. I claim that they are episodes of the activity of reasoning. In the preceding chapters, we get a sense of what that activity involves. Here I argue that the materials developed there put us in a position to understand what epistemic reasons are. This account incorporates the insights of rival positions while sidestepping familiar objections to them. The resulting picture is in line with the non-reductive approach to the epistemic developed so far. In fact, it goes further than other “reasons-first” approaches to Epistemology by claiming that reasons are not only basic within Epistemology, but they are also basic full-stop. One key consideration for my argument here is that reasons are, by their very nature, competitors. Although this point is generally acknowledged in the literature on reasons, its consequences for the metaphysics of reasons hasn’t been. Participants in the debate about the metaphysics of reasons typically try to identify reasons with something (e.g., facts or mental states) that are either not competitors, or only competitors insofar as they constitute, or bear on the epistemic assessment of, episodes of reasoning. (shrink)

I focus on three mereological principles: the Extensionality of Parthood (EP), the Uniqueness of Composition (UC), and the Extensionality of Composition (EC). These principles are not equivalent. Nonetheless, they are closely related (and often equated) as they all reflect the basic nominalistic dictum, No difference without a difference maker. And each one of them—individually or collectively—has been challenged on philosophical grounds. In the first part I argue that such challenges do not quite threaten EP insofar as they are either self-defeating (...) or unsupported. In the second part I argue that they hardly undermine the tenability of EC and UC as well. (shrink)

Extensional scientific realism is the view that each believable scientific theory is supported by the unique first-order evidence for it and that if we want to believe that it is true, we should rely on its unique first-order evidence. In contrast, intensional scientific realism is the view that all believable scientific theories have a common feature and that we should rely on it to determine whether a theory is believable or not. Fitzpatrick argues that extensional realism is immune, (...) while intensional realism is not, to the pessimistic induction. I reply that if extensional realism overcomes the pessimistic induction at all, that is because it implicitly relies on the theoretical resource of intensional realism. I also argue that extensional realism, by nature, cannot embed a criterion for distinguishing between believable and unbelievable theories. (shrink)

Ethical extensionism is a common argument pattern in environmental and animal ethics, which takes a morally valuable trait already recognized in us and argues that we should recognize that value in other entities such as nonhuman animals. I exposit ethical extensionism’s core argument, argue for its validity and soundness, and trace its history to 18th century progressivist calls to expand the moral community and legal franchise. However, ethical extensionism has its critics. The bulk of the paper responds to recent criticisms, (...) including (1) environmental ethicists’ objection against its austere conception of moral value (2), feminist ethicists’ claim that extensionism fails to account for the moral significance of difference, (3) disability theorists’ concern that ethical extensionist arguments are offensive, and (4) animal rights theorists’ lament that extensionism is a practical failure. While something is to be gained from each criticism, I argue that they ultimately fail and that extensionism remains compelling. (shrink)

Intensional evidence is any reason to accept a proposition that is not the truth values of the proposition accepted or, if it is a complex proposition, is not the truth values of its propositional contents. Extensional evidence is non-intensional evidence. Someone can accept a complex proposition, but deny its logical consequences when her acceptance is based on intensional evidence, while the logical consequences of the proposition presuppose the acceptance of extensional evidence, e.g., she can refuse the logical consequence (...) of a proposition she accepts because she doesn’t know what are the truth-values of its propositional contents. This tension motivates counterexamples to the negation of conditionals, the propositional analysis of conditionals, hypothetical syllogism, contraposition and or-to-if. It is argued that these counterexamples are non-starters because they rely on a mix of intensionally based premises and extensionally based conclusions. Instead, a genuine counterexample to classical argumentative forms should present circumstances where an intuitively true and extensionally based premise leads to an intuitively false conclusion that is also extensionally based. The other point is that evidentiary concerns about intensionally based beliefs should be constrained by the truth conditions of propositions presented by classical logic, which are nothing more than requirements of coherence in distributions of truth value. It is argued that this restriction also dissolves some known puzzles such as conditional stand-offs, the Adams pair, the opt-out property and the burglar’s puzzle. (shrink)

Neo-Fregean approaches to set theory, following Frege, have it that sets are the extensions of concepts, where concepts are the values of second-order variables. The idea is that, given a second-order entity $X$, there may be an object $\varepsilon X$, which is the extension of X. Other writers have also claimed a similar relationship between second-order logic and set theory, where sets arise from pluralities. This paper considers two interpretations of second-order logic—as being either extensional or intensional—and whether either (...) is more appropriate for this approach to the foundations of set theory. Although there seems to be a case for the extensional interpretation resulting from modal considerations, I show how there is no obstacle to starting with an intensional second-order logic. I do so by showing how the $\varepsilon$ operator can have the effect of “extensionalizing” intensional second-order entities. (shrink)

This paper reconstructs the function argument of Aristotle’s Eudemian Ethics 2.1. The argument seeks to define happiness through the method of division; shows that the highest good is better than all four of the goods of the soul, not only two, as commentators have thought; and unlike the Nicomachean argument, makes the highest good definitionally independent of the human function.

In this paper, I identify a central problem for conceptual engineering: the problem of showing concept-users why they should recognise the authority of the concepts advocated by engineers. I argue that this authority problem cannot generally be solved by appealing to the increased precision, consistency, or other theoretical virtues of engineered concepts. Outside contexts in which we anyway already aim to realise theoretical virtues, solving the authority problem requires engineering to take a functional turn and attend to the functions (...) of concepts. But this then presents us with the problem of how to specify a concept’s function. I argue that extant solutions to this function specification problem are unsatisfactory for engineering purposes, because the functions they identify fail to reliably bestow authority on concepts, and hence fail to solve the authority problem. What is required is an authoritative notion of conceptual function: an account of the functions of concepts which simultaneously shows why concepts fulfilling such functions should be recognised as having authority. I offer an account that meets this combination of demands by specifying the functions of concepts in terms of how they tie in with our present concerns. (shrink)

Function talk is a constant across different life sciences. From macro-evolution to genetics, functions are mentioned everywhere. For example, a limb’s function is to allow movement and RNA polymerases’ function is to transcribe DNA. Biochemistry is not immune from such a characterization; the biochemical world seems to be a chemical world embedded within biological processes. Specifically, biochemists commonly ascribe functions to biomolecules and classify them accordingly. This has been noticed in the recent philosophical literature on biochemical kinds. But (...) while a lot has been written on biological and psychological functions, little has been said explicitly about biochemical fuctions. Here, I explore functional attribution to biochemical molecules. I argue that if we accept this attribution, then biochemical functions are constituted by chemical dispositional properties that causally contribute to selected biological processes. In section 2, I discuss the controversy concerning the characterization of biochemical functions. In section 3, I consider whether a biological or a chemical under- standing of function can be applied to biochemical functions, illustrating the account with the example of vitamin B12. The result is that none of the theories on their own provides an adequate characterization. In section 4, I present an account of biochemical functions. In section 5, I assess this account taking into consideration common requirements for a theory of functions and an objection. (shrink)

What is the function of morality? On this question, something approaching a consensus has recently emerged. Impressed by developments in evolutionary theory, many philosophers now tell us that the function of morality is to reduce social tensions, and to thereby enable a society to efficiently promote the well-being of its members. In this paper, I subject this consensus to rigorous scrutiny, arguing that the functional hypothesis in question is not well supported. In particular, I attack the supposed evidential relation between (...) an evolutionary genealogy of morals and the functional hypothesis itself. I show that there are a great many functionally relevant discontinuities between our own culture and the culture within which morality allegedly emerged, and I argue that this seriously weakens the inference from morality’s evolutionary history to its present-day function. (shrink)

The functional approach to scientific progress has been mainly developed by Kuhn, Lakatos, Popper, Laudan, and more recently by Shan. The basic idea is that science progresses if key functions of science are fulfilled in a better way. This chapter defends the function approach. It begins with an overview of the two old versions of the functional approach by examining the work of Kuhn, Laudan, Popper, and Lakatos. It then argues for Shan’s new functional approach, in which scientific progress (...) is defined as an increase of usefulness of exemplary practices. (shrink)

Various prominent theories of pain assume that it is pain’s biological function to inform organisms about damage to their bodies. I argue that this is a mistake. First, there is no biological evidence to support the notion that pain was originally selected for its informative capacities, nor that it currently contributes to the fitness of organisms in this specific capacity. Second, neurological evidence indicates that modulating mechanisms in the nociceptive system systematically prevent pain from serving a primarily informative role. These (...) considerations threaten to undermine standard perceptual and representational accounts of pain. (shrink)

Many believe that, if true, reason-statements of the form ‘that X is F is a reason to φ’ describe a ‘favouring-relation’ between the fact that X is F and the act of φing. This favouring-relation has been assumed to share many features of other, more concrete relations. This combination of views leads to immediate problems. Firstly, unlike statements about many other relations, reason-statements can be true even when the relata do not exist, i.e., when the relevant facts do not obtain (...) and the relevant acts are not done. Secondly, the previous combination of views also makes it very difficult to draw the distinction between agent-relative and agent-neutral reasons. I argue that we should think that the predicate ‘is a reason to’ creates non-extensional contexts in the statements in which it is used. This would both solve the previous problems and avoid the awkward consequences of the so-called slingshot argument. (shrink)

A proper function of an entity is a beneficial effect that helps explain the persistence of the entity. Proper functions thereby arise through feedback mechanisms with beneficial effects as inputs and persistence as outputs. We continue to make assertions because they benefit speakers by benefiting speakers. Hearers benefit from true information. Speakers benefit by influencing hearer belief. If hearers do not benefit, they will not form beliefs in response to assertions. Speakers can then only maintain influence by providing true (...) information, often enough. The function of assertion is then inducing true hearer belief. When interests conflict, however, some mechanism must ensure that speakers provide true information often enough, instead of deceiving, or providing information regardless of quality. In humans, a core mechanism stabilizing true assertion involves social norms for truth telling. We tell the truth partly because we prescribe and enforce telling the truth. (shrink)

There are two main ways in which the notion of mereological fusion is usually defined in the current literature in mereology which have been labelled ‘Leśniewski fusion’ and ‘Goodman fusion’. It is well-known that, with Minimal Mereology as the background theory, every Leśniewski fusion also qualifies as a Goodman fusion. However, the converse does not hold unless stronger mereological principles are assumed. In this paper I will discuss how the gap between the two notions can be filled, focussing in particular (...) on two specific sets of principles that appear to be of particular philosophical interest. The first way to make the two notions equivalent can be used to shed some interesting light on the kind of intuition both notions seem to articulate. The second shows the importance of a little-known mereological principle which I will call ‘Mild Supplementation’. As I will show, the mereology obtained by adding Mild Supplementation to Minimal Mereology occupies an interesting position in the landscape of theories that are stronger than Minimal Mereology but weaker than what Achille Varzi and Roberto Casati have labelled ‘Extensional Mereology’. (shrink)

This paper argues that proper functions are proximal functions. In other words, it rejects the notion that there are distal biological functions – strictly speaking, distal functions are not functions at all, but simply beneficial effects normally associated with a trait performing its function. Once we rule out distal functions, two further positions become available: dysfunctions are simply failures of proper function, and pathological conditions are dysfunctions. Although elegant and seemingly intuitive, this simple view (...) has had surprisingly little uptake in the literature. Indeed, our position departs from that of almost every theorist who has engaged with the issue at any depth. We start by presenting three arguments for the position that proper functions are proximal: one from the specificity of functions, one from their relation to intervention, and one from their relation to pathology. We then consider two case studies evidencing the trouble that accepting distal functions causes for philosophical reflection on the nature of pathological conditions. Finally, we anticipate and respond to three objections: that there can be failure of function without dysfunction; that our account is unacceptably revisionary in respect of normal function-talk; and that our thesis over-generalises from a narrow set of cases. (shrink)

Different cognitive functions recruit a number of different, often overlapping, areas of the brain. Theories in cognitive and computational neuroscience are beginning to take this kind of functional integration into account. The contributions to this special issue consider what functional integration tells us about various aspects of the mind such as perception, language, volition, agency, and reward. Here, I consider how and why functional integration may matter for the mind; I discuss a general theoretical framework, based on generative models, (...) that may unify many of the debates surrounding functional integration and the mind; and I briefly introduce each of the contributions. (shrink)

This is a short overview of the biological functions debate in philosophy. While it was fairly comprehensive when it was written, my short book ​A Critical Overview of Biological Functions has largely supplanted it as a definitive and up-to-date overview of the debate, both because the book takes into account new developments since then, and because the length of the book allowed me to go into substantially more detail about existing views.

This article presents a distinct sense of ‘mechanism’, which I call the functional sense of mechanism. According to this sense, mechanisms serve functions, and this fact places substantive restrictions on the kinds of system activities ‘for which’ there can be a mechanism. On this view, there are no mechanisms for pathology; pathologies result from disrupting mechanisms for functions. Second, on this sense, natural selection is probably not a mechanism for evolution because it does not serve a function. After (...) distinguishing this sense fromsimilar explications of ‘mechanism’, I argue that it is ubiquitous in biology and has valuable epistemic benefits. (shrink)