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)

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)

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)

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)

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)

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.

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)

Object x being a member of itself or not and x being a member of R or not constitute two vastly different concepts. This paper attempts to locate the reflection of such an utter difference within the formal structure of the axiom of extensionality. -/- .

If one takes seriously the idea that a scientific language must be extensional, and accepts Quine’s notion of truth-value-related extensionality, and also recognizes that a scientific language must allow for singular terms that do not refer to existing objects, then there is a problem, since this combination of assumptions must be inconsistent. I will argue for a particular solution to the problem, namely, changing what is meant by the word ‘extensionality’, so that it would not be the truth-value (...) that had to be preserved under the substitution of co-extensional expressions, but the state of affairs that the sentence described. The question is whether or not elementary sentences containing empty singular terms, such as ‘Vulcan rotates’, are extensional in the substitutivity sense. Five conditions are specified under which extensionality in the substitutivity sense of such sentences can be secured. It is demonstrated that such sentences are state-of-affairs-as-extension-related extensional. This implies that such sentences are also truth-value-related extensional in Quine’s sense, but not truth-value-as-extension-related extensional. (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)

The original interest of this article lies in existential import. It provides a broader view on the problem by reference to modern, symbolic logic (ch.1). Gradually, however, our interest will change into the amalgamated expressions often used in logic; that is, why are such expressions as “x is a round triangle” applied in logic? We critically discuss this question from an extensional viewpoint, namely model theoretic semantics (ch.2). We also touch on Church’s λ-calculus in the appendix (app.2).

Bermúdez argues for rational framing effects in the form of quasi-cyclical preferences. This is supposed to refute the extensionality principle in standard decision theory. In response, I argue that it is better to analyze seemingly quasi-cyclical preferences as ceteris paribus preferences. Furthermore, if frames are included as objects of choice, we can acknowledge rational framing effects without rejecting extensionality.

In this paper, I argue that current attempts at classifying life–mind continuity (LMC) feature several important ambiguities. We can resolve these ambiguities by distinguishing between the extensional, categorical, and systematic relationships that LMC might encompass. In Sect. 1, I begin by introducing the notion of LMC and the theory behind it. In Sect. 2, I show how different ideas of mind shape different approaches to continuity and how to achieve its aim. In Sect. 3, I canvas various canonical formulations and (...) classifications of LMC; I then demonstrate that they retain important ambiguities. Section 4 builds on this by arguing that we must conceive of the extensional and categorical aspects of continuity independently. In Sect. 5, I show further that current literature has underexplored multiple systematic aspects of continuity. I then take a constructive approach in Sect. 6 by providing a classification model for LMC based on extensional and categorical commitments. Here, I comment on aspects of the thesis omitted from the model but essential for a full classification and thorough comparison between various approaches to LMC. All of these arguments lay the foundation for more exhaustively classifying accounts of LMC. (shrink)

In this paper, I present what I call the symmetry conception of God within 1st order, extensional, non-well-founded set theory. The symmetry conception comes in two versions. According to the first, God is that unique being that is universally symmetrical with respect to set membership. According to the second, God is the universally symmetrical set of all sets that are universally symmetrical with respect to set membership. I present a number of theorems, most importantly that any universally symmetrical set is (...) identical to its essence, that show that the two symmetry conceptions intersect with some dominant theological conceptions of God. The theorems also show that both of the symmetry conceptions of God entail that God has a fractal like structure. (shrink)

Much of the ontology made in the analytic tradition of philosophy nowadays is founded on some of Quine’s proposals. His naturalism and the binding between existence and quantification are respectively two of his very influential metaphilosophical and methodological theses. Nevertheless, many of his specific claims are quite controversial and contemporaneously have few followers. Some of them are: (a) his rejection of higher-order logic; (b) his resistance in accepting the intensionality of ontological commitments; (c) his rejection of first-order modal logic; and (...) (d) his rejection of the distinction between analytic and synthetic statements. I intend to argue that these controversial negative claims are just interconnected consequences of those much more accepted and apparently less harmful metaphilosophical and methodological theses, and that the glue linking all these consequences to its causes is the notion of extensionality. (shrink)

In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathematics, at least according (...) to some speculative research programs. (shrink)

In “Psychopower and Ordinary Madness” my ambition, as it relates to Bernard Stiegler’s recent literature, was twofold: 1) critiquing Stiegler’s work on exosomatization and artefactual posthumanism—or, more specifically, nonhumanism—to problematize approaches to media archaeology that rely upon technical exteriorization; 2) challenging how Stiegler engages with Giuseppe Longo and Francis Bailly’s conception of negative entropy. These efforts were directed by a prevalent techno-cultural qualifier: the rise of Synthetic Intelligence (including neural nets, deep learning, predictive processing and Bayesian models of cognition). This (...) paper continues this project but first directs a critical analytic lens at the Derridean practice of the ontologization of grammatization from which Stiegler emerges while also distinguishing how metalanguages operate in relation to object-oriented environmental interaction by way of inferentialism. Stalking continental (Kapp, Simondon, Leroi-Gourhan, etc.) and analytic traditions (e.g., Carnap, Chalmers, Clark, Sutton, Novaes, etc.), we move from artefacts to AI and Predictive Processing so as to link theories related to technicity with philosophy of mind. Simultaneously drawing forth Robert Brandom’s conceptualization of the roles that commitments play in retrospectively reconstructing the social experiences that lead to our endorsement(s) of norms, we compliment this account with Reza Negarestani’s deprivatized account of intelligence while analyzing the equipollent role between language and media (both digital and analog). (shrink)

This continues from Part 1. It is shown how an intensional interpretation of physics object languages can be formalised, and how a syntactic compositional time reversal operator can subsequently be defined. This is applied to solve the problems used as examples in Part 1. A proof of a general theorem that such an operator must be defineable is sketched. A number of related issues about the interpretation of theories of physics, including classical and quantum mechanics and classical EM theory are (...) discussed. (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)

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)

x and y are at least weakly indiscernible if they are distinct with respect to two predicates F and G (FxGy or FyGx and not both) but for all z except x and y, Fz if and only if Gz.

According to the Bad Company objection, the fact that Frege’s infamous Basic Law V instantiates the general definitional pattern of higher-order abstraction principles is a good reason to doubt the soundness of this sort of definitions. In this paper I argue against this objection by showing that the definitional pattern of abstraction principles – as extrapolated from §64 of Frege’s Grundlagen– includes an additional requirement (which I call the specificity condition) that is not satisfied by the Basic Law V while (...) is satisfied by other higher-order abstractions such as Hume’s Principle. I also show that the failure of this additional requirement in the case of Basic Law V is engendered by an essential feature of Frege’s conception of logic and thus that Frege himself should not have regarded the Basic Law V as a definition by abstraction. (shrink)

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. (...) In this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)

This paper is about both an application of virtue ethics, and about virtue ethics itself. A popular application of neo-Aristotelian virtue ethics to environmental issues is called interpersonal extensionism. It argues that we should view the normative range of traditional interpersonal virtues, such as compassion and humility, as extending beyond our interactions with people to also include our interactions with non-human environments. This paper uncovers an unaddressed problem for this view, then proposes a solution by revising how we understand neo-Aristotelian (...) virtue ethics itself. The tenet in question, defended by virtue ethicists such as Hursthouse and Foot, claims that a character trait counts as a virtue only if it is strictly necessary for human flourishing. This tenet threatens interpersonal extensionism because, as I show, the extended or environment-regarding aspects of virtues such as compassion and humility are not strictly speaking necessary for human flourishing: people can in principle flourish without those. But I then argue that diversities across both people and environments give us good, seldom acknowledged, reasons to revise neo-Aristotelian virtue ethics so that it no longer imposes the tenet that led to this problem. Neither a trait nor an aspect of it need be necessary for human flourishing in order to count as a neo-Aristotelian virtue. Indeed, marked variation between people and between environments can be complementary with respect to flourishing. Sometimes, for instance, part of the reason an environment-regarding aspect of compassion is virtuous is because of its distinct role in creating conditions that increase the chance that others will flourish. To show these things, I draw from work in philosophy of science on cluster approaches to categories and constitution, and from experiences working with diverse people in Canada's diverse national and provincial parks. (shrink)

The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and inter-subjective knowledge about these fragments, called here, in brief, language adequacy. This problem is formulated in several aspects, the most being: the compatibility of language syntax with its bi-level semantics: intensional and extensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formal-logical theory T of any categorial language L generated by the so-called classical (...) categorial grammar, and also on the ground of its extension to the bi-level, intensional and extensional semantic-pragmatic theory ST for L. In T, according to the token-type distinction of Ch.S. Peirce, L is characterized first as a language of well-formed expression-tokens (wfe-tokens) - material, concrete objects - and then as a language of wfe-types - abstract objects, classes of wfe-tokens. In ST the semantic-pragmatic notions of meaning and interpretation for wfe-types of L of intensional semantics and the notion of denotation of extensional semanics for wfe-types and constituents of knowledge are formalized. These notions allow formulating a postulate (an axiom of categorial adequacy) from which follow all the most important conditions of the language adequacy, including the above, and a structural one connected with three principles of compositionality. (shrink)

In the paper, original formal-logical conception of syntactic and semantic: intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically: in the spirit of some Husserl’s ideas of pure grammar, Leśniewski-Ajukiewicz’s theory syntactic/semantic categories and in accordance with Frege’s ontological canons, Bocheński’s famous motto—syntax mirrors ontology and some ideas of Suszko: language should be a linguistic scheme of ontological reality and simultaneously a tool of its (...) cognition. In the logical conception of language L, its expressions should satisfy some general conditions of language adequacy. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic, and semantic compatibility, correspondence guaranteed by the acceptance of a postulate of categorial compatibility syntactic and semantic categories of expressions of L. From this postulate, three principles of compositionality follow: one syntactic and two semantic already known to Frege. They are treated as conditions of homomorphism partial algebra of L into algebraic models of L: syntactic, intensional, and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, of course, an idealization, but only expressions with high degrees of precision of their senses, after due justification, may become theorems of science. (shrink)

One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...) for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics. (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)

According to the principle of compositionality, the meaning of a composed expression depends only on its logical form and the meaning of its descriptive sub-expressions. This dependence can be understood as the substitutivity of expressions that have the same meaning without changing the meaning of the composed expression. In this book the hidden complexity of Frege's and Quine's conceptions of extensionality is revealed. The insights gained by this analysis as well as two versions of the principle of compositionality are (...) used in a formal reconstruction of Gödel's and Quine's versions of the slingshot argument. (shrink)

Empty individual expressions are needed to reconstruct the actual use of scientific language as well as to make logic free from existence assumptions. According to Quine, a language must be extensional to be adequate for the purposes of science. By means of Lambert's non-extensionality argument it can be demonstrated that a language containing empty individual expressions cannot be extensional as long as truth-values are the extensions of sentences. This book investigates the soundness of Lambert's argument and examines the question (...) of whether and how extensionality of a language for free logic can be secured. To achieve these aims, the notion of extensionality is thoroughly analyzed and two new semantic approaches to free logic are developed in which states of affairs, but not truth-values, are the extensions of sentences. These two semantic approaches are defended against the slingshot argument. In this way, two possible solutions to the problem of extensionality arise which use non-existent objects in two different ways: whereas in dual domain semantics non-existent objects serve as referents of empty singular terms, in single domain semantics they serve as hole marker objects that mark the holes in states of affairs where an object is missing due to an irreferental individual expression. (shrink)

In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and (...) semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic (extensional and intensional) categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two semantic ones already known to Frege. They are treated as conditions of homomorphism of partial algebra of L into algebraic models of L: syntactic, intensional and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, obviously, an idealisation. The syntactic and semantic unambiguity of its expressions is not, of course, a feature of natural languages, but every syntactically and semantically ambiguous expression of such languages may be treated as a schema representing all of its interpretations that are unambiguous expressions. (shrink)

Hans Reichenbach’s pragmatic treatment of the problem of induction in his later works on inductive inference was, and still is, of great interest. However, it has been dismissed as a pseudo-solution and it has been regarded as problematically obscure. This is, in large part, due to the difficulty in understanding exactly what Reichenbach’s solution is supposed to amount to, especially as it appears to offer no response to the inductive skeptic. For entirely different reasons, the significance of Bertrand Russell’s classic (...) attempt to solve Hume’s problem is also both obscure and controversial. Russell accepted that Hume’s reasoning about induction was basically correct, but he argued that given the centrality of induction in our cognitive endeavors something must be wrong with Hume’s basic assumptions. What Russell effectively identified as Hume’s (and Reichenbach’s) failure was the commitment to a purely extensional empiricism. So, Russell’s solution to the problem of induction was to concede extensional empiricism and to accept that induction is grounded by accepting both a robust essentialism and a form of rationalism that allowed for a priori knowledge of universals. So, neither of those doctrines is without its critics. On the one hand, Reichenbach’s solution faces the charges of obscurity and of offering no response to the inductive skeptic. On the other hand, Russell’s solution looks to be objectionably ad hoc absent some non-controversial and independent argument that the universals that are necessary to ground the uniformity of nature actually exist and are knowable. This particular charge is especially likely to arise from those inclined towards purely extensional forms of empiricism. In this paper the significance of Reichenbach’s solution to the problem of induction will be made clearer via the comparison of these two historically important views about the problem of induction. The modest but important contention that will be made here is that the comparison of Reichenbach’s and Russell’s solutions calls attention to the opposition between extensional and intensional metaphysical presuppositions in the context of attempts to solve the problem of induction. It will be show that, in effect, what Reichenbach does is to establish an important epistemic limitation of extensional empiricism. So, it will be argued here that there is nothing really obscure about Reichenbach’s thoughts on induction at all. He was simply working out the limits of extensional empiricism with respect to inductive inference in opposition to the sort of metaphysics favored by Russell and like-minded thinkers. (shrink)

There are at least two different concepts that philosophers might target when analyzing causation: a pre-selective notion and a selective notion. This paper argues that these two distinct conceptions have been conflated to date, citing the puzzles of overdetermination, extensionality, and transitivity as evidence. The primary aim of the paper is to help reset the methodological scene concerning analyses of causation.

Resumo: O projeto semântico de Davidson toma a forma de reducionismo que visa explicar as noções intencionais com base em noções puramente extensionais. O objetivo desse trabalho consiste na investigação do fracasso do projeto de Davidson como um argumento indireto contra sua suposição segundo a qual a chamada interpretação radical seria o fundamento do significado linguístico e do pensamento. Abstract: Davidson's semantic program is a form of semantic reductionism that aims to account for intensional notions on a purely extensional basis. (...) My aim in this paper is not to show that Davidsons fails in addressing the so-called extensionality problem. That is no novelty. Even Davidsonians recognize Davidson's failure. My main goal is to explore Davidson's failure as an indirect argument against his key assumption that the radical interpretation is the basis of sense and hence the possibility of thought. There is no priority of language over thought. This is a remnant of the so-called linguistic turn that Davidson inherited from the analytical tradition. The moral is the following: we must come back to Lockean common sense that to learn a natural language and to translate an alien tongue into our own is merely to learn a vehicle for communicating and expressing thoughts we have already had. (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)

In the following the details of a state-of-affairs semantics for positive free logic are worked out, based on the models of common inner domain - outer domain semantics. Lambert's PFL system is proven to be weakly adequate (i.e., sound and complete) with respect to that semantics by demonstrating that the concept of logical truth definable therein coincides with that one of common truth-value semantics for PFL. Furthermore, this state-of-affairs semantics resists the challenges stemming from the slingshot argument since logically equivalent (...) statements do not always have the same extension according to it. Finally, it is argued that in such a semantics all statements of a certain language for PFL are state-of-affairs-related extensional as well as salva extensione extensional, even though their salva veritate extensionality fails. (shrink)

The search for the extensions of sentences can be guided by Frege’s “principle of compositionality of extension”, according to which the extension of a composed expression depends only on its logical form and the extensions of its parts capable of having extensions. By means of this principle, a strict criterion for the admissibility of objects as extensions of sentences can be derived: every object is admissible as the extension of a sentence that is preserved under the substitution of co-extensional expressions. (...) The question is: what are the extensions of elementary sentences containing empty singular terms, like ‘Vulcan rotates’. It can be demonstrated that in such sentences, states of affairs as structured objects (but not truth-values) are preserved under the substitution of co-extensional expressions. Hence, such states of affairs are admissible (while truth-values are not) as extensions of elementary sentences containing empty singular terms. (shrink)

The relationship of part to whole is one of the most fundamental there is; this is the first and only full-length study of this concept. This book shows that mereology, the formal theory of part and whole, is essential to ontology. Peter Simons surveys and criticizes previous theories, especially the standard extensional view, and proposes a more adequate account which encompasses both temporal and modal considerations in detail. 'Parts could easily be the standard book on mereology for the next twenty (...) or thirty years.' Timothy Williamson, Grazer Philosophische Studien. (shrink)

In this paper, we seek a reliabilist account of justified credence. Reliabilism about justified beliefs comes in two varieties: process reliabilism (Goldman, 1979, 2008) and indicator reliabilism (Alston, 1988, 2005). Existing accounts of reliabilism about justified credence comes in the same two varieties: Jeff Dunn (2015) proposes a version of process reliabilism, while Weng Hong Tang (2016) offers a version of indicator reliabilism. As we will see, both face the same objection. If they are right about what justification is, it (...) is mysterious why we care about justification, for neither of the accounts explains how justification is connected to anything of epistemic value. We will call this the Connection Problem. I begin by describing Dunn’s process reliabilism and Tang’s indicator reliabilism. I argue that, understood correctly, they are, in fact, extensionally equivalent. That is, Dunn and Tang reach the top of the same mountain, albeit by different routes. However, I argue that both face the Connection Problem. In response, I offer my own version of reliabilism, which is both process and indicator, and I argue that it solves that problem. Furthermore, I show that it is also extensionally equivalent to Dunn’s reliabilism and Tang’s. Thus, I reach the top of the same mountain as well. (shrink)

Seen from the point of view of evaluation conditions, a usual way to obtain a connexive logic is to take a well-known negation, for example, Boolean negation or de Morgan negation, and then assign special properties to the conditional to validate Aristotle’s and Boethius’ Theses. Nonetheless, another theoretical possibility is to have the extensional or the material conditional and then assign special properties to the negation to validate the theses. In this paper we examine that possibility, not sufficiently explored in (...) the connexive literature yet.We offer a characterization of connexive negation disentangled from the cancellation account of negation, a previous attempt to define connexivity on top of a distinctive negation. We also discuss an ancient view on connexive logics, according to which a valid implication is one where the negation of the consequent is incompatible with the antecedent, and discuss the role of our idea of connexive negation for this kind of view. (shrink)

Knowledge-first theories of justification are theories of justification that give knowledge priority when it comes to explaining when and why someone has justification for an attitude or an action. The emphasis of this article is on knowledge-first theories of justification for belief. As it turns out, there are a number of ways of giving knowledge priority when theorizing about justification, and what follows is a survey of more than a dozen existing options that have emerged in the early 21st century (...) since the publication of Timothy Williamson’s *Knowledge and Its Limits*. This article traces several of the general theoretical motivations that have been offered for putting knowledge first in the theory of justification. This is followed by an examination of existing knowledge-first theories of justification and their standing objections. These objections are largely, but not exclusively, concerned with the extensional adequacy of knowledge-first theories of justification. There are doubtless more ways to give knowledge priority in the theory of justified belief than are covered here, but the survey is instructive because it highlights potential shortcomings that would-be knowledge-first theorists of justification may wish either to avoid or else to be prepared with a suitable error theory. This entry concludes with a reflection about the extent to which the short history of, arguably, failed attempts to secure an unproblematic knowledge-first account of justified belief has begun to resemble the older Gettier dialectic. (shrink)

Possible world semantics has been gradually fine-grained over the years. First, simple extensional semantics was fine-grained by relativizing it to worlds considered as counterfactual, thus generating standard possible-world semantics, which was later further fine-grained by relativizing it to worlds considered as actual, thus generating two-dimensional semantics. However, worlds considered as actual were only considered with respect to the empirical facts obtaining in such worlds. This paper shows that no less of an important role is played by another feature of actual (...) worlds, namely, the criteria of identity that obtain in such worlds. (shrink)

Many theories of rational belief give a special place to logic. They say that an ideally rational agent would never be uncertain about logical facts. In short: they say that ideal rationality requires "logical omniscience." Here I argue against the view that ideal rationality requires logical omniscience on the grounds that the requirement of logical omniscience can come into conflict with the requirement to proportion one’s beliefs to the evidence. I proceed in two steps. First, I rehearse an influential line (...) of argument from the "higher-order evidence" debate, which purports to show that it would be dogmatic, even for a cognitively infallible agent, to refuse to revise her beliefs about logical matters in response to evidence indicating that those beliefs are irrational. Second, I defend this "anti-dogmatism" argument against two responses put forth by Declan Smithies and David Christensen. Against Smithies’ response, I argue that it leads to irrational self-ascriptions of epistemic luck, and that it obscures the distinction between propositional and doxastic justification. Against Christensen’s response, I argue that it clashes with one of two attractive deontic principles, and that it is extensionally inadequate. Taken together, these criticisms will suggest that the connection between logic and rationality cannot be what it is standardly taken to be—ideal rationality does not require logical omniscience. (shrink)

The aim of the consequentializing project is to show that, for every plausible ethical theory, there is a version of consequentialism that is extensionally equivalent to it. One challenge this project faces is that there are common-sense ethical theories that posit moral dilemmas. There has been some speculation about how the consequentializers should react to these theories, but so far there has not been a systematic treatment of the topic. In this article, I show that there are at least five (...) ways in which we can construct versions of consequentialism that are extensionally equivalent to the ethical theories that contain moral dilemmas. I argue that all these consequentializing strategies face a dilemma: either they must posit moral dilemmas in unintuitive cases or they must rely on unsupported assumptions about value, permissions, requirements, or options. I also consider this result's consequences for the consequentializing project. (shrink)

ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result of a confusion between higher-order vagueness and the distribution of the objects of a Sorites series into extensionally non-overlapping non-empty classes.

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)

According to hardcore actualism (HA), all modal truths are grounded in the concrete constituents of the actual world. In this paper, I discuss some problems faced by HA when it comes to accounting for certain alleged possibilities of non‐existence. I focus particular attention on Leech (2017)'s dilemma for HA, according to which HA must either sacrifice extensional correctness or admit mere possibilia. I propose a solution to Leech's dilemma, which relies on a distinction between weak and strong possibility. It remains (...) the case, however, that HA cannot capture certain iterated de re possibilities of non‐existence and that it is committed to a stock of necessary existents. But I still think that the virtues of the view outweigh these costs. (shrink)

Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type of Alexandroff spaces was (...) used by Ian Rumfitt to elucidate the logic of vague concepts in a new way. According to his approach, conceptual spaces such as the color spectrum give rise to classical systems of concepts that have the structure of atomic Boolean algebras. More precisely, concepts are represented as regular open regions of an underlying conceptual space endowed with a topological structure. Something is subsumed under a concept iff it is represented by an element of the conceptual space that is maximally close to the prototypical element p that defines that concept. This topological representation of concepts comes along with a representation of the familiar logical connectives of Aristotelian syllogistics in terms of natural settheoretical operations that characterize regular open interpretations of classical Boolean propositional logic. In the last 20 years, conceptual spaces have become a popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy, mainly due to the work of Peter Gärdenfors and his collaborators. By using prototypes and metrics of similarity spaces, one obtains geometrical discretizations of conceptual spaces by so-called Voronoi tessellations. These tessellations are extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. This class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox (Rumfitt). Further, they provide a semantics for the logic of clearness (Bobzien) that overcomes certain problems of the concept of higher2 order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The crucial role of order theory for Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and nonprototypical stimuli in favor of a more fine-grained gradual distinction between more-orless prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem” (Douven et al.) and problems of selecting a unique metric for similarity spaces. Finally, it is shown that only the Alexandroff account can deal with an issue that is gaining more and more importance for the theory of conceptual spaces, namely, the role that digital conceptual spaces play in the area of artificial intelligence, computer science and related disciplines. Keywords: Conceptual Spaces, Polar Spaces, Alexandroff Spaces, Prototypes, Topological Tessellations, Voronoi Tessellations, Digital Topology. (shrink)

It is often assumed that believing that p for a normative reason consists in nothing more than (i) believing that p for a reason and (ii) that reason’s corresponding to a normative reason to believe that p, where (i) and (ii) are independent factors. This is the Composite View. In this paper, we argue against the Composite View on extensional and theoretical grounds. We advocate an alternative that we call the Prime View. On this view, believing for a normative reason (...) is a distinctive achievement that isn’t exhausted by the mere conjunction of (i) and (ii). Its being an achievement entails that (i) and (ii) are not independent when one believes for a normative reason: minimally, (i) must hold because (ii) holds. Apart from its intrinsic interest, our discussion has important upshots for central issues in epistemology, including the analysis of doxastic justification, the epistemology of perception, and the place of competence in epistemology. (shrink)