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 analyzes recent work in psychology on the nature of the representation of complex forms of knowledge with the goal of understanding how theories are represented. The analysis suggests that, as a psychological form of representation, theories are mental structures that include theoretical entities (usually nonobservable), relationships among the theoretical entities, and relationships of the theoretical entities to the phenomena of some domain. A theory explains the phenomena in its domain by providing a conceptual framework for the (...) phenomena that leads to a feeling of understanding in the reader/hearer. The explanatory conceptual framework goes beyond the original phenomena, integrates diverse aspects of the world, and shows how the original phenomena follow from the framework. This analysis is used to argue that mental models are the subclass of theories that use causal/mechanical explanatory frameworks. In addition, an argument is made for a new psychologism in the philosophy of science, in which the mental representation of scientific theories must be taken into account. (shrink)

This paper investigates a puzzle about commitment. On the one hand, it is natural to hold that agents can be committed to propositions that they do not believe. On the other hand, because they are not logically omniscient, agents often have beliefs which are logically inconsistent. But then, since an inconsistent set of propositions entails every proposition, it seems that we have to hold that most or all agents are committed to every proposition. This consequence threatens to trivialize the idea (...) of commitment. To resolve this puzzle about commitment, this paper draws on a structural similarity between theories of commitment and Robert Stalnaker’s account of belief. Stalnaker holds that agents can have fragmented beliefs: they can be related to multiple internally consistent but jointly incompatible belief states. When this happens, they can believe inconsistent propositions without believing every proposition as long as the inconsistent propositions are located in different fragments. the paper develops a similar strategy for thinking about commitment: beliefs can either be co-believed or not, and an agent is committed to the consequences of a set of beliefs only if those beliefs are co-believed. (shrink)

If properties are to play a useful role in semantics, it is hard to avoid assuming the naïve theory of properties: for any predicate Θ(x), there is a property such that an object o has it if and only if Θ(o). Yet this appears to lead to various paradoxes. I show that no paradoxes arise as long as the logic is weakened appropriately; the main difficulty is finding a semantics that can handle a conditional obeying reasonable laws without engendering (...) paradox. I employ a semantics which is infinite-valued, with the values only partially ordered. Can the solution be adapted to naïve set theory? Probably not, but limiting naïve comprehension in set theory is perfectly satisfactory, whereas this is not so in a property theory used for semantics. (shrink)

Recent work on children’s inferences concerning biological and chemical categories has suggested that children (and perhaps adults) are essentialists— a view known as psychological essentialism. I distinguish three varieties of psychological essentialism and investigate the ways in which essentialism explains the inferences for which it is supposed to account. Essentialism succeeds in explaining the inferences, I argue, because it attributes to the child belief in causal laws connecting category membership and the possession of certain characteristic appearances and behavior. This suggests (...) that the data will be equally well explained by a non-essentialist hypothesis that attributes belief in the appropriate causal laws to the child, but makes no claim as to whether or not the child represents essences. I provide several reasons to think that this non-essentialist hypothesis is in fact superior to any version of the essentialist hypothesis. (shrink)

In their recent paper, “Practical Knowledge without Luminosity,” Bob Beddor and Carlotta Pavese (2022) claim that the doctrine of essentially intentional actions, or “essentialism,” is false. Essentialism states that some actions are essentially intentional, such that, “whenever they are performed, they are performed intentionally” (2022, p. 926). Beddor and Pavese work to reject essentialism, which figures as a key premise in Juan Piñeros Glasscock’s anti-luminosity argument against the knowledge condition for intentional action (Piñeros Glasscock, p. 1240). Historically, essentialism has received (...) little attention from philosophers since its inception in Elizabeth Anscombe’s Intention (2000, §47). However, I believe that essentially intentional actions can play an important role in an ontology of action. In my paper, I develop and argue for a variety of essentialism in the context of naive action theory, which I call naive essentialism. Naive essentialism is a two-fold thesis, which claims that (1) essentially intentional actions exist, and (2) that essentially intentional actions ground accidentally intentional actions. My paper has four parts. In the first part, I distinguish between essentially and accidentally intentional actions, and unpack the relevant principles of naive action theory. Second, I present the grounding thesis that accidentally intentional actions are grounded in essentially intentional actions. Next, I provide an argument for the existence of essentially intentional actions. Lastly, I briefly respond to a possible objection to my argument. The upshot of my arguments is that essentially intentional actions form the metaphysical and explanatory bedrock in a naive ontology of action, and that there are good reasons for accepting a key premise in Piñeros Glasscock’s anti-luminosity argument. (shrink)

This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in which it occurs. (...) The theory predicts several phenomena of reasoning about absolute probabilities, including typical biases. It correctly predicts certain cognitive illusions in inferences about relative probabilities. It accommodates reasoning based on numerical premises, and it explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem. Finally, it dispels some common misconceptions of probabilistic reasoning. (shrink)

Fairley and Manktelow (1997) have mistaken an error of presentation for an error of substance. My causal the- ory remains the same: Causal reasoning scenarios that require the reasoner to decide whether or not an effect will occur in the presence of a viable cause trigger considera- tion of disabling conditions—that is, factors that could prevent the effect from occurring in the presence of a vi- able cause. Scenarios that require the reasoner to decide whether or not a particular cause (...) has produced an ob- served effect trigger consideration of possible alternative causes. The data reported by Cummins (1995) and Cum- mins, Lubart, Alksnis, and Rist (1991) are consistent with this theoretical analysis. (shrink)

In a recent series of papers, I and others have advanced new logical approaches to familiar paradoxes. The key to these approaches is to accept full classical logic, and to accept the principles that cause paradox, while preventing trouble by allowing a certain sort ofnontransitivity. Earlier papers have treated paradoxes of truth and vagueness. The present paper will begin to extend the approach to deal with the familiar paradoxes arising in naive set theory, pointing out some of the promises and (...) pitfalls of such an approach. (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 main aim is to extend the range of logics which solve the set-theoretic paradoxes, over and above what was achieved by earlier work in the area. In doing this, the paper also provides a link between metacomplete logics and those that solve the paradoxes, by finally establishing that all M1-metacomplete logics can be used as a basis for naive set theory. In doing so, we manage to reach logics that are very close in their axiomatization to that of the (...) logic R of relevant implication. A further aim is the use of metavaluations in a new context, expanding the range of application of this novel technique, already used in the context of negation and arithmetic, thus providing an alternative to traditional model theoretic approaches. (shrink)

This paper outlines a theory and computer implementation of causal meanings and reasoning. The meanings depend on possibilities, and there are four weak causal relations: A causes B, A prevents B, A allows B, and A allows not‐B, and two stronger relations of cause and prevention. Thus, A causes B corresponds to three possibilities: A and B, not‐A and B, and not‐A and not‐B, with the temporal constraint that B does not precede A; and the stronger relation conveys only the (...) first and last of these possibilities. Individuals represent these relations in mental models of what is true in the various possibilities. The theory predicts a number of phenomena, and, contrary to many accounts, it implies that the meaning of causation is not probabilistic, differs from the meaning of enabling conditions, and does not depend on causal powers or mechanisms. The theory also implies that causal deductions do not depend on schemas or rules. (shrink)

Two distinct and apparently "dual" traditions of non-classical logic, three-valued logic and paraconsistent logic, are considered here and a unified presentation of "easy-to-handle" versions of these logics is given, in which full naive set theory, i.e. Frege's comprehension principle + extensionality, is not absurd.

The question "Why?" that is deployed in these exchanges evidently bears the "special sense" Elizabeth Anscombe has linked to the concepts of intention and of a reason for action; it is the sort of question "Why?" that asks for what Donald Davidson later called a "rationalization".2 The special character of what is given, in each response, as formulating a reason ── a description, namely, of the agent as actually doing something, and, moreover, as..

The naive set theory problem is to begin with a full comprehension axiom, and to find a logic strong enough to prove theorems, but weak enough not to prove everything. This paper considers the sub-problem of expressing extensional identity and the subset relation in paraconsistent, relevant solutions, in light of a recent proposal from Beall, Brady, Hazen, Priest and Restall [4]. The main result is that the proposal, in the context of an independently motivated formalization of naive set theory, leads (...) to triviality. (shrink)

This chapter discusses the way in which the familiar arguments against Sense-Datum Theory (SDT) are indeed wrong-headed. What kinds of real difficulties and new questions do we face if we adopt SDT, for example, in looking for a locus in the brain at which colours, and other phenomenal qualities, are assembled in a Phenomenal Array? If we initially formulate SDT in a relatively simple-minded—Naive—way, what kinds of issues do we encounter? The chapter offers some illustrations of issues likely to be (...) encountered and also examine in a beginning way how SDT might have to be less Naive. (shrink)

In [7], a naive set theory is introduced based on a polynomial time logical system, Light Linear Logic (LLL). Although it is reasonably claimed that the set theory inherits the intrinsically polytime character from the underlying logic LLL, the discussion there is largely informal, and a formal justification of the claim is not provided sufficiently. Moreover, the syntax is quite complicated in that it is based on a non-traditional hybrid sequent calculus which is required for formulating LLL.In this paper, we (...) consider a naive set theory based on Intuitionistic Light Affine Logic (ILAL), a simplification of LLL introduced by [1], and call it Light Affine Set Theory (LAST). The simplicity of LAST allows us to rigorously verify its polytime character. In particular, we prove that a function over {0, 1}* is computable in polynomial time if and only if it is provably total in LAST. (shrink)

Dialetheism is the metaphysical claim that there are true contradictions. And based on this view, Graham Priest and his collaborators have been suggesting solutions to a number of paradoxes. Those paradoxes include Russell’s paradox in naive set theory. For the purpose of dealing with this paradox, Priest is known to have argued against the presence of classical negation in the underlying logic of naive set theory. The aim of the present paper is to challenge this view by showing that there (...) is a way to handle classical negation. (shrink)

Reasonning in naive set theory (with unlimited comprehension), we derive a paradox (a formal contradiction) which can be seen as a variant of the Burali-Forti paradox.

Perceptions are externally-directed—they present us with a mind-independent reality, and thus contribute to our abilities to think about this reality, and to know what is objectively the case. But perceptions are also internally-dependent—their phenomenologies depend on the neuro-computational properties of the subject. A good theory of perception must account for both these facts. But naive realism has been criticized for failing to accommodate internal-dependence. This paper evaluates and responds to this criticism. It first argues that a certain version of naive (...) realism, often called “selectionism”, does indeed struggle with internal-dependence. It then develops an alternate version of naive realism which does not. This alternate version, inspired by an idea of Martin’s, accommodates the internal-dependence of perceptions by recognizing the role that the subject’s neuro-computational properties play in shaping perceptual phenomenology. At the same time, it retains the distinctive naive realist account of the external-directedness of perceptions. (shrink)

To the memory of Prof. Grigori Mints, Stanford UniversityBorn: June 7, 1939, St. Petersburg, RussiaDied: May 29, 2014, Palo Alto, California.

In this paper a logic for reasoning disquotationally about truth is presented and shown to have a standard model. This work improves on Hartry Field's recent results establishing consistency and omega-consistency of truth-theories with strong conditional logics. A novel method utilising the Banach fixed point theorem for contracting functions on complete metric spaces is invoked, and the resulting logic is shown to validate a number of principles which existing revision theoretic methods have heretofore failed to provide.

This paper describes a modal conception of sets, according to which sets are 'potential' with respect to their members. A modal theory is developed, which invokes a naive comprehension axiom schema, modified by adding `forward looking' and `backward looking' modal operators. We show that this `bi-modal' naive set theory can prove modalized interpretations of several ZFC axioms, including the axiom of infinity. We also show that the theory is consistent by providing an S5 Kripke model. The paper concludes with some (...) discussion of the nature of the modalities involved, drawing comparisons with noneism, the view that there are some non-existent objects. (shrink)

ABSTRACT In our response Field's ‘Properties, Propositions and Conditionals’, we explore the methodology of Field's program. We begin by contrasting it with a proof-theoretic approach and then commenting on some of the particular choices made in the development of Field's theory. Then, we look at issues of property identity in connection with different notions of equivalence. We close with some comments relating our discussion to Field's response to Restall’s [2010] ‘What Are We to Accept, and What Are We to Reject, (...) While Saving Truth from Paradox?’. (shrink)

Recently Feferman has outlined a program for the development of a foundation for naive category theory. While Ernst has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a ‘cookbook recipe’ is used for constructing categories, and it is explicitly shown (...) with a formalized argument that this “foundationless” naive category theory therefore contains a paradox similar to the Russell paradox of naive set theory. (shrink)

The naive structuralist definition of truthlikeness is an idealization in the sense that it assumes that all mistaken models of a theory are equally bad. The natural concretization is a refined definition based on an underlying notion of structurelikeness.In Section 1 the naive definition of truthlikeness of theories is presented, using a new conceptual justification, in terms of instantial and explanatory mistakes.

A naive validity theory can formally express its own notion of logical consequence. To block the inevitable Curry paradox, it is well known that a logic without the metarule of contraction will suffice. However, there ought to be a reason, independent of merely blocking paradoxes, to suppose that contraction fails. In this paper I provide such an argument, showing that naive validity has both explanatory and expressive roles—local and global dimensions, that make it naturally unfit for contraction.

I begin by describing what I call simple naïve realism. Then I describe relevant empirical results. Next, I develop two new empirical arguments against simple naive realism. Then I briefly look at two new, more complex forms of naïve realism: one due to Keith Allen and the other due to Heather Logue and Ori Beck. I argue that they are not satisfactory retreats for naive realists. The right course is to reject naive realism altogether. My stalking horse is (...) contemporary naive realism but there is a larger, positive lesson: new empirical results support a brain-based theory of sensory consciousness. (shrink)

It is part of the current wisdom that the Liar and similar semantic paradoxes can be taken care of by the use of certain non-classical multivalued logics. In this paper I want to suggest that bivalent logic can do just as well. This is accomplished by using a non-deterministic matrix to define the negation connective. I show that the systems obtained in this way support a transparent truth predicate. The paper also contains some remarks on the conceptual interest of such (...) systems. (shrink)

The project of a 'naive physics' has been the subject of attention in recent years above all in the artificial intelligence field, in connection with work on common-sense reasoning, perceptual representation and robotics. The idea of a theory of the common-sense world is however much older than this, having its roots not least in the work of phenomenologists and Gestalt psychologists such as K hler, Husserl, Schapp and Gibson. This paper seeks to show how contemporary naive physicists can profit from (...) a knowledge of these historical roots of their discipline, which are shown to imply above alla critique of the set-theory-based models of reality typically presupposed by contemporary work in common-sense ontology [1]. (shrink)

This paper elaborates on an argument in my book *Perception*. It has two parts. In the first part, I argue against what I call "basic" naive realism, on the grounds that it fails to accommodate what I call "internal dependence" and it requires an empirically implausible theory of sensible properties. Then I turn Craig French and Ian Phillips’ modified naïve realism as set out in their recent paper "Austerity and Illusion". It accommodates internal dependence. But it may retain the (...) empirically implausible theory of sensible properties. And it faces other empirical problems. Representationalism about experiences avoids those problems and is to be preferred. (shrink)

This chapter introduces the thesis of naive realism, which claims that the conscious aspects of our experiences are shaped by the external world. It clarifies the terminology of phenomenal character and explains how naive realism has a particular view of the phenomenal character of our experiences. It then considers various extant motivations for naive realism, including phenomenological motivations, John McDowell's claim that it can help to undermine skepticism, and motivations that concern our knowledge of demonstrative reference and the possibility of (...) representational content. (shrink)

A unified answer is offered to two distinct fundamental questions: whether a nonclassical solution to the semantic paradoxes should be extended to other apparently similar paradoxes and whether a nonclassical logic should be expressed in a nonclassical metalanguage. The paper starts by reviewing a budget of paradoxes involving the logical properties of validity, inconsistency, and compatibility. The author’s favored substructural approach to naive truth is then presented and it is explained how that approach can be extended in a very natural (...) way so as to solve a certain paradox of validity. However, three individually decisive reasons are later provided for thinking that no approach adopting a classical metalanguage can adequately account for all the features involved in the paradoxes of logical properties. Consequently, the paper undertakes the task to do better, and, building on the system already developed, introduces a theory in a nonclassical metalanguage that expresses an adequate logic of naive truth and of some naive logical properties. (shrink)

A source of much difficulty and confusion in the interpretation of quantum mechanics is a naive realism about operators. By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about measuring operators that occurs when the subject is quantum mechanics. Without a specification of what should be meant by measuring a quantum observable, such an expression can have no clear meaning. A definite specification is provided by (...) Bohmian mechanics, a theory that emerges from Schrödinger's equation for a system of particles when we merely insist that particles means particles. Bohmian mechanics clarifies the status and the role of operators as observables in quantum mechanics by providing the operational details absent from standard quantum mechanics. It thereby allows us to readily dismiss all the radical claims traditionally enveloping the transition from the classical to the quantum realm — for example, that we must abandon classical logic or classical probability. The moral is rather simple: Beware naive realism, especially about operators! (shrink)