The Knower Paradox has had a brief but eventful history, and principles of epistemic closure (which say that a subject automatically knows any proposition she knows to be materially implied, or logically entailed, by a proposition she already knows) have been the subject of tremendous debate in epistemic logic and epistemology more generally, especially because the fate of standard arguments for and against skepticism seems to turn on the fate of closure. As far as I can tell, however, no one (...) working in either area has emphasized the result I emphasize in this paper: the Knower Paradox just falsifies even the most widely accepted general principles of epistemic closure. After establishing that result, I discuss five of its more important consequences. (shrink)

Three misrepresentations of informal and formal logic by two feminist writers are discussed. Andrea Nye's criticism that the semantics for formal logic abstracts from context is a misrepresentation of formal logic because Nye ignores the development of intensional logics. Second, Nye's criticism that informaIlogicians ignore the origins of arguments is a misrepresentation of fallacy theory. Prominent writers in the field specifiy numerous cases where the origins of an argument are relevant to its evaluation. Third, Valerie Plumwood's criticism that negation in (...) classical logic rests on an exclusivistic dualism that encourages the exclusion of women is shown to be false. (shrink)

This paper explores the main philosophical approaches of David Hilbert’s theory of proof. Specifically, it is focuses on his ideas regarding logic, the concept of proof, the axiomatic, the concept of truth, metamathematics, the a priori knowledge and the general nature of scientific knowledge. The aim is to show and characterize his epistemological approach on the foundation of knowledge, where logic appears as a guarantee of that foundation. Hilbert supposes that the propositional apriorism, proposed by him to support mathematics, sustains (...) — on its turn — a general method for the treatment of the problem in other areas such as natural sciences. This method is axiomatic. Broadly speaking, we intend to recover and update the Hilbert’s philosophical thinking about the role of logic for scientific knowledge. (shrink)

The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription rule by (...) applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties. (shrink)

We are familiar with various set-theoretical paradoxes such as Cantor's paradox, Burali-Forti's paradox, Russell's paradox, Russell-Myhill paradox and Kaplan's paradox. In fact, there is another new possible set-theoretical paradox hiding itself in Wittgenstein’s Tractatus. From the Tractatus’s Picture theory of language we can strictly infer the two contradictory propositions simultaneously: the world and the language are equinumerous; the world and the language are not equinumerous. I call this antinomy the world-language paradox. Based on a rigorous analysis of the Tractatus, with (...) the help of the technical resources of Cantor’s naive set theory and Zermelo-Fraenkel set theory with the axiom of choice, I outline the world-language paradox and assess the unique possible solution plan, i.e., the mathematical plan utilizing ‘infinity’. I conclude that Wittgenstein cannot solve the hidden set-theoretical paradox of the Tractatus successfully unless he gives up his finitism. (shrink)

Michael Kremer defines fixed-point logics of truth based on Saul Kripke’s fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point logic of truth, when thought of as consequence relation, is highly complex: it is not even analytic. We also (...) consider variants, engendered by a stronger notion of ‘fixed point’, and by variant supervaluation schemes. A ‘logic’ is often thought of, not as a consequence relation, but as a set of sentences – the sentences true on each interpretation. We axiomatize the supervaluation fixed-point logics so conceived. (shrink)

In response to the liar’s paradox, Kripke developed the fixed-point semantics for languages expressing their own truth concepts. Kripke’s work suggests a number of related fixed-point theories of truth for such languages. Gupta and Belnap develop their revision theory of truth in contrast to the fixed-point theories. The current paper considers three natural ways to compare the various resulting theories of truth, and establishes the resulting relationships among these theories. The point is to get a sense of the lay of (...) the land amid a variety of options. Our results will also provide technical fodder for the methodological remarks of the companion paper to this one. (shrink)

This essay considers arguments for and against syntactical constraints on the proper formalization of definitions, originally owing to Alfred Tarski. It discusses and refutes an application of the constraints generalized to include a prohibition against not only object-place but also predicate-place variables in higher-order logic in a criticism of a recent effort to define the concept of heterologicality in a strengthened derivation of Grelling's paradox within type theory requirements. If the objections were correct, they would offer a more general moral (...) for the proper formal definition of terms in philosophical logic. The criticism nevertheless seems mistaken both in the substance and specific application with respect to legitimate synctactical constraints on definitions of key concepts in the case of Grelling's paradox. As such, the critique provides no justification for overturning previous conclusions concerning the possibility of resurrecting a type-observant version of Grelling's heterologicality paradox. (shrink)

The object of this paper is to sketch an approach to propositions, meaning and names. The key ingredients are a Twin-Earth-inspired distinction between internal and external meaning, and a middle-Wittgenstein-inspired conception of internal meaning as role in language system. I show how the approach offers a promising solution to the problem of the meaning of proper names. This is a plea for a neglected way of thinking about these topics.

This paper aims at providing an account of juridical acts that forms a suitable starting point for the creation of computational systems that deal with juridical acts. The paper is divided into two parts. This second part of the paper deals in some detail with the operation of juridical acts. Topics dealt with include: power and competence, capacity, form requirements, partial validity, avoidance and representation.

The Idea behind Tarski's Definition of Truth. In Tarski's presentations of his truth-definition, the steps of the construction are not sufficiently explained. It is not clear, on what general strategy the construction is based, what the fundamental ideas are, how some crucial steps work, and especially how the transition from the definition of satisfaction to the definition of truth should be understood. The paper shows that the account given in the model-theoretic literature, which is supported by Tarski's lemmata A and (...) B, is unsatisfactory, because Tarski's notion of truth can't be interpreted as ‘truth independent of the assignment of values to the variables’. Moreover, a satisfactory account of all the crucial steps is given. (shrink)

We forward an epistemological perspective regarding non-classical logics which restores the universality of logic in accordance with the thesis of global pluralism. In this perspective every non-classical truth-theory is actually a theory of some metalinguistic concept which does not coincide with the concept of truth (described by Tarski's truth theory). We intend to apply this point of view to Quantum Logic (QL) in order to prove that its structure properties derive from properties of the metalinguistic concept of testability in Quantum (...) Physics. To this end we construct a classical language L cand endow it with a classical effective interpretation which is partially inspired by the Ludwig approach to the foundations of Quantum Mechanics. Then we select two subsets of formulas in L cwhich can be considered testable because of their interpretation and we show that these subsets have the structure properties of Quantum Logics because of Quantum Mechanical axioms, as desired. Finally we comment on some relevant consequences of our approach (in particular, the fact that no non-classical logic is strictly needed in Quantum Physics). (shrink)

This paper gives an account of Anderson and Belnap’s selection criteria for an adequate theory of entailment. The criteria are grouped into three categories: criteria pertaining to modality, those pertaining to relevance, and those related to expressive strength. The leitmotif of both this paper and its prequel is the relevant legitimacy of disjunctive syllogism. Relevant logics are commonly held to be paraconsistent logics. It is shown in this paper, however, that both E and R can be extended to explosive logics (...) which satisfy all of Anderson and Belnap’s selection criteria, provided the truth-constant known as the Ackermann constant is available. One of the selection criteria related to expressive strength is having an “enthymematic” conditional for which a deduction theorem holds. I argue that this allows for a new interpretation of Anderson and Belnap’s take on logical consequence, namely as committing them to pluralism about logical consequence. (shrink)

What does it take for two logics to be mere notational variants? The present paper proposes a variety of different ways of cashing out notational variance, in particular isolating a constraint on any reasonable account of notational variance which makes plausible that the only kinds of translations which can witness notational variance are what are sometimes called definitional translations.

This paper is an attempt to convince anti-realists that their correct intuitions against the metaphysical inflationism derived from some versions of mathematical realism do not force them to embrace non-standard, epistemic approaches to truth and existence. It is also an attempt to convince mathematical realists that they do not need to implement their perfectly sound and judicious intuitions with the anti-intuitive developments that render full-blown mathematical realism into a view which even Gödel considered objectionable. I will argue for the following (...) two theses: that realism, in its standard characterization, is our default position, a position in agreement with our pre-theoretical intuitions and with the results of our best semantic theories, and that most of the metaphysical qualms usually related to it depends on a poor understanding of truth and existence as higher-order concepts. (shrink)

Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so (...) that ignorance of their nature is profound. (shrink)

In this paper I argue that pluralism at the level of logical systems requires a certain monism at the meta-logical level, and so, in a sense, there cannot be pluralism all the way down. The adequate alternative logical systems bottom out in a shared basic meta-logic, and as such, logical pluralism is limited. I argue that the content of this basic meta-logic must include the analogue of logical rules Modus Ponens and Universal Instantiation. I show this through a detailed analysis (...) of the ‘adoption problem’, which manifests something special about MP and UI. It appears that MP and UI underwrite the very nature of a logical rule of inference, due to all rules of inference being conditional and universal in their structure. As such, all logical rules presuppose MP and UI, making MP and UI self-governing, basic, unadoptable, and required in the meta-logic for the adequacy of any logical system. (shrink)

This paper offers a framework for extending Arnon Avron and Iddo Lev’s non-deterministic semantics to quantified predicate logic with the intent of resolving several problems and limitations of Avron and Anna Zamansky’s approach. By employing a broadly Fregean picture of logic, the framework described in this paper has the benefits of permitting quantifiers more general than Walter Carnielli’s distribution quantifiers and yielding a well-behaved model theory. This approach is purely objectual and yields the semantical equivalence of both α-equivalent formulae and (...) formulae differing only by codenotative terms. Finally, we make a brief excursion into non-deterministic model theory, proving a strong Łoś’ Theorem and compactness for all finitely-valued, non-deterministic logics whose quantifiers have intensions describable in a first order metalanguage. (shrink)

According to tradition, logic is normative for reasoning. According to many contemporary philosophers of logic, there is more than one correct logic. What is the relationship between these two strands of thought? This paper makes two claims. First, logic is doubly normative for reasoning because, in addition to constraining the combinations of beliefs that we may have, logic also constrains the methods by which we may form them. Second, given that logic is doubly normative for reasoning, a wide array of (...) logical pluralisms are inconsistent with the normativity of logic as they entail contradictory claims about how agents ought to reason. Thus, if logic is normative for reasoning, these pluralisms are untenable. (shrink)

The point of scientificity, or pos,represents a place in history whereeducational administration was founded as ascience. A pos creates a field of memoryand a field of studies. A pos isepistemologically sustained in its claim forscientific status by a line of demarcation orlod. A lod is supported by truthclaims based on various forms ofcorrespondence. As these forms have beeninterrogated and abandoned, correspondence hasgiven way to coherentism and finally to testsof falsification. As falsification has shownto contain serious flaws when compared to theactual (...) history of scientific discoveries, theentire project of a distinct and unitaryfield known as educational administration isseriously cast into doubt. Contemporaryexaminations in educational administrationdiscourse show that even when the lod hasbeen undermined by epistemological shifts, theinitial pos has remained to supportclaims regarding the project of a ``science ofleadership.'' The analysis contained in thisarticle show, however, that when claims of thelod are demonstrably unsustainable, theinitial pos must be similarly abandoned. With that collapse the concept of a fieldis likewise effaced. The epistemologicalalternative is to envision fields ofstudy which do not require a lod, excepton a longitudinal basis to ascertain whether aresearch program shaped and sustained by it isprogressive or regressive. In short, there areno aprori meta-criteria to separate sciencefrom non-science in educationaladministration. (shrink)

There are two paradoxes of satisfaction, and they are of different kinds. The classic satisfaction paradox is a version of Grelling’s: does ‘does not satisfy itself’ satisfy itself? The Unsatisfied paradox finds a predicate, P, such that Px if and only if x does not satisfy that predicate: paradox results for any x. The two are intuitively different as their predicates have different paradoxical extensions. Analysis reduces each paradoxical argument to differing rule sets, wherein their respective pathologies lie. Having different (...) pathologies, they are paradoxes of different kinds. Furthermore, each of these satisfaction paradoxes has an analogue with the same pathology in set theory. Therefore, these analogues are respectively of the same two kinds. This level of abstraction is significant in that it tracks two related but different pathologies. Thus, not all paradoxes of semantics and set theory share the same pathology: there are at least two kinds of paradox cutting across the semantic and set-theoretic distinction. (shrink)

Starting from a concept of reasonableness as well-consideredness, it is discussed in what way science could serve as a model for reasonable argumentation. It turns out that in order to be reasonable two requirements have to be fulfilled. The argumentation should comply with rules which are both problem-valid and intersubjectively valid. Geometrical and anthropological perspectives don't meet these criteria, but a critical perspective does. It is explained that a pragma-dialectical approach to argumentation which agrees with this critical perspective is indeed (...) problem-valid and that strong pragmatic and utilitarian arguments can be given for its intersubjective validity. Thus, conventional validity is promoted for a code of conduct for discussants who want to resolve their disputes reasonably by way of a critical discussion. (shrink)

Logical nihilism is the view that the relation of logical consequence is empty: there are counterexamples to any putative logical law. In this paper, I argue that the nihilist threat is illusory. The nihilistic arguments do not work. Moreover, the entire project is based on a misguided interpretation of the generality of logic.

The knower paradox states that the statement ‘We know that this statement is false’ leads to inconsistency. This article presents a fresh look at this paradox and some well-known solutions from the literature. Paul Égré discusses three possible solutions that modal provability logic provides for the paradox by surveying and comparing three different provability interpretations of modality, originally described by Skyrms, Anderson, and Solovay. In this article, some background is explained to clarify Égré’s solutions, all three of which hinge on (...) intricacies of provability logic and its arithmetical interpretations. To check whether Égré’s solutions are satisfactory, we use the criteria for solutions to paradoxes defined by Susan Haack and we propose some refinements of them. This article aims to describe to what extent the knower paradox can be solved using provability logic and to what extent the solutions proposed in the literature satisfy Haack’s criteria. Finally, the article offers some reflections on the relation between knowledge, proof, and provability, as inspired by the knower paradox and its solutions. (shrink)

This volume recreates the received notion of reflective equilibrium. It reconfigures reflective equilibrium as both a cognitive ideal and a method for approximating this ideal. The ideal of reflective equilibrium is restructured using the concept of discursive strata, which are formed by sentences and differentiated by function. Sentences that perform the same kind of linguistic function constitute a stratum. The book shows how moral discourse can be analyzed into phenomenal, instrumental, and teleological strata, and the ideal of reflective equilibrium reworked (...) in these terms. In addition, the work strengthens the method of reflective equilibrium by harnessing the resources of decision theory and inductive logic. It launches a comparative version of decision theory and employs this framework as a guide to moral theory choice. It also recruits quantitative inductive logic to inform a standard of inductive cogency. When used in tandem with comparative decision theory, this standard can aid in the effort to turn the undesirable condition of reflective disequilibrium into reflective equilibrium. (shrink)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.

Tarski’s pioneering work on truth has been thought by some to motivate a robust, correspondence-style theory of truth, and by others to motivate a deflationary attitude toward truth. I argue that Tarski’s work suggests neither; if it motivates any contemporary theory of truth, it motivates conceptual primitivism, the view that truth is a fundamental, indefinable concept. After outlining conceptual primitivism and Tarski’s theory of truth, I show how the two approaches to truth share much in common. While Tarski does not (...) explicitly accept primitivism, the view is open to him, and fits better with his formal work on truth than do correspondence or deflationary theories. Primitivists, in turn, may rely on Tarski’s insights in motivating their own perspective on truth. I conclude by showing how viewing Tarski through the primitivist lens provides a fresh response to some familiar charges from Putnam and Etchemendy. (shrink)

One of the important challenges in the philosophy of mathematics is to account for the semantics of sentences that express mathematical propositions while simultaneously explaining our access to their contents. This is Benacerraf’s Dilemma. In this dissertation, I argue that cognitive science furnishes new tools by means of which we can make progress on this problem. The foundation of the solution, I argue, must be an ontologically realist, albeit non-platonist, conception of mathematical reality. The semantic portion of the problem can (...) be addressed by accepting a Chomskyan conception of natural languages and a matching internalist, mentalist and nativist view of semantics. A helpful perspective on the epistemic aspect of the puzzle can be gained by translating Kurt G ̈odel’s neo-Kantian conception of the nature of mathematics and its objects into modern, cognitive terms. (shrink)

This is a position paper concerning the role of empirical studies of human default reasoning in the formalization of AI theories of default reasoning. We note that AI motivates its theoretical enterprise by reference to human skill at default reasoning, but that the actual research does not make any use of this sort of information and instead relies on intuitions of individual investigators. We discuss two reasons theorists might not consider human performance relevant to formalizing default reasoning: (a) that intuitions (...) are sufficient to describe a model, and (b) that human performance in this arena is irrelevant to a competence model of the phenomenon. We provide arguments against both these reasons. We then bring forward three further considerations against the use of intuitions in this arena: (a) it leads to an unawareness of predicate ambiguity, (b) it presumes an understanding of ordinary language statements of typicality, and (c) it is similar to discredited views in other fields. We advocate empirical investigation of the range of human phenomena that intuitively embody default reasoning. Gathering such information would provide data with which to generate formal default theories and against which to test the claims of proposed theories. Our position is that such data are the very phenomena that default theories are supposed to explain. (shrink)

In this paper we discuss the difference between (...) proliferations of logic systems, the questions of relativity and universality of logic and the position and interaction of logic with regards to other sciences such as physics, biology, mathematics and computer science. (shrink)

At the heart of my pragmatic theory of truth and ontology is a view of the relation between language and reality which I term internal justification: a way of explaining how sentences may have truth-values which we cannot discover without invoking the need for the mystery of a correspondence relation. The epistemology upon which the theory depend~ is fallibilist and holistic ; places heavy reliance on modal idioms ; and leads to the conclusion that current versions of realism and anti-realism (...) are deficient. Just as my theory avoids the need for an epistemic 'given', it avoids the need for a metaphysical 'given' or 'joints'. I offer a view of the nature of philosophy and what it can properly achieve with respect to ontological questions ; since those views lead me to believe that philosophical discussion about what exists should be restricted to 'entities' discussed in non-philosophical contexts, my views on how we should understand claims made about the existence of middle-sized physical objects, theoretical entities in science, and abstract entities in mathematics, give the thesis a schematic completeness. My theory leads me to a conception of inquiry which defends the cognitive status of moral statements whilst being critical of Kantian and utilitarian approaches to morality. Chapter 1 explores the views of my closest philosophical allies: William James and Nelson Goodman. (shrink)

The causal theory of properties is standardly combined with a realist's ontology of universals or tropes. In this paper, I consider an uncharted alternative – a nominalist causal theory of properties. I discuss advantages and disadvantages of the resulting theory of properties, and explore the Rylean understanding of causal powers that emerges.

This thesis comprises three main chapters—each comprising one relatively standalone paper. The unifying theme is fragmentalism about truth, which is the view that the predicate “true” either expresses distinct concepts or expresses distinct properties. -/- In Chapter 1, I provide a formal development of alethic pluralism. Pluralism is the view that there are distinct truth properties associated with distinct domains of subject matter, where a truth property satisfies certain truth-characterizing principles. On behalf of pluralists, I propose an account of logic (...) and semantics that shows how they can answer central conceptual and logical challenges for their view. -/- In Chapter 2, I motivate and develop a modal account of propositions on the basis of an iterative conception of propositions, where the modality is logico-mathematical. The modal account of propositions takes the conception to motivate an inherently potential hierarchy of propositions. I show that the account helps provide satisfying solutions to the intensional paradoxes of Russell-Myhill, Kaplan, and Prior. -/- In Chapter 3, I propose that “true” is polysemous. I suggest that “true” is initially polysemous between correspondence truth and disquotational truth, and further polysemous between the meanings corresponding to the subconcepts of the concept truth generated by the indefinite extensibility of that concept. I show that the proposal provides satisfying solutions to the semantic paradoxes. (shrink)