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)

A number of important philosophical problems are problems in the overlap of logic and ontology. Both logic and ontology are diverse fields within philosophy, and partly because of this there is not one single philosophical problem about the relation between logic and ontology. In this survey article we will first discuss what different philosophical projects are carried out under the headings of "logic" and "ontology" and then we will look at several areas where logic and ontology overlap.

This paper discusses George Boole’s two distinct approaches to the explanatory relationship between logical and psychological theory. It is argued that, whereas in his first book he attributes a substantive role to psychology in the foundation of logical theory, in his second work he abandons that position in favour of a linguistically conceived foundation. The early Boole espoused a type of psychologism and later came to adopt a type of anti-psychologism. To appreciate this invites a far-reaching reassessment of his philosophy (...) of logic. (shrink)

The concern of this paper is not with the truth of any particular realist or anti-realist view, but rather with determining what it is to be a realist or anti-realist in the first place. While much skepticism has been voiced in recent years about the viability of such a project, my goal is to articulate interesting and informative conditions whereby any view in any domain of experience can count as either a realist or an anti-realist position.

Traditional correspondence theory of truth with the concept of fact encounters many serious difficulties, main one of which is that it is too difficult to explain clearly the concept of ‘fact’ and how propositions ‘correspond’ to facts. This does not mean that we should abandon the traditional correspondence theory of truth and turn to some other type theories of truth. In order to guarantee the objectivity of truth, any reasonable theory of truth must adhere to the core insight of the (...) traditional correspondence theory: it is not something in our language, nor in our mind, but something in the external world, that make the propositions we use to describe the states of affairs in the world either true or false. It is entirely possible to formulate a new correspondence theory of truth without the concept of fact but still adhering to the core insights mentioned above of the traditional correspondence theory. New correspondence theory of truth has its own metaphysical and epistemological assumptions, and also its assumption in the philosophy of language. Because of the generativity of language, in defining the concept of truth, the new correspondence theory of truth must resort to Tarskian recursive procedure. First, it gives the semantic value of the components of a proposition, defines the truth of its atomic propositions, then gradually defines the truth of its more and more complex propositions and finally of the whole proposition. Coherence is the intrinsic element of truth. The concept of truth is by no means trivial and insignificant; on the contrary, it is very substantive. The pursuit of truth is our mission. (shrink)

We advance an approach to logical contexts that grounds the claim that logic is a local matter: distinct contexts require distinct logics. The approach results from a concern about context individuation, and holds that a logic may be constitutive of a context or domain of application. We add a naturalistic component: distinct domains are more than mere technical curiosities; as intuitionistic mathematics testifies, some of the distinct forms of inference in different domains are actively pursued as legitimate fields of research (...) in current mathematics, so, unless one is willing to revise the current scientific practice, generalism must go. The approach is advanced by discussing some tenets of a similar argument advanced by Shapiro, in the context of logic as models approach. In order to make our view more appealing, we reformulate a version of logic as models approach following naturalistic lines, and bring logic closer to the use of models in science. (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)

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)

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)

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.

John Cook Wilson (1849–1915) was Wykeham Professor of Logic at New College, Oxford and the founder of ‘Oxford Realism’, a philosophical movement that flourished at Oxford during the first decades of the 20th century. Although trained as a classicist and a mathematician, his most important contribution was to the theory of knowledge, where he argued that knowledge is factive and not definable in terms of belief, and he criticized ‘hybrid’ and ‘externalist’ accounts. He also argued for direct realism in perception, (...) criticizing both empiricism and idealism, and argued for a moderate nominalist view of universals as being in rebus and only ‘apprehended’ by their particulars. His influence helped swaying Oxford away from idealism and, through figures such as H. A. Prichard, Gilbert Ryle, or J. L. Austin, his ideas were also to some extent at the origin of ‘moral intuitionism’ and ‘ordinary language philosophy’ which defined much of Oxford philosophy until the second half of the twentieth-century. Nevertheless, his name and legacy were all but forgotten for generations after World War II. Still, his views on knowledge are with us today, being in part at work in the writings of philosophers as diverse as John McDowell, Charles Travis, and Timothy Williamson. (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)

There is a certain argument against the principle of the indiscernibility of identicals, or the thesis that whatever is true of a thing is true of anything identical with that thing. In this argument, PInI is used together with the self-evident principle of the necessity of self-identity to reach the conclusion, which is held to be paradoxical and, thus, fatal to PInI. My purpose is to show that the argument in question does not have this consequence. Further, I argue that (...) PInI is a universally valid principle which can be used to prove the necessity of identity. (shrink)

Rejectivism is one of the most influential embodiments of pragmatism within contemporary philosophy of logic, advancing an explanation of the meaning of a logical notion, negation, in terms of the speech act of denial. This paper offers a challenge to rejectivism by proposing that in virtue of explaining negation in terms of denial, the rejectivist ought to be able to explain the concept of contradiction partially in terms of denial. It is argued that any failure to achieve this constitutes an (...) explanatory failure on the part of rejectivism, and reasons are then provided to doubt that the challenge can be successfully met. (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)

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)

Meta-ethical realism faces the serious epistemological problem of how to explain our epistemic access to moral reality. In the face of this challenge many are sceptical about non-naturalist realism. Nonetheless, there is good reason to acknowledge moral objectivity: morality shows all the signs of a truth-apt discourse but doesn’t exhibit the typical relativity inducing features. This suggests a middle-ground position, a theory that embraces the virtues of realism but does avoid its vices: objectivist antirealism. In this paper, I’ll discuss, mainly (...) following Crispin Wright’s account of moral truth as superassertibility, a promising version of objectivist antirealism and show how to cope with notorious problems, notably those arising from the thought that moral disagreement might be possible in which nobody is guilty of a cognitive shortcoming, which contradicts the antirealist claim that moral truth is not beyond our epistemic reach. The solution is to deny the possibility of cognitively faultless moral disagreement by arguing that cognitively blameless thinkers either agree or stay agnostic and, therefore, never disagree about any moral proposition. Since assuming an agnostic stance on the part of such thinkers contradicts the antirealist’s conception of truth—even within the limits of intuitionistic logic—I’ll propose an alternative logical revision for the moral discourse: a three-valued logic with epistemically construed truth-values. (shrink)

I would like to attack a certain view: The view that the concept of identity can fail to apply to some things although, for some positive integer n, we have n of them. The idea of entities without self-identity is seriously entertained in the philosophy of quantum mechanics. It is so pervasive that it has been labelled the Received View. I introduce the Received View in Section 1. In Section 2 I explain what I mean by entity, and I argue (...) that supporters of the Received View should agree with my characterization of the corresponding notion of entity. I also explain what I mean by identity, and I show that supporters of the Received View agree with my characterization of that notion. In Section 3 I argue that the concept of identity, so characterized, is one with the concept of oneness. Thus, it cannot but apply to what belongs to a collection with n elements, n being a positive integer. In Section 4 I add some considerations on the primitiveness of identity or unity and the status of the Identity of Indiscernibles. In Section 5 I address the problem of how reference to indiscernible objects with identity can be achieved. (shrink)

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)

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)

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)

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)

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)

n various publications over the past years, Floridi has developed a theory of semantic information as well-formed, meaningful, and truthful data. This theory is more or less orthogonal to the standard entropy-based notions of information known from physics, information theory, and computer science that all define the amount of information in a certain system as a scalar value without any direct semantic implication. In this context the question rises what the exact relation between these various conceptions of information is and (...) whether there is a real need to enrich these mathematically more or less rigid definitions with a less formal notion of semantic information. I investigate various philosophical aspects of the more formal definitions of information in the light of Floridi’s theory. The position I defend is that the formal treatment of the notion of information as a general theory of entropy is one of the fundamental achievements of modern science that in itself is a rich source for new philosophical reflection. This makes information theory a competitor of classical epistemology rather than a servant. In this light Floridi’s philosophy of information is more a reprise of classical epistemology that only pays lip service to information theory but fails to address the important central questions of philosophy of information. Specifically, I will defend the view that notions that are associated with truth, knowledge, and meaning all can adequately be reconstructed in the context of modern information theory and that consequently there is no need to introduce a concept of semantic information. (shrink)

In 1999, Jeffrey Ketland published a paper which posed a series of technical problems for deflationary theories of truth. Ketland argued that deflationism is incompatible with standard mathematical formalizations of truth, and he claimed that alternate deflationary formalizations are unable to explain some central uses of the truth predicate in mathematics. He also used Beth’s definability theorem to argue that, contrary to deflationists’ claims, the T-schema cannot provide an ‘implicit definition’ of truth. In this article, I want to challenge this (...) final argument. Whatever other faults deflationism may have, the T-schema does provide an implicit definition of the truth predicate. Or so, at any rate, I shall argue. (shrink)

This paper critically examines logical instrumentalism as it has been put forth recently in the anti-exceptionalism about logic debate. I will argue that if one wishes to uphold the claim that logic is significantly similar to science, as the anti-exceptionalists have it, then logical instrumentalism cannot be what previous authors have taken it to be. The reason for this, I will argue, is that as the position currently stands, first, it reduces to a trivial claim about the instrumental value of (...) logical systems, and second, by its denial that logic aims to account for extra-systemic phenomena it significantly differs from science, in contrast with the AEL agenda. I will conclude by proposing a different kind of logical instrumentalism that I take to have a broad appeal, but especially for anti-exceptionalists, for it is developed as analogous to—and thus much closer aligned with—scientific instrumentalism. (shrink)

We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value defined classically, (...) and everyaf is endowed with ajustification value, defined in terms of the intuitive notion of proof and depending on the truth values of its radical subformulas. In this framework, we define the notion ofpragmatic validity in P and yield a list of criteria of pragmatic validity which hold under the assumption that only classical metalinguistic procedures of proof be accepted. We translate the classical propositional calculus (CPC) and the intuitionistic propositional calculus (IPC) into the assertive part of P and show that this translation allows us to interpret Intuitionistic Logic as an axiomatic theory of the constructive proof concept rather than an alternative to Classical Logic. Finally, we show that our framework provides a suitable background for discussing classical problems in the philosophy of logic. (shrink)

This paper analyses the notion of ‘interpretation’, which is often tied to the semantic approach to logic, where it is used when referring to truth-value assignments, for instance. There are, however, other uses of the notion that raise interesting problems. These are the cases in which interpreting a logic is closely related to its justification for a given application. The paper aims to present an understanding of interpretations that supports the model-theoretic characterization of validity to the detriment of the proof-theoretic (...) one. This is done by making use of the hierarchy of ST-related logics. Finally, a localist conception of logic is defended as the natural view stemming from the model-theoretic approach. (shrink)

Dans ce travail, je vais m'efforcer de critiquer la thèse poppérienne de la dissymétrie entre les procédures de vérification et de réfutation des théories empiriques. Pour caractériser les théories empiriques, j'utiliserai le critère suivant: l'analyse des procédures discursives employées ne suffit pas comme base de discussion de leur valeur de vérité. On doit faire appel à quelque chose dont on considère que la donnée est en quelque façon, et du point de vue de la connaissance, extérieure à la théorie. Dans (...) le titre, j'ai employé «falsification» parce que c'était le terme habituel des traducteurs français de Popper jusqu'à une date récente. Je trouve cette terminologie peu claire et j'utiliserai les couples vérifier/réfuter, confirmer/infirmer. (shrink)

Prior's three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic $Q_t $ and give its axiomatization and semantics. We also argue that $Q_t $ provides a smooth solution to the problem of future contingents.